Wind Tunnels: Uses and Developments 9781536158991, 1536158992

Table of contents :
Chapter 1 Numerical Investigation of the Collector Geometry Effect on the Aerodynamic Characteristics of the Flow inside a Wind Tunnel --
Chapter 2 Study of the Diffuser Geometry Effect on the Aerodynamic Characteristics of the Flow Inside a Wind Tunnel --
Chapter 3 Effect of the Collector Inlet Radius on the Turbulent Flow Inside a Wind Tunnel --
Chapter 4 Study of the Rotating Area Effect on the Turbulent Flow around a Savonius Wind Rotor --
Chapter 5 Study of the Meshing Choice of a NACA2415 Airfoil Wind Turbine --
Chapter 6 Study of the Wedging Angle Effect of a NACA2415 Airfoil Wind Turbine in a Wind Tunnel --
Chapter 7 Study of the NACA Airfoil Effect of a Horizontal Axis Wind Turbine in a Wind Tunnel --
Chapter 8 Computer Simulation of the Aerodynamic Structure of Inclined Roof Obstacles with Different Heights in a Wind Tunnel --
Chapter 9 Wind Tunnel Tests of Delta Wing with Privileged Apex

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MECHANICAL ENGINEERING THEORY AND APPLICATIONS

WIND TUNNELS USES AND DEVELOPMENTS

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MECHANICAL ENGINEERING THEORY AND APPLICATIONS Additional books and e-books in this series can be found on Nova’s website under the Series tab.

MECHANICAL ENGINEERING THEORY AND APPLICATIONS

WIND TUNNELS USES AND DEVELOPMENTS

ZIED DRISS EDITOR

Copyright © 2019 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected].

NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the Publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data ISBN: HERRN Library of Congress Control Number:2019944363

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface Chapter 1

Chapter 2

Chapter 3

vii Numerical Investigation of the Collector Geometry Effect on the Aerodynamic Characteristics of the Flow inside a Wind Tunnel Sobhi Frikha, Zied Driss, Kamel Hchaychi and Sami Rihane Study of the Diffuser Geometry Effect on the Aerodynamic Characteristics of the Flow Inside a Wind Tunnel Sobhi Frikha, Kamel Hchaychi, Sami Rihane and Zied Driss Effect of the Collector Inlet Radius on the Turbulent Flow Inside a Wind Tunnel Sobhi Frikha, Sami Rihane, Zied Driss and Kamel Hchaychi

1

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37

vi Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Contents Study of the Rotating Area Effect on the Turbulent Flow around a Savonius Wind Rotor Sobhi Frikha, Zied Driss, Emna Ayadi, Zied Masmoudi and Mohamed Salah Abid Study of the Meshing Choice of a NACA2415 Airfoil Wind Turbine Sobhi Frikha, Zied Driss, Tarek Chelbi and Mohamed Salah Abid

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91

Study of the Wedging Angle Effect of a NACA2415 Airfoil Wind Turbine in a Wind Tunnel Tarek Chelbi, Zied Driss, Sobhi Frikha and Mohamed Salah Abid

107

Study of the NACA Airfoil Effect of a Horizontal Axis Wind Turbine in a Wind Tunnel Zied Driss, Tarek Chelbi, Sobhi Frikha and Mohamed Salah Abid

145

Computer Simulation of the Aerodynamic Structure of Inclined Roof Obstacles with Different Heights in a Wind Tunnel Slah Driss, Zied Driss, Imen Kallel Kammoun and Mohamed Salah Abid

169

Chapter 9

Wind Tunnel Tests of Delta Wing with Privileged Apex Iddir Boumrar and Zied Driss About the Editor

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Index

229

Related Nova Publications

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199

PREFACE The present book focus on uses and developments of wind tunnels which are a device for producing a controlled stream of air in order to study the effects of movement through air or resistance to moving air on models of aircraft and other machines and objects. This book consists on nine chapters presenting different study on the design, uses and developments of the wind tunnel in different applications like wind turbines, building and aircraft models. In the first chapter, numerical simulations were carried out to study the effect of the collector geometry on the aerodynamic characteristics of the flow inside an open wind tunnel. Particularly, the authors have compared four types of collectors. The numerical results from the application of the CFD code "Fluent" were presented in different transverse and longitudinal planes of the wind tunnel. In the second chapter, authors studied the effect of the diffuser geometry on the aerodynamic characteristics of the flow inside an open wind tunnel. The numerical model used is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. These equations are solved by a finite volume discretization method.

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In the third chapter, authors compared two types of collectors and studied the effect of the collector inlet radius on the aerodynamic characteristics of the flow inside an open wind tunnel. The numerical results from the application of the CFD code "Fluent" were presented in different transverse and longitudinal planes of the wind tunnel. In the fourth chapter, numerical simulation and experimental validation were performed to study the effect of the rotating area on the turbulent flow around a Savonius wind rotor. Authors were particularly interested in visualizing the velocity field, the static pressure, the dynamic pressure, the vorticity, the turbulent kinetic energy, the dissipation rate of the turbulent kinetic energy and the turbulent viscosity. The wind tunnel experiment results were compared to the numerical results in terms of velocity profile, dynamic torque, dynamic torque coefficient, power and power coefficient. The good agreements confirm the validity of the numerical method. In the fifth chapter, studied the meshing effect of a NACA2415 airfoil type wind turbine. The software "SolidWorks Flow Simulation" has been used to present the local characteristics in different transverse and longitudinal planes. Experiments have been also conducted on an open wind tunnel equipped by a small NACA2415 airfoil type wind turbine to validate the numerical results. In the sixth chapter, numerical simulations were carried out to study the wedging angle effect of a NACA2415 airfoil wind turbine, to determine the local characteristics of the flow and to evaluate its performance. The considered model was implemented in the softaware "SolidWorks Flow Simulation" which uses a finite volume scheme. In the seven chapter, studied the complex flow field developing around a horizontal axis wind turbine rotor. Particularly, the comparison was done between the NACA2415 and NACA4410 airfoil types. The Navier-Stokes equations were considered in conjunction with the standard k-ε turbulence model to study the effect of the NACA airfoil wind turbine. These equations were solved numerically to determine the local characteristics of the flow.

Preface

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In the eight chapter, authors interested in the study of the aerodynamic structure of inclined roof obstacles with different heights. By using the software "SolidWorks Flow Simulation", the governing equations of mass and momentum in conjunction with the standard k-ε turbulence model were solved with a finite volume discretization. The numerical results were compared with anterior results developed in a wind tunnel. The good agreements with the experimental results confirm the numerical method. In the nine chapter, various experimental studies are devoted to the aerodynamic of reduced aircraft models with particular contours and edges. The first studies were focused on observations and visualization in the wind tunnel. They suggest that delta wings with "privileged" apex can influence the wing aerodynamic characteristics and consequently could have repercussions on the performances of the aircraft. In addition, these same studies revealed that the apex vortex which develops on the suction face of this type of wings occupy positions corresponding to values of quantified angles, called "privileged angles". The present experimental study aims to validate these phenomenological aspects delivered by visualizations through measurements of aerodynamic coefficients of pressure Cp, drag CD and lift CL determined for all the considered configurations.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 1

NUMERICAL INVESTIGATION OF THE COLLECTOR GEOMETRY EFFECT ON THE AERODYNAMIC CHARACTERISTICS OF THE FLOW INSIDE A WIND TUNNEL Sobhi Frikha*, Zied Driss, Kamel Hchaychi and Sami Rihane University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations were carried out to study the effect of the collector geometry on the aerodynamic characteristics of the flow inside an open wind tunnel. Particularly, we have compared four types of collectors. The used numerical model is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε *

Corresponding Author’s E-mail: [email protected].

2

Sobhi Frikha, Zied Driss, Kamel Hchaychi et al. turbulence model. These equations are solved by a finite volume discretization method. The numerical results obtained from the application of the CFD code "Fluent" are presented in different transverse and longitudinal planes of the wind tunnel.

Keywords: Collector, wind tunnel, turbulent flow, CFD

INTRODUCTION A wind tunnel is a device for producing a controlled stream of air in order to study the effects of movement through air or resistance to moving air on models of aircraft and other machines and objects. There are two basic types of wind tunnels: the closed-circuit and the opencircuit. The open-circuit draws air from the ambient environment and exhausts it back to the ambient after exiting the fan, while in the closedcircuit, the air repeatedly circulates through the tunnel. The closedcircuit design delivers an improved efficiency and generates less noise, but it is more expensive and more difficult to manufacture. There are various studies in the literature related to the design of wind tunnels and the measurements in them. For example, Batill et al. [1] studied the vacuum effect created by a fan in the suction type wind tunnel and calculated the energy losses in the boundary layer flows due to this emerged effect. Senol [2] designed and performed the computer-aided flow simulation of an open circuit subsonic wind tunnel for vehicle aerodynamics experiments. Cogotti [3] described the evolution of the automotive wind tunnels in parallel with developments in measurement techniques and performed aerodynamics and aerostatics measurements in new cars. Chong et al. [4] designed and manufactured an open circuit type wind tunnel and tested its aero-acoustic performance. Arifuzzaman and Mashud designed a short length subsonic wind tunnel to validate its adequacy for aerodynamic analysis as well as to determine the velocity

Numerical Investigation of the Collector Geometry Effect …

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profile at different positions of the test section. After testing the performance, this newly designed tunnel was a good tool to provide steady flow with consistent speed through the test section without excessive turbulence [5]. Leifsson and Koziel [6] designed and optimized the contraction shape of the tunnel. The contraction speeds up and aligns the flow into test section. The CFD is used to optimize the design of the contraction. The variable of contraction such as inlet size, contraction area ratio, and length and wall shape are optimized. Perta et al. investigated the wind tunnel configuration at different air inlet velocities for the aerodynamics performance with the CFD [7]. Yadava et al. designed a low turbulence wind tunnel for studying the effect of the turbulence of bluff bodies. They replaced the settling and contraction section with the air blower. The advantage of replacing such a replacement was to produce less turbulence and uniform flow [8]. Over the last decade, CFD modeling has seen widespread growth in aerodynamics and wind engineering research [9-11]. In this chapter, we are interested in a numerical study of the aerodynamic characteristics on a wind tunnel. Our goal is to compare different geometry of the collector in order to choose the best one. For this reason, numerical results are presented in different transverse and longitudinal planes of the considered control volume.

1. NUMERICAL MODEL Numerical results are conducted within the computational fluid dynamic (CFD) code "Fluent". In this code, the used numerical model is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model.

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These equations are solved by a finite volume discretization method [12, 13].

1.1. Boundary Conditions In this work, the designed wind tunnel is composed of a tranquilization chamber, a collector, a test section, a diffuser and a fan [14]. The control volume of the wind tunnel is presented in figure 1. The boundary conditions of our application consists in the inlet velocity equal to V = 4.7 m.s-1 and the outlet pressure equal to the atmospheric pressure.

1.2. Collector Geometries Figure 2 shows the different parameters of the wind tunnel such as the length and the opening of the collector and the length and the divergence angle of the diffuser.

Figure 1. Wind tunnel control volume.

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Figure 2. Geometric parameters of the wind tunnel.

Figure 3. Wind tunnel geometries.

Four configurations are considered in this study: wind tunnel with curved collector, wind tunnel with rectilinear collector, wind tunnel with large opening of the collector and wind tunnel with long collector (Figure 3). Table 1 presents the geometric parameters of the collector for the different configurations.

1.3. Meshing The meshes were created using Gambit. Figure 4 presents the meshing of the control volume for the different geometries.

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Sobhi Frikha, Zied Driss, Kamel Hchaychi et al. Table 1. Geometric parameters of the collectors Wind tunnel type

Collector Collector length Collector type length Wind tunnel with curved Hc = 800 mm Lc = 1200 mm Curved collector Wind tunnel with Hc = 800 mm Lc = 1200 mm Rectilinear rectilinear collector Wind tunnel with large Hc = 1600 mm Lc = 1200 mm Rectilinear opening of the collector Wind tunnel with long Hc = 800 mm Lc = 1800 mm Curved collector

Figure 4. Meshing of the considered cases.

The first case consists of 158061 nodes. The second case consists of 156940 nodes. The third case consists of 159472 nodes. However, the fourth case consists of 179360 nodes.

2. NUMERICAL RESULTS In this section, the velocity field, the static pressure, the dynamic pressure and the turbulent kinetic energy are presented. Different longitudinal and transverse planes are considered (Figure 5).

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Figure 5. Visualized planes.

2.1. Velocity Field Figures from 6 to 10 present the distribution of the velocity field in the different longitudinal and transverse planes. According to these results, it has been observed that the velocity increases progressively downstream of the collector. The maximum values of the speed are reached in the test vein and then decrease at the entrance of the diffuser. The maximum value of the average velocity differs from one configuration to another. Indeed, the velocity is equal to 19.1 m s-1 for the curved collector geometry, whereas it reaches a value of 20.2 m s-1 for the rectilinear collector. Also, it has been noted that there is a concentration of the velocity in the test vein. For the large opening collector, the velocity reaches a maximum value of 21.4 m s-1. In addition, it has been noted that the area of uniformity decreases. Therefore, we decided to choose the first configuration. The low cost and the little space are the main advantages of this choice.

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Figure 6. Mean velocity in the longitudinal plane.

Figure 7. Velocity field in the longitudinal plane.

Numerical Investigation of the Collector Geometry Effect …

Figure 8. Mean velocity in the transverse plane placed in the inlet of the collector.

Figure 9. Mean velocity in the transverse plane placed in the outlet of the collector.

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Figure 10. Mean velocity in the transverse plane placed in the middle of the test vein.

2.2. Static Pressure Figures from 11 to 14 present the distribution of the velocity field in the different longitudinal and transverse planes. According to these results, it has been shown that the value of the static pressure is maximum in the collector but it varies from one geometry to another. Indeed, the pressure value is equal to 5.5 Pa for the rectilinear collector and it is equal to 1.93 Pa for the tunnel with a large collector opening. The value of the static pressure decreases progressively away from the collector for all of the geometries. Then, it increases outside the test vein. The static pressure distribution in the test vein differs from one geometry to another. It has been noted that the pressure distribution in the test vein for the curved collector is more uniform than for the other collectors. More precisely, the pressure uniformity area is small for the collectors.

Numerical Investigation of the Collector Geometry Effect …

Figure 11. Static pressure in the longitudinal plane.

Figure 12. Static pressure in the transverse plane placed in the inlet of the collector.

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Figure 13. Static pressure in the transverse plane placed in the outlet of the collector.

Figure 14. Static pressure in the transverse plane placed in the middle of the test vein.

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Moreover, the transverse planes clearly show this difference between the different geometries particularly at the collector outlet and in the middle of the test vein. Therefore, it can also be confirmed that the curved collector is the most suitable geometry.

2.3. Dynamic Pressure Figures from 15 to 18 present the distribution of the dynamic pressure in the different longitudinal and transverse planes. According to these results, it has been noted that a compression zone characteristic of the maximum values of the dynamic pressure is located in the test vein. The dynamic pressure remains quite high in the test vein of the wind tunnel. Far from this area, it quickly becomes very weak. The maximum value of the dynamic pressure differs from one structure to another.

Figure 15. Dynamic pressure in the longitudinal plane.

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Figure 16. Dynamic pressure in the transverse plane placed in the inlet of the collector.

Figure 17. Dynamic pressure in the transverse plane placed in the outlet of the collector.

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Figure 18. Dynamic pressure in the transverse plane placed in the middle of the test vein.

Indeed, the maximum value of the dynamic pressure reaches P = 225 Pa for the curved collector. However, it is equal to P = 233 Pa for the rectilinear collector. For the large collector opening, the dynamic pressure is equal to P = 248 Pa. In addition, the transverse planes show a clear difference between the different geometries, especially at the outlet of the collector and in the middle of the test vein.

2.4. Turbulent Kinetic Energy Figures from 19 to 22 present the distribution of the turbulent kinetic energy in the different longitudinal and transverse planes. According to these results, it has been noted that the wake zone characteristic of the maximum values of the turbulent kinetic energy is located at the walls of the test vein and at the inlet of the collector.

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Figure 19. Turbulent kinetic energy in the longitudinal plane.

Figure 20. Turbulent kinetic energy in the transverse plane placed in the inlet of the collector.

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Figure 21. Turbulent kinetic energy in the transverse plane placed in the outlet of the collector.

Figure 22. Turbulent kinetic energy in the transverse plane placed in the middle of the test vein.

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Far from the wall, the turbulent kinetic energy quickly becomes very weak. It has been found that the maximum value of the turbulent kinetic energy for the curved collector is equal to k = 1 m2s-2 at the inlet of the collector. However, the maximum value of the turbulent kinetic energy is equal to k = 1.15 m2s-2 for the rectilinear collector and the long collector. For the large opening wind tunnel, the maximum value of the turbulent kinetic energy is equal to 1 m2s-2. The numerical results confirm that the first solution is better than the others because the zones of turbulence are less frequent.

CONCLUSION In this work, numerical simulations have been developed to study the turbulent flow inside a wind tunnel using four types of collectors. Different longitudinal and transverse planes were considered to present the results from simulation, such as velocity, static pressure, dynamic pressure and turbulent kinetic energy. According to the numerical results, fluid flow characteristics differ from one configuration to another. In fact, it has been noted that the use of the curved collector is the most suitable geometry. This knowledge will be used in the construction of the wind tunnel.

REFERENCES [1]

[2]

Batill, S. M. and Hoffmann, J. J. (1986) The Aerodynamic Design of Three Dimensional Subsonic Wind Tunnel Inlets, AIAA Journal, V. 24, No. 2, pp. 268 - 269. Senol, S. (2006) Design and Computer-Aided Simulation of a Suction Type Subsonic Wind Tunnel, Master Thesis, Kocaeli University, Science Institute, Izmit.

Numerical Investigation of the Collector Geometry Effect … [3]

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Cogotti, A. (2008) Evolution of Performance of an Automotive Wind Tunnel, J. Wind Engineering and Industrial Aerodynamics, V. 96, pp. 667 - 700. [4] Chong, T. P., Joseph, P. F., Davies, P. O. A. L. (2009) Design and Performance of an Open Jet Wind Tunnel for Aero-Acoustic Measurement, Applied Acoustics, V.70, pp. 605 - 614. [5] Arifuzzaman, M. and Mohammad, M. (2012). Design construction and performance test of a low cost subsonic wind tunnel. IOSR Journal of Engineering, 2(10), 83 - 92. [6] Leifsson, L. and Koziel, S. (2015). Simulation-driven design of low-speed wind tunnel contraction. Journal of Computational Science, 7, 1 - 12. [7] di Perta, E. S., Agizza, M. A., Sorrentino, G., Boccia, L. and Pindozzi, S. (2016). Study of aerodynamic performances of different wind tunnel configurations and air inlet velocities, using computational fluid dynamics (CFD). Computers and Electronics in Agriculture, 125, 137 - 148. [8] Yadava, Y. R., Kumar, A. and Shettya, S. D. (2016). Design and Analysis of Moderate Suction Wind tunnel to study the effect of turbulence on bluff bodies. International Journal of Innovative and Emerging Research in Engineering, 3(11). [9] Ghani, S., Aroussi, A., Rice, E. (2001) Simulation of road vehicle natural environment in a climatic wind tunnel. Simulation practice and theory, 8.6: 359 - 375. [10] Launder, B., Brian, D. (1972) Lectures in mathematical models of turbulence. Academic Press, London, UK. [11] Gartmann, A., Wolfgang, F., Wolfgang, S. and Mathias, D. (2011) CFD modeling and validation of measured wind field data in a portable wind tunnel. Aeolian Research, 3, no. 3: 315 - 325. [12] Frikha, S., Driss, Z., Ayadi, E., Masmoudi, Z., Abid, M. S. (2016) Numerical and experimental characterization of multi-stage Savonius rotors, Energy, Volume 114, 1, pp. 382 - 404.

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[13] Frikha, S., Driss, Z., Hagui, M. A. (2015) Computational study of the diffuser angle effect in the design of a waste heat recovery system for oil field cabins, Energy, Volume 84, 1, Pages 219 238. [14] Damak, A., Driss, Z., Kchaou, H., Abid, M. S. (2001) Conception et réalisation d’une soufflerie à aspiration, 4ème Congrès International Conception et Modélisation des Systèmes Mécaniques [Design and realization of a suction blower, 4th International Congress Design and Modeling of Mechanical Systems] (CMSM’11), Sousse, Tunisie, pp. 1 - 7.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 2

STUDY OF THE DIFFUSER GEOMETRY EFFECT ON THE AERODYNAMIC CHARACTERISTICS OF THE FLOW INSIDE A WIND TUNNEL Sobhi Frikha*, Kamel Hchaychi, Sami Rihane and Zied Driss University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations were carried out to study the effect of the diffuser geometry on the aerodynamic characteristics of the flow inside an open wind tunnel. Particularly, we have compared four types of diffusers. The used numerical model is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε *

Corresponding Author’s E-mail: [email protected].

22

Sobhi Frikha, Kamel Hchaychi, Sami Rihane et al. turbulence model. These equations are solved by a finite volume discretization method. The numerical results obtained from the application of the CFD code "Fluent" are presented in different transverse and longitudinal planes of the wind tunnel.

Keywords: diffuser, wind tunnel, turbulent flow, CFD

INTRODUCTION Wind tunnels are facilities in which the wind is produced by fans or by compressed air to study and measure the action of the air flow around a solid. There are two basic types of wind tunnels: the closedcircuit and the open-circuit. Open-circuit draws air from the ambient environment and exhaust it back to the ambient after exiting the fan, while in closed-circuit, the air repeatedly circulates through the tunnel. The closed-circuit design delivers improved efficiency and generates less noise, but it is more expensive and more difficult to manufacture. There are various studies in the literature related to design of wind tunnels and the measurements in them. Inan [1] designed and manufactured a multi-purpose low-speed open-loop wind tunnel. He measured turbulence, flow rate and pressure in the test section of it. Senol [2] designed and performed the computer-aided flow simulation of an open circuit subsonic wind tunnel for vehicle aerodynamics experiments. Cogotti [3] described the evolution of the automotive wind tunnels in parallel with developments in measurement techniques and performed aerodynamics and aerostatics measurements in new cars. Chong et al. [4] designed and manufactured an open circuit type wind tunnel and tested aero-acoustic performance of it. Kulkarni et al. used the honeycomb and honeycomb-screen combination in an open-circuit wind tunnel to reduce both lateral and axial turbulence in the flow. The simulation has confirmed the effectiveness of honeycomb [5]. Leifsson

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and Koziel [6] designed and optimized the contraction shape of the tunnel. The contraction speeds up and aligns the flow into test section. The CFD is used to optimize the design of the contraction. The variables of contraction such as inlet size, contraction area ratio, and length and wall shape are optimized. Perta et al. [7] investigated the wind tunnel configuration at different air inlet velocities for the aerodynamics performance with the CFD. Yadava R.Y. et al. designed a low turbulence wind tunnel for studying the effect of the turbulence of bluff bodies. They replaced the settling and contraction section with the air blower. The advantage of replacing was to produce less turbulence and uniform flow [8]. Over the last decade, CFD modeling witnessed widespread growth in aerodynamics and wind engineering researches [9-11]. In this chapter, we are interested in a numerical study of the aerodynamic characteristics on a wind tunnel. Our goal is to compare different geometry of the diffuser in order to choose the best one. For this reason, numerical results are presented in different transverse and longitudinal planes of the considered control volume.

1. NUMERICAL MODEL Numerical results are conducted within the computational fluid dynamic (CFD) code "Fluent". In this code, the numerical model used is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. These equations are solved by a finite volume discretization method [12, 13].

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1.1. Boundary Conditions In this work, the designed wind tunnel is composed of a tranquilization chamber, a collector, a test section, a diffuser and a fan [14]. The control volume of the wind tunnel is presented in figure 1.

Figure 1. Wind tunnel control volume.

Figure 2. Geometric parameters of the wind tunnel.

The boundary conditions of our application consists in the inlet velocity equal to V = 4.7 m.s-1 and the outlet pressure equal to the atmospheric pressure.

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1.2. Geometrical Arrangements Figure 2 shows the different parameters of the wind tunnel such as the length and the angle of divergence of the collector and the length and the divergence angle of the diffuser. Four configurations are considered in this study: wind tunnel with curved diffuser, wind tunnel with large angle of the diffuser, wind tunnel with short diffuser and wind tunnel with long diffuser (Figure 3).

Figure 3. Wind tunnel geometries.

Table 1. Geometric parameters of the diffusers Wind tunnel type

Collector length

Wind tunnel with curved Hc = 800 mm diffuser Wind tunnel with large angle Hc = 800 mm of the diffuser Wind tunnel with short Hc = 1600 mm diffuser Wind tunnel with long Hc = 800 mm diffuser

Diffuser length Ld = 1200 mm

Divergence angle of the diffuser α/2=3,58°

Ld = 1200 mm

α/2=8,88°

Ld = 400 mm

α/2=14°

Ld = 2400 mm

α/2=2,38°

Table 1 presents the geometric parameters of the diffuser for the different configurations.

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1.3. Meshing The meshes were created using Gambit. Figure 4 presents the meshing of the control volume for the different geometries. The first case consists of 66255 nodes. The second case consists of 80221 nodes. The third case consists of 64953 nodes. However, the fourth case consists of 78875 nodes.

Figure 4. Meshing of the considered cases.

Figure 5. Visualized planes.

2. NUMERICAL RESULTS In this part, the velocity field, the static pressure, the dynamic pressure and the turbulent kinetic energy are presented. A longitudinal

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plane and a transverse plane placed in the outlet of the diffuser are considered (Figure 5).

2.1. Velocity Field Figures from 6 to 8 present the distribution of the velocity field in the different longitudinal and transverse planes. According to these results, it has been observed that there is a drop in the velocity at the diffuser for the geometry with a large angle of the diffuser. This appears as a dead zone that affects the functioning of the fan. As a result, we have noticed a separation of the boundary layer as the diffuser divergence angle increases.

Figure 6. Mean velocity in the longitudinal plane.

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Figure 7. Velocity field in the longitudinal plane.

Figure 8. Mean velocity in the transverse plane placed in the outlet of the diffuser.

For the short diffuser, the velocity drop is not very significant. Its value is equal to 12 m.s-1 at the diffuser outlet. This value is higher than

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that of the first solution which is equal to 7 m.s-1. Moreover, the zone with uniformity speed is not distributed in the same way. Indeed, it is concentrated in the wind tunnel with a short diffuser. Therefore, we decided to choose the first configuration. Le low cost and the little space are the advantage of this choice

2.2. Static Pressure Figures 9 and 10 present the distribution of the static pressure in the different longitudinal and transverse planes. According to these results, it has been shown that the static pressure distribution in the test section differs from one geometry to another. For the wind tunnel with a curved diffuser, the pressure distribution in the test section is more uniform than that in the wind tunnel with a large angle of the diffuser; precisely the pressure uniformity area is small.

Figure 9. Static pressure in the longitudinal plane.

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For the long and short diffuser configuration, we have noticed that there is not a lot of difference compared to the first solution.

Figure 10. Static pressure in the transverse plane placed in the outlet of the diffuser.

Figure 11. Dynamic pressure in the longitudinal plane.

Study of the Diffuser Geometry Effect …

31

Figure 12. Dynamic pressure in the transverse plane placed in the outlet of the collector.

