Rotodynamic Pumps [2 ed.] 1781830177, 9781781830178

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Citation preview

ROTODYNAMIC

PUMPS

[Centrifugal and Axial)

(SECOND EDITION)

K M SRINIVASAN Ex-Professor, Mechanical Engineering PSG College of Technology, Coimbatore, INDIA and Basrah University, IRAQ

New Academic Science New Age International (UK) Ltd. 27 Old Gloucester Street, London, WC1 N 3AX, UK www.newacademicscience.co.uk e-mail: [email protected]

Copyright © 2017 by New Academic Science Limited 27 Old Gloucester Street, London, WCIN 3AX, UK www.newacademicscience.co.uk • e-mail: [email protected] ISBN: 978 1 78183 172 4 All rights reserved. No part of this book may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the copyright owner. British Library Cataloguing in Publication Data A Catalogue record for this book is available from the British Library Every effort has been made to make the book error free. However, the author and publisher have no warranty of any kind, expressed or implied, with regard to the documentation contained in this book.

WIS 'BOO,!( is aeaicatea to

My Parents Sri. lJG :M'llwruJ2l!Mty P ILL!ilI

!4na Smt. lJGq: SJ2I!M'BOOI}{9t[J2I!M 5'ls We(( as

ero my Professor f})r. !il.!il. LO:M!il'l(I9t[

JInaguiae f})r. !il.9t£ PMII}{ Leningraa Pofyteclinu, Leningraa, lJ(;21, ruSI}{ (at present ca((ea as St. PetersbU1lJ Pofytecfmic, St. PetersbU1lJ, !R...,ussia)

Who brought me to this (eve(

PREFACE TO THE SECOND EDITION I am very much thankful and grateful, for the valuable suggestions given by the readers about my book on ROTODYNAMIC PUMPS, 1st edition. This book is mostly design and regulation oriented. In the lInd edition, I have included, further developments in these areas, (1) modified version of impeller design procedure, (2) modified version of double curvature design procedure, (3) the design procedure for vane diffuser, (4) the design procedure for the vane less diffuser, (5) the design procedure for the suction volute, (6) Computer programme for the new version of impeller and examples for the same, (7) Computer programme for the vane diffuser with return guide vanes and example for the same, (8) Computer programme for the circular x- section, constant velocity volute design and example for the same, (9) the calculation from the model to the proto type using model analysis, i.e., using non dimensional analyses, (10) Computer programme for the Axial Flow Pump Design, (11) Modified design of Domestic centripetal pump, and (12) a new method for balancing axial thrust in submersible pumps. I do hope that the included material will enable the readers to understand the basics and design the pump more precisely. I, once again request all the readers to read and send their suggestions to me. I am grateful to my wife Smt. S.Nalini, and for my two sons S. Jagan Mohan and S. Muthuraman for their help given to me in preparing the computerized version of the newly prepared material. I am grateful to Mis New Age International (P) Ltd., Publishers, New Delhi for publishing my book. Indeed my book has come out wonderfully well.

DR. K.M. SRINIVASAN

PREFACE TO THE FIRST EDITION It was my very long felt ambition to provide a detailed and full information about the theory, design,

testing, analysis and operation of different types of rotodynamic pumps namely Centrifugal, Radial, Diagonal and Axial flow types. I have learned a lot during the period 1959-62 about pumps at PSG College of Technology, Coimbatore, while working as Senior Research Assistant for CSIR Scheme on Pumps, Turbo Chargers and Flow Meters. At the same time, I was undergoing training in foundry, pattern making, moulding, production, testing and design for different pumps at PSG Industrial Institute, Coimbatore, and also during the period 1967 and 1975. I cannot forget my study at Leningrad Polytechnic, Leningrad K-21, USSR (now st. Petersburg Polytechnic, st. Petersburg, Russia), for my doctorate degree in pumps. Dr. A.A Lomakin, Dr. A.N. Papir, Dr. Gurioff, Dr. N.N. Kovaloff, Dr. A.N. Smirnoff, Dr. Staritski, Dr. Gorgidjanyan, and Dr. Gutovski are the key professors who made me to know more about pumps from fundamentals to updated technology. I am very much grateful to Dr. A.A. Lomakin and Dr. A.N. Papir, who were my professors and guides for my doctorate degree in pumps. As a consultant, for different pump industries in India and abroad, I could understand the field problems. My experience, since 1959 till date, has been put up in this book to enable the readers in industries, and in academic area, to design, to analyse and to regulate the pumps. Complete design process for pumps, losses and efficiency calculation, based on boundary layer theory for axial flow pumps are also given. Computer programmes for the design of pump and for profile loss estimation for axial flow pumps are also given. All the design examples in the last chapter are real working models. The results are also given with pump drawings. I do hope that the reader will be in a position to understand, design, test and analyse pumps, after going through this book. I shall be very much honoured if my book is useful in attaining this. I am grateful to my wife Smt. S. Nalini, my sons Sri S. Muthuraman and Sri S. Jaganmohan and my daughter Smt. S. Nithyakala, who were very helpful in preparing the manuscript and drawings. Last but not the least I am grateful to the editorial department of Mis New Age International (P) Ltd., Publishers, New Delhi for their untiring effort to publish the book in a neat and elegant form, in spite of so many problems they come across while formulating this book from the manuscript level to this level. Constructive criticisms and suggestions are highly appreciated for further improvement of the book.

DR. K.M. SRINIVASAN

CONTENTS PREFACE TO THE SECOND EDITION

(vii)

PREFACE TO THE FIRST EDITION

(ix)

1.

1-5

INTRODUCTION 1.1

2.

6-42

PUMP PARAMETERS 2.1

2.2 2.3 2.4 2.5

2.6 2.7

3.

Principle and Classification of Pumps 1

Basic Parameters of Pump 6 Pump Construction 15 Losses in Pumps and Efficiency 18 Suction Conditions 20 Similarity Laws in Pumps 22 Classification ofImpeller Types According to Specific Speed (n) 28 Pumping Liquids other than Water 30

THEORY OF ROTODYNAMIC PUMPS

3.2

Energy Equation using Moment of Momentum Equation for Fluid Flow through Impeller 43 Bernoulli's Equation for the Flow through Impeller 44

3.3

Absolute Flow ofIdeal Fluid Past the Flow Passages of Pump 47

3.4

Relative Flow ofIdeal Fluid Past Impeller Blades 49

3.5

Flow Over an Airfoil 52

3.6

Two Dimensional Ideal Flow 54

3.7 3.8

Axisymmetric Flow and Circulation in Impeller 57 Real Fluid Flow after Impeller Blade Outlet Edge 59

3.1

3.9 Secondary Flow between Blades 60 3.10 Flow of a Profile in a Cascade System-Theoretical Flow 61 3.11

Fundamental Theory of Flow Over Isolated Profile 62

3.12 Profile Construction as per N.E. Jowkovski and S.A. Chapligin 64 3.13 Development of Thin Plate by Conformal Transformation 67 3.14 Development of Profile with Thickness by Conformal Transformation 67

(xi)

43-73

(xii)

CONTENTS

3.15 Chapligin's Profile of Finite Thickness at Outlet Edge of the Profile 68 3.16 Velocity Distribution in Space between Volute Casing and Impeller Shroud 70 3.17 Pressure Distribution in the Space between Stationary Casing and Moving Impeller Shroud of Fluid Machine 72

4.

THEORY AND CALCULATION OF BLADE SYSTEMS IN CENTRIFUGAL PUMP 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

74-141

Introduction 74 One Dimensional Theory 74 Velocity Triangles 75 Impeller Eye and Blade Inlet Edge Conditions 78 Outlet Velocity Triangle: Effect due to Blade Thickness 82 Slip Factor as per Stodola and Meizelll 091 84 Coefficient of Reaction (p) 90 Selection of Outlet Blade Angle (~2) and its Effect 92 Effect of Number of Vanes 95

4.10 Selection of Eye Diameter (Do)' Eye Velocity (Co), Inlet Diameter of Impeller (D 1) and Inlet Meridional Velocity (Cm ) 98 1 4.11 Selection of Outlet Diameter of Impeller (D 2 ) 101 4.12 Effect of Blade Breadth (B 2 ) 101 4.13 Impeller Design 112 4.14 Determination of Shaft and Hub Diameters 115 4.15 Determination ofInlet Dimensions for Impeller 116 4.16 Determination of Outlet Dimensions of Impeller 117 4.17 Development of Flow Passage in Meridional Plane 119 4.18 Development of Single Curvature Blade-Radial Blades 121 4.19 Development of Double Curvature Blade System 124

5.

SPIRAL CASINGS (VOLUTE CASINGS) 5.1 5.2 5.3 5.4 5.5

142-179

5.6

Importance of Spiral Casings 142 Volute Casing at the Outlet of the Impeller 143 Method of Calculation for Spiral Casing 144 Design of Spiral Casing with Cur = Constant and Trapezoidal Cross-section 146 Calculation of Trapezoidal Volute Cross-section under Constant Velocity of Flow C v = Constant (Constant Velocity Design) 147 Calculation of Circular Volute Section with Cur = Constant 149

5.7 5.8 5.9

Design of Circular Volute Cross-section with Constant Velocity (C v) 150 Calculation of Diffuser Section of Volute Casing 151 (A) Diffuser 152

(xiii)

CONTENTS

(B) Calculation of Spiral Part of Diffuser Passage 153 (C) Calculation of Diverging Cone Part of the Diffuser 155 (D) Return Guide Vanes 156 5.10 Calculation of Vaned Diffuser 157

5.11 Vaned Return Guide Passage with Vaneless Diffuser 164 5.12 Suction Volute Casing 166 5.13 Design Procedure 175 5.14 Effects of Suction Spiral on Pump Performance 176 5.15 Effect Due to Volute 179

6.

LOSSES IN PUMPS 6.1

Introduction 180

6.2

(A) Mechanical Losses 180

180-196

(B) Losses due to Disc Friction (MlJ 180 (C) Losses in Stuffing Box (Mis) 182 (D) Bearing Losses (MlB) 187 6.3

(A) Leakage Flow through the Clearance between Stationary and Rotatory Wearing Rings 187 (B) Leakage Flow through the Clearance between Two Stages of a Multistage Pump 192

6.4

7.

AxIAL AND RADIAL THRUSTS

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12

8.

Hydraulic Losses 194

197-214

Introduction 197 Axial Force Acting on the Impeller 198 Axial Thrust in Semi-open Impellers 200 Axial Thrust due to Direction Change in Bend at Inlet 201 Balancing of Axial Thrust 202 Axial Thrust taken by Bearings 203 Radial Vanes at Rear Shroud of the Impeller 203 Axial Thrust Balancing by Balancing Holes 204 Axial Thrust Balancing by Balance Drum and Disc 205 Radial Forces Acting on Volute Casing 210 Determination of Radial Forces 210 Methods to Balance the Radial Thrust 213

MODEL ANALYSIS 8.1

Introduction 215

8.2

Similarity of Hydraulic Efficiency 224

215-234

(xiv)

CONTENTS

8.3 8.4 8.5 8.6

9.

CAVITATION IN PUMPS 9.1 9.2 9.3 9.4 9.5 9.6

10.

Similarity of Volumetric Efficiency 225 Similarity of Mechanical Efficiency 226 Construction of Impeller by Similarity 227 Development of Surface of Impeller as per the Vortex Theory of G.F. Proscura 231

Suction Lift and Net Positive Suction Head (NPSH) 235 Cavitation Coefficient (0") Thoma's Constant 240 Cavitation Specific Speed (C) 241 Cavitation Development 241 Cavitation Test on Pumps 243 Methods Adopted to Reduce Cavitation 251

AxIALFLOWPUMP 10.1 10.2 10.3

235-255

256-332

Operating Principles and Construction 256 Flow Characteristics of Axial Flow Pump 258 Kutta-Jowkovski Theorem 258

10.4 Real Fluid Flow Over a Blade 262 10.5 Interaction between Profiles in a Cascade System 263 10.6 Curved Plates in a Cascade System 264 10.7 Effect of Blade Thickness on Flow Over a Cascade System 273 10.8 Method of Calculation of Profile with Thickness in a Cascade System 274 10.9 (A)Pump Design by Direct Method (Jowkovski's Method, Lift Method) 283 (B) Design of Axial Flow Pump as per Jowkovski's Lift MethodAnother Method 287 10.10 Flow with Angle of Attack 295 10.11 Correction in Profile Curvature due to the Change from Thin to Thick Profile 296 10.12 Effect of Viscosity 299 10.13 Selection ofImpeller Diameter and Speed 300 10.14 Selection of Hub Ratio 301 10.15 Selection of 10.16 10.17 10.18 10.19 10.20 10.21

(~)

-Aspect Ratio at Periphery 303 pen

Calculation of Hydraulic Losses and Hydraulic Efficiency 308 Calculation of Profile Losses using Boundary Layer Thickness 8** /67, 105, 106/311, Cavitation in Axial Flow Pumps 323 Radial Clearance between Impeller and Impeller Casing 328 Calculation for Axial Flow Diffusers 329 Axial Thrust 331

(xv)

CONTENTS

11.

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9

12.

13.

Introduction 333 Pump Performance-Relation between Total Head and Quantity of Flow 333 Pump Testing 341 Systems and Arrangements 346 Combined Operation of Pumps and Systems 350 Stable and Unstable Operations in a System 352 Reverse Flow in Pump 355 Pump Regulation 357 Effect of the Pump Performance when Small Changes are made in Pump Parts 371

PUMP CONSTRUCTION AND ApPLICATION 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11

333-374

375-414

Classification 375 Pumps for Clear Cold Water and for Non Corrosive Liquids 375 Other Pumps 382 Axial Flow Pumps 392 Condensate Pumps 395 Feed Water Pumps 399 Circulating Pumps 401 Booster Pumps 403 Pump for Viscous and Abrasive Liquids 408 Light Weight High Speed Engine Driven Monoblock Pump 412 Shaftless Monoblock Centrifugal Pump 412

DESIGN OF PUMP COMPONENTS Design Design Design Design Design

No. No. No. No. No.