2.3. Dynamic Pressure Figures 11 and 12 present the distribution of the dynamic pressure in the different longitudinal and transverse planes. According to these results, it has been noted that the compression zone characteristic of the maximum values of the dynamic pressure is located in the test vein. For the large angle of the diffuser as well as the short and the long diffuser configurations, it has been noted that a low dynamic pressure zone appears with a value equal to 20 Pa. This zone does not appear in the first solution.

2.4. Turbulent Kinetic Energy Figures 13 and 14 present the distribution of the turbulent kinetic energy in the different longitudinal and transverse planes.

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Figure 13. Turbulent kinetic energy in the longitudinal plane.

Figure 14. Turbulent kinetic energy in the transverse plane placed in the outlet of the diffuser.

According to these results, it has been noted that the wake zone characteristic of the maximum values of the turbulent kinetic energy

Study of the Diffuser Geometry Effect …

33

values is located on the wall. Throughout the control volume, the turbulent kinetic energy remains quite high. Far from the wall, it quickly becomes very weak. The decrease in turbulent kinetic energy varies from one geometry to another. Indeed, the maximum value of the turbulent kinetic energy for the wind tunnel with large angle of the diffuser is equal to k = 1.44 m2s-2 at the collector inlet and diffuser outlet. However, as for the wind tunnel with short and long diffuser the maximum value is equal to 1.15 m2s-2. It is located at the walls of the test section and at the inlet of the collector. For the first solution, there is no turbulence at the diffuser outlet. The numerical results confirm that the first solution is better than the others because the zones of turbulence are less frequent.

CONCLUSION In this chapter, numerical simulations have been developed to study the turbulent flow inside a wind tunnel using four types of diffusers. Different longitudinal and transverse planes were considered and we have presented all the results from simulation, such as velocity, static pressure, dynamic pressure and turbulent kinetic energy. According to the numerical results, fluid flow characteristics differ from one configuration to another. In fact, it has been noted that the use of the curved diffuser is the most suitable geometry. This knowledge will be used in the construction of the wind tunnel.

REFERENCES [1]

İnan, A. T. (2003) Design of Multi-Purpose Low Speed Subsonic Air Tunnel and Turbulence Measurements, Ph.D. Thesis, Marmara University, Science Institute, Istanbul.

34 [2]

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Senol, S. (2006) Design and Computer-Aided Simulation of a Suction Type Subsonic Wind Tunnel, Master Thesis, Kocaeli University, Science Institute, Izmit. [3] Cogotti, A. (2008) Evolution of Performance of an Automotive Wind Tunnel, J. Wind Engineering and Industrial Aerodynamics, V. 96, pp. 667 - 700. [4] Chong, T. P., Joseph, P. F., Davies, P. O. A. L. (2009) Design and Performance of an Open Jet Wind Tunnel for Aero-Acoustic Measurement, Applied Acoustics, V.70, pp. 605 - 614. [5] Kulkarni, V., Sahoo, N. and Chavan, S. D. (2011). Simulation of honeycomb–screen combinations for turbulence management in a subsonic wind tunnel. Journal of wind engineering and industrial aerodynamics, 99(1), 37 - 45. [6] Leifsson, L. and Koziel, S. (2015). Simulation-driven design of low-speed wind tunnel contraction. Journal of Computational Science, 7, 1 - 12. [7] di Perta, E. S., Agizza, M. A., Sorrentino, G., Boccia, L. and Pindozzi, S. (2016). Study of aerodynamic performances of different wind tunnel configurations and air inlet velocities, using computational fluid dynamics (CFD). Computers and Electronics in Agriculture, 125, 137 - 148. [8] Yadava, Y. R., Kumar, A. and Shettya, S. D. (2016). Design and Analysis of Moderate Suction Wind tunnel to study the effect of turbulence on bluff bodies. International Journal of Innovative and Emerging Research in Engineering, 3(11). [9] Ghani, S., Aroussi, A., Rice, E. (2001) Simulation of road vehicle natural environment in a climatic wind tunnel. Simulation practice and theory, 8.6: 359 - 375. [10] Launder, B., Brian, D. (1972) Lectures in mathematical models of turbulence. Academic Press, London, UK. [11] Gartmann, A., Wolfgang F., Wolfgang, S. and Mathias, D. (2011) CFD modeling and validation of measured wind field data in a portable wind tunnel. Aeolian Research, 3, no. 3: 315 - 325.

Study of the Diffuser Geometry Effect …

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[12] Frikha, S., Driss, Z., Ayadi, E., Masmoudi, Z., Abid, M. S. (2016) Numerical and experimental characterization of multi-stage Savonius rotors, Energy, Volume 114, 1, pp. 382 - 404. [13] Frikha, S., Driss, Z., Hagui, M. A. (2015) Computational study of the diffuser angle effect in the design of a waste heat recovery system for oil field cabins, Energy, Volume 84, 1, Pages 219 238. [14] Damak, A., Driss, Z., Kchaou, H., Abid, M. S. (2001) Conception et réalisation d’une soufflerie à aspiration, 4ème Congrès International Conception et Modélisation des Systèmes Mécaniques [Design and realization of a suction blower, 4th International Congress Design and Modeling of Mechanical Systems], (CMSM’11), Sousse, Tunisie, pp. 1 - 7.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 3

EFFECT OF THE COLLECTOR INLET RADIUS ON THE TURBULENT FLOW INSIDE A WIND TUNNEL Sobhi Frikha*, Sami Rihane, Zied Driss and Kamel Hchaychi University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations were carried out to study the effect of the collector inlet radius on the aerodynamic characteristics of the flow inside an open wind tunnel. Particularly, we have compared two types of collectors. The numerical model used is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. These equations are solved by a finite volume discretization method. The numerical results from the application of the *

Corresponding Author’s E-mail: [email protected].

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Sobhi Frikha, Sami Rihane, Zied Driss et al. CFD code “Fluent” are presented in different transverse and longitudinal planes of the wind tunnel.

Keywords: collector, wind tunnel, turbulent flow, CFD

INTRODUCTION A wind tunnel is a device designed to generate air flows of various speeds through a test section. Wind tunnels are typically used in aerodynamic research to analyze the behavior of flows under varying conditions, both within channels and over solid surfaces. There are two basic types of wind tunnels: the closed-circuit and the open-circuit. Open-circuit draw air from the ambient environment and exhaust it back to the ambient after exiting the fan, while in closed-circuit, the air repeatedly circulates through the tunnel. The closed-circuit design delivers improved efficiency and generates less noise, but is more expensive and more difficult to manufacture. There are various studies in the literature related to design of wind tunnels and the measurements in them. Senol [1] designed and performed the computer-aided flow simulation of an open circuit subsonic wind tunnel for vehicle aerodynamics experiments. Batill et al., [2] studied the vacuum effect created by a fan in the suction type wind tunnel and calculated the energy losses in the boundary layer flows due to this effect emerged. Cogotti [3] described the evolution of the automotive wind tunnels in parallel with developments in measurement techniques and performed aerodynamics and aerostatics measurements in new cars. Chong et al., [4] designed and manufactured an open circuit type wind tunnel and tested aero-acoustic performance of it. Kulkarni et al., [5] used the honeycomb and honeycomb-screen combination in an open-circuit wind tunnel to reduce both lateral and axial turbulence in the flow. The simulation has confirmed the effectiveness of honeycomb. Arifuzzaman and Mashud designed a short length subsonic wind tunnel to validate its

Effect of the Collector Inlet Radius …

39

adequacy for aerodynamic analysis as well to determine the velocity profile at different positions of the test section. After testing the performance, this newly designed tunnel was a good tool to provide steady flow with consistent speed through the test section without excessive turbulence [6]. Perta et al., [7] investigated the wind tunnel configuration at different air inlet velocities for the aerodynamics performance with the CFD. Yadava et al., designed a low turbulence wind tunnel for studying the effect of the turbulence of bluff bodies. They replaced the settling and contraction section with the air blower. The advantage of replacing was to produce less turbulence and uniform flow [8]. Over the last decade, CFD modeling has seen widespread growth in aerodynamics and wind engineering research [9, 10, 11]. In this chapter, we are interested in a numerical study of the aerodynamic characteristics on a wind tunnel. Our goal is to compare two geometry of the collector in order to choose the best one. For this reason, numerical results are presented in different transverse and longitudinal planes of the considered control volume.

1. NUMERICAL MODEL Numerical results are conducted within the computational fluid dynamic (CFD) code “Fluent”. In this code, the numerical model used is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. These equations are solved by a finite volume discretization method [12, 13].

1.1. Boundary Conditions In this work, the designed wind tunnel is composed by a tranquilization chamber, a collector, a test section, a diffuser and a fan

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[14]. The control volume of the wind tunnel is presented in figure 1. The boundary conditions of our application consists of the inlet velocity equal to V = 4.7 m.s-1 and the outlet pressure equal to the atmospheric pressure.

Figure 1. Wind tunnel control volume.

1.2. Collector Geometries Two configurations are considered in this study: collector without inlet radius and collector with inlet radius (Figure 2).

(a) Collector without inlet radius Figure 2. Wind tunnel geometries.

(b) Collector with inlet radius

Effect of the Collector Inlet Radius …

41

1.3. Meshing The meshes were created using Gambit. Figure 4 presents the meshing of the control volume for the different geometries. The first case consists on 166255 nodes. However, the second case consists on 37353 nodes.

(a) collector without inlet radius

(b) collector with inlet radius

Figure 3. Meshing.

2. NUMERICAL RESULTS In this part, the velocity field, the static pressure, the dynamic pressure and the turbulent kinetic energy are presented. Different longitudinal and transverse planes are considered as presented in figure 4.

Figure 4. Visualized planes.

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2.1. Velocity Field Figures from 5 to 8 present the distribution of the velocity field in the different longitudinal and transverse planes. According to these results, it has been observed that the mean velocity reaches its maximum value for both geometries at the test section. This velocity drops downstream to the output of the control volume. The maximum value of the mean speed differs from one configuration to another. Also, we have noted that for the first configuration, the maximum velocity value is about 19.1 m.s-1 while for the second configuration, the maximum velocity value is about 20.1 m.s-1.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 5. Mean velocity in the longitudinal plane.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 6. Velocity field in the longitudinal plane.

The inlet radius of the collector affects the velocity profile in the test section and the uniformity area. On the transverse planes, the difference between the different geometries is clear particularly in the

Effect of the Collector Inlet Radius …

43

collector outlet and in the middle of the test section. Therefore, we propose to use the first configuration which gives better operating conditions.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 7. Mean velocity in the transverse plane placed in the outlet of the collector.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 8. Mean velocity in the transverse plane placed in the middle of the test vein.

2.2. Static Pressure Figures from 9 to 11 present the distribution of the static pressure in the different longitudinal and transverse planes. According to these results, it has been shown that with the wind tunnel with an inlet radius the distribution of pressure at the outlet of the diffuser is more uniform than the wind tunnel without an inlet radius.

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(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 9. Static pressure in the longitudinal plane.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 10. Static pressure in the transverse plane placed in the outlet of the collector.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 11. Static pressure in the transverse plane placed in the middle of the test vein.

2.3. Dynamic Pressure Figures from 12 to 14 present the distribution of the dynamic pressure in the different longitudinal and transverse planes. According to these results, it has been noted that the wake zone characteristic of

Effect of the Collector Inlet Radius …

45

the maximum values of the dynamic pressure is located in the test section. Also, the dynamic pressure reaches its maximum value for the collector with inlet radius; it is equal to 247 Pa. For the collector without inlet radius, the maximum value of the dynamic pressure is equal to 225 Pa. Indeed, the dynamic pressure distribution is less uniform in the second configuration.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 12. Dynamic pressure in the longitudinal plane.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 13. Dynamic pressure in the transverse plane placed in the outlet of the collector.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 14. Dynamic pressure in the transverse plane placed in the middle of the test vein.

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2.4. Turbulent Kinetic Energy Figures from 15 to 17 present the distribution of the turbulent kinetic energy in the different longitudinal and transverse planes. According to these results, it has been noted that the wake zone characteristic of the maximum values of the turbulent kinetic energy is located at the wall. Throughout the control volume, the turbulent kinetic energy remains quite high. Far from the wall, it quickly becomes very weak.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 15. Turbulent kinetic energy in the longitudinal plane.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 16. Turbulent kinetic energy in the transverse plane placed in the outlet of the collector.

The maximum value of the turbulent kinetic energy is reached for the wind tunnel with an inlet radius and it is equal to 1.29 m2s-2 at the collector inlet. However, for the wind tunnel without inlet radius, the maximum value is equal to 1 m2s-2. Particularly, the distribution of the

Effect of the Collector Inlet Radius …

47

turbulent kinetic energy is less uniform in the second configuration. Moreover, the numerical results confirm that the first solution is more adequate since it presents less turbulence.

(a) Collector without inlet radius

(b) Collector with inlet radius

Figure 17. Turbulent kinetic energy in the transverse plane placed in the middle of the test vein.

CONCLUSION In this chapter, numerical simulations have been developed to study the turbulent flow inside a wind tunnel using two types of collector. Different longitudinal and transverse planes were considered and we presented all the results from simulation, such as velocity, static pressure, dynamic pressure and turbulent kinetic energy. According to the numerical results, fluid flow characteristics differ from one configuration to another. In fact, it has been noted that the use the collector without inlet radius is the most suitable geometry. This knowledge will be used in the construction of the wind tunnel.

REFERENCES [1]

Senol, S. (2006) Design and Computer-Aided Simulation of a Suction Type Subsonic Wind Tunnel, Master Thesis, Kocaeli University, Science Institute, Izmit.

48 [2]

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Batill, S.M. and Hoffmann, J.J. (1986) The Aerodynamic Design of Three Dimensional Subsonic Wind Tunnel Inlets, AIAA Journal, V. 24, No. 2, pp. 268-269. [3] Cogotti, A. (2008) Evolution of Performance of an Automotive Wind Tunnel, J. Wind Engineering and Industrial Aerodynamics, V. 96, pp. 667-700. [4] Chong, T.P., Joseph, P.F., Davies, P.O.A.L. (2009) Design and Performance of an Open Jet Wind Tunnel for Aero-Acoustic Measurement, Applied Acoustics, V.70, pp. 605-614. [5] Kulkarni, V., Sahoo, N., & Chavan, S. D. (2011). Simulation of honeycomb–screen combinations for turbulence management in a subsonic wind tunnel. Journal of wind engineering and industrial aerodynamics, 99(1), 37-45. [6] Arifuzzaman, M., & Mohammad, M. (2012). Design construction and performance test of a low cost subsonic wind tunnel. IOSR Journal of Engineering, 2(10), 83-92. [7] di Perta, E. S., Agizza, M. A., Sorrentino, G., Boccia, L., & Pindozzi, S. (2016). Study of aerodynamic performances of different wind tunnel configurations and air inlet velocities, using computational fluid dynamics (CFD). Computers and Electronics in Agriculture, 125, 137-148. [8] Yadava Y. R., Kumar A and Shettya S. D (2016). Design and Analysis of Moderate Suction Wind tunnel to study the effect of turbulence on bluff bodies. International Journal of Innovative and Emerging Research in Engineering, 3(11). [9] Ghani, S., Aroussi A., Rice E. (2001) Simulation of road vehicle natural environment in a climatic wind tunnel. Simulation practice and theory8.6: 359-375. [10] Launder, B., Brian D. (1972) Lectures in mathematical models of turbulence. Academic Press, London, UK. [11] Gartmann, A., Wolfgang F., Wolfgang S., and Mathias D. (2011) CFD modeling and validation of measured wind field data in a portable wind tunnel. Aeolian Research 3, no. 3: 315-325.

Effect of the Collector Inlet Radius …

49

[12] Frikha S., Driss Z., Ayadi E., Masmoudi Z., Abid M. S. (2016) Numerical and experimental characterization of multi-stage Savonius rotors, Energy, Volume 114, 1, pp. 382-404. [13] Frikha S., Driss Z., Hagui M.A. (2015) Computational study of the diffuser angle effect in the design of a waste heat recovery system for oil field cabins, Energy, Volume 84, 1, Pages 219-238. [14] Damak A., Driss Z., Kchaou H., Abid M.S. (2001) Conception et réalisation d’une soufflerie à aspiration [Design and realization of a suction blower], 4ème Congrès International Conception et Modélisation des Systèmes Mécaniques (CMSM’11), Sousse, Tunisie, pp. 1-7.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 4

STUDY OF THE ROTATING AREA EFFECT ON THE TURBULENT FLOW AROUND A SAVONIUS WIND ROTOR Sobhi Frikha*, Zied Driss, Emna Ayadi, Zied Masmoudi and Mohamed Salah Abid University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulation and experimental validation were performed to study the effect of the rotating area on the turbulent flow around a Savonius wind rotor. We were particularly interested in visualizing the velocity field, the static pressure, the dynamic pressure, the vorticity, the turbulent kinetic energy, the dissipation rate of the turbulent kinetic energy and the turbulent viscosity. The software "SolidWorks Flow Simulation" has been used to present the local *

Corresponding Author’s E-mail: [email protected].

52

Sobhi Frikha, Zied Driss, Emna Ayadi et al. characteristics in different transverse and longitudinal planes. The considered numerical model is based on the resolution of the NavierStokes equations in conjunction with the standard k-ε turbulence model. These equations were solved by a finite volume discretization method. The wind tunnel experiment results were compared to the numerical results in terms of velocity profile, dynamic torque, dynamic torque coefficient, power and power coefficient. The good agreements confirm the validity of the numerical method.

Keywords: wind tunnel, turbulent flow, aerodynamic structure, rotating area, CFD

NOMENCLATURE Cp C1ε C2ε Cμ D m Fi Gk H k P Re

coefficient of the power, dimensionless constant of the k-ε turbulence model, dimensionless constant of the k-ε turbulence model, dimensionless constant of the k-ε turbulence model, dimensionless rotor diameter, m bucket thickness, m Force components, N production term of turbulence, kg.m-1.s-3 bucket height, W.m-3 turbulent kinetic energy, J.kg-1 pressure, Pas Reynolds number, dimensionless

ui

Velocity components, m.s-1

u i'

Fluctuating velocity components, m.s-1

xi x y z ε

Cartesian coordinate, m Cartesian coordinate, m Cartesian coordinate, m Cartesian coordinate, m dissipation rate of the turbulent kinetic energy, W.kg-1

Study of the Rotating Area Effect on the Turbulent Flow … μ μt ρ σk σε Ω

53

dynamic viscosity, Pa.s turbulent viscosity, Pa.s density, kg.m-3 constant of the k-ε turbulence model, dimensionless constant of the k-ε turbulence model, dimensionless angular velocity, rad.s-1

INTRODUCTION An interest in wind energy has been growing and researchers have attempted the development to introduce cost-effective, reliable wind energy conversion systems. Wind turbines can rotate around either a horizontal or a vertical axis. Vertical wind turbines consist of two major types, the Darrieus rotor and Savonius rotor. The Darrieus wind turbine rotates around a central axis due to the lift force produced by the rotating airfoils, whereas a Savonius rotor rotates due to the drag force created by its blades. The best qualities of the Savonius rotors are the simplicity, the reliability and the low noise production. Because of its low rotation speed, Savonius rotors show lower efficiencies and thus they are incapable of providing adequate electricity. To increase the efficiency of the wind turbine, the designing of blades plays a very important role and many works have been made on the design improvements of the original Savonius rotor. Grinspan et al. [1] developed a new blade shape with a twist for the Savonius rotor. They got a maximum power coefficient of 0.5. Saha and Rajkumar [2] performed work on twist bladed metallic Savonius rotor and compared the performance with conventional semi-circular blades having no twist. They got an efficiency of 0.14. Their rotor also produced good starting torque and large rotational speeds. Mohamed et al. [3] considered an improved design to increase the output power of a Savonius wind rotor with either two or three blades. Other works [4-6] performed unsteady simulation and compared improved version of

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Savonius wind rotor. Menet and Bourabaa [7] studied the influence of some geometrical parameters on the aerodynamic behavior of the flow around a Savonius rotor. Thus, they made a numerical simulation and compared results with experimental studies. They studied the effect of the overlap ratio, the shaft, the chassis and the Reynolds number. Influence of Reynolds number was investigated by Kamoji et al. [8] for a modified Savonius wind rotor without shaft. The coefficient of power increases by 19% as the Reynolds number increases from 80,000 to 150,000. The maximum coefficient of power increases with the increase of the Reynolds number. Ushiyama and Nagai [9] tested several parameters of the Savonius wind rotor including the gap ratio, the aspect ratio, the number of cylindrical buckets, the number of stages, the endplate effects, the overlap ratio and the bucket design. The highest efficiency of all tested configurations was 24% for a two-stage, two-bucket rotor. Akwa et al. [10] studied the influence of the buckets overlap ratio of a Savonius wind rotor on the averaged torque and power coefficients by changing the geometry of the rotor. It has been found that the maximum device performance occurs for buckets overlap ratios with values close to 0.15. Khan et al. [11] tested different blade profiles of a Savonius wind rotor both in tunnel and natural wind conditions and they varied the overlap. Roy et al. [12] reviewed the numerical works. They have shown that with a proper computational methodology, the design, the performance and the efficiency of a Savonius wind rotor can be enhanced. The highest Cp of 0.375 was achieved for a blade profile of S-section Savonius rotor at an optimum overlap ratio of 30%. Driss et al. [13] made a numerical simulation of the turbulent flow around a small incurved Savonius wind rotor and compare the results with experimental results conducted in an open wind tunnel. In comparison with a circular Savonius wind rotor, the flow circulation of this rotor is enhanced. Driss et al. [14] compared different designs of rotors characterized by the bucket angles equal to ψ=60°, ψ=75°, ψ=90° and ψ=130°. It has been noted that the depression zones increase with the increase of the bucket arc angle. The

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55

acceleration zone characteristic of the maximum velocity values are recorded was formed in the convex surface of the rotor bucket and gets greater as the bucket arc. The wakes characteristics of the maximum values of the turbulent kinetic energy are more developed with the increase of the bucket arc angle. Sharma et al. [15] studied the performance of a two-stage two-bladed configuration of the Savonius rotor. They conducted experiments in a subsonic wind tunnel. The studied parameters were the overlap, the tip speed ratio, the power coefficient (Cp) and the torque coefficient (Ct). The study showed that a maximum Cp of 0.517 was obtained at 9.37% overlap condition. Similarly, power and torque coefficients decrease with the increase of overlap from 9.37% to 19.87%. Saha et al. [16] conducted tests by varying the number of stages from one to three. They concluded that when the number of stages increased from one to two, the rotor shows better performance characteristics. However, the performance gets degraded when the number of stages becomes three. Chaitep et al. [17] has studied the effect of the operating conditions (tip speed ratio) to the starting rotation, reverse up rotation, power and torque coefficients of curved blades vertical axis wind turbine. This turbine was tested in the laboratory scale in wind tunnel with different velocities of 1.5, 2.0, 3.0, 4.0 and 5.0 m/s. Mahmoud et al. [18] conducted an experimental analysis by using a wind tunnel experimental setup. The experimental results show that two bladed Savonius rotors are more efficient than the three and four bladed Savonius rotors. The rotor with end plates gives higher efficiency than the one without end plates. Blades having overlap ratios are better than the blades without overlap ratios. By increasing the aspect ratio, coefficient of performance (Cp) also increases. Frikha et al. [19] studied the effect of multi-stage on the performance of a Savonius wind rotor. Five configurations with different numbers of stages were used. Basing on the obtained results, the number of stages affects the aerodynamic behavior of the turbulent flow around the Savonius wind rotor. Experiments were conducted in

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an open wind tunnel. The comparison of the local and the global characteristics with the experimental results presents a good agreement. According to these anterior studies, it is clear that the study of the Savonius wind rotor design is very important to improve the aerodynamic characteristics and the rotor performance. In this context, we are interested in the study of the numerical parameters effect and particularly the rotating area effect on the aerodynamic characteristics of the flow around a Savonius wind rotor. In addition, wind tunnel experiments are developed and compared to the numerical simulations to choose the most effective model.

1. MATERIAL AND METHOD 1.1. Savonius Wind Rotor In this study, we have an interest in a Savonius wind rotor, used for converting the force of the wind into torque on a rotating shaft. The wind turbine consists of a Plexiglas bucket with a height H=200 mm, a diameter D=173 mm, an aspect ratio H/D=1.15 and an overlap ratio m/D = 0.034. Figure 1 presents the configuration of the bucket geometry studied in this work.

Figure 1. Vertical axis Savonius rotor.

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57

1.2. Wind Tunnel The overall design of the open circuit wind tunnel is presented in figure 2. This tunnel is formed by a ventilation chamber (1), a diffuser (2), a test section (3), a collector (4), a plenum (5), a support (6) and a wind turbine (7). The total length of the wind tunnel is 3857 mm. The test vein is of 400 mm of width, 800 mm of length and 400 mm of height.

Figure 2. Wind tunnel components.

1.3. Experimental Method The rotor axis has been placed in the middle of the test vein. An anemometer AM-4204 was used to measure the wind speed in different positions with an accuracy of 0.1 m/s (Figure 3). The rotational speed of the wind turbine rotor was measured with a digital tachometer CA-27 model (Figure 4). To measure the static torque on the rotor shaft, a torque meter TQ-8800 model was used (Figure 5). The dynamic torque exerted on the rotor shaft was measured with a DC generator which transforms the torque on its axis at an electrical current. The generator

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is coupled to the dynamometer RZR-2102 model which provides mechanical power to the generator and displays simultaneously the speed and the dynamic torque. The calibration curve that connects the electric current supplied by the generator to the dynamic torque is shown in Figure 6. Figure 7 presents the Savonius rotor assembled with a dynamometer.

Figure 3. Anemometer. Description Velocity range Resolution Precision Alimentation Autonomy Dimension Weight

Figure 4. Characteristics of the tachometer.

Tachometer types CA 1725 6 to 100000 tr/min 0.0006 à 6 according to rating 10-4 of the reading ± 6 points 9V 250 measures 5 min with optical sensor 21 x 72 x 47 mm 250 g

Study of the Rotating Area Effect on the Turbulent Flow … Description Maker Measurement parameters Measurement range Resolution Precision Overload capacity Dimension

Static torque meter TQ 8800 Lutron Static torque Max 0-1471.1 N.cm 0.1 N.cm ± (1.5% +5d) 220.1 N.cm max 180×72×32 mm

Figure 5. Characteristics of the static torque meter.

Figure 6. Calibration curve.

Figure 7. Savonius rotor assembled with a dynamometer.