D1.A D1.Al D1.A2 D1.B D2

415-538

Design of Single Stage Centrifugal Pump 415 Centrifugal Pump Design Example - Radial Type 415 Impeller Design in C Programme 419 Design of a Multistage Centrifugal Pump 435 Spiral Casing Design 449

Design No. D2.1

Free Vortex Cur

Design No. D2.2

Volute Design Example-Circular Cross-Section

Design No. D2.3

Constant Velocity 450 Volute Design, Circular Cross-Section and Constant Velocity in C Programme 451

=

Constant Circular Cross-Section 449

(xvi)

CONTENTS

Design No. D2.4 Design No. D2.5 Design Design Design Design Design

No. No. No. No. No.

D2.6 D2.7 D3 D3.1 D3.A

Design No. D4 Design No. D4.1 Design No. D5 Design No. D5.1 Design Design Design Design Design

No. No. No. No. No.

D6 D6.1 D7 DB DB.1

Spiral Casing Design under Cur = Constant and Trapezoidal Cross-Section 453 Spiral Casing Design with C v = Constant and Trapezoidal Cross-section 456 Design of Diffuser Vane for Radial Pump 459 Design of Suction Volute 464 465 Design of Axial Flow Pump 465 Computer Programming for Axial Flow Pump Design (Applied for both Impeller and Diffuser Design) 470 479 Correction for Profile Thickness by Increasing Blade Curvature (~) 479 481 Calculation of Correction for Blade Thickness using Thickness Coefficient (X) 481 483 Design of Axial Flow Pump 483 525 534 Design of Axial Flow Pump-as per Method Suggested by Prof. N.E. Jowkovski 534

APPENDICES

539-560

Appendix I : Equations Relating C, Ymax , 0° for Different Profiles

539

Appendix IT : lSI Standards Appendix ITI : Units of Measurement-Conversion Factors

547 554

Y

l

LITERATURE-REFERENCES

561-570

INDEX

571-573

1 INTRODUCTION

1.1 PRINCIPLE AND CLASSIFICATION OF PUMPS 1.1.1 Principle Newton's First law states that "Energy can neither be created nor be destroyed, but can be transfonned from one fonn of energy to another fonn." Different fonns of energy exists, namely, electrical, mechanical, fluid, hydraulic and pneumatic, pressure, potential, dynamic, wave, wind, geothennal, solar, chemical, etc. A machine is a contrivance, that converts one fonn of energy to another fonn. The machine follows the Newton's second law, which states that all forces existing in the world must be converted into the time rate of change of momentum i.e.,

LF

oc

d (mv) , where Fis the force which is responsible dt

for the energy development, m is the mass of the element, v is the velocity of the moving substance and t is the time. Newton's second law states that all forces (past, present and future) must be converted into a moving force in order to do work i.e., to exist in the world. For example the muscle force ofthe human must be converted into moving force of the hand, in order to take food, so also to walk, to eat in mouth. The earth and infact all the planets, in the universe must convert their energy into moving energy and must rotate around sun, in order to live in the universe. A wind mill converts the air energy into Mechanical energy with the help of wings. The opposite ofthis is the ceiling fan we use in our house i.e., the mechanical energy is converted into air energy. An electric motor converts electrical energy to mechanical energy. An internal combustion engine converts chemical energy to mechanical energy, etc. A pump is a machine, which converts mechanical energy to fluid energy, the fluid being incompressible. This action is opposite to that in hydraulic turbines. Most predominant part of fluid energy in fluid machines are pressure, potential and kinetic energy. In order to do work, the pressure energy and potential energy must be converted to kinetic energy. In steam and gas turbines, the pressure energy of steam from boiler as well as gas and air mixture from combustion chamber is converted to kinetic energy in nozzle. In hydraulic turbine, the potential energy is converted to kinetic energy in nozzle. High velocity stream of fluid from turbine nozzle strikes a set of blades and makes the blades to move, thereby fluid energy is converted into mechanical energy. In pumps, however, this process is reversed, the movement of blade system moves the fluid, which is always in contact with blade thereby converting mechanical energy of blade system to kinetic energy. For perfect conversion, the moving blade should be in contact with the fluid at all places, at all times. In other words, the moving blade system should be completely immersed in fluid. 1

2

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

1.1.2 Classification of Pumps 1. 1.2. 1 Classification According to Operating Principle Pumps are classified in different ways. One classification is according to the type as positive displacement pumps and rotodynamic pumps. This classification is illustrated in Fig. 1.1. In positive placement pumps, fluid is pushed whenever pump runs. The fluid movement cannot be stopped, otherwise, the unit will burst due to instantaneous pressure rise theoretically to infinity, practically exceeding the ultimate strength of the material of the pump, subsequently breaking the material. The motion may be rotary or reciprocating or combination of both.

Centrifugal, Mixed and Axial Flow Regenerative Piston plunger

Vane, Lobe Screw, Gear Perialistic, Metering, Diaphram, Radial piston, Axial piston

Fig. 1.1. Pump classification

The principle of action, in all positive displacement pumps, is purely static. These pumps are also called as 'static pumps'. The pumps, operated under this principle, are reciprocating, screw, ram, plunger, gear, lobe, perialistic, diaphram, radial piston, axial piston, etc. In rotodynamic pumps, however, the energy is transferred by rotary motion and by dynamic action. The rotating blade system imparts a force on the fluid, which is in contact with the blade system at all points, thereby making the fluid to move, i.e., transferring mechanical energy ofthe blade system to kinetic energy of the fluid. Unlike turbine, where pure pressure or potential energy is converted to kinetic energy, in pumps, the kinetic energy of the fluid is converted into either, pressure energy or potential energy or kinetic energy or the combination of any two or all the three forms depending upon the end use. This is done in spiral or volute casing, which follows the impeller. In domestic, circulating and in agricultural pumps, the end use is in the form of potential energy, i.e., lifting water from low level to high level. In process pumps, used for chemical industries, the fluid is pumped from one chamber under pressure to another chamber under pressure. These chambers may be at the same level (only pressure energy conversion) or may be at different levels (pressure and potential energy conversion).

3

INTRODUCTION

Pumps used for fire fighting, for spraying pesticides, must deliver the liquid at very high velocity i.e., at very high kinetic energy. These pumps convert all available energy at the outlet of the impeller into very high kinetic energy. In turbines, the fluid is water or steam or chemical gas-air mixture at constant pressure and temperature, where as, pumps deal with fluid at different temperatures and viscosities such as water, acids, alkaline, milk, distilled water, and also cryogenic fluids, like liquid hydrogen, liquid oxygen, liquid nitrogen, liquid ammonia, which are in gaseous form under normal temperatures. Pumps are also used to pump solid-liquid, liquid-gas or solid-liquid-gas mixtures, with different percentage of concentration called 'consistency'. Hence pumps are applied in diversified field, the pumping fluid possessing different property, namely, viscosity, density, temperature, consistency, etc. A third category of pump, called jet pump, where in, the fluid energy input, i.e., high head low discharge of fluid is converted into another form of fluid energy, i.e., low head and high discharge. These pumps are used either independently or along with centrifugal pumps. The reverse of jet pump is 'Hydraulic Ram' where in low head and high discharge of water is converted into high head and low discharge. Hydraulic Rams are installed at hills near a stream or river. The natural hill slope is the low head input energy. Large quantity of water at low head is taken from the river. A portion of water is pumped at high pressure and is supplied to a near-by village as drinking water. Remaining water is sent back to the river. This system does not need any prime mover like diesel or petrol engine or electric motor. Repair and maintenance is easy, in hydraulic ram since moving part is only the ram.

1.1.2.2 Classification According to Head and Discharge Another classification of pump is according to the head and discharge or quantity of flow to be pumped. Any customer, who is in need of a pump specifies only these two parameters. A quick selection of the pump is made referring standard charts for selecting the pump. Figure 1.2 gives the selection of pump according to head and discharge. 10000 H.m

A

1./1 1000

V

II

PISTON

,

-

I:>

... f-

r--.

, I

I 10

- - --

1I

-

"

CENTRIFUGAL

100

r-

-

r~

AXIAL 10

100

1000

10000

100000 3

Q.m /hr

Fig. 1.2. Pump selection as per head and discharge

4

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

1. 1.2.3 Classification According to Specific Speed Most accurate method of pump selection is based on the non-dimensional parameter called' specific speed' which takes into account speed of the pump along with head and discharge. Specific speed,

... (1.1)

where ns-specific speed, n-speed in rpm, Q-discharge in m 3/s, H-head in m. If pressure rise is known instead of total head then p = yH, where p-pressure rise of pumping fluid in N/m 2 and y-specific weight of the fluid at the given temperature in N/m 3 . It is essential that all parameters must be converted to equivalent water parameters before substituting them in Eqn. 1.1. Figure 1.3 illustrates the pump selection according to the specific speed of the pump. Centrifugal (radial flow) Low

oD2o =2,5to 1,8

Medium

oD2o

=2to 1,8

High

D2

0 = 1,8to 1,4 o

Diagonal and mixed flow

Propeller and axial flow

ns= 300 + 500

ns= 500 + 1000

-

D2 = 1,4to 1,2 Do

H-Q

Fig. 1.3. Classification according to specific speed

From Fig. 1.3, it is evident that, centrifugal pumps, at low specific speeds; mixed flow pumps, at medium specific speeds and axial flow pumps, at high specific speeds are used. All of them are classified as rotodynamic pumps. At very low specific speeds, however, positive displacement pumps are used. Referring to the Eqn. (1.1), it is seen that positive displacement pumps are used for very high head-very low discharge conditions. Ship propellers and aircraft propellers are of very high specific speed units beyond 1200, i.e., used for very low head-very high discharge conditions.

5

INTRODUCTION

1.1.2.4 Classification According to Direction of Flow in Impeller Another classification of pumps is according to the direction of flow of fluid in impeller of the pump such as radial or centrifugal flow, mixed or diagonal flow and axial or propeller type flow. Figure 1.4 illustrates the position of blade system in the impeller passage of a pump according to the direction of flow. Considering the flow of fluid in impeller, (Fig. 1.4) ifthe flow direction is radial (2-1) and (3-1), i.e., perpendicular to the axis of rotation, the pump is called radial flow centrifugal pump. If the flow is axial (6-5), i.e., parallel to the axis of rotation, the pump is called axial flow pump. Ifthe flow is partly axial and partly radial (4-2) and (4-3), i.e., diagonal, it is called mixed flow pump or diagonal flow pump. It is evident, from Fig. 1.4, that all these pumps are rotodynamic pumps, i.e., rotary blade passage and dynamic action of blade system in the fluid passage. Outlet, Delivery of water

,. .

I

Inlet, entry of water

./

I I I

./

(a) Radial

(b) Mixed

(c) Axial

(d) Relative location

Fig. 1.4. Position of blade system in different types of impellers

2-1 Centrifugal - Radial flow - very high head and very low flow. 3-1 Centrifugal - Radial flow - high head and low flow. 4-2 Mixed flow - Medium head and medium flow - low flow. 4-3 Diagonal flow - Medium head and medium flow - higher flow. 6-5 Axial flow, propeller - low head and high flow. Radial type centrifugal pumps have higher impeller diameter ratio (outlet to inlet diameter) and the blade is longer. Mixed flow pumps have medium diameter ratio and axial flow pumps have equal inlet and outlet diameters. This indicates that radial flow pumps work mostly by centrifugal force and partly by dynamic force, whereas, in axial flow pumps, the pressure rise is purely by hydrodynamic action. In mixed and diagonal flow pumps, however, the pressure rise is partly by centrifugal force and partly by hydrodynamic force.

2 PUMP PARAMETERS 2.1 BASIC PARAMETERS OF PUMP A pump is characterised by three parameters, i.e., 1. Total head (If), 2. Discharge or quantity of flow (Q), and 3. Power (N).

2.1.1 Quantity of Flow or Discharge (Q) of a Pump Quantity of flow or rate of flow or discharge (Q) of a pump is the flow of fluid passing through the pump in unit time. The rate of flow or discharge in volumetric system is expressed as unit volume flow unit weight flow .. , i.e., m 3/s, m 3/hr, lis etc., and in gravimetric system as , i.e., umt tIme unit time tons/day, kGf/hr, kGf/s etc. The relation between gravimetric or weight (W) and volumetric (Q) flow rate is given by W = yQ, where y is specific weight of the fluid.

2. 1. 1. 1. Flow Measurement 1. Gravimetric Method: A collecting tank of 1 m length (L) x 1 m width (W) x 1 Y4 m height (If)

is placed on a weighing balance. The delivery of water from the pump is directed to the tank, so that water is collected in the tank. A gate valve is fitted at the bottom of the tank, in order to empty the tank, whenever necessary. At normal conditions, the water from the collecting tank will be directed to suction sump, by opening the gate valve. To start with, the pointer in the weighing balance dial is set for one particular reading [weight (WI)]. The bottom gate valve in the collecting tank is now closed completely. Water gradually gets collected in the collecting tank and the weight of water collected in the tank gradually increases. This is shown by the gradual increase in the weighing balance dial reading. A stop watch is started as soon as the weight of water collected in the collecting tank, reaches the set weight reading in the dial (tl = 0). The set weight reading in the dial now is set to a higher reading (W2). After specific time, the weight of water collected will reach the newly set reading (W2). The stop watch is stopped as soon as the weight of water collected in the tank reaches the newly set reading (12), Thus, the time taken (12 - II) to collect specific amount of weight of water from the pump (W2 - WI) in the collecting tank is known. From these readings, the weight of water from the pump for one second can be calculated. The bottom gate valve is opened now, immediately, so that water does not over flow from the collecting tank. Net weight of water collected (W) = (W2 - WI) in kGf 6

7

PUMP PARAMETERS

Time taken to collect this weight of water (t) Weight flow rate through the pump

W = -

t

= t2 - tl

in seconds

in kGf/s

This is the most accurate method. It includes variation in density also along with quantity. It gives an error of about 0.5 %. 2. Volumetric Method: A collecting tank of 1 m length (L) x 1 m width (W) x 1Y4 m height (H), fitted with a glass tube and a graduated scale, at the outside surface of the tank, in order to measure the height of water collected in the tank, is used to collect, the delivery of water from the pump. A gate valve is fitted at the bottom of the tank, in order to empty the tank, whenever necessary. At normal conditions, the water from the collecting tank will be directed to suction sump, by opening the gate valve. To start with, the gate valve in the collecting tank is closed completely. Water level in the tank gradually rises. This is shown by the corresponding rise in level in the glass tube. A stop watch is started at any water level (HI) in the collecting tank (tl = 0). For a specific rise in water level in the collecting tank (H2 - HI = 10 to 15 cms), the stop watch is stopped and the time is noted (t2). Thus, the time taken (t2 - t l ) to collect specific amount of water from the pump in the collecting tank is known. From these readings, the amount of water delivered by the pump for one second can be calculated. The bottom gate valve is opened now, immediately, so that water does not over flow from the collecting tank. Area ofthe collecting tank = Length (L) x Width (W) in m2 Net volume of water collected (V) = (H= h2 - hi) x Lx W in m 3 Time taken to collect this volume of water (t) = (t2 - t l ) in seconds Volume flow rate through the pump