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2. NUMERICAL MODEL 2.1. Governing Equations In this study, the continuity equation, the momentum equation, the turbulent kinetic energy (k) and the dissipation rate of turbulent kinetic energy (ε) equations have been solved with the software “Solid Works Flow Simulation.” The mathematical formulation is based on the Navier-Stokes equations. The equations for the conservation of the mass and momentum for the compressible and incompressible flow positions in the numerical analysis can be written in the Cartesian system. The continuity equation is:

ρ

(ρ u i )

t

xi

0

(1)

The Momentum equation is: (ρ u i )

(ρ u i u j )

P

t

xj

xi

xj

μ

uj

uj

2

xj

xi

3

δij 

ui

(-ρ u i' u 'j )

xi

xj

Fi

(2)

They appear a number of additional unknown (-ρ u i' u 'j ) defined by:

ρu i' u 'j

μt

ui

uj

2

xj

xi

3

ρ k δ ij

(3)

In the present work, we have used the k-ε turbulence model. The transport equations for the turbulent kinetic energy k and the dissipation rate of the turbulent kinetic energy ε are written as follows:

Study of the Rotating Area Effect on the Turbulent Flow … (ρ k)

(ρ u i k)

t

xi

(ρ ε)

(ρ u i ε)

t

xi

xj

xj

μ

μ

μt

k

σk

xj

μt

ε

σε

xj

C1ε

Gk

ε k

Gk

ρε

C 2ε ρ

61

(4)

ε2 k

(5)

The turbulent viscosity is defined by:

μ t =ρ Cμ

k2 ε

(6)

2.2. Boundary Conditions

Figure 8. Boundary conditions.

The computational domain is defined by the interior volume of the wind tunnel blocked by two planes. The first one is the tranquilization chamber entry and the second one is the exit of the diffuser. For the inlet velocity, we take a value of 3 m.s-1 and for the outlet pressure, a value of 101325 Pa. The Multi-Reference Frame (MRF) approach has

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been adopted to consider the rotor rotation defined by an angular velocity of Ω = 52 rd.s-1 (Figure 8).

2.3. Meshing

(a) 3-D view

(b) Plane x= 0 mm

(c) Plane y=0 mm Figure 9. Meshing.

In this study, we have used the local initial mesh option. This mesh option allows us to specify an initial mesh in a local region of the computational domain to better resolve the model geometry and flow particularities in this region. The initial mesh is constructed from the basic mesh by refining the basic mesh cells in accordance with the specified mesh settings. The Basic mesh is formed by dividing the

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63

computational domain into slices by parallel planes which are orthogonal to the global coordinate system's axes. In our simulations, we have used a number of cells equal to 66 946 cells (Figure 9).

3. LOCAL RESULTS To choose the best rotating area, we have tested four different diameters equal to 220 mm, 260 mm, 320 mm and 330 mm (Figure 10).

(a) D = 220 mm

(b) D = 260 mm

(c) D = 320 mm

(d) D = 330 mm

Figure 10. Studied rotating area.

As represented in Figure 11, two longitudinal planes defined by x=0 mm and y=0 mm and three transverse planes defined by z=-150 mm, z=150 mm and z=0 mm are considered to visualize the velocity field, the static pressure, the dynamic pressure, the turbulent kinetic energy, the dissipation rate of the turbulent kinetic energy, the turbulent viscosity and the vorticity.

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Figure 11. Visualization planes.

3.1. Velocity Field Figures 12 and 13 present the distribution of the velocity field respectively in the longitudinal planes defined by y=0 mm and x=0 mm and the transverse planes defined by z=-150 mm, z=0 mm and z=150 mm. According to these results, it has been noted that the velocity is weak in the inlet of the collector. Indeed, it is governed by the boundary condition value of the inlet velocity, which is equal to 3 m.s-1. In this region, the velocity field is uniform and increases progressively downstream of the collector. The flow deflection has been observed at the meeting of the wind turbine. Downstream of the rotor, the velocity keeps increasing till the outside of the test section. As shown in longitudinal plane y = 0 mm, a wake characteristic of the minimum value of the velocity has been observed downstream of the rotor in the middle of the test section. According to the distribution of the velocity

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(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

field in the transverse plane, the maximum values of the velocity are obtained with the fourth domain characterized by D=330 mm.

Figure 12. (Continued).

Sobhi Frikha, Zied Driss, Emna Ayadi et al.

(d) D = 330 mm

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(a) Plane y=0 mm

(b) Plane x=0 mm

(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Figure 12. Distribution of the Velocity fields in the longitudinal planes.

Figure 13. (Continued).

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(d) D = 330 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 13. Distribution of the Velocity fields in the transverse planes.

3.2. Mean Velocity

(a) D = 220 mm

Figures 14 and 15 present the distribution of the mean velocity respectively in the longitudinal planes defined by y=0 mm and x=0 mm and the transverse planes defined by z=-150 mm, z=0 mm and z=150 mm. According to these results, the maximum value of the velocity reaches V= 15 m.s-1 in the test vein. Also, a large wake characteristic of the maximum value of the mean velocity is developed. This wake is concentrated around the bucket and downstream of the rotor. According to the distribution of the mean velocity in the longitudinal and the transverse planes, it has been noted that the maximum values of the mean velocity are obtained with the rotating area characterized by D = 330 mm.

Figure 14. (Continued).

Sobhi Frikha, Zied Driss, Emna Ayadi et al.

(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

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(a) Plane y=0 mm

(b) Plane x=0 mm

Figure 14. Distribution of the average velocity in the longitudinal planes.

(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 15. Distribution of the mean velocity in the transverse planes.

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3.3. Static Pressure

(b) D = 260 mm

(a) D = 220 mm

Figures 16 and 17 present the distribution of the static pressure respectively in the longitudinal planes defined by x=0 mm and y = 0 mm and the transverse planes defined by z=0 mm, z=150 mm, and z=150 mm. According to these results, it has been noted that the pressure is maximum in the upstream of the rotor and it decreases downstream of the rotor. The distribution of the pressure in the plane defined by y=0 mm shows a compression zone in the convex surfaces of the buckets. Also, a depression zone is located in the concave surfaces of the rotor buckets and downstream of the rotor. The maximum depression is obtained with the fourth domain defined by D = 330 mm.

Figure 16. (Continued).

(d) D = 330 mm

(c) D = 320 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane y=0 mm

(b) Plane x=0 mm

(a) D = 220 mm

Figure 16. Distribution of the static pressure in the longitudinal planes.

Figure 17. (Continued).

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(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

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(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 17. Distribution of the static pressure in the transverse planes.

3.4. Dynamic Pressure Figures 18 and 19 present the distribution of the dynamic pressure respectively in the longitudinal planes defined by x=0 mm and y = 0 mm and the transverse planes defined respectively by z=0 mm, z=150 mm, and z=-150 mm. According to these results, the dynamic pressure is weak in the collector inlet and increases progressively through the collector. Around the rotor, a depression zone has been observed. Also, a depression zone characteristic of the minimum value of the dynamic pressure has been observed upstream of the rotor in the middle of the test vein. According to the distribution of the dynamic pressure in the longitudinal and the transverse planes, the maximum values of the

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(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

dynamic pressure are obtained with the fourth domain defined by D = 330 mm.

Figure 18. (Continued).

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(d) D = 330 mm

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(a) Plane y=0 mm

(b) Plane x=0 mm

(d) D = 330 mm (c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Figure 18. Distribution of the dynamic pressure in the longitudinal planes.

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 19. Distribution of the dynamic pressure in the transverse planes.

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3.5. Turbulent Kinetic Energy

(b) D = 260 mm

(a) D = 220 mm

Figures 20 and 21 present the distribution of the turbulent kinetic energy respectively in the longitudinal planes defined by x=0 mm, y= 0 mm and the transverse planes defined by z = 0 mm, z=150 mm and z=150 mm. From these results, it has been noted that the turbulent kinetic energy is very weak upstream of the rotor. A wake characteristic of the maximum value of the turbulent kinetic energy appears downstream of the rotor. An increase of the turbulent kinetic energy has been observed on the convex surface of the buckets. According to the distribution of the turbulent kinetic energy on the longitudinal and the transverse plane, the maximum value of the turbulent kinetic energy is obtained for the fourth domain defined by D = 330 mm.

Figure 20. (Continued).

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(d) D = 330 mm

(c) D = 320 mm

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(a) Plane y=0 mm

(b) Plane x=0 mm

(b) D = 260 mm

(a) D = 220 mm

Figure 20. Distribution of the turbulent kinetic energy in the longitudinal planes.

Figure 21. (Continued).

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(d) D = 330 mm

(c) D = 320 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 21. Distribution of the turbulent kinetic energy in the transverse planes.

3.6. Dissipation Rate of the Turbulent Kinetic Energy Figures 22 and 23 show the distribution of the dissipation rate of the turbulent kinetic energy respectively in the longitudinal planes defined by x=0 mm and y = 0 mm and the transverse planes defined by z=0 mm, z=150 mm, and z=-150 mm. According to these results, the dissipation rate of the turbulent kinetic energy is very weak upstream of the rotor. However, it increases in the rotating area and downstream of the rotor. Outsidethe test vein, it has been noted that the dissipation rate increases through the diffuser. In fact, a wake characteristic of the maximum values of the dissipation rate of the turbulent kinetic energy is developed around the wind turbine. Otherwise, it has been noted that the rotating area has a direct effect on the distribution of the dissipation rate of the turbulent kinetic energy. According to the distribution of the dissipation rate of the turbulent kinetic energy in the longitudinal and the transverse planes, the maximum values of the dissipation rate of the turbulent kinetic energy are obtained for the fourth domain defined by D = 330 mm.

Sobhi Frikha, Zied Driss, Emna Ayadi et al.

(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

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(a) Plane y=0 mm

(b) Plane x=0 mm

Figure 22. Distribution of the dissipation rate of the turbulent kinetic energy in the longitudinal planes.

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(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 23. Distribution of the dissipation rate of the turbulent kinetic energy in the transverse planes.

3.7. Turbulent Viscosity Figures 24 and 25 present the distribution of the turbulent viscosity respectively in the longitudinal planes defined by x=0 mm and y = 0 mm and the transverse planes defined by z=0 mm, z=150 mm, and z= 150 mm. According to these results, it has been noted that the turbulence viscosity is very weak in the collector and the test vein inlet.

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(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Out of the test vein, the turbulence viscosity increases. In the diffuser, it has been observed a wake characteristic of the maximum values of the turbulent viscosity. Otherwise, it has been noted that the rotating area has an effect on the distribution of the turbulent viscosity. In fact, the wake characteristic of the maximum values of the turbulent viscosity is more developed with the increase of the rotating area.

Figure 24. (Continued).

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(d) D = 330 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane y=0 mm

(b) Plane x=0 mm

(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

(a) D = 220 mm

Figure 24. Distribution of the turbulent viscosity in the longitudinal planes.

(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 25. Distribution of the turbulent viscosity in the transverse planes.

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3.8. Vorticity

(b) D = 260 mm

(a) D = 220 mm

Figures 26 and 27 present the distribution of the vorticity respectively in the longitudinal planes defined by x=0 mm and y=0 mm and the transverse planes defined by z=0 mm, z=150 mm and z=-150 mm. According to these results, it has been observed that the wake characteristic of the maximum value of the vorticity appears around the rotating area. Out of the test vein, the vorticity increases near the wall. A wake characteristic of the maximum value has been observed in the distributor outlet. According to the distribution of the vorticity in the longitudinal plane defined by y=0 mm, the maximum values of the viscosity are obtained with the first and the second domain.

Figure 26. (Continued).

(d) D = 330 mm

(c) D = 320 mm

Study of the Rotating Area Effect on the Turbulent Flow …

(a) Plane y=0 mm

(b) Plane x=0 mm

(a) D = 220 mm

Figure 26. Distribution of the vorticity in the longitudinal planes.

Figure 27. (Continued).

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(d) D = 330 mm

(c) D = 320 mm

(b) D = 260 mm

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(a) Plane z=0 mm

(b) Plane z=150 mm

(c) Plane z=-150 mm

Figure 27. Distribution of the vorticity in the transverse planes.

4. COMPARISON BETWEEN THE NUMERICAL AND THE EXPERIMENTAL RESULTS 4.1. Velocity Profiles Figure 28 presents the superposition of the numerical results gathered from the CFD code and the experimental results taken by the anemometer. The considered planes are defined by z= 150 mm and z= 150 mm. For each transverse plane, the velocity values are taken along the directions defined by x= - 150 mm, x= 150 mm, x= -100 mm, x= 100 mm, x= -50 mm and x= 50 mm. The different velocity profiles seem to have the same appearance but the velocity values depend on the

Study of the Rotating Area Effect on the Turbulent Flow …

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(c) x= -100 mm

(b) x= 150 mm

(a) x= -150 mm

rotating field area. Indeed the greater the rotating area gets the smaller the gap between numerical and experimental results is. The best agreement with the experimental results is obtained with the rotating field area equal to D = 330 mm.

Figure 28. (Continued).

Sobhi Frikha, Zied Driss, Emna Ayadi et al.

(f) x= 50 mm

(e) x= -50 mm

(d) x= 100 mm

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(a) Plane z=150 mm

Figure 28. Velocity profiles.

(b) Plane z=-150 mm

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4.2. Global Characteristics Figure 29 shows the variation of the dynamic torque and the power as a function of the rotating speed of the rotor and the dynamic torque coefficient and the power coefficient as a function of the tip speed ratio.

(a) Dynamic torque

(b) Dynamic torque coefficient

(c) Power

(d) Power coefficient

Figure 29. Global characteristics.

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Globally, these profiles present the same evolution of the curve. In fact, it has been observed that the dynamic torque and the power decrease when the rotation speed increases. Indeed, the dynamic torque coefficient and the power coefficient decrease when the tip speed ratio increases. Also, it has been noted that those parameters depend on the domain. The fourth domain characterized by D = 330 mm gives the best agreement with the experimental results. The comparison between the numerical and experimental results appears in a good agreement.

CONCLUSION In this paper, we have studied the rotating area effect on the aerodynamic structure developed with a Savonius wind rotor. Four configurations with different rotor diameters were used. Numerical results, such as velocity fields, mean velocity, pressure and turbulent characteristics are presented in different longitudinal and transverse planes of the considered wind tunnel. Basing on the obtained results, the rotating area affects the aerodynamic behavior of the turbulent flow around the Savonius wind rotor. In fact, the maximum values of the local characteristics are obtained with a rotor diameter equal to D=330 mm. Experiments were also conducted in an open wind tunnel. According to the velocity, the power and the torque distribution, the fourth domain characterized by D = 330 mm gives the best agreement with the experimental results.

REFERENCES [1]

Grinspan, A. S., Kumar, P. S., Saha, U. K., Mahanta, P., Ratnarao, D. V., Veda Bhanu, G. (2001). Design development & testing of Savonius wind turbine rotor with twisted blades, Proceedings of

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international conference on fluid mechanics & fluid power, India, 28-31. [2] Saha, U. K., Rajkumar, M. (2005). On the performance analysis of Savonius rotor with twisted blades, J. Renew. Energy, pp. 9601481. [3] Mohamed, M. H., Janiga, G., Thévenin E. Pap, D. (2010). Optimization of Savonius turbines using an obstacle shielding the returning blade, Renewable Energy 35, 2618-2626. [4] D'Alessandro, V., Montelpare, S., Ricci, R., Secchiaroli, A. (2010). Unsteady Aerodynamics of a Savonius wind rotor: a new computational approach for the simulation of energy performance, Energy 35, 3349-3363. [5] Dobreva, I, Massouh F. (2011). CFD and PIV investigation of unsteady flow through Savonius wind turbine, Energy Procedia 6, 711-720. [6] Zhou, T., Rempfer, D. (2013). Numerical study of detailed flow field and performance of Savonius wind turbines, Renewable Energy 51, 373-381. [7] Menet, J. L., & Bourabaa, N. (2004). Increase in the Savonius rotors efficiency via a parametric investigation. In: European wind energy conference & exhibition, London, UK. [8] Kamoji, M. A., Kedare, S. B., Prabhu, S.V. (2009). Experimental investigations on single stage modified Savonius rotor, Applied Energy, 86, 1064-1073. [9] Ushiyama, I., Nagai, H. (1988). Optimum design configurations and performances of Savonius rotors, Wind Eng. 12-1, 59-75. [10] Akwa, J. V., Júnior, G. A. Da S., Petry, A. P. (2012). Discussion on the verification of the overlap ratio influence on performance coefficients of a Savonius wind rotor using computational fluid dynamics, Renewable Energy 38, 141-149. [11] Khan, N., Tariq, I. M., Hinchey, M., Masek, V. (2009). Performance of Savonius Rotor as Water Current Turbine, Journal of Ocean Technology, 4, N. 2, pp. 27-29.

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[12] Roy, S., Saha U. K. (2013). Review on the numerical investigations into the design and development of Savonius wind rotors, Renewable and Sustainable Energy Reviews 24, 73-83. [13] Driss, Z., Mlayeh, O., Driss, D., Maaloul, M., & Abid, M. S. (2014). Numerical simulation and experimental validation of the turbulent flow around a small incurved Savonius wind rotor. Energy, 74, 506-517. [14] Driss, Z., Mlayeh, O., Driss, S., Driss, D., Maaloul, M., & Abid, M. S. (2015). Study of the bucket design effect on the turbulent flow around unconventional Savonius wind rotors. Energy, 89, 708-729. [15] Sharma K. K., Gupta R., Biswas, A. (2014) Performance Measurement of a Two-Stage Two-Bladed Savonius Rotor. International Journal of Renewable Energy Research, Vol.4, No.1. [16] Saha, U. K., Thotla, S., & Maity, D. (2008). Optimum design configuration of Savonius rotor through wind tunnel experiments. Journal of Wind Engineering and Industrial Aerodynamics, 96(8), 1359-1375. [17] Chaitep S., Chaichana T., Watanawanyoo P., Hirahara H. (2011). Performance Evaluation of Curved Blades Vertical Axis Wind Turbine, European Journal of Scientific Research, ISSN 1450216X Vol.57 No.3, pp.435-446, Euro Journal Publishing, Inc. [18] Mahmoud N. H., El-Haroun A. A., Wahba E., Nasef M. H. (2012).An experimental study on improvement of Savonius rotor performance‖ Alexandria Engineering Journal 51, 19–25. [19] Frikha S., Driss Z., Ayadi E., Masmoudi Z., Abid M. S. (2016), Numerical and experimental characterization of multi-stage Savonius rotors. Energy, 114, 382-404.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 5

STUDY OF THE MESHING CHOICE OF A NACA2415 AIRFOIL WIND TURBINE Sobhi Frikha*, Zied Driss, Tarek Chelbi and Mohamed Salah Abid University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM) Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations and experimental validation were carried out to study the meshing effect of a NACA2415 airfoil type wind turbine. The software "SolidWorks Flow Simulation" has been used to present the local characteristics in different transverse and longitudinal planes. The considered numerical model is based on the resolution of the Navier-Stokes equations in conjunction with the k-ε turbulence model. Experiments have been also conducted on an open wind tunnel equipped *

Corresponding Author’s E-mail: [email protected].

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Sobhi Frikha, Zied Driss, Tarek Chelbi et al. by a small NACA2415 airfoil type wind turbine to validate the numerical results.

Keywords: Naca 2415, wind tunnel, mesh, turbulent flow, aerodynamic structure, CFD

INTRODUCTION In recent years, the high consumption of energy has led to a deficiency in energy recovery current human needs. That’s why, the world has moved towards the exploitation of new and renewable energies. The wind energy is considered among the most important environmental friendly sources and wind turbines are used to convert the kinetic energy presented in the wind to a mechanical energy and into electricity. These turbines are classified in two main categories: the horizontal axis wind turbines and the vertical axis wind turbines. Horizontal axis wind turbines are turbines in which rotor axis is in the horizontal direction. Wind turbine design is one of the most important parameters of interest in any type of wind turbine. In this context, a lot of scientists have experimentally and numerically examined the effects of wind turbines parameters design. Strinath and Mittal [1] utilized a continuous adjoint method for the design of airfoils in unsteady viscous flows for α = 4° and Re = 104. A stabilized finite element method based on the SUPG/PSPG stabilizations has been used to solve, both, flow and adjoint equations. The airfoil surface is parametrized by a 4th order NURBS curve with 13 control points. The y-coordinates of the control points are used as the design parameters. Henriques et al. [2] showed that a pressure-load inverse design method was successfully applied to the design of a high-loaded airfoil for application in a small wind turbine for urban environment. Predescu et al. [3] described the experimental work in a wind tunnel on wind turbine rotors having different number of blades and different twist angles. The aim of the work is to study the effect of the number of blades, the blade tip angles

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and twist angle of the blades on the power coefficient of the rotor. Also, the experiments evaluate to what extent the power coefficient of the turbine rotor depends on the operating wind speed. Sicot et al. [4] investigated the aerodynamic properties of a wind turbine airfoil. Particularly, they studied the influence of the inflow turbulence level (from 4.5% to 12%) and of the rotation on the stall mechanisms in the blade. A local approach was used to study the influence of these parameters on the separation point position on the suction surface of the airfoil, through simultaneous surface pressure measurements around the airfoil. Duquette et al. [5] conducted a numerical study in order to examine the impact of rotor solidity and blade number on the aerodynamic performance of small wind turbines. Blade element momentum theory and lifting line based wake theory were utilized to assess the effects of blade number and solidity on rotor performance. An increase in power coefficients at low tip speed ratios was observed with an increase in the solidity. Also, the power coefficients increased with the increase in the blade number at a given solidity. Tahar Bouzaher [6] studied the flow around a NACA2415 airfoil, with an 18° angle of attack, and flow separation control using a rod. It involves putting a cylindrical rod-upstream of the leading edge in a vertical translation movement in order to accelerate the transition of the boundary layer by an interaction between the rod wake and the boundary layer. The rod movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). Results showed a substantial modification in the flow behavior and a maximum drag reduction of 61%. Lanzafame and Messina [7] presented a methodology which allows a horizontal axis wind turbine to work continuously at its maximum power coefficient according to a law of the rotor velocity rotation as a function of the wind speed. To determine this law, a calculation code based on Blade Element Momentum theory was produced to create a power curve and power coefficient as the rotational velocity of a wind rotor varied. Thumthae and Chitsomboon [8] proposed four pitch angles for an

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untwisted blade corresponding to the maximum power coefficient at four wind speeds. Jureczko et al. [9] developed a computer program to optimize wind turbine blades taking into account different criteria such as blade vibration, output power, blade material cost, local and global stabilities, and appropriate blade structure strength. They used a modified genetic algorithm for optimization with and without copying the best individual cases. Maalawi and Badr [10] presented a practical methodology for generating optimized wind rotor configurations, which produce the largest possible power output. The aerodynamic optimization of the rotor blades is associated with an optimization of the chord and twist distribution, number of blades, choice of airfoil shape, and the tip speed ratio. Vardar and Alibas [11] compared the rotation rates and the power coefficients of the small wind turbines using the different NACA profiles for the various geometrical parameters like the twist angle, blade angle and the number of blades. Out of four tested blade profiles (namely NACA 0012, NACA 4412, NACA 4415, and NACA 23012) tested, it was found that NACA 4412 profiles with 0 grade twisting angle, 5 grade blade angle and double blades had the highest rotation rate, while NACA 4415 profiles with 0 grade twisting angle, 18 grade blade angle, 4 blades had the highest power coefficient. In this paper, we are interested in studying the mesh effect of a NACA2415 airfoil type wind turbine. The numerical results computed by a computational fluid dynamics code "SolidWorks Flow Simulation" are compared with the experimental results conducted on an open wind tunnel to choose the adequate numerical model.

1. EXPERIMENTAL DEVICE The considered wind turbine is a horizontal axis with a NACA2415 airfoil type placed in the test section of the wind tunnel. The wind

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tunnel is an open type and provides a stable and uniform air flow in the test section through a downstream vacuum. The compounds of the wind tunnel are presented in figure 1. The wind turbine consists of three adjustable blades of a length L = 110 mm and a width C = 45 mm. The rotor radius of the turbine is equal to R = 157 mm (Figure 2). To determine the velocity profiles in different directions preselected in the test section of the wind tunnel, the anemometer type AM 4204 has been used (Figure 3). This anemometer measures wind speed in different positions with a range variation between 0.2 and 20 m.s-1 and a resolution reaching 0.1 m.s-1. The different characteristics of this anemometer are summarized in table 1.

Ref. 7 6 5 4 3 2 1 Figure 1. Wind tunnel.

designation Wind turbine Support Ventilation chamber Diffuser Test section Collector Plenum

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Figure 2. Geometric parameters of wind turbine.

Figure 3. Anemometer emplacement.

A tachometer type CA1725 is used for measuring the rotation speed of the rotor as presented in figure 4. The optical sensor can provide results without disrupting the movement of the rotor.

Study of the Meshing Choice … Table 1. Characteristics of the anemometer Description Maker Probe type Measurement parameters Resolution Precision Measuring range

Figure 4. Tachometer type CA1725.

Anemometer type AM 4204 Lutron telescopic Air velocity, temperature, gas flow Air velocity 0.1m.s-1 Temperature 0.1 °C Air velocity 5% Temperature ± 0.8 °C Velocity 0.1 m.s-1 Temperature from -20 °C to +70 °C

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Sobhi Frikha, Zied Driss, Tarek Chelbi et al. Table 2. Characteristics of the tachometer Description Speed range Resolution Precision Supply Autonomy Dimension Weight

Tachometer type CA1725 6 to 100000 rpm 0.0006 to 6 according size 10-4 reading ± 6 points 9V 250 steps of 5 min with optical sensor 21 × 72 × 47 mm 250 g

Tachometer features are summarized in table 2.

2. NUMERICAL MODEL 2.1. Numerical Method In this study, the continuity equation, the momentum equation, the turbulent kinetic energy (k) and the dissipation rate of the turbulent kinetic energy (ε) equations have been solved with the software “Solid Works Flow Simulation”. This code is based on solving Navier-Stokes equations with a finite volume discretization method. This technique consists in dividing the computational domain into elementary volumes around each node in the grid; it ensures a continuity of flow between nodes. The spatial discretization is obtained by following a procedure for the tetrahedral interpolation scheme. As for the temporal discretization, the implicit formulation is adopted. The transport equation is integrated over the control volume. In the present work, we have used the modified k-ε turbulence model with damping functions proposed by Lam and Bremhorst [12]. This model describes laminar, turbulent and transitional flows of homogeneous fluids consisting of the following turbulence conservation laws [13]. This model has been used

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in different anterior works and satisfactory results were obtained [14, 15].

2.2. Boundary Conditions The computational domain is defined by the interior volume of the wind tunnel blocked by two planes: the first one is in the tranquillization chamber entry and the second one is in the exit of the diffuser (Figure 5). The velocity inlet, measured in the tranquilization chamber, is equal to V = 3 m.s-1. The static pressure of the air flow through the drive section is made at the atmospheric conditions. For this reason, the pressure outlet is set equal to p = 101325 Pa.

Figure 5. Boundary conditions.

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2.3. Meshing SolidWorks Flow Simulation options allow us to manually adjust the computational mesh to the solved problem's features to resolve them better. The geometry can be resolved reasonably well. However, if we generate the mesh and zoom in a thin region, we will see that it may still unresolved. In order to resolve these regions properly, we have used the local initial mesh option. The local initial mesh option allows us to specify an initial mesh in a local region of the computational domain to better resolve the model geometry and flow particuliarities in this region. The local region can be defined by a component of the assembly, disabled in the component control dialogue box, or specified by selecting a face, edge or vertex of the model. Local mesh settings are applied to all cells intersected by a component, face, edge, or a cell enclosing the selected vertex. The local mesh settings do not influence the basic mesh but they are basic mesh sensitive: all refinement levels are set with respect to the basic mesh cell. To refine the mesh only in a specific region and avoid excessive splitting of the mesh cells in other parts of the model, we have applied a local initial mesh at the component surrounding this region. The component is created specially to specify the local initial mesh. The settings on the narrow channels tab control the mesh refinement in the model’s flow passages. A characteristic number of cells across a narrow channel box specifies the number of initial mesh cells (including partial cells) that flow simulation will try to set across the model’s flow passages in the direction normal to solid/fluid interface. If possible, the number of cells across narrow channels will be equal to the specified characteristic number. Otherwise, it will be close to the characteristic number. If this condition is not satisfied, the cells lying in this direction will be split to satisfy the condition. In this section, we are interested in the study of the mesh resolution’s effect.