V = -

t

in m 3/s

This is the second accurate method. It only considers variation in volume. The density variation is neglected. It gives an error of about 1 % to 1.5 %. 3. Flow Instruments: As per Bemouli's equation, a change in velocity along a closed conduit induces a change in pressure. This pressure drop is measured by a manometer, to determine the flow in any closed conduits. Change in velocity is done by a change in area of cross section of the conduit for the same flow (Q). Venturi meters, orifice meters, and nozzles are the three meters, used to measure the flow in closed conduits. Orifice meters are also used in tanks to measure the flow into or from a tank. Venturi meters are used mostly for incompressible fluid flow (water and oil) measurement. Orifice meters and Nozzles are used for both incompressible (water and oil) and compressible fluid flow (air and gas) measurement. All these three meters have similar construction. The main diameter at the entrance of the meter is gradually reduced to a throat diameter, in venturi meters and nozzles, where as there will be a sudden reduction from main diameter to throat diameter in orifice meters. These meters are connected in the pipe line with 4d to 6d (d is the pipe diameter) straight and free upstream and downstream length, in order to ensure uniform flow at the meters. Then only the readings taken from these meters will be correct. A manometer is connected between the main diameter and the throat diameter, in order to measure pressure difference. Quantity of flow through the meters Q

=

CD

~ ~a2 ~2

_

a; ~2gH, in m /s

Where, CD is the coefficient of discharge, which is a constant, 0.96 to 0.98 for venturi meters, 0.85 to 0.88 for nozzles and 0.62 to 0.64 for orifice meters

3

8

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

a 1 is the area at the main diameter (d1) of the meter, which is equal to pipe diameter,

~ = nd

2 1

4

in m 2

a2 is the area at the throat diameter (d2 ), which is given by the manufacturer, normally d2 = 0.5 d 1,

a

2

=

d

2

2 n_ inm2 4

g is the gravitational constant on earth = 9.81 mls2, H is the pressure drop across the main and the throat diameters of the meter, which is measured in m, by the mercury manometer, connected to the meter. This method is commonly used in industries. It gives an error of about 3% to 5%. 4. Flow Meters: Flow meters are directly connected in pipe lines, like flow instruments. They give the flow directly. A rotor with screw shaped blades will be rotating across the flow, inside pipes, whenever flow takes place. This rotation is connected to a dial through gears. The dial is graduated in flow rate. The rotation of rotor blades is proportional to flow rate. The flow meter will be calibrated after manufacture with a standard flow measuring device like volumetric method. These meters are used in industries, houses and other places where the flow rate is the only requirement. These meters give an error of approximately 10% to 15%. 5. Field Test: This method is used in fields, where tank or stopwatch or weighing balance or flow meters are not available. The flow rate of the pump purchased has to be determined, in the field, without any above said materials. Only pump with motor and suction and delivery pipes are available. The pump is mounted with and suction and delivery pipes, near the water source. Care should be taken so that the delivery of water through the delivery pipe is strictly in horizontal direction. Allow water from the delivery pipe to fall on the ground. Measure the horizontal distance between the delivery outlet and the point on the ground, where the delivered water touches the ground [distance X in the fig. 2.1] and the vertical distance from the water delivery point from the delivery pipe to the ground [distance Y in the fig. 2.1]. The following formulae are used to determine the flow rate from the pump. 4 to 8d

y

Fig. 2.1. Flow measurement in field

v

Y

=

=

X

X

t

v

-ort=-

... (2.1)

1 X2 (Yi) gt2 or - g 2

2

v

... (2.2)

9

PUMP PARAMETERS

V

where

_

-

~gX2 2Y

2.215

=

X JY

... (2.3)

v is the velocity in m/s. X is the horizontal distance of fall of water from the delivery pipe in meters (m). Y is the vertical distance between the pipe and the ground in meters (m). TABLE 2.1: Velocity of water coming out of the delivery pipe, (v), in mls

A

Xm Ym

5 m

6 m

7 m

8 m

9 m

10 m

11 m

12 m

13 m

2Y2m

7

8.41

9.81

11.21

12.61

14.00

15.41

16.81

18.21

3m

6.39

7.87

8.95

10.23

11.51

12.70

14.07

15.35

16.62

3 Y2m

5.92

7.10

8.29

9.47

10.66

11.84

13.02

14.21

15.39

nd 2

= 4.

A in sq. meters

= A in sq in x 6.4516/10000

TABLE 2.2: Area of pipe for the given diameter (d) Diameter in inches

Q (LIs)

=

(A) Area in sq. inches

(A) Area in sq. meters

1 Y2 in

1.7672 sq. in

1.14 x 10-3

2

in

3.1415 sq. in

2.02 x 10-3

2 Y2in

4.9087 sq. in

3.17 x 10-3

3

in

7.0686 sq. in

4.56 x 10-3

4

in

12.5664 sq. in

8.11 x 10-3

6

in

28.2743 sq. in

18.20 x 10-3 nd

2

A (sq. meters) x v (mls) x 1000 where A = 4

TABLE 2.3: Quantity of flow through the installed delivery pipe, (Q) in Lis (v)mls (d) inch

4 mls

5 mls

6 mls

7 mls

8 mls

9 mls

10 mls

1 Y2 2 2 Y2 3 4 6

4.56 8.08 12.67 18.24 32.43 72.80

5.70 10.10 15.14 22.80 40.54 91.00

6.86 12.12 19.00 27.36 48.65 109.20

7.98 14.14 22.10 31.92 56.76 127.40

9.12 16.16 25.34 36.48 64.16 145.60

10.26 18.18 28.50 41.04 72.97 163.80

11.40 20.20 31.67 45.60 81.08 182.00

10

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

2.1.2 Total Head or Head of a Pump (H) Total head of a pump (lI) is defined as the increase in fluid energy received by every kilogram of the fluid passing through the pump. In other words, it is the energy difference per unit weight of the fluid between inlet and outlet ofthe pump. Referring to Fig. 2.2, the energy difference per unit weight of the fluid (E) between inlet (E 1) and outlet (E2 ) will be Einlet

=

Eoutlet

E

=

c2

PI +Zl +_1

Y

1

E

= 2

2g

}

C2

P2 +Z2 +_2

Y

... (2.4 )

2g

+Z1 ... v....

Fig. 2.2 Head measurement in pumps

the pressure in N/m2 (pascal-Pa) Z - the level or position above or below reference level in 'm' C - the flow velocity of the fluid in mls y - specific weight of the fluid in kGf/m 3 (or) N/m3 g - acceleration due to gravity in m/s2 Suffix 1 - indicates inlet or suction condition of the pump 2 - indicates outlet or delivery condition of the pump Total head H will be,

where,

p -

... (2.5) and

.

IS

d kGf.m N.m expresse as - - or -N kGf

=

m.

2.1.3 Total Head of a Pump in a System A pump installation consists of pump and system. Pumps are selected to match the given condition of the system, which depends upon the system head (Hsy)' quantity of flow (Q), density (p), the viscosity (fl), consistency (C), temperature (T), and corrosiveness ofthe pumping liquid. Ifthe pumping

11

PUMP PARAMETERS

liquid is other than water at different temperatures and pressures such as milk, distilled water, acid, alkaline solutions, as well as liquid ammonia, liquid oxygen, liquid hydrogen, liquid nitrogen or any other chemical solutions under higher temperatures and pressures, solid-liquid solution, liquid-gas solutions etc., the pump parameters in liquid must be converted into equivalent water parameters. The quantity (Q) and the total head (If) ofthe pump must coincide with the conditions of external system such as pressure and location ofthe system. Normally, the pump is selected with 2 to 4% higher value in total head than the normal value of system head. A system consists of pipelines with fittings such as gate valve or butterfly valve or non-return valve or any other valve along with bends, tee joints, reducers, etc., at the delivery line of the pump as well as foot valve, strainer, bend, etc., at the suction line ofthe pump. The system is an already available pipeline in the field or at the working area, to suit the prevailing conditions in the field or working area. It is a fixed system for that particular place. System varies from place to place. Referring to Fig. 2.3, the pipe 2-d refers to the delivery side and s-l refers to the suction side of the system. For all calculations in a pumping system, the axis of the shaft of the horizontal pump is referred as reference line. For vertical pumps, the inlet edge of the blade of the impeller will be the reference line. Since the difference between the inlet edge of the blade and the centre line of the outlet edge of the blade is usually small, it is neglected and the centre line of the outlet edge ofthe blade is taken as reference line. Anything above or after the reference line is called delivery side (marked with suffix' d') and anything below or before the reference line is called suction side (marked with suffix's') of a pump. Referring to Fig. 2.3, the equation for suction and delivery pipelines of the system can be written as follows. Since no energy is added or subtracted in these lines during the flow through the system, For (2 - d) delivery line E2 = Ed + hf (2 - d)

i.e.,

P2 C2 -+Z2 +y 2g

2

=

Pd Cd -+Zd +-+h/(2-d) Y 2g

For (s-l) suction line Es = EI + hf(s-I)

. I.e.,

2

Cs Ps Z + -+ -

Y

s

2g

=

PI +Z + C? +h I /(,-1) Y 2g

... (2.6)

-

The values hf (2 _ d) and hf(s _ I) include major frictional losses and all minor losses. The total head of the pump as per Eqn. 2.5 is

H

x 1

t

C1

-+----++--(!) V

Fig. 2.3 Pump in a closed system

12

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

... (2.7) H

Hp= I(Q)

Q

Fig 2.4 Head of pump and system

Equation 2.7 shows that, if a pump is connected to a system, the pump and the system will operate only at a point where Hp = H sy. Figure 2.4 shows graphically this condition. For both major and minor losses combined together hf

C2

=

constant x 2g

=

Kfj2, where K is the

sum of all constants (major and minor). The system head Hsy= Pd -y Ps + hs + hd + (Kd + K) Q2. If a s curve Hsyst= f(Q) is drawn, it will be a parabola moving upwards, i.e., increase of head when the flow Q increases (Fig. 2.4).

Ifthis curve is superimposed with H-Q curve ofthe pump, the meeting point will be (Hp = Hsyst) the operating point of the pump for that system. Different Hsy curves can be drawn by changing hs or hd or Pd or Ps as well as by changing pipe size Dp ' pipe length ip ' in suction and delivery, or by adding or removing or changing bends, tee, crossjoints or by changing the valves in the system. Change of every individual parts mentioned above changes the Hsyst-Q curve. If these curves are superimposed on pump H-Q curve, the operating point for each system can be determined (Fig. 2.5).

13

PUMP PARAMETERS

H

P1 , P2 , P3 , P4 Operating points

Hsyst 4 - Q

E ""0

co

I

OJ

~I~

Hsyst 2 - Q

+" - - r - - "'1;2:::::::__....:.--:--:-~\- Hsyst 1 -

Q

.s::

+ .s::W II

•

I Oi

Q4! Q3 : Q2: Q1:

••

(Hp-Q)

--~--+-------~~~~~-------Q

3 Quantity m /s, Us.

Fig. 2.5 Different systems operating on one pump

Referring to Eqn. 2.7, if suction and delivery chamber pressures are very high, when compared to the potential and kinetic energies, then the pump is called process pump. Ifthe suction and delivery chambers are open type, then Pd= Ps = Palm and if hd, hs are very high, then these pumps are called domestic or agricultural or circulating pumps. If velocity C2 is very large, when compared to other parameters andPd= Ps = Palm and hs and hd may be positive or zero, then these pumps are called fire fighting pumps, sprayer pumps. Rearranging Eqn. 2.5, we get P2 Pd C 2 _C 2 +(Z -Z)+ d 2 +h Y Y d 2 2g f(2 - d)

Pd

=--::;-

+hd+hfd +

c1-c;

... (2.8)

2g

If a pressure gauge is connected very close to the delivery side of the pump at point 2, it will read the delivery chamber pressure

(p; ),

static delivery height (h d)' delivery line frictional losses (h ) (both f

major and minor losses) and the difference between the velocity head or kinetic energy at delivery chamber

casing

(~; ) and immediately after the delivery ofliquid from pump, Le"

(C~). If the delivery chamber is a closed one, then ~

at the outlet of the volute

Py will be real and normally above d

C2 atmosphere 2; will be equal to zero. The pressure gauge P2 will read

P2 Y

=

Pd + h + h _ C~ Y d fd 2g

... (2.9)

14

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

C2

where C2 is the velocity at the delivery pipe, and 2; will be the kinetic energy at the delivery pipe.

y

• •

Pd

In case the delIvery chamber IS open to atmosphere, then

C}

velocity Cd = C2 and the velocity head at the delivery pipe is

Palm

=

-y- and

-C22 2g

=

cl. 2i wIll be real. The

O. The pressure gauge (P2)

will read

P2 y

=

hd + hId (gauge pressure)

+ hd + hId (absolute pressure) ... (2.10) y If a pressure gauge is connected at the end of suction pipe and very near to the pump inlet at point 1, it will read =

Palm

2

2

) l!.!:..+(Z-Z)+ Cs _CI _ h ( Y s 1 2g f(s -

=

Ifthe suction chamber is closed,

PI y

~ =

Ps Y

_

h _h + s

1)

C 2 _C 2 ... (2.11)

1

s

2g

ft

will be read and Cs

C2 =

0,

2~

=

C? )

Ps _ (hs + h s + y fi 2g

O. Then

... (2.12)

where, C 1 is the fluid velocity at suction pipe.

l!.!:..