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Table 3. Time resolution and number of cells Cells size (mm) Number of cells Time resolution (min)

200 2095 1

Figure 6. 3D views of the meshing.

100 2969 1,25

50 3983 2

5 41374 28

4 58656 41

3 72047 60

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In fact, we are going to change the size of the mesh and compare the results with the values of the velocity collected from the test section obtained experimentally.The time resolution and the number of cells of each cell size are presented in the table 3. It has been observed that the time resolution increases with the decrease of the mesh cells size. Figures 6, 7 and 8 show the 3D and the 2D views of the meshing, in the longitudinal plane x = 0 mm and in the transversal plane z = 0 mm for different numbers of cells.

3. COMPARISON BETWEEN THE NUMERICAL AND THE EXPERIMENTAL RESULTS Figure 9 shows the different profiles of the average velocity for different cells size.

Figure 7. 2D views of the meshing in the longitudinal plane defined by x = 0 mm for different numbers of cells.

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Figure 8. 2D views of the meshing in the transverse plane defined by z = 0 mm for different numbers of cells.

Figure 9. Comparison of the average velocity profiles.

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It presents the superposition of the numerical results gathered from the software "Solid works Flow simulation" and the experimental results taken by the anemometer. The velocity profiles are measured at different altitudes of the plane defined by the position z = 100 mm, which corresponds to a plane located downstream of the turbine. According to these results, it has been noted that the different velocity profiles seem to have the same appearance. However, the velocity values depend on the cell size. Indeed the greater the cell size gets the larger the gap between numerical and experimental results is. The best result regarding precision and time is to be found in a cell of 3 mm size. Regarding to these results, the numerical model can predict the aerodynamic results with a good agreement.

CONCLUSION In this paper, we are interested in the study of the meshing effect on the numerical results of a horizontal axis wind turbine with a NACA2415 airfoil type. Particularly, we have changed the cells size and we have compared the numerical results with the values of the velocity collected experimentally from an open wind tunnel to choose the adequate numerical model. It has been noted that the greater the cell size gets, the larger the gap between numerical and experimental results is. The best result regarding precision and time is found to be in a cell of 3 mm size. In the future, we intend using the particle image velocimetry laser (PIV) system to determine the local characteristics.

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REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8] [9]

Srinath, D. N., Mittal, S. (2010). Optimal aerodynamic design of airfoils in unsteady viscous flows, Computer Methods in Applied Mechanics and Engineering, 199, 1976 - 1991. Henriques, J. C. C., Marques da Silva, F., Estanqueiro, A. I., Gato, L. M. C. (2009). Design of a new urban wind turbine airfoil using a pressure-load inverse method, Renewable Energy, 34 2728 2734. Predescu, M., Bejinariu, A., Mitroi, O., Nedelcu, A. (2009). Influence of the Number of Blades on the Mechanical Power Curve of Wind Turbines, International Conference on Renewable Energies and Power Quality. Sicot, C., Devinant, P., Loyer, S., Hureau, J. (2008). Rotational and turbulence effects on a wind turbine blade. Investigation of the stall mechanisms, Journal of Wind Engineering and Industrial Aerodynamics, 96, 1320 - 1331. Duquette, M. M., Visser, K. D. (2003). Numerical implications of solidity and blade number on rotor performance of horizontal-axis wind turbines. J. Sol. Energy Eng., 125(4):425 - 32. Tahar Bouzaher, M. (2014) Numerical study of flow separation control over a NACA2415 airfoil, world academy of science, engineering and technology. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 8: 782 785. Lanzafame, R., Messina, M. (2010). Horizontal axis wind turbine working at maximum power coefficient continuously. Renew Energy, 35:301 - 6. Thumthae, C., Chitsomboon, T. (2009). Optimal angle of attack for untwisted blade wind turbine. Renew Energy, 34:1279 - 84. Jureczko, M., Pawlak, M., Mezyk, A. (2005). Optimisation of wind turbine blades. J. Mater. Process Technol., 167:463 - 71.

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[10] Badr, M. A., Maalawi, K. Y. (2003). A practical approach for selecting optimum wind rotors. Renewable Energy, 28:803e22. [11] Vardar, A., Alibas, I. (2008). Research on wind turbine rotor models using NACA profiles. Renewable Energy, 33, 1721 1732. [12] Lam, C. K. G., Bremhorst, K. A. (1981), Modified Form of Model for Predicting Wall Turbulence. ASME Journal of Fluids Engineering, Vol. 103: pp. 456 - 460. [13] SolidWorks, Enhanced turbulence modeling in SolidWorks flow simulation (2013). Dassault Systèmes SolidWorks Corporation Waltham, USA, MKTURBMODWPENG0313. [14] Frikha, S., Driss, Z. and Hagui, M. A. (2015). Computational study of the diffuser angle effect in the design of a waste heat recovery system for oil field cabins. Energy, 84:219 - 238. [15] Frikha, S., Driss, Z., Ayadi, E., Masmoudi, Z., Abid, M. S. (2016). Numerical and experimental characterization of multi-stage Savonius rotors, Energy, Volume 114, pp. 382 - 404.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 6

STUDY OF THE WEDGING ANGLE EFFECT OF A NACA2415 AIRFOIL WIND TURBINE IN A WIND TUNNEL Tarek Chelbi, Zied Driss*, Sobhi Frikha and Mohamed Salah Abid University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations were carried out to study the wedging angle effect of a NACA2415 airfoil wind turbine and to evaluate its performance. The Navier-Stokes equations in conjunction with the standard k-ε turbulence model were considered. These equations were solved numerically to determine the local characteristics of the flow. The considered model was implemented in the softaware "SolidWorks Flow Simulation" which uses a finite volume scheme. *

Corresponding Author’s E-mail: [email protected].

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Keywords: wind tunnel, horizontal axis wind turbine, NACA2415 airfoil, wedging angle, CFD

1. INTRODUCTION In recent years, the high consumption of energy leads to a deficiency in energy recovery current human needs. However, facing economic problems due to large increases in fuel prices, the world has moved towards the exploitation of new and renewable energies. These are inexhaustible and inexpensive compared to the energies of noble viewpoint of electric power generation. This strategy is based on the principle of sustainable development. Indeed, these energies meet current needs without compromising the development of future generations. Also, they use the natural elements such as biomass, water, sun and wind. If the sun, wind and biogas energy are exploited, only the wind belongs to the oldest tradition. Although, for economic and technical reasons, wind energy is no longer well used. Although that clean energy finish, it appears blatantly that electricity contributes greatly to environmental degradation and the depletion of nonrenewable resources. Therefore, the steps to prepare a truly sustainable development is to increase the share of renewable resources for electricity generation. In this context, the production of electricity by wind turbines is playing a major role. A lot of scientists have experimentally and numerically examined the effects of such parameter design as blades number and airfoil profile. For example, Leifsson and Koziel [1] presented a transonic airfoil design optimization methodology that uses a computationally cheap, physics-based lowfidelity model to construct a surrogate of an accurate but CPU intensive high-fidelity model. The low-fidelity model, described by the transonic small-disturbance equation, is corrected by aligning its airfoil surface pressure distribution with the corresponding distribution of the high-

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fidelity model, the Euler equations. This alignment is carried out using a shape-preserving response prediction methodology and ensures a good generalization capability of the surrogate model with respect to both objectives and constraints (lift and wave drag). The resulting approach requires only a single high-fidelity model evaluation per iteration of the design process. Strinath and Mittal [2] utilized a continuous adjoint method for the design of airfoils in unsteady viscous flows for α = 4° and Re = 104. A stabilized finite element method based on the SUPG/PSPG stabilizations has been used to solve, both, flow and adjoint equations. The airfoil surface is parametrized by a 4th order NURBS curve with 13 control points. The y-coordinates of the control points are used as the design parameters. The results of an experimental investigation of the heat transfer coefficients for forced convection from a NACA-63421 airfoil are presented by Wang et al. [3]. Wind tunnel measurements of convection coefficients are obtained for air flow temperatures from 20 to 30 °C. The experimental data are correlated with respect to the Nusselt and Reynolds numbers. Both average and spatial variations of the heat transfer coefficients are nondimensionalized through modifications of a classical Hilpert correlation for cylinders in crossflow. It is shown that the functional form of the Hilpert correlation can effectively accommodate measured data for the NACA airfoil over a range of Reynolds numbers. An uncertainty analysis is performed to yield a 7.34% measurement uncertainty for experimental data correlated with the Nusselt number. Henriques et al. [4] showed that a pressure-load inverse design method was successfully applied to the design of a high-loaded airfoil for application in a small wind turbine for urban environment. Predescu et al. [5] described the experimental work in a wind tunnel on wind turbine rotors having different blades number and different twist angle. The aim of the work is to study the effects of the number of blades, the blade tip angles and the blades twist angle on the power coefficient of the rotor. Hirahara et al. [6] developed a unique and very small wind turbine with a diameter of 500 mm and a small aspect ratio for wide use in urban space. The

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basic performance was tested for various free stream and load resistance. The airflow around the turbine was investigated using a particle image velocimetry (PIV). Wright and Wood [7] showed that the acceleration and deceleration of the rotor at speeds below its controlled maximum speed for a range of wind speeds were calculated and compared with data. Schreck and Robinson [8] showed that wind turbine blade aerodynamic phenomena can be broadly categorized according to the operating state of the machine, and two particular aerodynamic phenomena assume crucial importance. At zero and low rotor yaw angles, increasing rotation determines blade aerodynamic response. At moderate to high yaw angles, dynamic stall dominates blade aerodynamic. The main goal of the Mirzaei et al. [9] investigation was to understand the flow field structure of the separation bubble formed on NLF-0414 airfoil with glaze-ice accretions using CFD and hot-wire anemometry and comparing these results with previous researches performed on NACA 0012 airfoil. Hu et al. [10] showed that Coriolis and centrifugal forces play important roles in 3D stall-delay. At the root area of the blade, where the high angles of attack occur, the effect of the Coriolis and centrifugal forces is dominant. Thus, it shows apparent stall-delay phenomenon at the inner part of the blade. However, by increasing the Reynolds number, the separation position has a stronger effect than by increasing the Coriolis and centrifugal forces. Sicot et al. [11] investigated the aerodynamic properties of a wind turbine airfoil. Particularly, they studied the influence of the inflow turbulence level (from 4.5% to 12%) and of the rotation on the stall mechanisms in the blade. A local approach was used to study the influence of these parameters on the separation point position on the suction surface of the airfoil, through simultaneous surface pressure measurements around the airfoil. Tahar Bouzaher [12] studied the flow around a NACA2415 airfoil, with a 18° angle of attack, and flow separation control using a rod. It involves putting a cylindrical rod upstream of the leading edge- in vertical translation movement in order to accelerate the transition of the boundary layer by interaction between

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the rod wake and the boundary layer. The rod movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). Results showed a substantial modification in the flow behavior and a maximum drag reduction of 61%. In this chapter, we are interested in studying of the effect of the wedging angle effect of a NACA2415 airfoil wind turbine. The numerical results obtained in six cases of the wedging angle are particularly studied.

2. GEOMETRICAL SYSYTEM

(a) Perspective vue

(b) Face vue

(c) Right vue

Figure 1. Geometric parameters of the wind turbine.

In the present work, we are interested in a wind turbine with adjustable blades with NACA profile type. The wind turbine consists of three blades of a length L and width C (Figure 1). This rotor is equipped with a mechanism for varying the wedging angle. This angle is measured between the plane of rotation of the wind turbine and the chord. Six different configurations defined by wedging angle equal to

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β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30° are considered in the present study (Figure 2).

(a) β = 5°

(b) β = 10°

(c) β = 15°

Figure 2. Different wedging angles.

Figure 3. Boundary conditions.

(d) β = 20°

(e) β = 25°

(f) β = 30°

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Figure 3 presents the conditions for use in the software SolidWorks Flow Simulation corresponding to our study. The choice of boundary conditions is an instruction which requires great precision for an accurate description of the problem in order to obtain satisfactory results. In these conditions, the velocity inlet is equal to V = 3 m.s-1 and the pressure outlet is equal to p = 101325 Pa.

3. NUMERICAL RESULTS In this section, we are interested in studying the influence of the wedging angle on the aerodynamic structure around the wind turbine. Particularly, we are interested in predicting the results in the longitudinal planes defined by x = 0 mm and y = 0 mm and in the transverse planes defined by z = 0 mm and z = -50 mm.

3.1. Velocity Fields Figures 4, 5, 6 and 7 show the velocity vectors colored by average velocity in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30° are studied. According to these results, it has been noted that the flow follows the wall of the wind tunnel. In the collector inlet, the average velocity is weak and it is equal to V = 3 m.s-1. This value is imposed by the boundary conditions. During the cross collector, a progressive increase of the flow is observed. This fact is due to the reduction of the transverse surface of the collector. At level of the test vein, the average velocity is equal to V = 11.5 m.s-1. At the test vein, the wind turbine has a direct effect on the

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velocity vectors distribution. In the wind turbine upstream, the velocity vectors are uniform and have a horizontal direction. On the meeting of the wind turbine, a flow deflection has been observed.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 4. Velocity fields in the longitudinal plane defined by x = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

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Figure 5. Velocity fields in the longitudinal plane defined by y = 0 mm.

At level of blades, an acceleration zone of the flow is appeared. In this region, the maximum average velocity is obtained and it is equal to V = 14 m.s-1. This region becomes very clear by increasing the wedging angle. In addition, a recirculation zone appears at the level of the wind turbine cover. In the wind turbine downstream, another recirculation zone appears. For thus, the wind turbine is considered as an obstacle in the out-flow front. After the exit of the test vein, it has been noted that the average velocity decreases along its crossing through the diffuser.

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Near the wall, the average velocity reaches a very weak value. Indeed, it has been noted that the wedging angle has a direct effect on the distribution of the velocity vectors. In fact, with β = 25° and β = 30°, the acceleration of the flow gets its maximum at the blades level.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(d) β = 20°

(f) β = 30°

Figure 6. Velocity field in the transverse plane defined by z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(d) β = 20°

(f) β = 30°

Figure 7. Velocity field in the transverse plane defined by z = -50 mm.

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3.2. Average Velocity

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 8. Average velocity distribution in the longitudinal plane defined by x = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 9. Average velocity distribution in the longitudinal plane defined by y = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 10. Average velocity distribution in the transverse plane defined by z = 0 mm.

Figures 8, 9, 10 and 11 show the distribution of the average velocity in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. The average velocity is weak in the collector inlet and it is equal to V = 3 m.s-1. This value is imposed by the boundary conditions. During the cross collector, a progressive increase of the flow is observed. This fact is due to the reduction of the transversal surface of the collector. At level of the test vein, the average velocity is thereabouts equal to V = 11.5 m.s -1. At the test vein, the wind turbine has a direct effect on the average velocity distribution. In fact, two large wakes, characteristic of the highly velocity average, are developed at the level of blades. In this region, the maximal average velocity is equal to V = 14 m.s -1. However, two others wakes, characteristic of the weak average velocity, are developed. The

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first one is observed at the level of the cover and the second one is observed in the wind turbine downstream. The weakest value is obtained in the wind turbine downstream. While moving away the wind turbine, all these wakes disappear. Through the diffuser, the magnitude velocity decreases along its crossing. However, ithas been noted that the wedging angle has a direct effect on the distribution of the average velocity. In fact, the average velocity gets its minimum in the blades downstream with β = 25° and β = 30°.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 11. Average velocity distribution in the transverse plane defined by z = -50 mm.

3.3. Static Pressure Figures 12, 13, 14 and 15 show the distribution of the static pressure in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to

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these results, it has been noted that the static pressure is maximum in the collector inlet of the wind tunnel and it is equal to p = 101328 Pa. During the collector, a progressive decrease of the static pressure has been observed. This fact is due to the reduction of the transversal surface of the collector. At the test vein, a large depression zone appears around the wind turbine. The minimum value, equal to p = 101328 Pa, is obtained in the wind turbine downstream particularly in the blades downstream. After the exit of the test vein, it has been noted

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 12. Static pressure distribution in the longitudinal plane defined by x = 0 mm.

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that the static pressure increases along its crossing through the diffuser until reaching atmospheric pressure. This value is imposed by the boundary conditions. However, it has been noted that the wedging angle has a direct effect on the distribution of the static pressure. In fact, with β = 25° and β = 30°, the wind turbine separates the compression and the depression zones.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 13. Static pressure distribution in the longitudinal plane defined by y = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 14. Static pressure distribution in the transverse plane defined by z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 15. Static pressure distribution in the transverse plane defined by z = -50 mm.

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3.4. Dynamic Pressure

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 16. Dynamic pressure distribution in the longitudinal plane defined by x = 0 mm.

Figures 16, 17, 18 and 19 show the distribution of the dynamic pressure in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for

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different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°,

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 17. Dynamic pressure distribution in the longitudinal plane defined by y = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 18. Dynamic pressure distribution in the transverse plane defined by z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 19. Dynamic pressure distribution in the transverse plane defined by z = -50 mm.

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β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to these results, it has been noted that during the collector, a progressive increase of the dynamic pressure is observed. This fact is due to the reduction of the transversal surface of the collector. At the test vein, a large compression zone appears around the wind turbine. However, it has been noted that the wedging angle has a direct effect on the distribution of the dynamic pressure. In fact, at level of blades, the maximum value of the dynamic pressure is obtained with β = 25° and β = 30°. The compression region becomes clearer by increasing the wedging angle. In the wind turbine downstream, a depression zone has been observed. For thus, the wind turbine is considered as an obstacle in the out-flow front. After the exit of the test vein, it has been noted that the dynamic pressure decreases along its crossing through the diffuser.

3.5. Turbulent Kinetic Energy Figures 20, 21, 22, and 23 show the distribution of the turbulent kinetic energy in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to these results, it has been noted that the turbulent kinetic energy is weak in all of the control volume excepted on the region around the wind turbine in the test vein. In this area, a wake zone characteristic of the highly value of the turbulent kinetic energy is developed. By approaching the wind turbine, this wake becomes large, particularly around the wind turbine where the turbulent kinetic energy gets its maximum. In addition, another wake is developed in the diffuser outlet. However, it has been noted that the wedging angle has a direct effect on

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the distribution of the turbulent kinetic energy. In fact, by increasing the wedging angle, another wake is developed in the diffuser outlet, observed clearly with β = 5° and it becomes smaller with β = 30°.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 20. Turbulent kinetic energy distribution in the longitudinal plane defined by x = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

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Figure 21. Turbulent kinetic energy distribution in the longitudinal plane defined by y = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 22. Turbulent kinetic energy distribution in the transverse plane defined by z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 20°

(f) β = 30°

Figure 23. Turbulent kinetic energy distribution in the transverse plane defined by z = 50 mm.

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3.6. Dissipation Rate of the Turbulent Kinetic Energy

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 24. Dissipation rate of the turbulent kinetic energy in the longitudinal plane x = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 25. Dissipation rate of the turbulent kinetic energy in the longitudinal plane y = 0 mm.

Figures 24, 25, 26 and 27 show the distribution of the dissipation rate of the turbulent kinetic energy in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0

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mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to these results, it has been noted that the dissipation rate of the turbulent kinetic energy is weak in all of the control volume excepted on the region around the wind turbine in the test vein. In fact, a wake zone characteristic of the highly value of the turbulent kinetic energy is developed around the wind turbine where it get its maximum. However, it has been noted that the wedging angle has a direct effect on the distribution dissipation rate of the turbulent kinetic energy. In fact, by increasing the wedging angle, another wake is developed in the diffuser outlet, observed clearly with β = 5° and it becomes smaller with β = 30°.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 26. Dissipation rate of the turbulent kinetic energy in the transverse plane z = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 27. Dissipation rate of the turbulent kinetic energy in the transverse plane z = 50 mm.

3.7. Turbulent Viscosity Figures 28, 29, 30 and 31 show the distribution of the turbulent viscosity in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Specially, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to these results, it has been noted that the turbulent viscosity is maximal in the collector and in the test vein inlet. In the wind turbine upstream, a reduced wake, characteristic of the highly turbulent viscosity, is developed. However, it has been noted that the wedging angle has a direct effect on the distribution of the viscosity. In fact, by increasing

Study of the Wedging Angle Effect …

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the wedging angle, another wake is developed in the diffuser outlet, observed clearly with β = 5° and it becomes smaller with β = 30°.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 28. Turbulent viscosity distribution in the longitudinal plane x = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 29. Turbulent viscosity distribution in the longitudinal plane y = 0 mm.

Study of the Wedging Angle Effect …

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 30. Turbulent viscosity distribution in the transverse plane z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 31. Turbulent viscosity distribution in the transverse plane z = -50 mm.

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3.8. Vorticity

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 32. Vorticity distribution in the longitudinal plane x = 0 mm.

Study of the Wedging Angle Effect …

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 33. Vorticity distribution in the longitudinal plane y = 0 mm.

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(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 34. Vorticity distribution in the transverse plane z = 0 mm.

(a) β = 5°

(b) β = 10°

(c) β = 15°

(d) β = 20°

(e) β = 25°

(f) β = 30°

Figure 35. Vorticity distribution in the transverse plane z = -50 mm.

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Figures 32, 33, 34 and 35 show the distribution of the vorticity in different longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm for different values of the wedging angle of the wind turbine. Particularly, the geometric configurations defined by the wedging angles equal to β = 5°, β = 10°, β = 15°, β = 20°, β = 25° and β = 30°, are studied. According to these results, it has been noted that the vorticity is very weak out of the test vein for all the values of the wedging angle. It increases around the wind turbine. The vorticity get its maximum in the blades downstream. However, it has been noted that the wedging angle has a direct effect on the distribution of the vorticity. In fact, by increasing the wedging angle, the maximum value of vorticity is observed clearly around the blades, particularly with β = 20°, β = 25° and β = 30°.

CONCLUSION In this chapter, we are interested in analyzing of the numerical results provided by the computational fluid dynamics code "SolidWorks Flow Simulation". The influence of the wedging angle is particularly investigated in a static state. For the studied configurations, we have presented the distribution of velocity fields, the average velocity, the static and dynamic pressure, and the turbulence characteristics of flow in different planes of the control volume. These findings have implemented the influence of the studied parameters. The use of the particle image velocimetry laser (PIV) system will be also crucial for a finer survey of the local characteristics.

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REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Leifsson, L., S. Koziel, Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction, Journal of Computational Science 1 (2010) 98-106. Srinath, D.N., S. Mittal, Optimal aerodynamic design of airfoils in unsteady viscous flows, Computer Methods in Applied Mechanics and Engineering 199 (2010) 1976-1991. Wang, X., E. Bibeau, G.F. Naterer, Experimental correlation of forced convection heat transfer from a NACA airfoil, Experimental Thermal and Fluid Science 31 (2007) 1073-1082. Henriques, J.C.C., F. Marques da Silva, A.I. Estanqueiro, L.M.C. Gato, Design of a new urban wind turbine airfoil using a pressureload inverse method, Renewable Energy 34 (2009) 2728-2734. Predescu, M., A. Bejinariu, O. Mitroi, A. Nedelcu, Influence of the Number of Blades on the Mechanical Power Curve of Wind Turbines, International Conference on Renewable Energies and Power Quality (2009). Hirahara, H., M.Z. Hossain, M. Kawahashia and Y. Nonomura, Testing basic performance of a very small wind turbine designed for multi-purposes, Renewable Energy 30 (2005) 1279-1297. Wrigh A.K., and D.H. Wood, The starting and low wind speed behaviour of a small horizontal axis wind turbine, Journal of Wind Engineering and Industrial Aerodynamics 92 (2004) 12651279. Schreck S.J., and M.C. Robinson, Horizontal Axis Wind Turbine Blade Aerodynamics in Experiments and Modeling, IEEE Transactions on Energy Conversion 22 (2007) 61-70. Mirzaei, M., M.A. Ardekani and M. Doosttalab, Numerical and experimental study of flow field characteristics of an iced airfoil, Aerospace Science and Technology 13 (2009) 267-27.

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[10] Hu, D., O. Hu and Z. Du, A study on stall-delay for horizontal axis wind turbine, Renewable Energy 31 (2006) 821-836. [11] Sicot, C., P. Devinant, S. Loyer and J. Hureau, Rotational and turbulence effects on a wind turbine blade: investigation of the stall mechanisms, Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 1320-1331. [12] Tahar Bouzaher, M., Numerical Study of Flow Separation Control over a NACA2415 Airfoil, World Academy of Science, Engineering and Technology International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering 8:4 (2014) 782-785.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 7

STUDY OF THE NACA AIRFOIL EFFECT OF A HORIZONTAL AXIS WIND TURBINE IN A WIND TUNNEL Zied Driss*, Tarek Chelbi, Sobhi Frikha and Mohamed Salah Abid University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT In this chapter, numerical simulations were carried out to gain an insight into the complex flow field developing around a horizontal axis wind turbine rotor. Particularly, the comparison was done between the NACA2415 and NACA4410 airfoil types. The Navier-Stokes equations were considered in conjunction with the standard k-ε turbulence model to study the effect of the NACA airfoil wind turbine. These equations were solved numerically to determine the local characteristics of the flow. The *

Corresponding Author’s E-mail: [email protected].