= Palm . The pressure PI will be negative y y y i. e., under vacuum. A vacuum gauge (V) instead of pressure gauge PI must be connected at point 1. The velocity Cs = 0 and so

If the suction chamber is open to atmosphere, then

C 2) (hs + hjs + -2g absolute C?) vacuum (hs + hjs + 2i

P y

~ -

or

=

I

... (2.13)

Vacuum gauge will read only vacuum. The same condition will exist if Ps , the suction chamber y pressure is not sufficiently higher than the vacuum in the suction side of the pump. In this case also, only vacuum gauge must be connected at point 1. That's why if the suction chamber is closed, a pressure cum vacuum gauge and if suction chamber is open to atmosphere a vacuum gauge is connected at point 1, i.e., at the end of suction pipe or immediately before the inlet ofthe pump. Since total head of the pump (Hp) = Total head of the system (Hsyst)

15

PUMP PARAMETERS

2

Hp

=

2

C

H syst = P 2 + V + X + ( 2; -

2~ ) for open system

C

= P - PI + X for closed system ... (2.14) 2 where X, is the difference in height between delivery pressure gauge (P 2 ) and suction gauge (P I or V). If P 2 is at a higher level than P l' X is positive. If P 2 is at a lower level than P l' then Xl is negative. If P2 and PI are at the same level, X= o.

2.1.4 Power (N) Power is defined as the amount of energy spent to increase the energy of the fluid passing through kgf.m N.m the pump from inlet to outlet of the pump and is expressed in - - or - - or watts or kilowatts. If s s 'W' is the weight of fluid passing through the pump and the energy increase per unit weight of the fluid between inlet and outlet of the pump is 'H', power N will be No

=

C

WH

onstant

=

C

yQH.

onstant

m kW or watts.

where W = YQ, if W is expressed in kgf, the constant will be 102, and if expressed in Newton, the constant will be 1000 in order to get the power in kW.

2.1.5 Efficiency (rt) The power supplied to the pump will be higher than the energy spent in converting mechanical energy to fluid energy due to various losses, namely, hydraulic, volumetric and mechanical losses. The ratio of actual power utilized to the power supplied is called efficiency (11). Power spent (No = 11 or

Nth

yQH

Const (C) Power supplied (Nth)

No

yQH

11

Const 11

) yQH

Const Nth ... (2.15)

2.2 PUMP CONSTRUCTION Any pump consists of an impeller having specified number of curved blades called vanes, kept in between two shrouds. The impeller is the rotating element responsible for the conversion of mechanical energy into fluid energy. This impeller is connected, through a shaft and coupled, to the prime mover for rotation. The connection may be a direct drive or indirect drive, through belt or gear system. The shaft is supported by one or two fixed bearing supports depending upon the pump duty and one floating sleeve bearing support along with either mechanical seal or asbestos packed stuffing box. This floating support is arranged to take care of liner thermal expansion of shaft, towards the impeller side but not at the prime mover side and at the same time acting as load bearing unit. The mechanical seal material

16

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

or the packing material is selected according to the type of pumping liquid such as acidic, alkaline, neutral, milk, distilled water, cryogenic liquids like ammonia, hydrogen, oxygen, nitrogen, two phase fluids such as solid-liquid, liquid-gas, etc. A gland provided in the stuffing box keeps the packing material or seal in position. The impeller is rotated inside a sealed spiral casing or volute casing. Suction and delivery pipes are connected to the suction side and delivery side of the spiral casing through respective flanges. Since volute casing is a non rotating part and impeller is a rotating element, sufficient clearance should be provided between them. The fluid enters the suction side of the impeller, called eye of the impeller with low energy. Due to conversion of mechanical to fluid energy, the fluid leaving the impeller will be with higher energy, mostly with more kinetic energy. Due to the energy difference between inlet and outlet of impeller and due to the clearance between volute casing and impeller, a part of fluid flows from impeller outlet to the eye of the impeller at the suction side and towards the stuffing box side at the back. In order to control this leakage flow, wearing rings, at the casing and at the impeller at front and back side are provided. The amount of clearance and different forms of wearing rings used depends upon the pumping fluid (temperature, consistency, etc.). The mechanical seal and the packing in stuffing box reduces this leakage still further at the rear side. The volute casing and the impeller with shaft are fitted to the bracket which has the bearings to support the shaft. This bracket base is mounted in a common base plate, which has the provision to mount the prime mover. The pump and prime mover will be kept on a common base plate. In Figs. 2.6, 2.7 and 2.8, three types of pump assemblies are given for single suction pumps. However, the construction differs for double suction pumps and multi stage pumps.

1. 2. 3. 4.

Suction flange Delivery flange Impeller Volute casings

5. 6. 7. 8.

Bearing bed Shaft Deep groove ball bearing Bush

9. 10. 11. 12.

Flexible coupling (pump side) Flexible coupling (motor side) Gland Bearing cap

13. 14. 15. 16.

Impeller nut Coupling nut Air cock Grease cup

Fig. 2.6. Single bearing supported pump with split type volute casing

17

PUMP PARAMETERS

1. 2. 3. 4. 5. 6. 7. 8.

Spiral casing Intermediate casing Cooling room cover Supporting foot Pump shaft Left-hand impeller Radial ball bearing Radial roller bearing (only for bearing bracket)

9. Bearing bracket 10. Bearing bracket intermediate 11. Bearing cover 12. Flat seal 13. Flat seal 14. Flat seal 15. Flat seal 16. Flat seal

17. 18. 19. 20. 21. 22. 23. 24. 25.

Flat seal Seal ring Radial seal ring Gland Stuffing box ring Bottom ring Block ring Stuffing box Splash ring

26. 27. 28. 29. 30. 31. 32. 33. 34.

Wearing ring Shaft sleeve Disk Pin Oil level regular Hexagon screw Hexagon screw Stud bolt Stud bolt

35. 36. 37. 38. 39. 40. 41. 42. 43. 44.

Stud bolt Stud bolt Locking screw Threaded pin Inner hexagon screw Nut Nut Impeller nut Fitting key Fitting key

Fig. 2.7. Back pullout-double bearing type pump with combine volute casing

Fig. 2.8. Heavy duty pump

Basically pump construction consists ofthree sub-assemblies namely (1) shaft assembly, (2) casing assembly, and (3) base assembly or bracket assembly. Shaft assembly, consists of impeller, impeller key, impeller nut, shaft, bushes at stuffing box, bearing inner races, pump coupling, key, and coupling nut, all mounted on a common shaft. The shaft is connected to the prime mover either through belt drive, or direct. This assembly is the only rotating assembly and hence this assembly must be perfectly balanced. But, all components in this assembly are machined components except impeller, viz., inside surface of shrouds and the blade surfaces. These surfaces are normally rough cast surfaces and could not be machined. Hence, impeller only is balanced and assembled on the shaft.

18

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Casing assembly consists of suction side or front side bracket, rear side or coupling side bracket of the volute casing. However, volute casing construction changes depending upon the pumping fluids. For pumping high consistency liquid, two phase fluids, suction side bracket, coupling side bracket and volute casing are made up of three separate pieces (Fig. 2.8). For ordinary pumping liquids like water, milk, etc. suction side bracket and volute casing are single unit (Fig. 2.7). In agricultural pumps, casing is made into two halves (Fig. 2.6). Suction side bracket and one half of the casing become one part. Coupling side bracket and other half the casing become another part. Coupling side bracket will also have stuffing box or mechanical seal chamber. For higher capacity pumps, the base assembly or bracket assembly consists of a bracket with provisions for assembling front and rear bearings, and bearing caps. In agricultural pumps (Fig. 2.6), however, the stuffing box and gland at the front side of the bracket and bearing chamber and bearing cap on the other side of the bracket will be the normal construction. In low capacity pumps, the bracket is fitted on a base plate along with the prime mover. The casing will be connected to the bracket. In such pumps, the entire weight of delivery pipe with fluid, the suction pipe with fluid and all minor fitting like valve, bend, etc., will be connected to the casing delivery side and suction side respectively as a overhung unit. Such assemblies are called 'back pull out' assembly (Fig. 2.7). This assembly is a convenient assembly, where in all parts, except casing can be removed by pulling the entire assembly backwards for any repair and maintenance. The pipe system need not be disturbed. However, the prime mover has to be removed from base plate, in order to remove the pump assembly parts. In higher and medium capacity pumps, pumps with heavy liquids, two phase fluids will have the base at the casing which is connected to the common base plate.

2.3 LOSSES IN PUMPS AND EFFICIENCY Theoretically, all the energy supplied to the pump by the prime mover, in the form of mechanical energy, should be converted into fluid energy. Owing to manufacturing inaccuracies and entirely different flow conditions prevailing in pump, entire energy input (mechanical energy) is not converted into fluid energy. Referring to Figs. 2.6, 2.7 and 2.8, the mechanical energy supplied at the coupling side of the pump by the prime mover is reduced, due to energy absorption in bearings, stuffing box, disc friction. Hence, the energy input at the impeller will be less than the energy input at the pump coupling. Due to surface roughness inside impeller and due to the leakage flow through clearance, there will be further reduction in the energy input to the impeller. Hence, the energy output from the pump is less than the energy input to the pump. The difference between energy input and energy output ofthe pump is called losses in pump. The ratio of energy usefully utilized for work to the energy supplied is called efficiency. In other words, efficiency is the ratio of output energy to the input energy of the machine in doing work. Three kinds oflosses prevail in fluid machines namely (1) Hydraulic loss, (2) Volumetric loss and (3) Mechanical loss. The sum of all losses will be the total loss. Overall efficiency is the product of hydraulic efficiency, volumetric efficiency and mechanical efficiency.

2.3.1 Hydraulic Loss and Hydraulic Efficiency (rth) Due to surface roughness at the inner side of the impeller, through which the fluid passes, losses due to friction and losses due to secondary flow, take place, as a result of which energy loss takes place. Actual head developed (Ha) will be less than the theoretical head (Hth ) by the amount fiH = Hth - H a, where, fiH is called the hydraulic loss. Hydraulic efficiency (llh) is the ratio between actual head to the theoretical head.

19

PUMP PARAMETERS

Hydraulic loss, Hydraulic efficiency,

fiH

=

Hth-Ha

11

=

-

h

Ha

Hth

=

M/ 1-Hth

Hth -M/ Hth

)

... (2.16)

2.3.2 Volumetric Loss and Volumetric Efficiency (rt) In order that the impeller can rotate inside the stationary casing, proper clearance is provided at the front and rear side of the impeller at wearing rings. Due to pressure difference between impeller outlet and impeller inlet at the front side of the impeller as well as the pressure difference between impeller outlet and slightly higher than atmospheric pressure at the stuffing box, part of fluid coming out of the impeller leaks through the clearances on both sides of the impeller. As a result, the quantity coming out of the pump, the actual quantity (Qa) will be less than the quantity passing through the impeller, i.e., theoretical quantity (Qth) by the amount of leakage quantity passing through the clearances (fiQ), i.e., fiQ = Qth - Qa· Volumetric efficiency (11) is the ratio between actual quantity and theoretical quantity fiQ

llv

Qth - Qa Qa Qth - fiQ

... (2.17)

2.3.3 Mechanical Loss and Mechanical Efficiency (rt m ) Energy loss in ball, roller or thrust bearings (fiNE)' in bush bearings at stuffing box or in mechanical seal portion (fiNs)' and the disc friction losses (fiND) due to the impeller rotation inside the volute casing, which is filled with fluid are classified as mechanical losses (fiN). The energy received at the impeller side of the shaft, i.e., actual power (Ni ) for energy conversion into fluid energy will be less than the energy supplied at the coupling side by the prime mover, i.e., theoretical power (Nth)' i.e., fiN = Nth - N( The ratio between actual power (Ni ) and the theoretical power (Nth) is the mechanical efficiency (11 m),

i.e.,

fiN

=

fiND + fiNE + fiNs

fiN

=

Nth-Ni fiN

=1-Nth

2.3.4 Total Losses and Overall Efficiency (rt) Total losses

=

Hydraulic loss + Volumetric loss + Mechanical loss

llv = Qth ' output energy (No) = YQaHa = yQthllv Hth llh

and since, =

fiH + fiQ + fiN.

Qa

Since,

where, Ni

=

power available at the impeller end of the shaft,

... (2.18)

20

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Therefore, . Overall efficIency, 11

=

No N

=

... (2.19)

11m 11v 11h

th

2.4 SUCTION CONDITIONS Normal and dependable operation of a pump depends mostly on suction conditions ofthe pump, i.e., pressure at the inlet edge ofthe impeller blade (Fig. 2.9). Referring to the Eqns. (2.11) and (2.12), the pressure PI at the impeller inlet is less than the pressure at the suction chamber P s ' If the suction chamber pressure P s is low or if the suction chamber is open to atmosphere, i.e.,ps = Palm' the pressure at point 1, at the inlet edge ofthe blade ofthe impeller will be under vacuum (Eqn. 2.10). If this pressure, PI is lower than the local vapour pressure of the pumping fluid, corresponding to the temperature of the liquid at impeller eye (Pvp)' then the liquid at this point will be boiling. In other words, liquid will not be in liquid form, instead it will be in gaseous form and pumping cannot be done. Hence, the pressure at the inlet ofthe impeller, i.e., at the eye of the impeller, must be above vapour pressure of the flowing fluid corresponding the temperature of the fluid. L'. h

2

Fig. 2.9. Suction conditions in a pump

PI

Y or

(~ - p~p )

~ _ (hs + hfs + C; ) > y

PS PVP) (-::;--::;-

2g

Pvp Y

(h s + hfs +"2g C;) >0

... (2.20)

21

PUMP PARAMETERS

. chamber IS . open to atInosphere, then -Ps If the suction y

Palm

= --

y

(~ -p;) ~ (p;" -p;p) -(h, + hi' + ~~ } (NPSH)Net or Hsv i.e.,

(~

_

=

0

(NPSH)A - (NPSH)R

p;p) must be greater than zero or in other words, it should always be positive, i.e.,

(p~", - P; ) 2 (h' + hi' + ~~ ) (NPSH)A

(

;::

(NPSH) R

vp . PI -y Pvp ) IS . terme d as Hsv and IS . ca11ed Net PosItive .. S ' Head (NPS H. ) (Palm uctlOn -y- - P ) IS ca11ed

Y

NPSH available. The two terms Palm and Pvp cannot be altered, since these values Palm is the atInospheric pressure at the place where pump is runnmg and Pvp is the vapour pressure, which depends upon the

temperat",e of the pumping liquid. These two values are fixed values. The term

(h' + hi' + ~~ ) is

called NPSH required which is depending upon the pump, viz., flow rate, pipe length and size, and the level of suction chamber with respect to the reference line of the pump. All these can be altered during pump erection at site. Hence, NPSH (Net) or (Hsv) = NPSH (available) - NPSH (required) II.

cr

(p~", - P; ) - (h' + hft + ~n C2

hs + his +_s ______ 2g

(H atm - Hvp) -

Hsv = - - = __________

~~

H

... (2.21)

~_L

H

... (2.22)

where cr is called Thoma's constant. All pump manufactures give this value, i.e., Hsv or cr by conducting test on water in the laboratory. Depending upon the site conditions, pump erection is carried out so that pump can work without cavitation. In order to have a safe operation, a reserve in the NPSH is introduced and suction lift or suction head is calculated accordingly. KIf.

~ (II",", - II,p) -

( h, + hi' +

~!

)

-

..

(2.23)

Normal values of Kwill be 1.15 to 1.40. Therefore, hs will be

h,

~ (II",", - II,p) -

(hi' +

~n

KIf.

...(2.24)

22

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

In case the pumping liquid is other than water =

H

Hsv(w)

S

sv (L)

... (2.25)

L

where SL is the specific gravity ofthe liquid 'h and Yw are the specific weights of liquid and water respectively. 12

c 11

E

-5

10

.ill

9

S

8

o

co

/

I /

8

II

I

V

c

e:!

5

OJ

~ e:!

4

0.:

3

OJ

o

0..

~

2

o

--10

/' ./

/

V

/

V /

/

V

20

30

40

50

60

70 80

Water Temperature °C (a)

/

90 100 110

o

/

/

100 125 150

175 200

225

Water Temperature °C

(b)

Fig. 2.10. Vapour pressure of water at different temperatures

2.5 SIMILARITY LAWS IN PUMPS 2.5.1 Similarity Laws A complete study of fluid flow and the flow pattern in impeller, in casing and in various other elements of pump by theoretical means could not be achieved. That is why, experimental coefficients are used along with the theoretical equations to solve the problems in pumps. These experimental coefficients are obtained by conducting experiments on different pumps and obtaining results with the help of similarity laws and dimensional analysis. Similarity and dimensional analysis is a process of obtaining the property and characteristics of another similar pump from the available property and characteristics of a pump on which experiment was carried out and the results known. A functional relationship between different parameters of the pump tested and the pump for which the calculations are needed, is established by this law. Using dimensional analysis under geometrical similarity, different expressions, connecting pump head (If), quantity (Q), power (N) and speed (n) with the impeller diameter (D), which is the standard reference linear dimension for a pump, and the properties of fluid, such as density (p), viscosity (fl) and gravitational acceleration (g) can be established. The following Table 2.4 gives the dimensions and units of different parameters used for non-dimensional analysis.

23

PUMP PARAMETERS

TABLE 2.4: Unit and dimensions Parameter

Dimension

l.

Head

H

2.

Quantity

Q

3.

Power

N

metre(m) m 3/second (s) Newton.m S

1

Symbol L L3/t ML2 -2

t

1 t

D

s m

L

Gravitational acceleration

g

m/s2

LIP

7.

Density

p

kg/m3

MIL3

8.

Viscosity

fl

kg ms

-

4.

Speed

n

5.

Diameter

6.

-

M

Lt

As per the laws of dimensional analysis, there are 8 parameters with 3 dimensions. Hence, (8 - 3) = 5 non-dimensional parameters can be evolved. After solving, we get the following nondimensional parameters,

(1)

~ which is Reynold's number (Re = pVL ) pnD ~

(2)

~

(3) (4)

which is Struhaul's number nD machines

(Sh =~) nL

and is called as unit discharge KQ in fluid

+, is called as unit power pn D JD is Froude number (F, ~ :: ) (KN)

H

(5)

D

Multiplying non-dimensional parameters (4) and (5), we get another non-dimensional number

~H2 . Since g is a constant, in practice ~ 2 is used, which is called unit head (KH ) in fluid machines. n D n D Based on the above non-dimensional parameters, a functional relationship between unit power (KN) and the unit discharge (KQ), i.e., KN = f (KQ) as well as unit head (KH) and unit discharge (KQ) viz., KH = f (KQ) can be established, ... (2.26)

24

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

IV,

~ pn3D5 f (R" n;3 )

... (2.27)

where, Ni (internal power) or the power input at the impeller unit, i.e., the power input at the coupling side minus mechanical losses in bearings, stuffing box, and disc friction. Also

gH n2D2

=

f

(11 Q) pn D2' nD3

= /

(R nD3Q)

... (2.28)

e,

Q)

2

n D2 f ( R ' - - 3 e ... (2.29) g nD Equations (2.27) and (2.29) give the relation between the internal power (Ni ) and head (H) with Reynold's number and unit discharge (KQ). The effect of Reynold's number is not considered, since the tests are conducted in auto model region, i.e., at high Reynold's number (Re> 10 5), where the coefficient of friction '/' remains constant and is independent Reynold's number (Re)' The value H will be approximate, since effect due to frictional losses is not considered. Considering two identical pumps viz., prototype (suffixp) and model (suffix m), i.e., pumps of the same series which are geometrically similar, i.e., linear dimensions are proportional and kinematically similar, i.e., flow directions are same within the impeller and in casing, i.e., blade angles are same, velocity triangles are identical. H

or

For Head

= --

gHp

or

... (2.30)

... (2.31 )

For Quantity

Qp

or

Qm Np For Power

or

3

=

npD~

=

nmDm

K3 (:p ) m

... (2.32)

Nm 5

3

5

3

5

3

5

ppnpDp

PmnmDm

Np

ppnpDp

Nm

PmnmDm

~ K' (::J (::l Ifthe pumping liquid is same for both prototype and for model Pp

... (2.33) =

Pm' then

25

PUMP PARAMETERS

NN

P

=

m

J;5

(2)3

..

nm

(2.34)

Equations (2.31), (2.32) and (2.33) are called similarity equations for pumps, and include the scale effect, i.e., include change in the effect of Reynold's number R

(~) .

=

e

~ pnD

and relative Roughness effect

However, exact values, which include the change in the corresponding efficiencies between prototype and model, are given below:

... (2.35)

llvp )

The value ( - - takes into account the change in volumetric efficiency connected with the ll vm change in the relative values of wearing clearances, balancing holes and usually connected with the change in scale K The value Reynold's number and scale

(llhP) llhm

is the change in hydraulic efficiency which is a function of

K The value (llmp) is the change in the relative values of mechanical llmm

losses in bearings, stuffing box and for disc friction. The equations developed under similarity laws for pumps are most important for test result analysis and widely used in pump industries, to analyse the performance of model tested in the laboratory, with the test results obtained from the prototype, tested in industries such as test at different speeds, test at different diameters, tests on liquids other than water, etc., and also to develop new pumps.

2.5.2 Specific Speed (ns) Specific speed (ns) is defined as the speed (n) of a geometrically similar pump which consumes 1 (metric) hp and develops 1 m of total head, the pumping liquid being water under normal temperature of 4°C and at atmospheric pressure of 1.0336 kg£'cm2, and y= 1000 kg£'m3, viscosity fl = 1 centipoise or v = 1 centistoke, i.e., n = ns' when N = 1 hp and H = 1 m. Since,

yQH

N(hp)

y

=

75 1000 kgf/m3

N (hp)

=

1 hp, H

Q

=

1x75 1000 x 1

Substituting the values

=

1m =

0.075 m 3/s.

26

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Referring to equation for unit power, KN , and substituting the values.

N pn D

1

where D is the reference diameter

= -3-5

- - 3-5

pnsDs

s

35

()3

N = pn D =~ ~ pn;D; ns gH

... (2.36)

g.1

--... (2.37)

or Combining Eqns. 2.36 and 2.37 2

N

H5 N

2

~ KlO(:,J

~ (:,J

~ KlO

and lIs

or n s4

(:J

n4 N 2 =

[is

nJN

ns H5!4

... (2.38)

yQH

N= - 75

Since,

ns

=

Since,

y

=

Hence,

ns -

(

VrY 7s

=

~ 1000 = 75

3.65)

nJQ

H3/4

1000 kgflm 3

_ n.[N _ H5/4

-

3.65

nfQ H3/4

... (2.39)

Equation (2.38) is used for turbines and Eqn. (2.39) is adopted for pumps.

2.5.3 Unit Specific Speed (nSq ) Unit Specific Speed (n sq ) is defined as the speed of a geometrically similar pump delivering 1 m 3 /s of discharge and develops 1m head, i.e., n = nsq where Q = 1 m 3 /s and H = 1 m, i.e.,

_ nJQ

nsq - H 3 / 4

•

sv

Combining

~H 2

n D

and

~ nD

or

into one by removing' D' or

27

PUMP PARAMETERS

gH oc n2]j2

D2

or

Q2 n2

Therefore,

n 4Q 2 g3 H 3

or

0c

-

gH n2

or

g3 H 3

or

oc~

=

Constant

3H 3 D6= -g-n6 6 n Q2 2 n g3 H3 = Constant n/Q (gH) 3/4

or

=

Constant (ns)

... (2.40)

Equation (2.40) is called non-dimensional specific speed (n sn ). Since g is a constant, it can be taken to the right hand side. . speci·fiIC speed ,n U mt sq

Similarly, combining

~H2

n D

gH oc n2 N

oc

nJQ H3/4 .

=

D2

and or

~ pn 3 D5

gH

n

g5 H 5 n

lO

or

r:;

or

or

D2 oc - 2

pn 3 D5 or D 5 oc

So,

into one and by removing 'D' in both expressions

V p g5/4 H5/4

N

pn N

oc

or

--3

2

or

p2n 6

=

Constant

=

Constant

=

DlO n

N

2

oc

lO

p2n 6 N2

g5 H5p2n6

=

Constant

nsn

... (2.41)

where nsn is the non-dimensional specific speed. Since N

=

Y QH = pg QH, substituting this value in the above equation =

Constant

or which is the same nsn as defined earlier. While calculating the specific speed, all efficiencies, i.e., volumetric, hydraulic, mechanical and overall efficiencies are assumed to remain same for one value ofns ' i.e., for one series, independent of size, capacity, head of the pump, of same ns. This is not correct since larger size and capacity pumps will have higher efficiency than smaller capacity units of same ns. This is the only drawback in the calculation of specific speed. Referring to the specific speed equation, it can be said that each value of specific speed, ns refers to one particular series of geometrically similar pumps, i.e., a number of pumps with different H, Q, n can be developed, all having same (ns) specific speed.

28

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

From the above discussions, it can be concluded that each value of ns refers one particular series of geometrically and kinematically similar pump, each pump in this series will be identical to the other. It can also be said that for the same value of head and discharge (H - Q) different types of pumps in different series can be obtained with different specific speed, by changing the speed n. Each pump will be different in type and construction. But due to limited suction conditions cavitation and subsequent vibration, noise and damage of pump parts at higher speeds, high speeds are not recommended unless otherwise needed. Moreover, maximum efficiency can be obtained only at a particular speed for the given head (If) and discharge (Q), i.e., for given ns only at one particular speed. In fact, the specific speed, ns is calculated at the maximum efficiency point only. Normally, pumps are driven by electric motor (speed will be 720, 960, 1450,2990 rpm) or by I.e. Engines (750 or 1000 rpm) or by Turbines (25000 to 50000 rpm). Hence, pumps are always selected or developed to give maximum efficiency at these speeds. The value of specific speed, the type of pump will be always selected for the given H - Q of pumps and from the speed, n of the prime mover coupled to the pump.

2.6 CLASSIFICATION OF IMPELLER TYPES ACCORDING TO SPECIFIC SPEED (ns) The shape and type of impeller depends upon the specific speed ns. For the same head and discharge, the specific speed (ns) is directly proportional to the speed (n). ns increases when the speed is increased. When the speed increases, the shape and type of impeller change. In first approximation, the pump head (If) is directly proportional to the peripheral velocity or blade velocity (u). This is evident from the non-dimensional equation Hoc n2D2 oc u2. When speed (n) decreases the diameter (D) increases. Outer diameter (D2 ) of the impeller is the characteristic linear dimension or the reference diameter D. So increase in speed n decreases the diameter D2 and correspondingly the size and weight of the pump are reduced which is naturally most advantageous, provided suction conditions do not have any limitations. The eye diameter (Do) or the inlet diameter (D)) is determined from the quantity of flow (Q). Do or D) slightly reduces when speed is increased. So the ratio D2 or D2 reduces with the increase of ns. Also Do D) for the given quantity, the diameter D2 reduces, the breadth b2 increases. So .!!1... increases with the D increase of ns. When ns the specific speed increases, the flow rate (Q) increase~ and total head (If) decreases. High head-low discharge pumps have low specific speed. The pumps have higher value of (D/D)) and low value of (b/D 2). Impeller blades are in radial direction and of single curvature design. These pumps are called radial flow centrifugal pumps. Medium head-medium discharge pumps have medium specific speed. These pumps have medium D

value of D2 and 1

B --t-. At lower range of medium specific speed, the impeller blades have double 2

curvature at inlet and single curvature at outlet. The outlet edge of the blade is parallel to the axis. The inlet edge of the blade extends towards the eye of the impeller in order to reduce blade loading since outer diameter D2 is reduced. When the specific speed increases further, the inlet and outlet edges are inclained, i. e., neither radial nor axial. The blades have double curvature design. Flow through the impeller is neither radial nor axial, but is in mixed or diagonal direction. These pumps are called mixed flow pumps or diagonal flow pumps.

29

PUMP PARAMETERS

Low head-high discharge pumps have high specific speed. Inlet and outlet edges of impeller blade are almost perpendicular to the flow direction. The blades are of double curvature design. These pumps are called axial flow pumps. Very low head and very high discharge conditions give very high specific speed. The fluid flow direction in impeller is axial. Ship propellers belong to this category. In general, pumps are classified as radial, mixed, or diagonal and axial, depending upon the fluid flow through the impeller passage. All positive displacement pumps have very low discharge and very high head and hence very low specific speed. Theoretically, specific speed changes from 0 to 00, i.e., from zero discharge to zero head as well as change in speed. Practically very low speed and very high speed could not be attained, so also, very low head and very high discharge are limited and hence the specific speed. D

A 80

350

450

ns

800

D2 Fig. 2.11. Form and shape of impeller for D 1

Figures (1.3) and (2.11) give different forms or shapes of impellers and their range of specific speeds as well as the range of diameter ratio (D/D j ).