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Keywords: airfoil effect, NACA2415, NACA4410, wind turbine, wind tunnel, turbulent flow

1. INTRODUCTION Subsidy programs were required, to stimulate the installation of such a large wind energy capacity, since Wind energy is the fastest growing source of energy. As such, there is still a lot of work needed to develop the technology, so that it is cost competitive with conventional sources. For example, Hu [1] developed an experimental investigation on the properties of the near wake behind the rotor of a horizontal-axis wind turbine at model scale. Measurements were made with a stationary slanted hot-wire anemometer using the technique of phase-locked averaging. The primary aim is to study the formation and development of the three-dimensional wake. Five axial locations were chosen within four chord lengths of the blades over a range of tip speed ratios. The results show that during the downstream development of the wake, the wake centre traces a helical curve with its rotation direction opposite to that of the rotor. Grant et al. [2] described a wind-tunnel study of the wake dynamics of an operational, horizontal-axis wind turbine. The behaviour of the vorticity trailing from the turbine blade tips was considered. Laser sheet visualisation (LSV) techniques were used to measure the trajectories of the trailing vorticity under various conditions of turbine yaw and blade azimuth. Selected results obtained in the experimental study were compared with the predictions of a prescribed wake model and are being used in the further development of the method. Barnsley and Wellicome [3] made surface pressure and near rotor velocity measurements, using a laser Doppler facility, at six radial positions for a 1 m diameter two-bladed rotor, over the stalling

Study of the NACA Airfoil Effect of a Horizontal Axis Wind … 147 range of tip speed ratios at typical Reynolds’ numbers of 300000. Velocity measurements have been used to quantify local incidence and results illustrate clearly the development of enhanced lift incidence due to a delay in the loss of leading edge suction peaks compared to 2D behaviour. Static hysteresis in the stall behaviour has also been identified. Power comparisons with full scale data indicate fairly good agreement in peak power coefficient and tip speed ratio at the onset of stall but also show significant Reynolds number effects in the stalling and post stall regions. Ting et al. [4] developed wind chiller in CCT Lab. Directly uses wind force to drive refrigeration system and hence reduces two times energy conversions between mechanical and electrical energies. The wind chiller needs high wind speed for its effective work due to the large working torque is required by the compressor. For the purpose of enlarging the applied wind field by the wind machine, this work aims to develop a dual system of wind chiller integrated with wind generator. The integrated wind generator can use the wind energy which cannot effectively drive the compressor. Therefore, the new developed dual system can apply larger range of the wind field and further increase the total working efficiency of the wind machine. Chen and Liou [5] quantitatively investigated the effects of tunnel blockage on the turbine power coefficient in wind tunnel tests of small horizontal-axis wind turbines. The blockage factor was determined by measuring the tunnel velocities with and without rotors using a pitot-static tube under various test conditions. Results showed that the BF depends strongly on the rotor tip speed ratio, the blade pitch angle, and the tunnel blockage ratio (BR). This study also showed that the blockage correction is less than 5% for a BR of 10%, which confirms that no blockage correction for a BR less than 10% in literatures is acceptable. Leifsson and Koziel [6] presented a transonic airfoil design optimization methodology that uses a computationally cheap, physics-based low-fidelity model to construct a surrogate of an accurate but CPU intensive high-fidelity model. The low-fidelity model, described by the transonic small-disturbance equation, is

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corrected by aligning its airfoil surface pressure distribution with the corresponding distribution of the high-fidelity model, the Euler equations. This alignment is carried out using a shape-preserving response prediction methodology and ensures a good generalization capability of the surrogate model with respect to both objectives and constraints (lift and wave drag). The resulting approach requires only a single high-fidelity model evaluation per iteration of the design process. Strinath and Mittal [7] utilized a continuous adjoint method for the design of airfoils in unsteady viscous flows for α = 4° and Re = 104. A stabilized finite element method based on the SUPG/PSPG stabilizations has been used to solve, both, flow and adjoint equations. The airfoil surface is parametrized by a 4th order NURBS curve with 13 control points. The y-coordinates of the control points are used as the design parameters. The results of an experimental investigation of the heat transfer coefficients for forced convection from a NACA63421 airfoil are presented by Wang et al. [8]. Wind tunnel measurements of convection coefficients are obtained for air flow temperatures from 20 to 30°C. The experimental data are correlated with respect to the Nusselt and Reynolds numbers. Both average and spatial variations of the heat transfer coefficients are nondimensionalized through modifications of a classical Hilpert correlation for cylinders in crossflow. It is shown that the functional form of the Hilpert correlation can effectively accommodate measured data for the NACA airfoil over a range of Reynolds numbers. An uncertainty analysis is performed to yield a 7.34% measurement uncertainty for experimental data correlated with the Nusselt number. Henriques et al. [9] showed that a pressure-load inverse design method was successfully applied to the design of a high-loaded airfoil for application in a small wind turbine for urban environment. In this chapter, we are interested in studying of the effect of the NACA airfoils wind turbine. The numerical results obtained in these cases are considered the NACA2415 and NACA4410 airfoil types.

Study of the NACA Airfoil Effect of a Horizontal Axis Wind … 149

2. GEOMETRICAL SYSTEM Figure 1 presents the overall design of a suction wind tunnel open circuit. This wind tunnel is composed by:  



  

Plenum: it is used to reduce the air turbulence, to ensure an air flow parallel and slows the air flow. Test section: its role is to facilitate the visualization of phenomena that occur around the prototype studied in experimental tests. Collector: This item can suck a large volume of air at low speed and low pressure and reduce it to a small volume of high velocity air without creating turbulence. Diffuser: it helps straighten the flow of air entering the blower. Ventilation chamber: it allows control of air flow flowing in the wind tunnel. Support: it eliminates all kinds of vibration and ensures a good stability of the tunnel during the experimental tests.

Ref. 1 2 3 4 5 6 7

Figure 1. Wind tunnel.

Designation Ventilation chamber Diffuser Test section Collector Support of the blower Plenum Wind turbine

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Zied Driss, Tarek Chelbi, Sobhi Frikha et al. Table 1. Airfoil points coordinates (a) NACA2145 airfoil x y z 45 0 0.072 42.75 0 0.603 40.5 0 1.1025 36 0 1.9845 31.5 0 2.745 27 0 3.375 22.5 0 3.8565 18 0 4.1625 13.5 0 4.221 11.25 0 4.1265 9 0 3.915 6.75 0 3.5865 4.5 0 3.0735 3.375 0 2.727 2.25 0 2.2815 1.125 0 1.6695 0.5625 0 1.2195 0 0 0 0.5625 0 - 0.927 1.125 0 - 1.287 2.25 0 - 1.728 3.375 0 - 2.0115 4.5 0 - 2.205 6.75 0 - 2.439 9 0 - 2.547 11.25 0 - 2.565 13.5 0 - 2.529 18 0 - 2.3625 22.5 0 - 1.986 27 0 - 1.755 31.5 0 - 1.3725 36 0 - 0.9675 40.5 0 - 0.5265 42.75 0 - 0.306 45 0 - 0.072

(b) NACA4410 airfoil x y z 50 0 0 49.9465 0 0.195 48.6735 0 0.466 47.422 0 0.858 46.6505 0 1.083 44.834 0 1.5855 42.6775 0 2.1415 41.4835 0 2.4315 36.057 0 3.6135 33.036 0 4.1705 31.4705 0 4.429 29.8775 0 4.6705 28.263 0 4.8925 16.964 0 5.6805 2.578 0 2.8765 0.4805 0 1.2445 0.214 0 0.827 0.0535 0 0.4125 0 0 0.0375 0.0535 0 - 0.283 12.5 0 - 1.987 13.943 0 - 1.9225 15.433 0 - 1.85 16.964 0 - 1.7735 34.567 0 - 0.798 36.057 0 - 0.715 37.5 0 0.6385 38.8895 0 - 0.568 40.219 0 - 05.3 45.7865 0 - 0.251 46.6505 0 - 0.2155 47.422 0 - 0.182 48.6735 0 - 0.1135 49.9465 0 - 0.0055 50 0 0

Study of the NACA Airfoil Effect of a Horizontal Axis Wind … 151

(a) NACA2415 airfoil

(b) NACA4410 airfoil

Figure 2. Three-blades wind turbine types.

In the present application, we are interested to a horizontal axis wind turbine with three blades. Particularly, we are interested in the studying of the NACA2415 and NACA4410 airfoil types, as presented in Figure 2.

3. NUMERICAL RESULTS In this section, we are interested in studying the effect of the NACA airfoil wind turbine. The numerical results obtained in the cases of the airfoils type NACA2415 and NACA4410 are particularly studied with a wedging angle equal to β = 30°. The results, from application of the software “SolidWorks flow simulation”, are presented in the transverse and longitudinal planes of the considered control volume.

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3.1. Velocity Vectors Figures 3, 4, 5 and 6 compare the distribution of velocity vectors for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it has been noted that the flow follows the wall of the wind tunnel. In the collector inlet, the average velocity is weak and it is equal to V = 3 m.s-1. This value is imposed by the boundary conditions. During the cross collector, a progressive increase of the flow is observed. This fact is due to the reduction of the transverse surface of the collector. At level of the test vein, the average velocity is equal to V = 11.5 m.s-1. At the test vein, the wind turbine has a direct effect on the velocity vectors distribution. In the wind turbine upstream, the velocity vectors are uniform and have a horizontal direction. On the meeting of the wind turbine, a flow deflection has been observed. At the blades level, an acceleration of the flow is appeared. In this region, the maximum average velocity is obtained and it is equal to V = 14 m.s-1. Otherwise, it has been noted that the airfoil type have an effect on the velocity vectors distribution. In fact, with the NACA2415 airfoil, a developed recirculation zone appears in the wind turbine downstream. Within a NACA4410 airfoil, the same fact has been observed. However, it has been noted that the airfoil type has a direct effect on the recirculation zone shape less developed with the NACA4410 airfoil.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 3. Velocity fields in the longitudinal plane defined by x = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 4. Velocity fields in the longitudinal plane defined by y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 5. Velocity fields in the transverse plane defined by z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 6. Velocity fields in the transverse plane defined by z = - 50 mm.

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3.2. Average Velocity Figures 7, 8, 9 and 10 compare the distribution of average velocity for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it is clear that the average velocity is uniform in the inlet of the control volume. The average velocity is weak in the collector inlet and it is equal to V = 3 m.s-1. This value is imposed by the boundary conditions. During the cross collector, a progressive increase of the flow has been observed. This fact is due to the reduction of the transverse surface of the collector. At level of the test vein, the average velocity is equal to V = 11.5 m.s-1. Otherwise, it has been noted that the airfoil type have an effect on the velocity vectors distribution. In fact, two large wakes, characteristic of the highly values of the average velocity, are developed at the blades level. However, two others wakes, characteristic of the weak average velocity, are developed. The first one has been observed at the cover level and the second one has been observed in the wind turbine downstream. While comparing these results relative to the NACA2415 and NACA4410 airfoil type, it has been noted that all observed wakes are wider with the NACA4410 airfoil type.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 7. Average velocity distribution in the longitudinal plane defined by x = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 8. Average velocity distribution in the longitudinal plane defined by y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 9. Average velocity distribution in the transverse plane defined by z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 10. Average velocity distribution in the transverse plane defined by z = - 50 mm.

3.3. Static Pressure Figures 11, 12, 13 and 14 compare the distribution of static pressure for the NACA2415 and NACA4410 airfoil type. These results are

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presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it is clear that the static pressure is uniform in the inlet of the control volume. Also, it has been noted that the static pressure is maximum in the collector inlet of the wind tunnel and it is equal to p = 101328 Pa. During the collector, a progressive decrease of the static pressure has been observed. This fact is due to the reduction of the transverse surface of the collector. At the test vein, a large depression zone appears around the wind turbine. While comparing these results relative to the NACA2415 and NACA4410 airfoil type, it has been noted that this depression zone is wider with the NACA4410 airfoil type.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 11. Static pressure distribution in the longitudinal plane defined by x = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 12. Static pressure distribution in the longitudinal plane defined by y = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 13. Static pressure distribution in the transverse plane defined by z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 14. Static pressure distribution in the transverse plane defined by z = - 50 mm.

3.4. Dynamic Pressure Figures 15, 16, 17 and 18 compare the distribution of the dynamic pressure for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = -50 mm. According to these results, it is clear that the dynamic pressure is uniform in the inlet of the control volume. Also, it has been noted that during the collector, a progressive increase of the dynamic pressure has been observed. This fact is due to the reduction of the transversal surface of the collector. The dynamic pressure increases with the air flow advancement. While approaching to the wind turbine, the dynamic pressure decreases again. The same fact has been observed in the wind turbine downstream where the wake zone is developed more and more.

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At the blades level, the maximum value of the dynamic pressure is obtained. While comparing these results relative to the NACA2415 with NACA4410 airfoil type, it has been noted that the maximum value of the dynamic pressure is gotten within a NACA4410 airfoil type.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 15. Dynamic pressure distribution in the longitudinal plane defined by x = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 16. Dynamic pressure distribution in the longitudinal plane defined by y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 17. Dynamic pressure distribution in the transverse plane defined by z = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 18. Dynamic pressure distribution in the transverse plane defined by z = - 50 mm.

3.5. Turbulent Kinetic Energy Figures 19, 20, 21 and 22 compare the distribution of the turbulent kinetic energy for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it has been noted that the turbulent kinetic energy is weak in all of the control volume excepted of region around the wind turbine in the test vein. A wake zone, characteristic of the highly values of the turbulent kinetic energy, is developed in the wind turbine upstream. This wake became wider around the wind turbine. Another wake, developed in the diffuser outlet, is wider with the NACA2415.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 19. Turbulent kinetic energy distribution in the longitudinal plane x = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 20. Turbulent kinetic energy distribution in the longitudinal plane y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 21. Turbulent kinetic energy distribution in the transverse plane z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 22. Turbulent kinetic energy distribution in the transverse plane z = - 50 mm.

3.6. Turbulent Dissipation Rate Figures 23, 24, 25 and 26 compare the distribution of the dissipation rate of the turbulent kinetic energy for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal

Study of the NACA Airfoil Effect of a Horizontal Axis Wind … 161 and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it has been noted that the dissipation rate of the turbulent kinetic energy is weak in all of the control volume excepted of region around the wind turbine in the test vein. A wake zone, characteristic of the highly values of the dissipation rate of the turbulent kinetic energy, is developed around the wind turbine. Another wake, developed in the diffuser outlet, is wider with NACA4410.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 23. Dissipation rate of the turbulent kinetic energy in the longitudinal plane x = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 24. Dissipation rate of the turbulent kinetic energy in the longitudinal plane y = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 25. Dissipation rate of the turbulent kinetic energy in the transverse plane z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 26. Dissipation rate of the turbulent kinetic energy in the transverse plane z = - 50 mm.

3.7. Turbulent Viscosity Figures 27, 28, 29 and 30 compare the distribution of the turbulent viscosity for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it has been noted that the turbulent viscosity is maximum in the collector and in the test vein inlet. In addition, a reduce wake, characteristic of the highly turbulent viscosity, is developed in the wind turbine upstream. Another wake, developed in the diffuser outlet, is wider with the NACA4410 airfoil.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 27. Turbulent viscosity distribution in the longitudinal plane x = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 28. Turbulent viscosity distribution in the longitudinal plane y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 29. Turbulent viscosity distribution in the transverse plane defined by z = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 30. Turbulent viscosity distribution in the transverse plane defined by z = - 50. mm.

3.8. Vorticity Figures 31, 32, 33 and 34 compare the distribution of the vorticity for the NACA2415 and NACA4410 airfoil type. These results are presented in the longitudinal and transverse planes defined respectively by x = 0 mm, y = 0 mm, z = 0 mm and z = - 50 mm. According to these results, it has been noted that the vorticity is very weak out of the test vein. It increases around the wind turbine. The vorticity get its maximum in the blades downstream. A wake, characteristic of the highly values of the vorticity, is developed around the wind turbine, especially in the wind turbine downstream. The vorticity gets its maximum with NACA4410.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 31. Vorticity distribution in the longitudinal plane defined by x = 0 mm.

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(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 32. Vorticity distribution in the longitudinal plane defined by y = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 33. Vorticity distribution in the transverse plane defined by z = 0 mm.

(a) NACA2415 airfoil type

(b) NACA4410 airfoil type

Figure 34. Vorticity distribution in the transverse plane defined by z = - 50 mm.

CONCLUSION In this chapter, we are interested in analyzing of the numerical results provided by the software “SolidWorks flow simulation”. The influence of the airfoil type is particularly investigated by considering

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the NACA2415 and NACA4410 airfoils type. For the studied configurations, we have presented the distribution of velocity fields, the average velocity, the static and dynamic pressure, and turbulence characteristics of flow in different planes of the control volume. Our goal is to study, analyze and optimize different aerodynamic characteristics to compare the performance of wind energy systems in terms of energy captured and delivered power. Indeed, these findings have implemented the influence of the studied parameters.

REFERENCES [1] [2]

[3]

[4]

[5]

[6]

Hu, D. Near wake of a model horizontal-axis wind turbine, Journal of Hydrodynamics, 21 (2), 285-291, 2009. Grant, I; Mo, M; Pan, X; Parkin, P; Powell, J; Reinecke, H; Shuang, K; Coton, F; Lee, D. An experimental and numerical study of the vortex laments in the wake of an operational, horizontal-axis, wind turbine, Journal of Wind Engineering and Industrial Aerodynamics, 85, 177-189, 2000. Barnsley, MJ; Wellicome, JF. Wind tunnel investigation of stall aerodynamics for a 1.0 m horizontal axis rotor, Journal of Wind Engineering and Industrial Aerodynamics, 39, 11-21, 1992. Ting, CC; Lai, CW; Huang, CB. Developing the dual system of wind chiller integrated with wind generator, Applied Energy, 88, 741-747, 2011. Chen, TY; Liou, LR. Blockage corrections in wind tunnel tests of small horizontal-axis wind turbines, Experimental Thermal and Fluid Science, 35, 565-569, 2011. Leifsson, L; Koziel, S. Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction, Journal of Computational Science, 1, 98-106, 2010.

Study of the NACA Airfoil Effect of a Horizontal Axis Wind … 167 [7]

[8]

[9]

Srinath, DN; Mittal, S. Optimal aerodynamic design of airfoils in unsteady viscous flows, Computer Methods in Applied Mechanics and Engineering, 199, 1976-1991, 2010. Wang, X; Bibeau, E; Naterer, GF. Experimental correlation of forced convection heat transfer from a NACA airfoil, Experimental Thermal and Fluid Science, 31, 1073-1082, 2007. Henriques, JCC; Marques da Silva, F; Estanqueiro, AI; Gato, LMC. Design of a new urban wind turbine airfoil using a pressure-load inverse method, Renewable Energy, 34, 2728-2734, 2009.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 8

COMPUTER SIMULATION OF THE AERODYNAMIC STRUCTURE OF INCLINED ROOF OBSTACLES WITH DIFFERENT HEIGHTS IN A WIND TUNNEL Slah Driss, Zied Driss, Imen Kallel Kammoun and Mohamed Salah Abid University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM) Sfax, Tunisia

ABSTRACT In this chapter, we are interested in the study of the aerodynamic structure of inclined roof obstacles with different heights. By using the software “SolidWorks Flow Simulation,” the governing equations of mass and momentum in conjunction with the standard k-ε turbulence model were solved with a finite volume discretization. The numerical 

Corresponding Author’s Email: [email protected].

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Slah Driss, Zied Driss, Imen Kallel Kammoun et al. results were compared with anterior results developed in a wind tunnel. The good agreements with the experimental results confirm the numerical method.

Keywords: inclined roof obstacles, high effect, wind tunnel, aerodynamic structure.

1. INTRODUCTION Social considerations can be related to building like clean air and natural light. The study of geometry parameters effects on airflow patterns can be done inside wind tunnels, where airflow conditions are controlled. For example, Ntinas et al. [1] predicted the airflow around buildings. A time-dependent simulation model has been applied for the prediction of the turbulent airflow around obstacles with arched and pitched roof geometry, under wind tunnel conditions. To verify the reliability of the model an experiment was conducted inside a wind tunnel and the air velocity and turbulent kinetic energy profiles were measured around two small-scale obstacles with an arched-type and a pitched-type roof, respectively. Luo et al. [2] studied models of cuboid obstacles to characterize the three-dimensional responses of airflow behind obstacles with different shape ratios to variations in the incident flow in a wind-tunnel simulation. Wind velocity was measured using particle image velocimetry (PIV). The flow patterns behind cuboid obstacles were complicated by changes in the incidence angle of the approaching flow and in the obstacle’s shape ratio. Tominaga and Stathopoulos [3] reviewed current modeling techniques in CFD simulation of near-field pollutant dispersion in urban environments and discussed the findings to give insight into future applications. Key features of near-field pollutant dispersion around buildings from previous studies were identified and discussed. Jiang et al. [4] studied three ventilation cases, single-sided ventilation with an opening in

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windward wall, single-sided ventilation with an opening in leeward wall, and cross ventilation. In the wind tunnel, a laser Doppler anemometry was used to provide accurate and detailed velocity data. The numerical results from LES are in good agreement with the experimental data, in particular with the predicted airflow patterns and velocities around and within, and the surface pressures over, the models. Ahmad et al. [5] provided a comprehensive literature on wind tunnel simulation studies in urban street canyons/intersections including the effects of building configurations, canyon geometries, traffic induced turbulence and variable approaching wind directions on flow fields and exhaust dispersion. Smolarkiewicz et al. [6] performed largeeddy simulations (LES) of the flow past a scale model of a complex building. Calculations are accomplished using two different methods to represent the edifice. De Paepe et al. [7] simulated five different wind incidence angles using a turntable, in order to quantify their effect on indoor air velocities. The responses in local air velocities could largely be attributed to the relative position of the end walls of the scale models orientated towards the wind. This crucial position allows the measured air velocity trends to be explained. The estimated airflow rates gradually decreased for larger wind incidence angles. Lim et al. [8] presented a numerical simulation of flow around a surface mounted cube placed in a turbulent boundary layer which, although representing a typical wind environment. The presented results include detailed comparison between measurements and LES computations of both the inflow boundary layer and the flow field around the cube including mean and fluctuating surface pressures. Becker et al. [9] studied the structure of the flow field around three-dimensional obstacles of different aspect ratios, in two different types of boundary layers. The dimensions of the rectangular block obstacles were chosen to represent generic shapes of buildings. In order to study the flow field around a building structure in a wind tunnel test, the simulation of a boundary layer similar to the atmospheric boundary layer was a crucial issue.

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De Melo et al. [10] developed two Gaussian atmospheric dispersion models incorporating the PRIME algorithm for plume rise and building downwash, are intercompared and validated using wind tunnel data on odour dispersion around a complex pig farm facility comprising of two attached buildings. Richards et al. [11] used as input data for generating typical weather data required as input for building and heating, ventilation and air-conditioning (HVAC) system models in order to study the energy budgets of buildings and assess the performance of airconditioning (A/C) systems. A series of wind tunnel experiments were conducted in which the mean velocity and temperature field within the vicinity of a single block building (a cube) with leeward wall heating were measured. The ratio of Grashof number to the square of Reynolds number was used to model thermal effects within the vicinity of the model, but some compromises were needed in order to obtain a practical model while at the same time fulfilling the objectives of the task set. Gousseau et al. [12] used Large-Eddy Simulation (LES) to investigate the turbulent mass transport mechanism in the case of gas dispersion around an isolated cubical building. Close agreement is found between wind-tunnel measurements and the computed average and standard deviation of concentration in the wake of the building. Since the turbulent mass flux is equal to the covariance of velocity and concentration, a detailed statistical analysis of these variables was performed to gain insight into the dispersion process. Meslem et al. [13] observed changes in the prediction of local and global mean-flow quantities as a function of the considered turbulence model and by the lack of consensus in the literature on their performance to predict jet flows with significant three-dimensionality. In this chapter, we are interested in the study of the aerodynamic structure of inclined roof obstacles with different heights in a wind tunnel.

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2. COMPUTATIONAL DOMAIN Figure 1 presents the considered computational domains around the inclined roof obstacles with different heights equals to h = 0, h = H, h = 2H and h = 3H. Each domain is defined by the interior volume of the wind tunnel blocked by two planes: the first one is in the entry and the second one is in the exit. Figure 2 shows the geometrical arrangments of the considered system consisting on inclined roof obstacles. All these obstacles present a width equal to L2 = 118 mm. The distances separated the obstacle with the inlet and the outlet are equal respectively to L1 = 152 mm and L3 = 530 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 1. Computational domain for different heights.

h

h

L1

L2

L3

h

Parameters Parameters H L1 L22 L L3 L3

Values Values 63 mm 63 mm 152 152mm mm 118 118mm mm 530 mm 530 mm

Figure 2. Schematic representation of the pitched type obstacle

Figure 2. Schematic representation of the pitched type obstacle.

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3. NUMERICAL MODEL 3.1. Boundary Conditions A boundary condition is required anywhere fluid enters or exits the system and can be set as a pressure, mass flow, volume flow or velocity. For the inlet velocity, we will take as a value V = 0.32 m.s-1 and for the outlet pressure a value of P = 101325 Pa will be considered which means that at this opening the fluid exits the model to an area of static atmospheric pressure. In the computational domain characterized by h = H, a summary of the boundary conditions is given in Figure 3.

Figure 3. Boundary conditions in the computational domain characterized by h = H.

3.2. Mesh The local mesh settings do not influence the basic mesh but are basic mesh sensitive. All refinement levels are set with respect to the basic mesh cell. To refine the mesh only in a specific region and avoid excessive splitting of the mesh cells in other parts of the model, we apply a local initial mesh at the component surrounding this region. The component is created specially to specify the local initial mesh.

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Figure 4. Meshing of the computational domain.

4. NUMERICAL RESULTS By using the software “SolidWorks Flow Simulation”, the governing equations of mass and momentum in conjunction with the standard k-ε turbulence model were solved with a finite volume discretization [14-17]. Figure 5 presents the longitudinal and transverse planes defined by z = 0 mm, x = 90 mm, x = 179 mm and x = 269 mm. These planes are considered to visualize the velocity field, the total pressure, the dynamic pressure, the turbulent kinetic energy, the dissipation rate of the turbulent kinetic energy and the vorticity.

Figure 5. Presentation planes.

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4.1. Velocity Field Figures 6, 7, 8 and 9 present the distribution of the velocity field respectively in the longitudinal plane defined by z = 0 mm and the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 6. Distribution of the velocity field in the plane z = 0 mm.

According to these results, it has been noted that the velocity is weak in the inlet of the computational domain. Indeed, it is governed by the boundary condition value of the inlet velocity which is equal to V = 0.32 m.s-1. In this region, the velocity field is found to be uniform and increases progressively downstream of the entry. While the position of the obstacle is characterized by the high velocity. Downstream of the inclined type obstacle, the velocity keeps increasing progress. Then, a decrease has been noted through the exit where the minimum velocity values are recorded in he lateral walls. The maximum velocity values are located in the top of the roof according to the distribution shown in the plane defined by z = 0 mm. However, in the obstacle downstream a dead zone has been observed in the transverse plane showing a symmetric distribution in the plane defined by x = 90 mm. Indeed, it’s

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clear that the height of the obstacle has a direct effect on the velocity field. In fact, the maximum value of the velocity field increases with the increase of the obstacle height. Also, the extension of the dead zone created in the obstacle downstream is more developed with the height equal to h = 3H.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 7. Distribution of the velocity field in the plane x = 90 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 8. Distribution of the velocity field in the plane x = 179 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 9. Distribution of the velocity field in the plane x = 269 mm.

4.2. Average Velocity Figures 10, 11, 12 and 13 present the distribution of the average velocity respectively in the longitudinal plane defined by z = 0 mm and the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. According to these results, it has been noted that the velocity is weak in the inlet of the test section, it is indeed governed by the boundary condition value of the inlet velocity which is equal to V = 0.32 m.s-1. In this region, the velocity field is found to be uniform and increases progressively downstream of the entry, while the position of the obstacle is characterized by the high velocity. Downstream of the arched type obstacle, the velocity keeps increasing progress. Then, a decrease is noted through the exit where the minimum velocity values are recorded in the lateral walls. The maximum velocity values are located in the top of the roof according to the distribution shown in the plane defined by z = 0 mm. However, in the obstacle downstream a dead zone has been observed in the transverse planes showing a symmetric distribution in the planes defined by x = 90 mm and x = 179

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mm. Indeed, it is clear that the height of the obstacle has a direct effect on the average velocity. In fact, the maximum value of the average velocity increases with the increase of the obstacle height. Also, the extension of the dead zone created in the obstacle downstream is more developed with the height equal to h = 3H.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 10. Distribution of the average velocity in the plane z = 0 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 11. Distribution of the average velocity in the plane x = 90 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 12. Distribution of the average velocity in the plane x = 179 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 13. Distribution of the average velocity in the plane x = 269 mm.