TABLE 2.5: Specific speed of pumps Type of

_ 3.65n.[Q nsH3/4

Positive displacement pumps

8-35

D2 ~

-

Centrifugal Radial Mixed Normal Low Higher discharge discharge discharge

40-80

~

2.5

Mixed

Axial

Diagonal

Propeller

Propeller

Ship propellers

80-150

150-300

300-400

400-600

600-1200

1200-1800 and above

~2

1.8-1.4

1.3-1.15

1.15-1.1

0.8-0.6

0.6-0.55

n.[Q nsv = H3/4

2-10

10-22

22-41

41-82

82-110

110-165

165-330

330-495

n.[Q n =--sn (gH)3/4

0.36-1.8

1.8-4.0

4.0-7.4

7.4-14.8

14.8-19.8

19.8-29.8

29.8-59.5

59.5-89.3

30

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

2.7 PUMPING LIQUIDS OTHER THAN WATER 2.7.1 Total Head, Flow Rate, Efficiency and Power Determination for Pumps when Pumping Liquids other than Water Unlike turbines; pumps are used not only for pumping clear cold water at normal temperatures, but also for pumping liquids with different properties such as different densities, different viscosities and different consistencies, pumping not only at normal temperatures, but also at cold or hot temperatures. Liquids may be corrosive or non-corrosive, two phase fluids such as gas-liquid or solid-liquid mixtures, milk, distilled water, acids, alkaline solutions, cryogenic liquids like liquid hydrogen, liquid oxygen, liquid nitrogen, liquid ammonia, molasses, tar, petrol, diesel, crude-oil, etc. It is not possible to design each pump for each liquid and test them in the laboratory with the pumping liquid at the actual field working conditions.

Pump design is always carried out for clear water at normal temperature. Water is considered as reference liquid for all the liquids mentioned above. For pumping liquids with viscosity and consistency, correction coefficients K H , KQ and KTf (or Ke) are used for converting the liquid parameters to equivalent water parameters. These coefficients are taken from standard recommended graphs and tables. These values are the consolidated results from a number of experiments by many authors and recommended by International Hydraulic Institute and Bureau of Indian Standards 146 I. Suitable pump is then selected from the commercially available water pumps for which performance characteristics are known.

2.7.2 Effect of Temperature Increase in the temperature of the liquid decreases the density, viscosity, consistency and increases vapour pressure of the liquid. Due to high temperature of pumping liquid, the dimensions of pump parts change at running condition, due to thermal expansion of the material of the pump parts. Extra dimensional allowances in clearances are given depending upon the temperature of the pumping liquid and coefficient of thermal expansion of the material of the pump parts. These pumps are brought to the running temperature by filling with the pumping liquid or by external heating, before starting the pump for smooth and vibration free operation. These pumps will not be started at normal temperatures and also should not be used for liquids at other than the recommended temperature. Increase in vapour pressure due to increase in temperature of the pumping liquid changes the net NPSH value and also reduction in suction lift. The system at suction side of the pump must be suitably altered for cavitation free operation of the pump. Recommended changes are given in Chapter 9 ofthis book.

2.7.3 Density Correction (p or y) Pumping pressure 'p' and the total head (lI) are related by the hydrostatic equation p = yH = Pg H where 'y' is the specific weight and 'p' is the density ofthe pumping liquid and 'g' is the gravitational acceleration. For the same pumping pressure, total head of the pump changes according to the specific weight (y) or the density (p) or the specific gravity (S) of the pumping liquid, i.e., p

=

Yw Hw

=

Yv Hv

=

Sv Yw Hv

31

PUMP PARAMETERS

Since, Yv

=

Sv Yw· Suffix 'w' is for water and suffix 'v' is for the viscous liquid. H w

= YvHv =S H Yw v v

Although, theoretically density has no influence on flow rate, i.e., Q w = Qv' practically Q v changes by 2 to 3% Qw and even up to 5% at higher density of pumping liquid due to the influence of surface tension. For high temperature liquid pumping at tOC, the density of pumping liquid (pto e ) is calculated as (Eqn. 2.42).

PtOe where,

(~td

=

. .. (2.42)

l+~toc(roC -15°c)

is the coefficient and (P15d is the density at t

=

15°C.

Table 2.6 gives the values of (~td for different values of (P15d.

TABLE 2.6: Density correction coefficients P15°e

0.7

0.8

0.85

0.9

0.95

~tOe

82 x 10-10

77 x 10-5

72 x 10-5

64 x 10-5

60 x 10-5

2.7.4 Viscosity Correction 2.7.4.1 ISO Method Performance of centrifugal pump changes when the viscosity ofthe pumping liquid changes. For higher viscous liquids, total head (Hv)' flow rate (Qv) and efficiency (llv) reduce considerably. Correspondingly, power consumption (Niv ) increases. Head-discharge graph droops down more. Overall efficiency reduces. Optimum efficiency shifts to lower flow rate condition. Power consumption increases considerably especially at high viscous liquid pumping due to higher reduction in efficiency. However, shut off head of viscous liquid remains same as that of water. Figure 2.15 shows the change in pump parameters when viscosity of the pumping liquid changes. However, up to liquid viscosity 20 C.S., pump performance for viscous liquid pumping does not change with respect to the pump performance pumping with water. Correction is applied only if the pumping liquid viscosity is more than 20 C.S. Figure 2.12 and 2.13 give the values of coefficient for flow rate (KQ), coefficient for total head (KH ) and coefficient for efficiency (KT) or Ke) for different values of Qv' Hv and v v' where v v is the viscosity of liquid in (S or SSU). Ifthe temperature of pumping liquid is higher, viscosity (v tOe) at the temperature (t0C) is calculated as 0.01775 v tOe(C.S.) = 1 + 0.0337 to + 0.00023 t02 ... (2.43) Calculated value ofvtoe only should be taken while referring Figs. 2.12 and 2.13. However, this graph can be referred only for : (a) Pumps of radial type centrifugal pumps under the normal operating range, having open or closed impellers. It cannot be used for mixed and axial flow pumps or for pumps of special design of impellers such as s-type impellers, single blade or two blade impellers or for non-

32

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

unifonn liquids like, slurries paperstocks, etc., since it may produce widely varying results, depending upon the particular characteristics of the liquids. (b) Sufficient NPSH should be available in water parameters in order to avoid cavitation.

Relation between viscous and water parameters is expressed as Qv =KQ Q w

Hv=

KH Hw

llv

KT} 1Jw

=

... (2.44)

N= IV

2.7.4.1.1 Determination of Water Parameters for the Given Head, Quantity and Viscosity of the Pumping Liquid For the given total head (H), quantity (Q), efficiency (11) and specific gravity (S) at the pumping temperature (t0C) of the viscous liquid to be pumped, equivalent water parameters (Hw' Qw' ll w' N iw ) can be detennined referring the graph (Figs. 2.12 and 2.13). The procedure is as follows: From the point of given viscous quantity (Q) (point A) in X -axis, a vertical line is drawn to meet the given viscous head (H) line (point B). From this meeting point of Hv and Qv (point B) a horizontal line, either left or right, is drawn to intersect the given viscosity (v) line (point C). From the point C, a vertical line is drawn to meet the correction curves KT}' KQ and KH at peak water efficiency points D, E, F, respectively. The values KT}' KQ and KH are the correction coefficients. By using Eqn. (2.44), equivalent water parameters Qw' H w' llw can be calculated. For multistage pumps, the total head (H) must be the total head per stage only, i.e., Hv = [(Hv) multistage/number of stages]. Based on the water parameters (Hv and Qv)' suitable pump can be selected from the commercially available pumps.

2.7.4.1.2 Determination of Viscous Parameters When Water Parameters are Known For the given Hw' Qw' llw values of water pump, equivalent viscous parameters Hv' Qv' and llv can be detennined, referring the graph (Figs. 2.12 and 2.13). From the perfonnance characteristics of the available water pump, namely Hw = f(Qw)' llw= f(Qw) and N iw = f(Qw)' where Qw is the quantity at the maximum efficiency condition and H w' ll w' N w are the corresponding values head, effciency and power at Qw' are detennined. The values of Hw' ll w' N w for 0.6 Qw' 0.8 Qw' 1.0 Qwand 1.2 Qw are detennined. As first approximation, all the above detennined water parameters are assumed as viscous liquid parameters, so that graph (Figs. 2.12 and 2.13) can be referred to find K H , K Q, and KT} for all four capacities, following the same procedure as mentioned. Using the Eqn. (2.41), equivalent values of H v' 11 v' and Qv can be calculated for all four Qw capacities. Two graphs Hw' 11 v' N w = f(Qw) and Hv' 11 v' N v = f(Qv) are drawn taking shut offhead is same for water and for viscous liquid pumping. From this curve, Q v can be found out for the given value of Qw and other values. One such graph is given in Fig. 2.14.

33

PUMP PARAMETERS 100 90 80

"C

co

Ol

I

70

I""

I-

I-

~~

I'-.

r::: ~~

'" " ~r-... :::'

Il-

60

'

~~ I 20

I-

-100

1"1"

I90 80

.z:"0 co co

70

0.

()

60 50

~

I-

70

(;'

c Ol "0

60

if: w

50 40

I-

"\ 1\

I-

\

\ '\ \ \ \

II-

\

II-

\

I-

~ I

-

(;' c

Ol

"0

if: Ol

\ 1\ \ ~I\J\

" E

\ \

\ \

~

0. Cl _c co "+=

\

"- 0 Ol-

ClCO

co

1\ 1\

Ci)U

\

c.CO

~ ~ ~V 15

20

140

50

I

I I I I

40

50 6070 80 100

40 50 60

I

I 150

200

\~ ~~ ~~

),cr-\ \

K \NI 1\

I I 300

I

I I I I

70

60

80 300 200 150 100 75 50 40 30 20 15 10

300

400

\ \

~ f.-'

5m

V 1'1'

~0'1\>""2\1\ I\~

r-.I\

I~ r-.

I\

1\1\1\

3

o

0

~

00

600 800:5 ....--

....--

....-- C\J

I

400 5006007008001000

~ ~~

~\

\\ .\1\ \~ l\ \

150 200

90

~~

\' \\ \ l\ \~1,\ ~

80 toO

"1\

~ ~~

IIV ~~

\

\

Water pump peak efficiency %

'1'\

\\' \ \ 1\ \I} l\' \

30

90

r-...

,

\

:i

X\ \\ \\ 1\1\

V

I'" I'- r-...~ 40 50 607080

l~"0-

Q

Y'( (\

~~~/ 30

30

~

-%; r0 ~ ~ ~~ ~ ~ ~ ~ f;::: ~~ 30O~

to

:1\ r{,

~ ~ ~~ ~ '\

Is

\~ ~t'-

~

\

~ ~ ~ ~ ~~ ~ ~~

~ ~~~

co2 Ol co

g:?a g~

\

\\ ~ ~ ~ ~~ ~ ~~

\1\

~ ~ ~~

Ol"C~

20 15 10 7 5 4 3 2 15

\

\ \ .\

\ 1\1\ 1\ ~~

co.

~

\

\

\\'6\\

1\

E Ol ~

:::l

No.

~~~~~\%~ ~O\~ %f~I\9-1~~%

tdq. Ol

co

\1

\

\

30

Water pump peak efficiency %

\

1\ 1\' ,1\"

1

liO

50 60

~"

"1\

20

I-

\

\

\

20

Q

,,'

r1-1' . " I \20 I ~ I I ~ ~ ........ ,I "\'\ ~ ~ ~ '\ ~ ~~ l'-

30 I-

10

~" "::::

~

I" ~

I'~ t-.: I""~

~~

40

30

90 80 70

........

"

Il-

['..

~ ~~ ~ ~ I'-. ,~ ~ ~~

"

I-

l90

"

~ ~ ~ ~ >1

I-

-100

80

Water pump peak efficiency %

:::::::::: ~ ~ ~ ~b~ ;: ....... r-...: ::::~ ~ ~~ ....... '~ r-.....

I 2000

a3

~

m/hr

I I I I

3000 4000500060008000 imp gpm

Fig. 2.12. A viscosity correction nomogram based on that quoted by (from Davidson (3), 1993, Process Pump Selection-A System Approach, Second Edition IMechE, London)

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

34

1.0

I

1llllllIllllllIlIllllrtmllt~1

E:: aJ

0.6.

·u"

1.0

LL

o

Q)

-I-- I--

~ 0.9 () 0.8

II II KQ

r--.....

0.7

r-...

0.6

I'

0.5 0.4

~

0.3 0.2

IN000

.... "'m

+-- Centistokes

(l)C\I~

~C\I'"

1\

\ ~\ \ \ 1\[\1\ \ 1\ \ \

200 150 100 80 60 40 30 25 20 15 10 8 6 4

~

~

1\

~ ~~ ~ ~~

\ 1\

C!G ~

\

~

~~ ~

~

,

~ ~ '\

~~

~ .-.::

"

o

0

C\I

'"

a

LO

a

(!)

a T"""

~

t:Sc: ~ ~ K\~

\1\1\

~1\~ ~ \\1\ \1\1\ \ \1\1\

o

'"

l\

c,

'"

7.10 3 , the coefficient kQ' kHare nearly equal to (i.e., kQ = kH= 1), which indicates thatthe increase in hydraulic losses between water pumping and viscous pumping is same, i.e., the effect of viscosity is negligible. The drop in overall efficiency k1) indicates that disc friction losses are increasing. At Re < 7.10 3 , the hydraulic friction losses considerably increase, which is responsible for reduction in efficiency. The disc friction loss will be low. In practice, it is found that pump performance comparison for viscous liquid pumping with that of water with respect to Reynold's number gives an error of ±5% for ns = 85 to 130.

2.7.5 Effect of Viscosity on Performance The performance of water pumps, when used for viscous liquid pumping, changes considerably from water performance. Many authors have already worked on this area. Prof. A. A. Burdhakoff, Prof. R.W. Sheshenko, Prof. D.A. Suhanoff, Prof. B.D. Baklanoff, Prof. M.D. Aizentein, Prof. A. T. Ippan 1 4 I, Prof. A.J. Stepanpoff 1 112 1 are a few authors to be mentioned. In chemical industries, mostly centrifugal pumps, of ns = 80 to 135, are used for pumping viscous liquids. Spiral casings are used, instead of diffusers, in most of the pumps, because, when pumping viscous liquids, the flow velocity in pump parts is less than that for water pumping. Coefficient of reaction p = 0.7 and number of blades Z = 5 to 6, depending upon the viscosity ofthe pumping liquid. Figure 2.17 gives the test results of a pump of ns = 85, for different viscous liquid pumping.

41

PUMP PARAMETERS Hm 50 47 44

I~ :--...

--"'-

:" ~ \

41 38

\

35

\

32

I t--:::

....... ...........

""

'" '"

H=I(O)~

"-

I

.....-/ ./

"-

I--

:;:.oc:: /""

c-

./

/......... /' .........

11=1(0)

V

72 64

--

V /"

f--

...- V

...- l-

V---- V

V f--

32 24 16 8

V/

h :/"

/"

./ V ./

--

If/. v: --::. 10

/

.........

20

/'

--

/'

_

C/)'V

,,:~

V V

v =0,009

--

. / v=0.0093 Water

1---0

J

- r--

-

lL ....::-

,,/

-

~.138

/

_f-"

.....-

1.50

Water

V

-

-

18.80

~ 0.595

.>-

~

8.55

12.28

~

V r"'~ V

3.69

~3.69

_f-"

V V /,~ V"

A~ ~ ~ ~V

--

- ...-

//"

'\ V

56

40

--

12.28 8.55

;;;k

...- ...- ...-

11=1(0)

48

--

I-I--

I---

18.80

12

80

0.595

C/)'V

/'

16

11%

~

.... 1.50

'y

18

6

""- " ~ ,0.138

"- ,/

/\

NkW

8

~ /'

2

cm /sec water

~~

\~0

20

10

"/V r-....

v- 0.009

"""'" '" V"- \:-"- "- "'" '""/ - - -- - --

23

4

r--.....

i'- R ~

.......

26

14

.......

..........

\

29

I

....... b

r--

0.595

1.50 3.69 8.55 12.28 18.80

I 30

40

50

60

70

80

Fig. 2.17. Actual performance variation due to change viscosity of liquids test results conducted on the same pump ns = 85 n = 2875 rpm

2.7.6 Effect of Consistency on Pump Performance Pumps in chemical and process industries handle two phase fluids, i.e., liquid with another nonmixing liquid, liquids with solids in suspension, gas particles in liquids. Apparently average specific gravity of such mixtures is different from specific gravity of liquid alone. The problem becomes more difficult, if the liquid is other than water, which is very common in chemical industries. As a result, the net pumping head, flow rate, power, NPSH of the mixture change. So the pump parameters of the mixture is converted into equivalent water parameters by using experimental coefficients called' consistency factor' . 'Consistency' is defined as the percentage by volume or by weight (or specific gravity) of the solid content or gas content or other liquid present in suspension in the whole pumping mixture. It is the property of material by which a permanent change of shape is resisted and is also defined by the complete force-flow relationships. As done for viscous fluids, the experimentally determined conversion factors are used to determine the liquid parameters. The following equations are used for such conversion:

42

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

. Water rating (Q or H )

w

w

Pulp (or) stock rating for Q or H (Q, or HJ } Conversion factor for Q or H (Eq or E H )

= --"-----------''--------'----'-

... (2.52)

Hs = E H • Hw' Qs = E Q . Q w Water efficiency (llw) x Conversion factor (El) = Pulp or stock efficiency (lls)

llw x El) = lls Table 2.8 gives the conversion factor for pulp or stock pumping at different consistency conditions 15 I.

TABLE 2.8: Consistency conversion coefficient Pulp or stock consistency %

EQ

F1I

El)

1.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

0.99 0.99 0.98 0.97 0.96 0.92 0.87 0.80 0.72 0.62 0.52 0.42

1.00 1.00 1.00 1.00 0.99 0.98 0.97 0.95 0.93 0.90 0.87 0.83

0.99 0.99 0.98 0.97 0.95 0.90 0.85 0.76 0.67 0.56 0.45 0.35

Such conversion factors are available for different liquid mixtures from the manufactures such as KSB pumps, Pump Manual or International Hydraulic Institute Standards. Rotodynamic pumps can be used only up to 7% consistency. For consistencies above 7%, positive displacement pumps must be used. Correct design, construction and material of pump parts must be followed especially for impeller blade shape, casing shape and location, sealing arrangement, and cooling arrangements such as external cooling or mother liquid circulation for cooling and sealing to suit the pumping fluid and operating conditions. In this book, water handling pumps and their constructions are only dealt with and discussed in Chapter 13. For special pumps, however, handling hydrocarbons and other high consistency liquids, specific manufacturer's recommendation must be referred.

2.7.7 Special Consideration in Pump Selection Normally pumps are manufactured as per the manufacturer's standard of production range. Any customer selects pump for his requirement from the available standard ranges. Sometimes, pumps are selected according to space availability in the field such as in ships, rigs, railways, in general for transport systems and sometimes to replace the existing pump with the new pump especially in mechanical and process industries. In such cases, efficiency is not considered as a major factor, instead functional applications such as fitting the pump in the space available, non-stop or continuous operation even at emergency conditions are considered as important. Such conditions change from field to field and installation to installation. Pumps must not only be designed and constructed but also must work as per the requirement of prevailing conditions at the fluid.

3 THEORY OF ROTODYNAMIC PUMPS

3.1 ENERGY EQUATION USING MOMENT OF MOMENTUM EQUATION FOR FLUID FLOW THROUGH IMPELLER Energy transfer from the impeller blade to the fluid, per unit mass (or weight) of fluid flow, when fluid passes through the impeller, can be developed by using momentum equation between point '0', just before the impeller blade and point '3' just after the blade. The cylindrical contour surface passing through point 0 and point 3 are shown in Fig. 3.1. The contour circles drawn with radius 'rj' passing through the point 0 and with radius 'r 2 ' passing through point 3 are connected to the front and rear shrouds (Fig. 3.1). Pressure and velocity forces, on both sides of the shrouds, are equal and opposite and hence get cancelled. Only two forces, due to absolute velocities, one acting on the outer cylindrical surface 3 and another on the inner cylindrical surface '0' are responsible for energy transfer. Taking moment ofthis momentum at inlet and at outlet, i.e., moment oftangential component ofthese forces with respect to the centre ofthe circle and since lo= ro cos ao' ro= rl' Co cos a o= Cu = C u and l3 = r3 cos a 3, r 3 = r2' C3 cos a 3 = Cu3 = Cu2' the reactive moment due to the tangential fo~ces 1cting on the cylindrical surfaces 3 and 0 will be

Contour L

n I I I

~N: ~~

--~-: I I I

:

Fig. 3.1. Moment of momentum equation as applied to impeller

Moment M 3 = C3l3 = C3 r3 cos a 3 = CU3 r3 = CU2 r2

... (3.1)

Taking into account, moment Mf due to friction, created due to the fluid passing through blade passages, total moment M will be

44

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

... (3.2) For ideal fluid flow, M;-= O. Energy transfer per unit weight of fluid flow through the impeller of a pump, i.e., the theoretical head developed under infinite number of blades, with infinitesimally smaller vane thickness, will be H

M 0) yQ

=

thoo

where MO)

=N,

YQ = Wand u

=

[CU2 - CUI J

... (3.3)

g

= O)r.

Equation 3.3 is the Eular's equation for the head developed by a pump.

3.2 BERNOULLI'S EQUATION FOR THE FLOW THROUGH IMPELLER Eular's equation for an elementary flow along a streamline (S) is given by

dC

1 dp dC dC ds dC dC dC d Fs - ds = d(=-at+a;at = -at+a;C =-at+ ds

P

[C

2

"2

)

where, Fs p

= =

Resolved component unit of mass along the direction of the streamline S Pressure

C

=

Velocity (absolute)

... (3.4)

p = Density For an elementary length 'ds' on the streamline, the Eqn. (3.4) can be written as F ds _ s

..

.!. dp ds -i.[~)dS = dC ds p ds

ds

For steady flow condition

dC at

Therefore,

1dpd s -d- [C F ds - s p ds ds 2

=

... (3.5)

dt

2

O. 2 )

... (3.6)

_ ds-O.

The force due to unit mass is the gravitational force 'g' ( =

7: )

which is directed downwards.

F g =-g. Taking vertically upward direction of Z-axis as +ve direction

/'..

dZ

Fs -Fg (cosZ , ds)=-gds

and

... (3.7)

Substituting this value of Fs in Eqn. 3.6 and changing the sign

dZ 1 dp d [C + g -ds+--ds+ds

or

P ds

ds

2

2

)

ds -_ 0

dp C2 gdZ+-+d- = 0

P

2

... (3.8)

45

THEORY OF ROTODYNAMIC PUMPS

For compressible flow, density 'p' is a function of the pressure p i.e., p equation (3.8) with respect to ds. For unit mass of fluid as

f

C2 +p 2

dp

gZ + -

=

=

f(p). Integrating

Constant

... (3.9)

For incompressible fluid, the density' p , is constant. The specific weight y = pg. Hence, equation (3.9) can be written for unit weight of fluid as, 2

p

C

y

2g

-+ Z + -

=

Constant

... (3.10)

Equations (3.8), (3.9) and (3.10) are called Bernoulli's equation derived from fundamental Eular's equation of motion under steady absolute flow condition along a streamline. It is evident that this equation cannot be applied for the change of energy of ideal fluid under unsteady absolute motion of fluid in impellers. Perhaps this equation can be applied for other elements like approach pipe with or without inlet blades, volute casing, diffuser, return passage of multistage pumps, which are non-moving or stationary elements, where steady flow prevails under optimum conditions. For impellers, however, steady flow condition can be applied for relative velocity of flow of fluid, since this velocity is actual velocity flowing past the blades. Referring equation (3.7), the force Fs in impeller blades consists ofthe gravitational force Fg and inertia force (since blade is moving) namely centrifugal force F CF and Coriolis force Fc . . .. (3.11) Fs =Fg +FCF+Fc For unit mass flow along the streamline'S', the gravitational force F

= -

g

towards downward direction. The centrifugal force FCF

=

ol- r, where

g dZ and is directed ds

'(0' is the angular velocity and /'..

'r' is the radius, and is directed towards radial direction. Coriolis force, Fc = (0 w sin ((0 w), is directed

normal to the direction of relative velocity, vector 'w' and angular velocity '(0'. Since ds = w dt along the streamline, the resolved component of the total mass force Fs will be /'..

Fs

=

/'..

/'..

Ig cos (Fg.ds) + FCF cos (r.ds) + Fc cos (Fc· ds )

Fig. 3.2. Vector diagram for Coriolis component Fa determination of Mz

46

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Taking axis of rotation vertically upwards as +ve direction the resolved component of the mass force in relative motion along a streamline will be Fs

=

dz ds

2

dr ds

-+(0 -

-g

... (3.12) /'..

substituting the value of ~ in equation (3.6) and since, Fes = Fe cos (~.ds) = 0, because ofthe direction of Fe normal to the direction of w on the elemental strip' ds' where the relative velocity 'w' is tangential to the streamline dZ 2 dr 1 dp d (W2 -g -ds+(O r -ds---ds-- -

ds

... (3.13)

gdZ - d( '~ )+ d; +d( ~l 0

... (3.14)

P ds

ds

Simplifying,

)

0

ds

ds

2

=

O

Wm2= W2co sin PA2

C>O

Cm3 =C3co sin(X3 =Wm3 =W3 co sinA3 ... (4.14) P The outlet velocity triangle before and after the outlet edge ofthe blade is given in Fig. 4.7. C>O

(a)

C>O

(b)

Fig. 4.7. Outlet velocity triangle--effect of blade thickness

In order to get higher head and efficiency, the outlet edge of the blade is made as sharp edged as shown in continuous lines (Fig. 4.7). This reduces the area blocked by blade at outlet and the flow resembles like flow with infinite number of blades with infinitesimally smaller thickness. However, angle of sharpness must be properly selected, so that there should not be any flow separation. The outlet velocity triangle A2 B2 C2 due to area increase and subsequent reduction in flow velocity Cm2 to Cm3 ,will change into A3 B2 C2 . Correspondingly, the direction and magnitude of absolute and relative velocities change (Fig. 4.7).

4.5.1

Outlet Velocity Triangle: Effect of Finite Number of Blades

The direction of the flow of fluid at outlet of the impeller, under elementary theory of blade system, must be tangential to blade position at outlet. In other words, the fluid angle will be same as blade angle at outlet. Also under infinite number of blades with infinitesimally smaller vane thickness, the flow velocity distribution i.e., the relative velocity wand the meridional velocity Cm at any radius, across the channel, should be equal i.e., from the trailing side or suction side ofthe blade to the leading side or pressure side ofthe next blade (Ref. Fig. 3.3). Correspondingly, the velocity has the same value at leading and trailing sides of the impeller blade. Considering any blade in such a system, as per Bemouli's equation the pressures between the leading side and the trailing side of the blade are same due to equal velocity on both sides. Under this condition, there cannot be energy transfer from mechanical to fluid by the blade system. In other

84

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

words, pumping will not exist. In order to have pumping or to change mechanical energy to fluid energy, the pressure at the leading side of the blade must be higher than the pressure at the trailing side ofthe blade. Correspondingly, the velocity (wand Cm) at the trailing side will be higher than the velocity at the leading side of the blade. When impeller rotates, the leading side of the blade exerts a force on the fluid in contact and makes the fluid to move. This unequal velocity distribution within the impellers passage can be considered as consisting of two types of flow: (1) Constant velocity of flow across the entire impeller passage combined with, and (2) A circulating velocity moving from trailing edge to the leading edge and then back to the trailing edge (Fig. 3.6). Due to this circulatory motion, a tangential velocity is created at the outlet edge ofthe blade, which is opposite to the direction of motion of blade and is in the same direction of blade motion at the inlet edge of the blade. Considering the outlet, the tangential velocity (L1C u) created in the opposite direction reduces the original tangential velocity C to C ,correspondingly the total head is reduced from H to H . Both ~= ~ = m these total heads are connected by the equation H= = (1 + p)Hm' where 'p' is the correction coefficient. Various authors derived different methods to determine the value of the coefficient 'p'.