4.3. Total Pressure Figures 14, 15, 16 and 17 present the distribution of the total pressure respectively in the longitudinal plane defined by z = 0 mm and

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the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. According to these results, it has been noted that a compressure zone appears in the obstacle upstream of the obstacle. However, a depressure zone appears in the downstream of the obstacle. In the top of the test section, the total pressure keeps a uniform distribution. It is clear that the height has a direct effect on the total pressure distribution. In fact, the maximum value of the total pressure increases with the increase of the obstacle height. Downstream of the inclined type obstacle, the total pressure keeps increasing progress. The maximum pressure values are located in the top of the roof according to the distribution shown in the plane y = 0 mm. The transverse planes show a symmetric distribution in the planes defined by x = 90 mm and x = 179 mm. For example, in the longitudinal plane z = 0 mm the maximum value of the total pressure is equal to Pt = 102308.89 Pa for the obstacle height of 3h. However, the maximum value of the total pressure is equal to Pt = 101466, 81 Pa for the obstacle height h = H.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 14. Distribution of the total pressure in the plane z = 0 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 15. Distribution of the total pressure in the plane x = 90 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 16. Distribution of the total pressure in the plane x = 179 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

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Figure 17. Distribution of the total pressure in the plane x = 269 mm.

4.4. Dynamic Pressure Figures 18, 19, 20 and 21 present the distribution of the dynamic pressure respectively in the longitudinal plane defined by z = 0 mm and the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. According to these results, it has been noted that a compressure zone appears in the obstacle upstream of the obstacle. However, a depressure zone appears in the downstream of the obstacle. In the top of the test section, the dynamic pressure keeps a uniform distribution. It is clear that the height has a direct effect on the dynamic pressure distribution. In fact, the maximum value of the dynamic pressure increases with the increase of the obstacle height. Downstream of the inclined type obstacle, the dynamic pressure keeps increasing progress.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 18. Distribution of the dynamic pressure in the plane z = 0 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 19. Distribution of the dynamic pressure in the plane x = 90 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 20. Distribution of the dynamic pressure in the plane x = 179 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 21. Distribution of the dynamic pressure in the plane x = 269 mm.

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The maximum dynamic pressure values are located in the top of the roof according to the distribution shown in the plane defined by y = 0 mm. The transverse planes show a symmetric distribution in the planes defined by x = 90 mm and x = 179 mm. For example, in the longitudinal plane z = 0 mm, the maximum value of the total pressure is equal to Pd = 519.58 Pa for the obstacle height of h = 3H. However, the maximum value of the total pressure is equal to Pd = 135.02 Pa for the obstacle height of h = H.

4.5. Turbulent Kinetic Energy Figures 22, 23, 24 and 25 present the distribution of the turbulent kinetic energy respectively in the longitudinal plane defined by z = 0 mm and the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. According to these results, it has been noted that the turbulent kinetic energy is weak in the inlet of the entry. In this region, the turbulent kinetic energy is found to be uniform and increases progressively downstream of the test section. Downstream of the inclined type obstacle the turbulent kinetic energy keeps increasing progress. Then, a decrease has been noted through the exit where the minimum energy values are recorded in the lateral walls. The maximum value of the turbulent kinetic energy are located in the top of the roof according to the distribution shown in the plane defined by z = 0 mm. However, in the obstacle downstream, a dead zone has been observed in the transverse plane defined by x = 90 mm and x = 179 mm plane. Indeed, it is clear that the height of the obstacle has a direct effect on the turbulent kinetic energy distribution. In fact, the maximum value of the turbulent kinetic energy increases with the increase of the obstacle height.

Computer Simulation of the Aerodynamic Structure…

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 22. Distribution of the turbulent kinetic energy in the plane z = 0 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 23. Distribution of the turbulent kinetic energy in the plane x = 90 mm

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 24. Distribution of the turbulent kinetic energy in the plane x = 179 mm.

(a) h = 0

(b) h = H

(c) h = 2H (d) h = 3H Figure 25. Distribution of the turbulent kinetic energy in the plane x = 269 mm

Figure 25. Distribution of the turbulent kinetic energy in the plane x = 269 mm.

4.6. Dissipation Rate of the Turbulent Kinetic Energy Figures 26, 27, 28 and 29 present the distribution of the dissipation rate of the turbulent kinetic energy respectively on the longitudinal

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planes defined by z = 0mm and on the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. From these results, it has been noted that the dissipation rate of the turbulent kinetic energy is weak in the inlet of the test section. In this region, the dissipation rate of the turbulent kinetic energy is found to be uniform and increases progressively downstream of the test section. Downstream of the inclined type obstacle, the dissipation rate of the turbulent kinetic energy keeps increasing progress. Then, a decrease has been noted through the exit where the minimum values of the dissipation rate of the

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 26. Distribution of the turbulent dissipation rate in the plane z = 0 mm.

turbulent kinetic energy are recorded in the lateral walls. The maximum values of the dissipation rate of the turbulent kinetic energy are located in the top of the roof according to the distribution shown in the plane defined by z = 0 mm. However, in the obstacle downstream, a dead zone has been observed in the transverse plane showing a symmetric distribution in the planes defined by x = 90 mm and x = 179 mm plane. Indeed, it is clear that the height of the obstacle has a direct effect on

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the dissipation rate of the turbulent kinetic energy. In fact, the maximum value of the dissipation rate of the turbulent kinetic energy increases with the increase of the obstacle height.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 27. Distribution of the turbulent dissipation rate in the plane x = 90 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 28. Distribution of the turbulent dissipation rate in the plane x = 179 mm.

Computer Simulation of the Aerodynamic Structure…

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

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Figure 29. Distribution of the turbulent dissipation rate in the plane x = 269 mm.

4.7. Vorticity Figures 30, 31, 32 and 33 present the distribution of the vorticity respectively in the longitudinal plane defined by z = 0 mm and the transverse planes defined by x = 90 mm, x = 179 mm and x = 269 mm. From these results, it has been noted that vorticity is weak in the inlet of the test section. In this region, the vorticity is found to be uniform and increases progressively downstream of the test section. Downstream of the inclined type obstacle the vorticity keeps increasing progress. Then, a decrease has been noted through the exit where the minimum vorticity values are recorded in the lateral walls. The maximum vorticity values are located in the top of the roof according to the distribution shown in the plane defined by z = 0 mm. However, in the obstacle downstream a dead zone has been the transverse plane showing a symmetric distribution in the planes defined by x = 90 mm and x = 179 mm.

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Indeed, it is clear that the height of the obstacle has a direct effect on the vorticity. In fact, the maximum value of the vorticity increases with the increase of the obstacle height.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 30. Distribution of the Vorticity in the plane z = 0 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 31. Distribution of the Vorticity in the plane x = 90 mm.

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(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 32. Distribution of the Vorticity in the plane x = 179 mm.

(a) h = 0

(b) h = H

(c) h = 2H

(d) h = 3H

Figure 33. Distribution of the Vorticity in the plane x = 269 mm.

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5. EXPERIMENTAL VALIDATION

h = 3H (Numerical) h = H (Numerical) h = H (Experimental [1])

Figure 34. Comparison between the numerical and the experimental velocity profiles for x = 3H.

Figure 34 shows the velocity profiles along the centre section defined by x = 3H for the inclined obstacles with hights h = H and h = 3H. From these results, it is clear that the hight of the obstacle presents a direct effect on the velocity value presenting an increase, especially near the obstacle head. The comparison of the predicted averaged velocity results with the measured data founded from the litterature presents a small discrepancie. These good agreement confirms the validity of the numerical method.

CONCLUSION A numerical simulation was developped to predict the aerodynamic structure of the inclined roof obstacles with different heights in a wind tunnel. The numerical results consist on the visualization of the local results such as the velocity field, the total pressure, the dynamic pressure, the turbulent kinetic energy, the dissipation rat of the turbulent

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kinetic energy and the vorticity. These results confirm that the inclined roof obstacles heights have a direct effect on the airflow patterns and the local characteristics on the roof and downstream of the obstacles, but did not affect significantly their upstream side. The satisfactory agreement between the numerical simulation and the experimental results, obtained by wind tunnel tests, validated the used mathematical model.

REFERENCES [1]

[2]

[3]

[4]

[5]

Ntinas G. K., Zhang G., Fragos V. P., Bochtis D. D., NikitaMartzopoulou Ch., Airflow patterns around obstacles with arched and pitched roofs:Wind tunnel measurements and direct simulation, European Journal of Mechanics B/Fluids 43 (2014) 216–229. Luo W., Dong Z., Qian G., Lu J., Wind tunnel simulation of the three-dimensional airflow patterns behind cuboid obstacles at different angles of wind incidence, and their significance for the formation of sand shadows, Geomorphology 139–140 (2012) 258– 270. Tominaga Y., Stathopoulos T., CFD simulation of near-field pollutant dispersion in the urban environment: A review of current modeling techniques, Atmospheric Environment 79 (2013) 716730. Jiang Y.,Alexander D., Jenkins H., Arthur R., Chen Q., Natural ventilation in buildings: measurement in a wind tunnel and numerical simulation with large-eddy simulation, J. Wind Eng. Ind. Aerodyn. 91 (2003) 331-353. Ahmad K., Khare M., Chaudhry K. K., Wind tunnel simulation studies on dispersion at urban street canyons and intersections- a review, J. Wind Eng.

196 [6] [7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

Slah Driss, Zied Driss, Imen Kallel Kammoun et al. Ind. Aerodyn. 93 (2005) 697-717. Smolarkiewicz P. K., Sharman R., Weil J., Perry S. G., Heist D., Bowker G., Building resolving large-eddy simulation and comparison with wind tunnel experiments, Journal of computational Physics 227 (2007) 633-653. De Paepe M., Pieters J. G., Cornelis W. M., Gabriels D., Merci B., Demeyer P., Airflow measurements in and around scale-model cattle barns in a wind tunnel: Effect of wind incidence angle, Biosystems Engineering 115 (2013) 211-219. Lim H. C., Thomas T. G., Castro I. P., Flow around a cube in a turbulent boundary layer: LES and experiment /J. Wind Eng. Ind. Aerodyn. 97 (2009) 96-109. Becker S., Lienhart H., Durst F., Flow around three-dimensional obstacles in boundary layers, J. Wind Eng. Ind. Aerodyn. 90 (2002) 265-279. De Melo A. M. V., Santos J. M., Mavrroidis I., Costa Reis Junior N., Modelling of odour dispersion around a pig farm building complex using AERMOD and CALPUFF. Comparison with wind tunnel results, A. M. Vieira de Melo et al./Building and Environment 56 (2012) 8-20. Richards K., Schatzmann M., Leitl B., Wind tunnel experiments modelling the thermal effects within the vicinity of a single block building with leeward wall heating, J. Wind Eng. Ind. Aerodyn. 94 (2006) 621-636. Gousseau P., Blocken B., Heijst G. J. F, Large-Eddy Simulation of pollutant dispersion around a cubical building: Analysis of the turbulent mass transport mechanism by unsteady concentration and velocity statistics, Environmental Pollution 167 (2012) 47-57. Meslema A., Bodeb F., Croitorub C., Nastaseb I., Comparison of turbulence models in simulating jet flow from a cross-shaped orifice: European Journal of Mechanics B/Fluids 44 (2014) 100120.

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[15] Driss Z., Mlayeh O., Driss D., Maaloul M., Abid M. S., Numerical simulation and experimental validation of the turbulent flow around a small incurved Savonius wind rotor, Energy (2014) 74. 506-517. [16] Driss S., Driss Z., Kallel Kammoun I., Study of the Reynolds Number Effect on the Aerodynamic Structure around an Obstacle with Inclined Roof, Sustainable Energy, 2014, Vol. 2, No. 4, 126133. [17] Driss Z., Bouzgarrou G., Chtourou W., Kchaou H., Abid MS., Computational studies of the pitched blade turbines design effect on the stirred tank flow characteristics, European Journal of Mechanics B/Fluids 29 (2010) 236-245. [18] Ammar M., Chtourou W., Driss Z., Abid MS., Numerical investigation of turbulent flow generated in baffled stirred vessels equipped with three different turbines in one and two-stage system, Energy 36 (2011) 5081-5093.

In: Wind Tunnels: Uses and Developments ISBN: 978-1-53615-898-4 Editor: Zied Driss © 2019 Nova Science Publishers, Inc.

Chapter 9

WIND TUNNEL TESTS OF DELTA WING WITH PRIVILEGED APEX Iddir Boumrar1, and Zied Driss2 1

University Mouloud Mammeri of Tizi-Ouzou, Mechanical Engineering Department, Tizi-Ouzou, Algeria 2 University of Sfax, National School of Engineers of Sfax (ENIS), Laboratory of Electro-Mechanic Systems (LASEM), Sfax, Tunisia

ABSTRACT Various experimental studies are devoted to the aerodynamic of reduced aircraft models with particular contours and edges. The first studies were focused on observations and visualization in the wind tunnel. They suggest that delta wings with "privileged" apex can influence the wing aerodynamic characteristics and consequently could have repercussions on the performances of the aircraft. In addition, these same studies revealed that the apex vortex which develops on the suction face of this type of wings occupy positions corresponding to values of quantified angles, called "privileged angles". The present experimental 

Corresponding Author’s Email: [email protected], [email protected].

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Iddir Boumrar and Zied Driss study aims to validate these phenomenological aspects delivered by visualizations through measurements of aerodynamic coefficients of pressure Cp, drag CD and lift CL determined for all the considered configurations. The obtained experimental results are encouraging, but the mechanisms of interactions between the values of the apex angle and the flow are still to date too badly known to consider the optimization of aerodynamic form for a real application.

Keywords: wind tunnel, delta wing aircraft, privileged apex angle, defect pressure, lift, drag, apex vortex, delta wing-fuselage interaction, external aerodynamic, fuselage

NOMENCLATURE A CD CL Cp -Cp d e g i icr ivb lo L LEVs Oxyz Ox Oy Oz R

Wing surface (m2), Drag coefficient, Lift coefficient, Pressure coefficient, Defect pressure coefficient, fuselage diameter (m), delta wing thickness (m), Acceleration of gravity (m/s2), Angle of attack (AOA°): incidence (°), Critical incidence (°), Vortex breakdown incidence (°), Wing chord (m), Wing span (m), Leading Edge Vortex, Cartesian coordinates axis, Median axis on the wing surface, Transverse axis on the wing surface, Vertical axis, Polar coordinate of the pressure taps (m),

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vortex Generators, Wind tunnel velocity (m/s), height in the multi-manometer (mm).

Greek Letters α1 α2 β 𝜆= ρ ρH

Angle between the principal vortices directions (°), Angle between the secondary vortices directions (°), Apex angle (°), 𝐿2 𝐴

𝛽

= 4𝑡𝑔( 2 )Aspect ratio, Air density (kg/m3), Oil density (kg/m3).

1. INTRODUCTION During the last few decades, flow structure over delta wings has been a major field of interest due to the increasing applications on unmanned combat air vehicles (UCAV), unmanned air vehicles (UAV), and micro air vehicles (MAV), which can be represented by these simplified plan forms. In today’s competitive world, demands for more maneuverable and stealthy air vehicles have encouraged the development of new control concepts for separated flows. The goal of these works is to describe experimental and numerical flow passive and active control techniques used to manipulate the vortical structures and particularly to delay three dimensional separations from the surface of the plan form (stall) over slender delta wings at high angles of attack. Flow over delta wing is dominated by two counter rotating vortices shed from the leading edges generated closer to the wing surface, the vortex core location leads to distinctive features as a result of interaction between the boundary layer on wing and vortices. This

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interaction might result in separation of the LEVs into two rotating vortex structure, dual vortex structure, which is reported both experimentally and numerically in low incidences and low Reynolds numbers. The passive control strategies include geometry or material modifications having an obvious advantage of not requiring energy input to the flow field. Modification of leading edge shape, modification of trailing edge, using elastic materials in plan form structure, and using flaps can be listed as most common approaches in passive control. For example, Zhen et al. [1] carried out experimental and numerical works where an array of vortex generators (VGs) was attached on Aludra UAV’s wing to determine the effects of these passive VGs on the aerodynamic characteristics. In the numerical investigation, the RANS code Fluent 6.3 was used and the comparison to the experimental results reveals a satisfactory agreement. The parametric study shows that higher maximum lift coefficient was achieved when the VGs are placed nearer to the separation point. In addition to this, shorter spanwise distance between the VGs also increases the maximum lift coefficient, rectangular and curve-edge VG performs better than triangular V. G. Wang [2] performed experiments on a 82.5° sweep flat-plate delta wing combined with a dorsal fin of height 0.6 of the wing semi-span at Reynolds number based on the wing root chord of 3.32 × 105, in which a pair of small and short dielectric barrier discharge plasma actuators were employed at the wing leading edge near the apex of the wing to effect flow control. Measured pressure distributions over the model were investigated. Lateral flow control was achieved at angle of attack of 30° by the plasma actuators. Flow induced by the leading-edge plasma actuator in still air was also studied. Rehman [3] presented an investigation of the vortex flow structure over non-slender delta wing with leading edge sweep angle, Λ = 45°. A seven-hole pressure probe measurements for axial vorticity, axial velocity, vortex trajectory and pressure variations were presented at various chordwise stations and angles of incidences. Passive apex flap has been used to control the leading edge vortices and to delay the

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vortex breakdown. It is recognized that vortex breakdown was delayed by 8% with downward apex flap deflection. Leading edge control surfaces were investigated by Panta et al. [4] as an alternative actuation solution with the potential to enhance control authority and rapidity. In this study, flow visualization of leading edge control surface revealed that higher deflection rates delayed flow separation and this was expected to enhance control forces. Higher actuation rates produced dominant leading edge vortices and hence a transient lift enhancement over the airfoil. Lift spikes from high rate actuations could be exploited to compensate the high frequency perturbations from gusts. Robert [5] developed a design methodology for optimized flutter control of an aeroelastic delta wing. The approach rests on two main premises. The first application of linear modeling and control design techniques was used to control the predominantly nonlinear phenomenon of flutter by preventing its onset. The second lies in the spatial optimization of actuator and sensor parameters to facilitate control of targeted modes while providing roll-off of higher order modes without the need for phase-inducing filters. The experiments employing these optimized transducers show substantially increased flutter control authority over no optimized systems, and point to the importance of this spatial coupling as well as the transducer mass and stiffness effects. Çelik et al. [6] studied the effect of passive bleeding on flow structure of a 45° swept delta wing using techniques of laser-illuminated smoke visualization, surface-pressure measurements and Particle Image Velocimetry. Three different bleeding configurations were tested to identify the effectiveness of the control technique compared to a base plan form. The results confirm that the bleeding might effectively be used to eliminate the surface separation on no slender delta wing. Magness et al. [7] investigated the unsteady flow structure of leadingedge vortices on a delta wing using new types of experimental techniques, in order to provide insight into the consequences of various forms of active control. These investigations involve global control of the entire wing and local control. The localized control at long and short

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time-scales involved application of various transient forms of suction and blowing using small probes upstream and downstream of the location of vortex breakdown, as well as distributed suction and blowing along the leading-edge of the wing applied in a direction tangential to the feeding sheet. These local control techniques can result in substantial alteration of the location of vortex breakdown. In some cases, it is possible to accomplish this without net mass addition to the flow field. Mitchell et al. [8] examined two promising and different pneumatic flow control methods for the control of vortex breakdown over slender delta wings: open-loop, along-the-core blowing and periodic blowing and suction along the leading edges. These studies consist of both experimental and computational analysis of subsonic flow fields around 70° delta wings over a broad range of angles of attack and root-chord Reynolds numbers. In the study of Nelson et al. [9], plasma actuators placed just below the leading edge were found to augment the lift. The configuration was implemented in a full-span model that was mounted on a sting that allowed free-to-roll motion. The ability of the plasma actuator arrangement to produce roll maneuvers was then investigated for a range of angles of attack and free- stream speeds. The results indicated excellent roll control with roll moment coefficients that are comparable to conventional moving surfaces. The study of Çelik and Yavuz [10] aimed to control the flow structure and particularly to delay stall on a non-slender delta wing by passive control. This study investigated the sole effect of bio-inspired geometry modification on flow structure and stall characteristic of a 45° swept delta wing using laser illuminated smoke visualization technique. The bio-inspired geometry was derived from fluke geometries due to apparent physical similarity. The fluke geometry was obtained from the literature, which is a white-sided female dolphin of sweep angle 47.7°. The fore body of the fluke is adapted to have 45° of sweep. The adaptation point was chosen such that the shoulder on the geometry was kept without any change, to cover a broad range of operation with different flow characteristics. Greenblatt et al. [11] considered the

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active control of a leading edge vortex on a semi span delta wing wind tunnel model, by means of a pulsed dielectric barrier discharge (DBD) plasma actuator. The main objectives were to maximize aerodynamic performance, study combined active (DBD actuator) and passive (Gurney flap) control, and investigate the flow field corresponding to optimum control conditions. The flow field data acquired above the wing, and normal to the root chord, indicated that the major contribution to lift enhancement occurred near the delta wing apex. Anton et al. [12] studied the aerodynamic coefficients and stability derivatives for the X-31 model aircraft. To improve the stability derivative calculations for a delta-wing aircraft in the subsonic regime, a compendium of new methods was programmed into a new code, FDerivatives. All the required geometrical data relative to the aerodynamic coefficient estimation of the X-31 aircraft were calculated for the wing–body–tail configuration. The FDerivatives code gives very good results in comparison with experiments. An analysis of longitudinal motion, based on FDerivatives results, was presented. Williams [13] investigated the effects of active flow control by oscillatory blowing at the leading edge of a no slender delta wing with a 50° sweep angle. Pressure measurements and Particle Image Velocimetry measurements were conducted on a half wing to investigate the formation of leading edge vortices for oscillatory blowing, compared to the stalled flow for the no blowing case. Stall has been delayed by up to 8°, and significant increases in the upper surface suction force have been observed. Phase averaged measurements reveal the perturbation due to the pulsed blowing, its interaction with the shear layer and vortex, apparent displacement of the vortex core, and relaxation of the reattachment region. According to anterior studies interesting more the phenomenological analyses, it is clear that the obtained results tend to generalize the existence of privileged angles, or discretization of the angles, which are formed in the Helium Supra Fluid flow between the helicoids swirls and their respective axis, with broad fields interesting

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as well science of nature, medicine (physiology, anatomy) architecture, physics and mechanics. While being limited to the fluid mechanics, stability and optimization of flows would correspond to the wealth of privileged angles present in the studied geometrical forms. In case of aerodynamics, studies based primarily on many visualizations in wind tunnel of flows around bodies and simple delta wings, show that the angle formed by the apex swirls are affected by the wing apex angle value. In the same way of fluid mechanics, it would prove through comparisons between planes provided with delta wings, that the wings with privileged apex have advantages concerning the stability of the aircraft and their fuel consumption. Beyond visualizations and phenomenological analyses existing in the literature, the study suggested here wants to be a work of quantification through the aerodynamic coefficients. The objective is to dissociate the wings with privileged apex of the wings with non-privileged apex and later to allow consequently a choice of optimal delta wings. In the present work many pressure taps are placed under the delta wings principal apex vortex in order to determine the longitudinal distribution of the defect pressure coefficient -Cp. Also, we carried out measurements of the coefficients of lift CL and drag CD, a confrontation of the obtained experimental results is presented. Three delta wings with apex angle (β = 75, 80 and 85°) are considered in the present experimental study. The results relating to the aerodynamic coefficients show that the wing with privileged apex angle β = 80° has an advantage of presenting the greatest values of depression and lift; while the two other delta wings with non-privileged apex angles (β = 75 and 85°) present the low values of depression and lift. The drag values are almost identical for the three studied wings. The whole of these results suggest in conclusion that it is preferable to use delta wings with privileged apex angle which provide better aerodynamic performances in terms of pressure, lift and drag coefficients (– Cp, CL and CD).

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2. FACILITIES AND MEASUREMENT TECHNIQUES Aerodynamic studies based on visualizations were carried out by Benkir [14]. They prove through comparisons that the bodies provided with privileged angles at their different contours have advantages concerning the stability of the flow and a better repartition of the complex swirling structures. The criterion of privileged angles was introduced at the microscopic scale in the atoms and extended at the macroscopic scale in the case of the Helium II supra fluid flow. These privileged angles are given in [14] with the following relation: cos 𝛽 =

𝑚 √𝑙(𝑙+1)

l and m integers with −𝑙 < 𝑚 < +𝑙

(1)

where m and l are integers m ≤ l; The first family is defined by m = l (which corresponds to β = 45°,35°3,30°,26°6,24°1,22°2…). The second family is defined by m = 2 and l > 2 (β = 54°7,63°4,68°6,72°,74°5…). The experimental device, described in detail in [15], is composed by a subsonic wind tunnel having a test section with 100 cm of length, 30 cm of width and 30 cm of height (Figure 1). The flow velocity Vo is adjustable from 0 to 45 m/s. A multi-manometer with 24 tubes allows measurements of pressure by reading the heights of oil prevailing in the tubes. The velocity measurement of the air flow in the test section is ensured by a double Pitot probe connected to the multi-manometer. An aerodynamic balance with strain gauges connected to a data acquisition system, allow us the measurements of the two principal aerodynamic loads lift (L) and drag (D) exerted on the models. Therefore, the corresponding lift and drag coefficients (CL and CD ) are defined respectively by the following equations:

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Iddir Boumrar and Zied Driss CL = 1 2

L ρV20 A

(2)

and D

CD = 1

ρV20 A

(3)

2

The pressure have been determined via the measurements of the oil heights, and read on the manometer, which led then to determine the corresponding pressure coefficient Cp using the following equations: Cp =

P−P0 1 ρV20 2

(4)

with 2ρH gΔz

Vo = √

ρ

(5)

Figure 1. Wind tunnel.

Special suitable supports are developed in order to allow the fixation of the models in the test section and the connection of the pressure taps to the multi-manometer.

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2.1. Delta Wing Models Before the realization of the scaled reduced models, we established a drawing design which defines all the models to be carried out with their respective geometrical dimensions (Tables 1 and 2). Table 1. Geometrical characteristics of the studied delta wings β (°) 75 (NP) 80 (P) 85 (NP)

lo (cm) 9.97 9.55 9.13

L(cm) 15.31 16.03 16.73

A(cm2) 76.54 76.54 76.54

λ 3.07 3.36 3.66

P: privileged; NP: non privileged.

2.1.1. Models for Lift and Drag Measurement The delta wing models were produced from a Plexiglass flat plate of thickness e = 5 mm (Figure 2), on which we draw the various wings with an inhibiting pen thereafter each wing was cute out using a saw then adjusted using a milling machine; the choice of Plexiglass is not fortuitous since it offers a facility of machining (realization of grooves, drilling of holes…). Half of realized wings are intended for the measurement of the pressure coefficient Cp, in addition the other wings were carried out for the measurement of the coefficients of lift CL and drag CD.

(a) Delta wing without fuselage

(b) Delta wing in the wind tunnel test section.

Figure 2. Delta wing model for CL and CD measurement.

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2.1.2. Models For Pressure Measurement The realized pressure taps are located under the delta wing apex vortex, the three wings intended for the measurement of the defect pressure coefficient -Cp must undergo the following operations:

      

Tracing lines of pressure taps at located points, Milling to obtain some 2.5 depth mm grooves being used as drain for the capillary tubes, Drilling the holes to receive the tubes, Placement of the copper tubes bent beforehand, Fixation of the tubes in the grooves using a fast adhesive, Replacement of the matter removed by cement for sheets, Smooth the surface of cement.

Because the pressure taps localization must be done with precision, we must take in account especially α1 position of the principal apex vortex. According to visualizations of Benkir [14], we deduce that the values of angles α1 and α2 between the delta wings vortices carried out are given in the Table 2.

Figure 3. Different views of the delta wing apex vortex.

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Table 2. Principal and secondary vortices positions by Benkir [14] β (°) 75 (NP) 80 (P) 85 (NP)

α1 (°) angle between the principal vortex 45 (i = 8 to 26) 54.7 (i = 8 to 22) 54.7 (i = 8 to 22)

(a) Model without fuselage

α2 (°) angle between the secondary vortex 63.4 (i = 8 to 20) 63.4 (i = 8 to 20) 63.4 (i = 8 to 20)

(b) Model with fuselage of diameter d

Figure 4. Pressure taps localization under the apex vortex of the studied delta wings.

2.2. Realization of the Delta Wings Supports The presence of any object in the wind tunnel test section, except the wing models, is considered as an obstacle which can generate disturbances of the air flow, and bring an additional error to the considered measurements. This allows us to conceive supports able to support the wing models with not very significant influence on the experimental results (measurement of Cp, CL and CD). 2.2.1. Support for Lift and Drag Measurement The realization of this support is simple. It is composed by the following elements:



a semi-cylindrical bar with a diameter 10 mm and length 270 mm. Its smooth surface quality was obtained by assigning to the machine a high rotation velocity, a low depth of cut and a slow

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

movement in advance of the tool, follow-up of some master keys of milling which enable us to obtain the semi-cylinder. a small screw which will make it possible to fix the various wings on the support.

The first extremity is cylindrical over a 45 mm length and connected to the wind tunnel balance by the intermediary of an embedding at 40 mm of the torsion movement which could intervene during the wind tunnel tests and is eliminated using a pin fixed at the wind tunnel balance. At 60 mm of the other extremity, we bore a hole of 4 mm diameter tapped to receive a compatible screw which allows the fixation of the models in order to place the models in the center of the wind tunnel test section.

Figure 5. Support for CL and CD measurements.

2.2.2. Realization of Support for Pressure Measurement The number of tests and delta wing models provided with pressure taps, allow us to carry out a rigid attachment unit but easily dismountable, since each time, there is placing a model, to carry out tests, and to remove it to replace another. The mechanism of fixing the wing model provided with pressure taps is represented by two principal parts: The support conceived is a hollow tube of 30 cm of length, with external diameter 18.5 cm and

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internal diameter of 16.5 cm through which pass 24 tubes connected to the capillary tubes leaving the wings via vinyl polychloride pipes, on the other extremity the same tubes communicate with the multimanometer. The same support provides in its medium by a leg used to maintain the model. On this leg, we bored two holes of diameter 3 mm and two others in each model, fixing is obtained using two screws and two nuts. The distance which separated the wings from the cylindrical tube is sufficiently large 10 cm in order to avoid an additional disturbance of the results.

(a) Final assembly of the model in the wind tunnel

(b) Final assembly of the combination delta wing fuselage in the wind tunnel

Figure 6. Pressure measurement system.

We choose screws and nuts of low dimensions with diameter (2.5 mm). We filed them in order to decrease their dimensions. We placed the heads of the two screws in holes prepared for this purpose on each wing. We covered them by a smooth surface, to reduce the effects of the disturbances of the air flow around these screws and nuts and to minimize the additional lift caused by their swirls. The support is equipped in its end with a small bar which is encased in an opening of the vertical wall of the section test to eliminate the vibration while allowing a rotation around its axis. At the other end, it is connected a drum which is encased in the test section wall.

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2.3. Incidence Adjustment System The attachment unit comprises also screws latch-tightening and a graduated dial of degree in degree, giving the incidence of the wing and the combination delta wing-fuselage.

Figure 7. Incidence adjustment system.

3. RESULTS ANALYSIS The models were tested at two flow velocities (Vo = 20.3 m/s and 31 m/s) and several angles of attack varying from i = 0° to 45° with a step of 5 degrees. This is necessary in order to study effects of Reynolds number and angle of attack on models aerodynamic characteristics. The results were obtained in terms of defect pressure coefficient -Cp, lift coefficient CL and drag coefficient CD evolutions.

3.1. Pressure Measurement The pressure measurement provides detailed information on the flow field particularly under apex vortex of the models.

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For measurement of depression the various steps below are followed during model testing in the wind tunnel test section: 1. The model is installed in the wind tunnel test section at a considered incidence, 2. All the tubes issued from the various pressure taps are connected to the multi-manometer, 3. Regulate the angle of attack, 4. The air flow is actuated at the velocity Vo=20.3 m/s, 5. Readings of the pressure gauge are taken, 6. Repeat steps 4 and 5 for the velocity Vo = 31 m/s, 7. Repeat steps 3 to 7 according to another angle of attack. 3.1.1. Privileged Apex Angle (β = 80°) Effects Curves of Figure 8 present the defect pressure coefficient distribution under the apex vortex of tested wings without fuselage at two different flow rates. As r/lo increases it is noticed that -Cp decreases for the three wings. Maximum values of -Cp are reached at the immediate vicinity of the wings apex. Different pressure distribution shown on Figures 8, 10 and 11 prove clearly that there is effect of the privileged angle apex β=80°, value of the most significant -Cp is reached by models with privileged apex angle β = 80°. 3.1.2. Apex Vortex Bursting The defect pressure coefficient -Cp increases with the angle of attack, an abrupt fall of -Cp values is obtained at a criticize incidence ivb [8, 14], as presented in Figures 9,12 and 13, which translates the apex vortex breakdown. The pressure distribution under the apex swirls, developed on the suction face of the studied delta wings, are shown on Figure 9 before and after bursting of the apex vortices, at two flow velocities Vo = 20.3 m/s and 31 m/s. According to these results, we notice that the increase

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of the angle of attack to i = 30°, decreases the defect pressure abruptly for all the examined flow rates. A new pace of the pressure distribution is noticed since we have vortex bursting for the delta wings.

(a) i=5°, Vo=20.3 m/s

(c) i=10°, Vo=20.3 m/s

(b) i=5°, Vo=31 m/s

(d) i=10°, Vo=31 m/s

(e) i=15°, Vo=20.3 m/s (f) i=15°, Vo=31 m/s Figure 8. Effects of the privileged apex angle for delta wings without fuselage.

Figure 8. Effects of the privileged apex angle for delta wings without fuselage.

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(a) i=15°, Vo=20.3 m/s

217

(b) i=30°, Vo=20.3 m/s

(c) i=15°, Vo=31 m/s (d) i=30°, Vo=31 m/s Figure 9. Defect pressure coefficient –Cp distribution before and after vortex Figure 9. Defect pressure coefficient –Cp distribution andfuselage. after vortex bursting bursting (breakdown) on the wingsbefore without (breakdown) on the wings without fuselage.

When r/lo increases, the distance between the curves of -Cp along the apex vortex direction decreases (Figures 8 and 9). Moving downstream to r/lo = 0.6, the three curves tend towards the same value of -Cp = 0.5 before the swirls bursting and –Cp = 0.8 after unhooking. We observe a small variation of the pressure coefficient along the apex swirl at various Reynolds numbers. For r/lo> 0.6 the three evolutions become more stable and confused. 3.1.3. Fuselage Diameter Effects At the incidences i = 5°, 10° and 15° we observe on Figure 10, the pressure distribution under the apex vortex of tested combinations delta

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wing-fuselage with diameter d = 20 mm at the two considered velocities. Beyond the value r/lo = 0.75, as r/lo increases, it is noticed that -Cp decreases for the three models. A small area of significant -Cp appears for 0.5 < r/lo < 1. The results proved that this flow state occurs for all the Reynolds numbers. We have also a superposition of two flows above the two sides of the combinations delta wing-fuselage:

(a) (a)i=5°, i=5°,VVo=20.3 m/s o=20.3m/s

(b)i=5°, i=5°,VVo=31 m/s (b) o=31m/s

(c) i=10°, Vo=20.3 m/s (c) i=10°, Vo=20.3 m/s

(d) i=10°, Vo=31 m/s (d) i=10°, Vo=31 m/s

(e) i=15°, Vo=20.3 m/s (f) i=15°, Vo=31 m/s Vothe =20.3 m/s (f) i=15°, Vo=31 m/s Figure(e) 10.i=15°, Role of privileged apex angle for the combinations delta wing-fuselage with Figure 10. Role of the privileged apex angle for mm. the combinations delta wing-fuselage with diameter d=20 diameter d=20 10. Role of the privileged apex angle formm. the combinations delta wing-fuselage

Figure with diameter d = 20 mm.

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the first flow resulting from the delta wing leading edges the second is a vortical flow developed on the wing fuselage. The pressure distribution under the apex swirls on the suction face of the combinations delta wing -fuselage are shown on Figures 10 and 11 at incidences i = 5°, 10° and 15° for Vo = 20.3 m/sand Vo = 31 m/s. Firstly we deduce that effect of Reynolds number is negligible. Increasing the angle of attack we notice that –Cp value corresponding to the privileged apex β = 80° are dominant.

(a) i=5°, i=5°, V Vo=20.3 =20.3 m/s m/s (a) o

(b) i=5°, i=5°, V Vo=31 =31 m/s m/s (b) o

(c) i=10°, i=10°, V Vo=20.3 =20.3 m/s m/s (c) o

(d) i=10°, i=10°, V Vo=31 =31 m/s m/s (d) o

(e) i=15°, i=15°, V Vo=20.3 =20.3 m/s m/s (f) i=15°, i=15°, V Vo=31 =31 m/s m/s (e) (f) o o Figure 11. 11. Role Role of of the the privileged privileged apex apex angle angle for for the the combinations combinations delta delta wing-fuselage wing-fuselage with with Figure diameter d=30mm. diameter Role of the privileged apex angled=30mm. for the combinations delta wing-fuselage

Figure 11. with diameter d = 30mm.

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3.2. Lift and Drag Measurement Figures 12 and 13 show the evolution of lift and drag coefficients. According to these results, the three curves are quasi-confused and have the same bursting angle. According to Figure 12 we notice that the CL and CD evolutions for the various wings without fuselage are identical in particular before the bursting. In these curves, the effects of the privileged apex angle appear slightly in particular before bursting. The same results are reproduced for the curves of Figure13, with Vo = 31 m/s. When the angle of attack is increased up to i = 25°, turbulences translated by the evolution of CL and CD are remarkable. This is due to the vortex entirely burst at this critical angle of attack.

Figure 12. Evolution of CL and CD for the delta wings without fuselage at the velocity o=20.3 m/s. Figure 12. Evolution of CL and CD forVthe delta wings without fuselage at the velocity Vo = 20.3 m/s.

Figure 13. CL and CD evolutions for the delta wings without fuselage at the velocity Vo=31 m/s. wings without fuselage at the velocity Figure 13. CL and CD evolutions for the delta Vo = 31 m/s.

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4. MEASUREMENT UNCERTAINTIES Measuring drag, lift or pressure coefficients, various experimental errors are added to measurements; these experimental errors are due primarily to the preliminary determination of flow rates before each test on a considered model (misreading of the oil heights in the multimanometer columns), the errors of the parallax (made during the reading of the incidence angle values) and the effects of temperature in particular on the density. Thus for the pressure coefficient given by eq.4, we use the logarithmic derivative and we obtain: 1

ln Cp = ln(p − po ) − ln(ρ) − ln (2 . Vo 2 )

(6)

After differentiation, we will have: dCp Cp

=

dp p−po

−

dpo p−po

−

dρ

− 2.

ρ

dVo

(7)

Vo

While passing to the uncertainties we write: ∆Cp Cp

=

∆p p−po

+

∆po p−po

+

∆𝜌 𝜌

+ 2.

∆Vo

(8)

Vo

After differentiation of equation.(5) we obtain: 2.

dVo Vo

=

dρH ρH

+

dg g

dz

dz

+ 2. z−z − 2. z−zo − o

o

dρ ρ

(9)

And passing to uncertainties: 2.

∆Vo Vo

=

∆ρH ρH

+

∆g g

∆z

∆z

+ 2. z−z − 2. z−zo − o

o

∆ρ ρ

(10)

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Iddir Boumrar and Zied Driss Finally we obtain:

∆Cp Cp

= 11%

In the same way for the two other aerodynamic coefficients defined respectively by eq.2 and eq.3: We obtain: ∆CL CL

=

∆s s

+

∆𝜌 𝜌

+

∆A A

+ 2.

∆Vo Vo

(11)

And: ∆CD CD

=

∆D D

+

∆𝜌 𝜌

+

∆A A

+ 2.

∆Vo Vo

(12)

A is the delta wing surface, defined as follows: A=

L𝑙o

(13)

2

Thereafter, we obtain: ∆A A

=

∆L L

+

∆𝑙o

(14)

𝑙o

What enables us to determine the two relative error: ∆CL CL

= 12% and

∆CD CD

= 12%

CONCLUSION The contribution of this work aims at improving aerodynamic passive optimization based on phenomenological considerations. Thus, we are interested by the influence of the apex angles values called privileged angles on the aerodynamic performances of delta wings and

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the interaction delta wing-fuselage with geometrical characteristics close to those of the military aircrafts. The obtained results are in agreement with those published recently and coincide well with those met in the literature. The defect pressure coefficient –Cp evolutions under the apex vortex show that the depression decreases when we move from the wing apex towards the trailing edge. Indeed, we note easily that an increase of the incidence involves a significant increase in the depression until the apex vortex bursting. The comparative analysis carried out through the influence of the angle of apex β on the defect pressure coefficient –Cp evolution, under the principal apex vortex of the various wings submitted for testing, reveals the role of the privileged apex angle of the second family β = 80°. The behavior analysis of the apex vortex corresponding to the wing with privileged apex (β = 80°) is characterized by optimal aerodynamic parameters than the two other apexes in particular the measured values of defect pressure, lift and drag. The beneficial effects of the privileged apex are obtained once again for combinations delta wing-fuselage. In this context, the choice of the wings with privileged apex make it sure to obtain prevalence aerodynamic parameters, where the phenomenological studies show a better stability of the flow developing at the delta wings suction face.

REFERENCES [1]

[2]

Zhen, T. K., Zubair, M., Ahmad, K. A., (2011). Experimental and Numerical Investigation of the Effects of Passive Vortex Generators on Aludra UAV Performance. Chinese Journal of Aeronautics, 24 (5), 577-583. Wang, J. L., Li, H. X., Meng,X. S., Liu, F., Luo, S. J., (2011). Plasma Flow Control over Slender Delta Wing and Low Dorsal Fin Combination. AIP Conference Proceedings, 1376 (1), 518.

224 [3]

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Rehman, H. L., (2011). Control of Leading Edge Vortices using Apex Flap over Non-Slender Delta Wing. Recent Progresses in Fluid Dynamics Research, Vol 1376, 518-520. [4] Panta, A., Petersen P., Marino M., Watkins S., Fisher A. and Mohamed, A., (2017). Qualitative Investigation of the Dynamics of a Leading Edge Control Surfaces for MAV Applications. 9th International Micro Air Vehicle Conference and Flight Competitioin, Toulouse, France, 1-8. [5] Robert, E. R. and Robert, L. C., (2003). Delta Wing Flutter Control Using Spatially Optimized Transducers. Journal of Intelligent Material Systems and Structures, 14 (11), 677-691. [6] Çelik, A., Çetin,C., and Yavuz, M. M., (2017). Effect of Passive Bleeding on Flow Structure over a Nonslender Delta Wing. AIAA Journal, 55 (8), 2555-2565. [7] Magness, C., Robinson, O., and Rockwell, D., (1989). Control of Leading-Edge Vortices on A Delta Wing. 2nd Shear Flow Conference, Tempe, USA. [8] Mitchell, A., Morton, S., Molton, P., Guy, Y., (2001). Flow Control of Vortical Structures and Vortex Breakdown over Slender Delta Wings. RTO Applied Vehicle Technology Panel (AVT), Symposium held in Loen, Norway. [9] Nelson, R. C., Corke, T. C., He, C., Othman, H., Matsuno, T., Patel, M. and Ng, T., (2007). Modification of the Flow Structure over a UAV Wing for Roll Control. 45th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings, Reno, Nevada, USA. [10] Çelik, A., and Yavuz, M. M., (2016). Effect of Edge Modifications on Flow Structure of Low Swept Delta Wing. AIAA Journal, 54 (5), 1789-1797. [11] Greenblatt, D., Kastantin, Y., Nayeri, C. N., and Paschereit, C. O., (2008). Delta Wing Flow Control Using Dielectric Barrier Discharge Actuators. AIAA Journal, 46 (6), 1554-1560.

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[12] Anton, N., Botez, R. M., and Popescu, D., (2011). Stability Derivatives for a Delta-Wing X-31 Aircraft Validated using Wind Tunnel Test Data. Journal of Aerospace Engineering, 225(4), 403-416. [13] Williams, N. M., Wang, Z., Gursul, I. (2008). Active Flow Control on a Nonslender Delta Wing. Journal of Aircraft, 45 (6), 2100-2110. [14] Benkir, M., (1990). Persistance et Destruction des Structures Tourbillonnaires Concentrées en Particulier au Dessus d’Ailes Delta: Critères Angulaires de Stabilité aux Ecoulements, Ph.D. Dissertation, University of Valenciennes, France. [Persistence and Destruction of the Swirling Structures Concentrated in particular Upper Delta wings: Angular criteria of Stability to the Flows]. [15] Boumrar, I., (2012). Comportement des Ailes delta à Apex Privilégiés avec et sans Fuselage- Étude Expérimentale et Simulation Numérique, PhD. Dissertation, Department of Mechanical Engineering, Mouloud Mammeri University of TiziOuzou, Algeria. [Behavior of Delta wings with Privileged Apex with and without Fuselage- Experimental Study and Numerical Simulation].

ABOUT THE EDITOR Zied Driss, PhD Professor, Laboratory of Electromechanical Systems (LASEM), National School of Engineers of Sfax (ENIS), University of Sfax (US), Sfax, Tunisia

Prof. Zied Driss is Full Professor in the Department of Mechanical Engineering at National School of Engineers of Sfax (ENIS). He received his Engineering Diploma in 2001, his Master Degree in 2003, his PhD in 2008 and his HDR in 2013 in Mechanical Engineering from ENIS at University of Sfax, Tunisia. He is interested on the development of numerical and experimental techniques for solving problems in mechanical engineering and energy applications. Also, his research has been focused on the interaction between Computational Fluid Dynamics (CFD) and Computational Structure Dynamics (CSD) codes. As a result of his research, he is principal or co-principal investigator on more than 130 papers in peerreviewed journals, more than 300 communications to international conferences, 15 books and 50 books chapters. Also, he is the main inventors of 3 patents.

228

About the Editor

Currently, Prof. Driss is a Chief of Project in the Laboratory of Electromechanical Systems (LASEM), an Editorial Board Member and reviewer for different international journals, an Editor for different books, a General Chair of two bi-annual international conferences and an active member in different national and international associations.

INDEX A acceleration of the flow, 116, 152 acceleration zone, 55, 115 accurate description, 113 adequacy for aerodynamic analysis, 2, 39 adequate numerical model, 94, 104 adjustable blades, 95, 111 advancement, 157 aero-acoustic performance, 2, 22, 38 aerodynamic, vii, viii, ix, 1, 3, 18, 19, 21, 23, 34, 37, 38, 39, 48, 52, 54, 56, 88, 92, 93, 104, 105, 110, 113, 142, 166, 167, 169, 170, 172, 194, 197, 199, 202, 205, 206, 207, 214, 222 aerodynamic balance, 207 aerodynamic characteristics, vii, viii, 1, 3, 21, 23, 37, 39, 56, 166, 202, 214 aerodynamic coefficients, 205, 206, 222 aerodynamic of reduced aircraft models, ix, 199 aerodynamic optimization, 94 aerodynamic parameters, 223 aerodynamic passive optimization, 222

aerodynamic performance(s), 19, 34, 48, 93, 205, 206, 222 aerodynamic phenomena, 110 aerodynamic propertie(s), 93, 110 aerodynamic research, 38 aerodynamic results, 104 aerodynamic structure, ix, 52, 88, 92, 113, 169, 170, 172, 194, 197 aerodynamic studies, 207 aerodynamics, 2, 3, 19, 22, 23, 34, 38, 48, 89, 90, 105, 142, 143, 166, 206 aerodynamics experiments, 2, 22, 38 aerodynamics performance, 3, 23, 39 aeroelastic delta wing, 203 aerostatics measurements, 2, 22, 38 air blower, 3, 23, 39 air flow(s), 38, 95, 109, 148, 149 air velocity, 97, 170 aircraft, vii, 2, 205, 225 airflow, 110, 170, 195, 196 airflow patterns, 170, 195 airfoil, viii, 91, 92, 105, 107, 108, 111, 142, 143, 145, 146, 148, 150, 151, 152, 154, 155, 157, 159, 160, 162, 164, 165, 203 airfoil effect, 146 airfoil profile, 108

230

Index

airfoil shape, 94 airfoil surface, 92, 108, 148 airfoil type(s), viii, 145, 148, 151, 152, 154, 155, 157, 159, 160, 162, 164, 165 algorithm, 94 anemometer, 57, 58, 84, 95, 96, 97, 104, 146 anemometer emplacement, 96 angle of attack, 93, 105, 110, 200, 202, 214, 215, 216, 219, 220 angle of divergence, 25 angles of attack, 110, 201, 204, 214 anterior works, 99 apex, ix apex angles, 206, 222 atmospheric pressure, 4, 24, 40, 122 average velocity, 7, 102, 103, 113, 115, 117, 118, 119, 120, 141, 152, 154, 155, 166, 178, 179, 180

B basic mesh, 62, 100, 174 basic mesh sensitive, 100, 174 basic performance, 110, 142 behavior of flows, 38 beneficial effects of the privileged apex, 223 best agreement, 85, 88 better repartition of the complex swirling structures, 207 biogas, 108 biomass, 108 blade aerodynamic, 110 blade angle, 94 blade number, 93, 105 blade profiles, 54, 94 blade shape, 53 blade tip angles, 92, 109 blades number, 108 blades twist angle, 109

boundary conditions, 4, 24, 40, 61, 99, 112, 113, 119, 122, 152, 154, 174 boundary layer flows, 2, 38 bucket bucket angles, 54 bucket arc, 54 bucket design, 54, 90 bucket geometry, 56 buckets, 54, 70, 75 buckets overlap, 54 building configurations, 171 buildings, 170, 172, 195

C calculations, 171, 205 calibration, 58 calibration curve, 58 calibration curve, 59 cell size, 102, 104 cell(s) size, 101, 102, 104 cfd code, vii, viii, 2, 22, 38, 84 chord, 94, 111, 146, 200, 202, 205 circular Savonius wind rotor, 54 closed-circuit, 2, 22, 38 closed-circuit design, 2, 22, 38 coefficient, 52, 54, 88, 93, 200, 202, 205, 214 collector, vii, viii, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 24, 25, 31, 33, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 57, 64, 72, 79, 95, 113, 119, 121, 127, 134, 149, 152, 154, 156, 157, 162 collector geometry, vii, 1 collector inlet, viii, 33, 37, 46, 72, 113, 119, 121, 152, 154, 156 collector inlet radius, viii, 37 collector with inlet radius, 40, 41, 42, 43, 44, 45, 46, 47 collector without inlet radius, 40, 41, 42, 43, 44, 45, 46, 47

Index collectors, vii, viii, 1, 6, 10, 18, 37 color, iv complex building, 171 complex flow field, viii, 145 compounds, 95 compression, 13, 31, 70, 122, 127 compression XE "compression" zone, 13, 31, 70, 127 computational domain(s), 61, 62, 98, 99, 100, 173, 174, 175, 176 computational fluid dynamic, 3, 19, 23, 34, 39, 48, 89, 94, 141 computational fluid dynamic(s) (CFD), vii, viii, 2, 3, 19, 22, 23, 34, 38, 39, 48, 52, 84, 89, 92, 94, 108, 110, 141, 170, 195, 227 computational fluid dynamic(s) (CFD), 3, 19, 23, 34, 39, 48, 89, 94, 141 computational fluid dynamics, 19, 34, 48, 89, 94, 141 computational mesh, 100 computational methodology, 54 computations, 171 computer, 2, 22, 38, 94 computer program, 94 computer simulation, 169 computer aided flow simulation, 2, 22, 38 conference, 89 configuration, 3, 7, 18, 23, 29, 30, 33, 39, 42, 45, 47, 55, 56, 90 Congress, iv conservation, 60, 98 conservation laws, 98 conservation of the mass, 60 considered control volume, 3, 23, 39, 151 construction, 18, 19, 33, 47, 48 consumption, 92, 108 continuity equation, 60, 98 contraction, 3, 19, 23, 34, 39 contraction section, 3, 23, 39 control design techniques, 203

231

control volume, 4, 5, 24, 26, 33, 40, 41, 42, 46, 98, 127, 133, 141, 154, 156, 157, 159, 161, 166 controlled stream of air, vii, 2 convection coefficients, 109, 148 convex surfaces, 70 coriolis and centrifugal forces, 110 correlation, 109, 142, 148, 167 cost, 7, 19, 29, 48, 53, 94, 146 cost-effective, 53 counter rotating vortices, 201 criterion of privileged angles, 207 curved collector, 5, 6, 7, 10, 13, 15, 18 cylindrical buckets, 54

D Darrieus rotor, 53 dead zone, 27, 176, 178, 186, 189, 191 defect pressure, 200, 206, 210, 214, 215, 216, 217, 223 defect pressure coefficient, 200, 206, 210, 214, 215, 217, 223 deficiency in energy recovery, 92, 108 delivered power, 166 delta wing(s), ix, 199, 200, 201, 204, 205, 206, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 222, 225 delta wing-fuselage, 200, 214, 218, 219, 223 delta wing-fuselage interaction, 200 depletion of nonrenewable resources, 108 depression, 54, 70, 72, 121, 122, 127, 156 depression zone, 54, 70, 72, 121, 122, 127, 156 design, vii, 2, 3, 18, 19, 20, 22, 23, 33, 34, 35, 38, 47, 48, 49, 53, 57, 88, 89, 90, 92, 105, 106, 109, 142, 148, 149, 166, 167, 197, 203 design of airfoils, 92, 105, 109, 142, 148, 167 design of wind tunnels, 2, 22, 38

232

Index

design process, 109, 148 designed tunnel, 3, 39 designing of blades, 53 different heights, ix, 169, 172, 173, 194 different shape ratios, 170 diffuser, vii, 4, 7, 20, 21, 22, 23, 24, 25, 27, 28, 33, 35, 39, 49, 57, 61, 77, 80, 95, 99, 106, 115, 120, 122, 127, 133, 135, 149, 159, 161, 162 diffuser geometry, vii, 21 diffuser outlet, 28, 33, 127, 133, 135, 159, 161, 162 digital tachometer, 57 discretization, vii, ix, 2, 4, 22, 23, 37, 39, 52, 98 discretization of the angles, 205 dissipation rat of the turbulent kinetic energy, 195 distribution, 7, 10, 13, 15, 27, 29, 31, 42, 43, 44, 46, 64, 67, 70, 72, 75, 77, 79, 82, 88, 94, 108, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 141, 148, 152, 154, 155, 156, 157, 158, 159, 160, 162, 163, 164, 165, 166 disturbances of the air flow, 211, 213 divergence, 4, 25, 27 divergence angle, 4, 25, 27 divergence angle of the diffuser, 4, 25 downstream vacuum, 95 drag, ix, 53, 93, 109, 148, 200, 206, 207, 209, 211, 214, 220 drag force, 53 drawing design, 209 drive section, 99 dual vortex structure, 202 dynamic mesh technique, 93, 111 dynamic pressure, viii, 6, 13, 14, 15, 18, 26, 30, 31, 33, 41, 44, 45, 47, 51, 63, 72, 74, 124, 125, 126, 127, 141, 157, 158, 159, 166, 175, 183, 184, 185, 186, 194

dynamic torque, viii, 52, 57, 87 dynamic torque coefficient, viii, 52, 87 dynamic viscosity, 53 dynamometer, 58, 59

E economic problem, 108 economic problems, 108 effectiveness of the control technique, 203 efficiency, 2, 22, 38, 53, 89, 147 elastic materials, 202 electric current, 58 electricity, 53, 92, 108 electricity generation, 108 energies, 92, 105, 108, 142, 147 energy, viii, 2, 6, 15, 16, 17, 18, 26, 31, 32, 33, 38, 41, 46, 47, 51, 52, 53, 60, 63, 75, 76, 77, 78, 79, 89, 92, 98, 108, 127, 128, 129, 130, 131, 132, 133, 134, 146, 159, 160, 161, 162, 166 energy captured, 166 energy losses, 2, 38 energy recovery, 92, 108 engineering, 3, 23, 34, 39, 48, 105 environment, 2, 19, 22, 34, 38, 48, 92, 109, 148 environmental degradation, 108 environmental friendly sources, 92 evolution, 2, 22, 38, 88 excessive splitting, 100, 174 excessive turbulence, 3, 39 experiment results, viii, 52 experiment(s), viii, 52, 170, 196 experimental and computational analysis, 204 experimental and numerical flow, 201 experimental and numerical works, 202 experimental data, 109, 148, 171 experimental device, 207 experimental errors, 221

Index experimental investigation, 89, 109, 146 experimental results, ix, 54, 84, 85, 88, 94, 104, 170, 195, 200, 202, 206, 211 experimental studies, ix, 54, 199 experimental techniques, 203, 227 experimental validation, viii, 51, 90, 91, 197 experimental work, 92, 109 exploitation, 92, 108 external aerodynamic, 200

F fan, 2, 4, 22, 24, 27, 38, 39 fidelity, 108, 142, 147, 166 finite element method, 92, 109, 148 finite volume, vii, viii, ix, 2, 4, 22, 23, 37, 39, 52, 98, 107, 146, 169, 175 finite volume discretization, vii, ix, 2, 4, 22, 23, 37, 39, 52, 98, 169, 175 finite volume discretization method, vii, 2, 4, 22, 23, 37, 39, 52, 98 finite volume scheme, viii, 107, 146 flow, vii, viii, ix, 1, 3, 21, 22, 37, 38, 51, 54, 56, 60, 62, 64, 89, 91, 92, 94, 97, 98, 100, 104, 105, 106, 107, 109, 113, 115, 119, 127, 141, 142, 143, 145, 148, 149, 151, 152, 154, 165, 169, 170, 175, 196, 197, 200, 201, 204, 205, 207, 214, 215, 218, 221,223, 224, 225 flow circulation, 54 flow deflection, 64, 114, 152 flow field, viii, 89, 110, 142, 145, 171, 202, 205, 214 flow field structure, 110 flow particuliarities, 100 flow patterns, 170 flow separation, 93, 105, 110, 203 flow simulation, 100, 104, 106, 151, 165 flow structure, 201, 203, 204 flow visualization, 203 fluctuating velocity components, 52

233

fluid, vii, viii, 2, 3, 18, 19, 22, 23, 33, 34, 38, 39, 47, 48, 52, 84, 89, 92, 94, 100, 108, 110, 141, 170, 195, 207, 227 fluid flow, 18, 33, 47, 205, 207 fluid mechanics, 206 force, 53, 56, 147 formation, 146 fuel prices, 108 fuselage, 200, 209, 211, 213, 215, 216, 217, 218, 220, 225 future generations, 108

G gap between numerical and experimental results, 85, 104 gap ratio, 54 generator, 57, 147 geometric configurations, 113, 119, 120, 125, 127, 133, 134, 141 geometric parameters, 5, 6, 24, 25, 96, 111 geometrical arrangments, 173 geometrical characteristics, 209, 223 geometrical parameters, 54, 94 geometry, vii, 1, 3, 7, 10, 13, 18, 21, 23, 27, 29, 33, 39, 47, 54, 56, 62, 100 global characteristics, 56, 87 global mean-flow, 172 good agreement(s), viii, ix, 52, 56, 88, 104, 147, 170, 171, 194 governing equations, ix, 169, 175 growth, 3, 23, 39

H heat transfer, 109, 142, 148, 167 heat transfer coefficients, 109, 148 height, 52, 56, 57 heights, 195, 207, 208, 221 high consumption of energy, 92, 108 high effect, 170

234

Index

higher deflection, 203 higher maximum lift coefficient, 202 highest efficiency, 54 homogeneous fluids, 98 honeycomb, 22, 34, 38, 48 honeycomb-screen, 22, 38 horizontal axis, viii, 92, 94, 104, 105, 108, 142, 143, 145, 151, 166 horizontal axis wind turbine, viii, 92, 104, 108, 142, 143, 145, 151 horizontal axis wind turbine(s), viii, 92, 104, 105, 108, 142, 143, 145, 146, 151, 166 hot-wire anemometry, 110 human, 92, 108 hysteresis, 147

I image, 104, 110, 141, 170 implicit formulation, 98 improvements, 53 incidence, 147 incidence angles, 171 incident flow, 170 inclined roof obstacles, ix, 169, 170, 172, 173, 194 India, 89 injury, iv inlet radius, 42, 43, 46 inlet velocity, 4, 24, 40, 61, 64, 174, 176, 178 interaction delta wing-fuselage, 223 interface, 100 interior volume, 61, 99, 173 iteration, 109, 148

J JCC, 167 jet flows, 172

K kinetic energy, viii, 15, 18, 33, 46, 47, 51, 60, 63, 75, 77, 92, 98, 127, 133, 159, 161, 175, 186, 189

L laboratory scale, 55 laminar, 98 large angle of the diffuser, 25, 27, 29, 31, 33 large opening, 5, 6, 7, 18 laws, 98 leading edge control, 203 leading edge shape, 202 leading edge vortices, 202, 205 length, 2, 3, 4, 6, 23, 25, 38, 57, 95, 111, 207, 211, 212 less noise, 2, 22, 38 less turbulence, 3, 23, 39, 47 lift, ix, 53, 109, 147, 200, 202, 205, 206, 207, 209, 211, 213, 214, 220, 221, 223 lift and drag, 206, 207, 220, 223 lift or pressure coefficients, 221 local characteristics, viii, 52, 88, 91, 104, 107, 141, 145, 195 local initial mesh, 62, 100, 174 local initial mesh option, 62, 100 local mesh settings, 100, 174 local region, 62, 100 local results, 194 long collector, 5, 6, 18 long diffuser, 25, 31, 33 longitudinal plane(s), vii, viii, 2, 3, 8, 11, 13, 16, 22, 23, 27, 28, 29, 30, 32, 38, 39, 42, 44, 45, 46, 52, 63, 64, 66, 67, 70, 71, 72, 74, 75, 77, 78, 79, 80, 81, 82, 83, 91, 102, 113, 114, 115, 117, 118, 121, 122, 124, 125, 128, 129, 131, 132, 135, 136, 138, 139, 151, 152, 153, 154, 155, 156,

Index 158, 159, 160, 161, 163, 164, 165, 176, 178, 180, 183, 186, 189, 191

M management, 34, 48 mass, ix, 60, 169, 172, 174, 175, 196, 203 mass flow, 174 mathematical formulation, 60 matter, iv mean velocity, 8, 9, 10, 27, 28, 42, 43, 67, 69, 88, 172 measured data, 109, 148, 194 measurement, 2, 22, 38, 109, 148 measurement techniques, 2, 22, 38 measurements, ix, 2, 22, 33, 38, 93, 109, 146, 171, 196, 200, 202, 205, 206, 207, 208, 211, 212, 221 measurements of aerodynamic coefficients of pressure, ix, 200 mechanisms of interactions, 200 mesh, 62, 92, 94, 100, 102, 174 mesh refinement, 100 meshing choice, 91 meshing effect, viii, 91, 104 methodology, 54, 93, 109, 148 micro air vehicles, 201 microscopic scale, 207 military aircrafts, 223 modeling techniques, 170, 195 models, vii, ix, 2, 19, 34, 48, 106, 146 modifications, 109, 148 modified Savonius wind rotor, 54 momentum, ix, 60, 93, 98, 169, 175 momentum equation, 60, 98 momentum equation, 60 multi-manometer, 201, 207, 208, 213, 215, 221 multi-reference frame, 61 multi-stage, 19, 35, 49, 55, 90, 106

235 N

NACA airfoil, viii, 109, 142, 145, 148, 151, 167 NACA Airfoil Effect, 145 NACA airfoils wind turbine, 148 NACA profiles, 94, 106 naca2415 airfoil type, viii, 91, 94, 104 narrow channels, 100 natural light, 170 navier-stokes equations, vii, viii, 1, 3, 21, 23, 37, 39, 52, 60, 91, 98, 107, 145 Navier-Stokes equations, vii, viii, 1, 3, 21, 23, 37, 39, 52, 60, 91, 98, 107, 145 new and renewable, 92, 108 nodes, 6, 26, 41, 98 non-slender delta wing, 202, 204 number of blades, 92, 109 number of cells, 63, 100, 101, 102 number of stages, 54 numbers, 55, 102, 103, 109, 147, 202 numerical, vii, viii, ix, 1, 3, 6, 18, 19, 21, 23, 26, 33, 35, 37, 39, 41, 47, 49, 51, 54, 56, 60, 84, 88, 89, 90, 91, 93, 94, 98, 102, 104, 105, 106, 107, 111, 113, 141, 142, 143, 145, 148, 151, 165, 166, 169, 171, 174, 175, 194, 195, 197, 202, 223, 225, 227 numerical analysis, 60 numerical investigation, 90, 197, 202 numerical method, ix, 170 numerical model, vii, 1, 3, 21, 23, 37, 39, 52, 91, 104 numerical parameters, 56 numerical results, vii, viii, ix, 2, 3, 18, 22, 23, 33, 37, 39, 47, 52, 84, 88, 92, 94, 104, 111, 141, 148, 151, 165, 170, 171, 194 numerical simulation(s), vii, viii, 1, 18, 21, 33, 37, 47, 51, 54, 56, 90, 91, 107, 145, 171, 194, 195, 197

236

Index

numerical study, 3, 23, 39, 89, 93, 105, 166 Nusselt number, 109, 148

O obstacles, ix, 170, 173, 194, 195, 196 oil, 20, 35, 49, 106 open circuit subsonic wind tunnel, 2, 22, 38 open circuit type wind, 2, 22, 38 open circuit type wind tunnel, 2, 22, 38 open circuit wind tunnel, 57 open wind tunnel, vii, viii, 1, 21, 37, 54, 88, 91, 94, 104 open-circuit, 2, 22, 38 open-circuit wind tunnel, 22, 38 opening of the collector, 4 operating wind speed, 93 optical sensor, 58, 96, 98 optimization, 94, 108, 142, 147, 166 optimization method, 108, 147 optimization of aerodynamic, 200 optimized wind rotor configurations, 94 outlet of the diffuser, 27, 28, 30, 32, 43 outlet pressure, 4, 24, 40, 61, 174 overlap, 54, 56, 89 overlap ratio, 54, 56, 89

P parallel, 2, 22, 38, 63, 149 parameter design, 108 parametric study, 202 particle image velocimetry, 104, 110, 141, 170 passive and active control techniques, 201 passive apex flap, 202 passive control, 202, 204 passive control strategies, 202 performance, viii, 3, 19, 34, 39, 48, 53, 89, 90, 107, 166, 172, 223

performance of wind energy XE "energy" systems, 166 performed aerodynamics, 2, 22, 38 permission, iv phase averaged measurements, 205 phenomenological analyses, 205 phenomenological aspects, ix, 200 phenomenological considerations, 222 phenomenological studies, 223 physics, 108, 142, 147, 166 pitch, 93, 147 pitched roof geometry, 170 pitched type obstacle, 173 pitched-type roof, 170 playing, 108 plenum, 57, 95, 149 plexiglass flat plate, 209 power, viii, 52, 53, 87, 88, 89, 93, 105, 108, 142, 147 power coefficient, viii, 52, 53, 87, 93, 105, 109, 147 power coefficient of the rotor, 93, 109 power coefficients, 54, 93 power generation, 108 practical methodology, 94 precision, 58, 59, 97, 98, 104, 113, 210 predicted airflow patterns, 171 predicted averaged velocity results, 194 predominantly nonlinear phenomenon, 203 preparation, iv presentation planes, 175 pressure, 4, 10, 13, 15, 22, 24, 29, 31, 40, 43, 44, 45, 52, 70, 72, 88, 92, 99, 105, 108, 113, 120, 121, 122, 124, 127, 142, 146, 149, 155, 156, 157, 167, 174, 180, 181, 183, 186, 200, 202, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 221, 223 pressure coefficient, 200, 208, 209, 217, 221, 223 pressure measurements, 93, 110, 203, 205 pressure uniformity, 10, 29

Index principal apex vortex, 206, 210, 223 privileged angles, ix, 199, 205, 207, 222 privileged apex, 199, 200, 206, 215, 216, 218, 219, 220, 223, 225 privileged apex angle, 200, 206, 215, 216, 218, 219, 220, 223 production of electricity, 108 prototype, 149

Q quantified angles, ix, 199

R radius, viii, 37, 40, 41, 42, 43, 44, 45, 46, 47, 95 ratio(s), 3, 23, 54, 88, 94, 109, 147, 170, 172 reading, 58, 98 real application, 200 recirculation zone, 115, 152 recommendations, iv recovery, 20, 35, 49, 106 rectilinear collector, 5, 6, 7, 10, 15, 18 refinement levels, 100, 174 reliability, 53, 170 reliability of the model, 170 reliable wind energy conversion systems, 53 renewable resources, 108 repercussions on the performances of the aircraft, ix, 199 requiring energy input, 202 researchers, 53 resistance, vii, 2, 110 resolution, vii, 1, 3, 21, 23, 37, 39, 52, 58, 59, 91, 95, 97, 98, 100, 101, 102 resources, 108 response, 109, 142, 148, 166 results, ix, 6, 7, 10, 13, 15, 18, 26, 27, 29, 31, 32, 33, 41, 42, 43, 44, 46, 47, 54, 63,

237

64, 67, 70, 72, 75, 77, 79, 82, 84, 88, 93, 94, 96, 102, 104, 109, 113, 121, 127, 133, 134, 141, 146, 151, 152, 154, 155, 157, 159, 160, 162, 164, 170, 171, 175, 176, 178, 181, 183, 186, 189, 191, 194, 195, 196, 203, 205, 206, 213, 214, 215, 218, 220, 223 Reynolds number, 52, 54, 109, 147, 172, 202, 214, 217, 218 rights, iv rigid attachment, 212 root, 110 rotating, viii, 51, 52, 53, 56, 63, 67, 77, 80, 82, 85, 87, 88, 202 rotating area, viii, 51, 52, 56, 63, 67, 77, 80, 82, 85, 88 rotating speed, 87 rotation speed, 88, 96 rotor blades, 94 rotor diameters, 88 rotor performance, 56, 93, 105 rotor shaft, 57 rotor solidity, 93

S satisfactory agreement, 195, 202 satisfactory results, 99, 113 Savonius rotor(s), 19, 35, 49, 53, 56, 58, 59, 89, 90, 106 Savonius Wind Rotor, 51, 56 Savonius wind rotor design, 56 science, 105 semi-circular blades, 53 sensor, 58, 96, 98 separated flows, 201 separation point, 93, 110, 202 services, iv shaft, 54, 56, 57 shape, 3, 23, 53, 94, 109, 142, 148, 152, 166 shed, 201

238

Index

short diffuser, 25, 28, 30 shorter spanwise, 202 simplicity, 53 simulation, viii, ix, 2, 18, 19, 22, 33, 34, 38, 47, 48, 51, 53, 60, 89, 90, 91, 94, 98, 100, 104, 106, 107, 113, 141, 146, 151, 165, 169, 170, 172, 175, 195, 196, 225 simulations, vii, viii, 1, 18, 21, 33, 37, 47, 56, 63, 91, 107, 145 small aspect, 109 small horizontal-axis wind turbines, 147, 166 small incurved Savonius wind rotor, 54, 90, 197 small NACA2415 airfoil type wind turbine, viii, 92 small wind turbine(s), 92, 109, 142, 148 small-scale obstacles, 170 software, viii, ix, 51, 60, 91, 98, 104, 113, 146, 151, 165 solid surfaces, 38 solid/fluid interface, 100 solution, 18, 29, 30, 31, 33, 47 span delta wing wind tunnel model, 205 spatial discretization, 98 spatial optimization, 203 S-section Savonius rotor, 54 stability, 149 stability of the aircraft, 206 stability of the flow, 207, 223 stabilized finite element method, 92, 109, 148 stall mechanisms, 93, 105, 110, 143 standard k-ε turbulence model, vii, viii, ix, 2, 3, 22, 23, 37, 39, 52, 107, 145, 169, 175 state, 110, 141 static, viii, 6, 10, 11, 12, 18, 26, 29, 30, 33, 41, 43, 44, 47, 51, 57, 59, 63, 70, 71, 99, 120, 121, 122, 123, 141, 147, 155, 156, 157, 166, 174

static pressure, viii, 6, 10, 11, 12, 18, 26, 29, 30, 33, 41, 43, 44, 47, 51, 63, 70, 71, 99, 120, 121, 122, 123, 155, 156, 157 static state, 141 static torque, 57, 59 structure, ix, 13, 52, 88, 92, 94, 110, 113 subsonic wind tunnel, 2, 19, 34, 38, 48, 55, 207 suitable geometry, 13, 18, 33, 47 support, 57, 95, 149, 211, 212, 213 sustainable development, 108

T tachometer, 58, 96, 97, 98 techniques, 2, 22, 38, 146 technology, 105, 146 temperature, 97 temporal discretization, 98 test section, 3, 4, 22, 23, 24, 29, 33, 38, 39, 42, 45, 57, 64, 94, 95, 102, 149, 178, 181, 183, 186, 189, 191, 207, 208, 213 test vein, 7, 10, 12, 13, 15, 17, 31, 43, 44, 45, 47, 57, 67, 72, 77, 79, 82, 113, 115, 119, 121, 127, 133, 134, 141, 152, 154, 156, 159, 161, 162, 164 tested models, 146 testing, 3, 39, 88 tetrahedral interpolation, 98 the air flow, 22, 99, 149, 157, 207, 215 three blades, 53, 111, 151 time resolution, 101, 102 tip speed ratio, 55, 87, 93, 146 total pressure, 175, 180, 181, 182, 183, 186, 194 trailing edge, 202, 223 tranquilization chamber, 4, 24, 39, 61, 99 translation, 93, 110 transonic airfoil design, 108, 147 transport, 60, 98 transport equation, 60, 98

Index transverse plane(s), 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 27, 28, 29, 30, 31, 32, 33, 41, 42, 43, 44, 45, 46, 47, 63, 64, 66, 67, 69, 70, 72, 74, 75, 76, 77, 79, 81, 82, 84, 88, 103, 113, 116, 119, 120, 123, 124, 126, 127, 130, 132, 133, 134, 137, 140, 141, 152, 153,154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 175, 176, 178, 181, 183, 186, 189, 191 turbine, 53, 89, 90, 92, 95, 104, 109, 111, 113, 115, 119, 121, 122, 127, 133, 134, 141, 146, 152, 157, 159, 161, 164 turbine power coefficient, 147 turbulence, vii, viii, ix, 2, 3, 18, 19, 22, 23, 33, 34, 37, 38, 39, 47, 48, 52, 53, 60, 79, 91, 93, 98, 105, 106, 107, 110, 141, 143, 145, 149, 166, 169, 172, 175, 196 turbulence characteristics, 141, 166 turbulence model, 52, 53, 60, 91, 98, 106, 172, 196 turbulence of bluff bodies, 3, 23, 39 turbulent, viii, 2, 6, 15, 16, 17, 18, 22, 26, 31, 32, 33, 37, 38, 41, 46, 47, 51, 52, 53, 54, 60, 61, 63, 75, 76, 77, 78, 79, 80, 81, 88, 90, 92, 98, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 146, 159, 160, 161, 162, 163, 164, 170, 172, 175, 186, 187,188, 189, 190, 191, 194, 196, 197 turbulent flow, viii, 2, 18, 22, 33, 37, 38, 47, 51, 52, 54, 88, 90, 92, 146, 197 turbulent kinetic energy, viii, 6, 15, 16, 17, 18, 26, 31, 32, 33, 41, 46, 47, 51, 52, 55, 60, 63, 75, 76, 77, 78, 79, 98, 127, 131, 132, 133, 134, 159, 160, 161, 162, 170, 175, 186, 187, 188, 194 turbulent viscosity, viii, 51, 53, 61, 63, 79, 80, 81, 134, 135, 136, 137, 162, 163, 164 twist, 53, 92, 109 twist angle, 92, 109 twist bladed, 53 two-bucket rotor, 54

239

two-stage two-bladed, 55

U uniform, 3, 10, 23, 29, 39, 43, 45, 47, 64, 95, 114, 152, 154, 156, 157, 176, 178, 181, 183, 186, 189, 191 uniform flow, 3, 23, 39 unmanned air vehicles, 201 unmanned combat air vehicles, 201 unsteady viscous flows, 92, 105, 109, 142, 148, 167 urban, 92, 105, 109, 142, 148, 167, 170, 195 urban environment(s), 92, 109, 148, 170, 195 USA, 106

V vacuum, 2, 38, 95 validation, viii, 19, 34, 48, 51, 90, 91 validity, viii, 52, 194 validity of the numerical method, viii, 52, 194 values of the apex angle, 200 variables, 23 variations, 109, 148 various wings, 209, 212, 220, 223 vein, 7, 10, 12, 13, 15, 17, 31, 43, 44, 45, 47, 57, 67, 72, 77, 79, 82, 113, 115, 119, 121, 127, 133, 134, 141, 152, 154, 156, 159, 161, 162, 164 velocities, 3, 19, 23, 34, 39, 48, 55, 147, 171, 214, 215, 218 velocity, viii, 2, 4, 6, 7, 8, 9, 10, 18, 24, 26, 27, 28, 33, 39, 40, 41, 42, 43, 47, 51, 52, 53, 55, 58, 61, 63, 64, 66, 67, 69, 84, 85, 86, 88, 93, 95, 97, 99, 102, 103, 104, 113, 114, 115, 116, 117, 118, 119, 120, 141, 146, 149, 152, 153, 154, 155, 166,

240

Index

171, 172, 174, 175, 176, 177, 178, 194, 196, 201, 202, 207, 211, 215, 220 velocity components, 52 velocity XE "velocity" field(s), viii, 6, 7, 8, 10, 26, 27, 28, 41, 42, 51, 63, 64, 66, 67, 88, 114, 115, 116, 141, 152, 153, 166, 175, 176, 177, 178, 194 velocity measurements, 146 velocity profile, viii, 3, 39, 42, 52, 84, 85, 86, 95, 104, 194 velocity vectors, 113, 116, 152, 154 ventilation, 57 ventilation chamber, 57 ventilation chamber, 95, 149 vertical axis wind turbines, 92 vertical wind turbines, 53 vibration, 94, 149 viscosity, viii, 51, 53, 61, 63, 79, 80, 81, 82, 134, 135, 136, 137, 162, 163, 164 visualization, ix, 149 visualizations, ix, 200, 206, 207, 210 volume flow, 174 vortex core, 201, 205 vortex structure(s), 202 vortical structures, 201 vorticity, viii, 51, 63, 82, 83, 84, 138, 139, 140, 141, 146, 164, 165, 175, 191, 192, 193, 195, 202 vorticity trailing, 146

W wake zone, 15, 32, 44, 46, 127, 133, 157, 159, 161 waste, 20, 35, 49, 106 waste heat, 20, 35, 49, 106 wedging angle, viii, 107, 108, 111, 112, 113, 115, 119, 120, 122, 125, 127, 133, 134, 141, 151 wind, viii, ix, 1, 2, 3, 4, 5, 6, 13, 18, 19, 21, 22, 23, 24, 25, 29, 33, 34, 37, 38, 39, 40,

43, 46, 47, 48, 51, 52, 53, 56, 57, 61, 64, 77, 88, 89, 90, 91, 92, 94, 95, 96, 99, 105, 106, 107, 108, 111, 113, 115, 119, 120, 121, 125, 127, 133, 134,141, 142, 143, 145, 146, 149, 151, 152, 154, 156, 157, 159, 161, 162, 164, 166, 167, 169, 170, 172, 173, 194, 195, 196, 199, 200, 201, 206, 208, 209, 211, 212, 213, 215, 225 wind energy, 53, 89, 92, 108, 146 wind engineering, 3, 23, 34, 39, 48 wind speed, 57, 93, 94, 95, 110, 142, 147 wind tunnel control volume, 4, 24, 40 wind tunnel experiments, 56, 90, 172, 196 wind tunnel measurements, 109, 148, 195 wind tunnel simulation, 171, 195 wind tunnel test section, 209, 211, 212, 215 wind tunnel tests, 147, 166, 195, 199, 212 wind tunnel(s), viii, ix, 1, 2, 3, 4, 5, 6, 13, 18, 19, 21, 22, 23, 24, 25, 29, 33, 34, 37, 38, 39, 40, 43, 46, 47, 48, 52, 55, 56, 57, 61, 88, 90, 92, 94, 95, 99, 107, 108, 109, 113, 121, 145, 146, 147, 149, 152, 156, 166, 169, 170, 172, 173, 194, 195, 196, 199, 200, 201, 206, 208, 209, 211, 212, 213, 215, 225 wind turbine, vii, viii, 53, 56, 57, 64, 77, 88, 89, 90, 91, 92, 94, 95, 96, 105, 106, 107, 108, 111, 113, 115, 119, 120, 121, 125, 127, 133, 134, 141, 142, 143, 145, 146, 149, 151, 152, 154, 156, 157, 159, 161, 162, 164, 166, 167 wind turbine airfoil, 93, 105, 110, 142, 167 wind turbines, vii, 53, 89, 92, 105, 108, 147, 166 wind turbines parameters design, 92 wind-tunnel measurements, 172 wing aerodynamic characteristics, ix, 199 wing model(s), 211, 212 wing surface, 200, 201 wings with privileged apex, 206, 223