4.6 SLIP FACTOR AS PER STODOLAAND MEIZEL 11091 Due to the flow change from theoretical to actual, in the impeller passage, outlet blade angle 132 reduces, and the relative velocity w 2 increases (Fig. 4.10).

Fig. 4.8. (a) Determination of effective radius

Fig. 4.8. (b) Flow in impeller passage

THEORY AND CALCULATION OF BLADE SYSTEMS IN CENTRIFUGAL PUMP

85

Stodola and Meizel suggested that L1w 2 is proportional to u 2 . The blade velocity at outletL1w2 = XU2 . In order to detennine the value of x, Meizel considered the flow in impeller passages consists of (1) flow with constant velocity in impeller passage along with (2) a circulatory flow with an angular velocity (0, rotating opposite to the blade rotation. He assumed that maximum value of relative circulation velocity L1w2max occurs at the middle ofthe passage. The plain flow with equal velocity is along the streamline, whereas the velocity vector of the circulatory flow is perpendicular to this plain flow direction, with the result, combined velocity w 2 is changed from one end to another end in impeller passages. Applying Stokes theorem, and referring to Fig. 4.8 (b) the circulation along the contour ABC will be

r

=

2(OA =

rAB + rBC + rCA

where, A is the area ABC. Since contour AB and BC are perpendicular to the streamline, circulation

r AB

= 0 and

r BC

= 0 and

rAC

= L1wi = L1w2

2nr2

z

,since t =

2nr2

Z

r Area

x=

If

B2

is increased the value x is also increased

... (4.15) The following assumptions were made by Meizel in deriving the above equation: 1. The circulatory velocity vector is perpendicular to the main flow streamline, which is not always correct. 2. The circulatory vortex moves in a closed contour which is not correct since inlet and outlet passages are open for flow. Only two sides of the blades act as closed contour.

86

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

3. The relative velocity w 2 = is tangential to the blade at outlet i.e., B2 of flow

=

B2 ofthe blade

and flow is parallel to each other at all points of impeller outlet passage. This is correct only for more number of blades (z 210). For smaller number of blades, the correction factor called slip factor does not agree. Also it is assumed that inlet flow conditions will not affect outlet flow conditions, which is also not true. In general, the slip factor equation given by Stodola and Meizel agrees with the experimental results for higher number of impeller blades.

4.6.1 Slip Factor as defined by Karl Pfliderer

1971

Karl pfliderer established a relationship for slip factor based on the blade loading (Fig. 4.9) which is based on the following assumptions: 1. Pressure drop across the unit length of middle streamline is constant in meridional section.

2. Unequal pressure and relative velocity distribution exists in impeller passage before the outlet edge of the impeller blade i.e., high relative velocity and low pressure at the trailing side ofthe impeller blade and low relative velocity and high pressure at the leading side of the blade. High relative velocity at the trailing face remains same, whereas the low velocity at the leading side gradually increases and becomes equal to the high velocity at the outlet edge. Hence for the normal entry condition (C = 0), Karl pfliderer

/r";"'--f+_..---

r

___________________ 1__

Ul

defined a relation between H= and Hm (equation 4.10) with a slip coefficient 'p' as

where,

dr

Fig. 4.9. (a) Slip factor as per Pfliderer

\If r~ p=--

Z S

Z -

No. of impeller blades.

\jf -

Coefficient depending upon the blade configuration.

S -

Static moment of the central streamline

r2

Ifthe blades are radial or nearly radial ds

f rdr =

=

r2

p

\If

2 -

r1

2

rl

and,

f r ds.

dr 2

r2

S =

=

2

... (4.16)

87

THEORY AND CALCULATION OF BLADE SYSTEMS IN CENTRIFUGAL PUMP

YH

z 12

10

8 5

4

0,6

3 2

0,4

°

30

~epad

60

0,2

°

0,4

0,6

0,8

r/r2

K 1,0 0,8 0,7 0,6 0,5

IA

~

0,4 0,35 0,3 0,25

~

0,2 0,16 0,14 0,12 0,10

'I

"'"

h'll

V/J. I I

/ VIllI I

7)7r2

VI , II II I

/ /

I I

/

V

/

/

,

/

0,08 0,07 0,06 0,05

/

/

0,03 0,02

/

0,01

V

V

/

I

/ I

If

/

I

I

I

I

(b) YH = f ( 15 10

5

I

0

(c) k = f (

r _1 =

r2

°

~:) when ~ = 90° ~: ' z, ~)

/ I

/

/

V

0,03 0,040,05

I

I 45/25/ 20

/

(a) YH = f(~) when

I

/ 1/ I

I

45/

V

J 0,02

/

/

90/

0,04

0,01

All

0,1

/,

II

0,2

0,3

0,4 0,5 0,6 0,8(r/r2)

Fig. 4.9. (b) Correction coefficient for finite number of vanes as per S.S. Rudinoff 11041

Karl pfliderer recommended the value of coefficient as \jf =

(0.55 to 0.68) + 0.6 sin B2

... (4.17)

The value of \jf, calculated as per the above equation, coincides with practical results, only for radial type pumps, having

..1.. < 0.5 and with backward curved blades. For radial blades B2 = 90° r2

1.8 i.e., nearly 50% more than normal value. For forward curved blades, it increases further. The corrected value of \jf as recommended by pfliderer is

\jf '"

\jf =

(0.6 to 0.65) (1 + sin B2)

... (4.18)

88

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

This equation is applicable for diffuser type pumps, where the inlet edge of the diffuser is kept very near to the impeller outlet edge. \jf increases if this distance increases. For volute pumps and for vaneless diffuser pumps, \jf values becomes higher. The approximate values are given below: \jf = 0.65 to 0.85 for volute \jf

=

0.68 for vaned diffuser

\jf

=

0.85 to 1.0 for vaneless diffuser

Also when (Xl S 10°, \jf increases approximately by 30%. A normal value of (Xl '" 20° is recommended for pumps for which \jf is minimum. When \jf is minimum, the power consumption is also reduced. pfliderer's slip factor gives a good result for pumps n S 150 with backward curved vanes. Slip factor 'p' increases with the increase of ns ' and it depends upon the surface roughness of the flow passage also. Extending the inlet edge towards the eye side as well as change in the static moment ofthe middle streamline'S' does not change the slip factor and hence Hm does not increase. In general, Hm calculated as per Stodota-Meizel formula is found to be nearer to the experimentally determined value of Hm than Hm calculated as per pfliderer.

4.6.2 Slip Factor as per Proscura

1931

Professor Proscura mentioned that the flow of fluid in rotating curved blades of impeller is the combination of two flows: (1) plain flow with uniform and constant relative velocity across the entire flow passage width from leading side of one blade to the trailing side of the next blade of a stationary curved blade cascade system, determined by using conformal mapping from the stationary straight blade cascade system and (2) axial vortex flow. Considering the flow due to axial vortex (2m) developed within the impeller flow passage, he gave the relation between H m and H = as

~2 + ( ~) sin ~l 2

1t

sin

1+Z

Considering equation (4.1),

H=

=

... (4.19)

1-(~r

(1 + p) H m , the value 'p' is 2

1t

P

=

Z

------l.(--=-"-:)2-1-

~

2\jf

1

- ZI-(~ J

THEORY AND CALCULATION OF BLADE SYSTEMS IN CENTRIFUGAL PUMP

89

where,

... (4.20) which is similar to equation (4.13) determined by pfliderer. Equation (4.15) is determined only for ideal fluid flow with finite number of blades and not for real fluid having friction losses due to viscosity. Before leaving the outlet edge, due to the slip factor, the relative velocity at outlet w 2 = deviates from the original direction (Fig. 4.10). Since flow rate is = C and the outlet blade angle reduces same C m2=

m2

from 132= to 13 2 ,

W2

> W 2=, C2 < C 2=,

(X2> (X2=

13w u2=' Cu2 R=--=5.43~S 11:

'18

2. The distance between the parallel lines in the cylinder M does not depend upon ~S, hence can be selected suitably. 3. It is recommended and advisable that the starting point of the blade construction should not be at the inlet edge. 4. While marking ~li on streamline (Fig. 4.29 a), the following rule must be followed:

M=

M

RT"v.

However, at the beginning it is better to give rav and find ~l. Afterwards rav is checked and corresponding ~l is calculated correctly by equation (4.61). 5. To mark the length Mi on streamline a, b, c (Fig. 4.29b), which can be shown as streamline on conformal spreading cylinder, the inlet edge is marked approximately. 6. The conformal mapping lines on transfer, with inlet and outlet vane angles 13 1 and 132 , must be smooth without any abrupt changes. The angles 13 1 and 132 are marked from the point a only (Fig. 4.29b). Abrupt change comes only, if the points a, b, c of inlet edge lie in the section between the directions with angles 13 1 and 132 marked from the point A. While transforming the streamline by conformal transformation on cylinder, the profiling must be done in such a way that the inlet edge lies along one meridional plane (a', bl • cl ). The inlet edge of streamline can be located only with one and the same value ofw = J(s) along the stream. It is necessary to get nearly same angle of coverage ofthe blade '8' in plan for all streamlines i.e., ai' bi' ci' etc., the location of inlet edge in one single meridional plane, simplifies the production process and control. In some cases, it provides a good anti cavitating quality in impeller. C

I

0 C

a

3

2

4

3

5

4 (a)

III

~

A

2

I

.........

" "- " ...............

...... '"

(b)

Fig. 4.30. Correction in entrance and in exit edge of the blades on conformal transformation diagram

Profiling the vanes on conformal cylinder is done on the meridional sections. The points of intersection of meridional sections with the vane on conformal net of the cylinder are marked. Then these points are transferred to the meridional plane ofthe impeller. Marking I, II, III etc., the skeleton of the vane sections (ai' bi' c) are obtained. Then the profile thickness is added (Fig. 4.29b), to get the leading and trailing edge of the blade in meridinal plane of the impeller. While transferring, it is essential to observe that the meridional part should not lie in the plane of evaluation, but must be located above. The distance between two meridional sections along the streamline must change if not, smoothness on the profile cannot be obtained.

133

THEORY AND CALCULATION OF BLADE SYSTEMS IN CENTRIFUGAL PUMP

4.19.7. Method of Construction of Vane on Conformal Mapping (Development of Cylinder) The difficulty lies when the impeller drawings are prepared for the pump having ns = 300 to 350, especially with the outer streamline' c', because during the profiling the vane becomes very short. This can be improved by 1. Increasing the vane angle. 2. Straightening the outlet end (Fig. 4.30a). 3. Bending the edge in the meridional plane (Fig. 4.30b). After construction of meridional parts of vanes, it is essential to check the profile thickness and its effect on flow. cr The coefficient of flow reduction, \If = 1 - - , where 't' is the pitch t

21tr = -.

Z

The vane thickness

along the circumferential direction (cr) (Fig. 4.28) at any radius' r' is for cylindrical blades cr = _._8_ and

sml\

for three dimensional blades cr =

8

tan l3v sin A,

, where A, is the angle between the section and the streamline

(Fig. 4.27). This angle should not be 60, because of the difficulty in manufacturing and poor flow pattern. If the flow is not straight but inclained at an angle, then A, must be checked at the shrouds also, where the conditions are poor.

4.19.8. Calculation of Velocities and Moments of Velocity in Impellers The calculation of moments and velocities are done for each streamline, from inlet to outlet. This is drawn graphically in the form of (CuJ),

l3v' w=, _t_, t - cr

1

rtanl3v

,~ \If

and v the streamline distance from s

inletto outlet. [Streamlines are at' -a2 (rl to r 2), b l - b2]. From the graph, all values ofw= and (CuJ) are found out. Corrections are made if necessary so as to get smooth change from inlet to outlet of all parameters, which provides uniform change in thickness. The change in w = gives the diffuser effect of the impeller channel. The flow pattern in blades is known from the change of (CuJ). (CuJ) must increase for pumps from inlet to outlet, whereas it should reduce for turbines. It remains constant at non-working regions. First Cm' the meridional velocity along the channel is determined from the elevations or meridional plane of the impeller. C'

=

Cm

\If

m

The coefficient \If is determined from the conformal net of

l3v· The relative velocity

c'

i

w= = sin

is determined from the velocity triangle. For infinitesimal blade, the value Cu is determined as C

= u=

C'

u--m-+(C r) tanl3v u =

... (4.62)

134

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Next is to construct the values ofw, e, Cm , for each streamline (al' a2 ). Similarly for other stream lines bl - b2 etc., at inlet C l = O. However, (Cu ' r l ) is not equal to 0 at inlet due to the provisions of /

U

angle of attack, (C r l ) U

1

C Q360 = Q total

a=

Ae = he ( he tan

b 3 =mm.

0

~ +b

a

3 )

Qe=AexCy

a e = 2he tan

'2 + b 3

For check up

149

SPIRAL CASINGS (VOLUTE CASINGS)

TABLE 5.3: Calculation of flow rate at different (Cv = const., trapezoidal cross-section)

e

S.No.

1 2 3

e values Qe

0

0

45° to 360° at constant

Q = Q360

interval

The height of the last trapezoidal section is detennined as h360 = (KpX r 2 ) - r 3, where Kp is an experimental coefficient given in Fig. 5.5. The value of Kp given are for double suction pumps. For single suction pumps, the value be less by 10 to 15%.

Kp

will

5.6 CALCULATION OF CIRCULAR VOLUTE SECTION WITH C u r= CONSTANT Applying equation 5.5 for a circular crosssection (Fig. 5.6) volute design with Cur = constant. Quantity Q e at an angle 8 from initial position will be Q

e

1

-r;

=

21t

~ Since, b (r)

B

fR b(r) dr r

r3

r+- Ja;

-pi

1

2 ~p~ - (r - aJ2

=

Fig. 5.6. Volute design with circular crosssection and free vortex (Cur = const.)

e

Since

Qe = 360 Q360·

Substituting this value in the above equation

8° where K

=

360r B Q360

Since a

=

=

nOng

Hm

co

Q360

=

3~~:B

(a _~a2 _ p2 ) K(a _~a2 _ p2 =

)

r3 + p, substituting this value and after simplification, we get

P

=

80 *0

-

K

+

2-r K

3·

... (5.10)

150

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

eo values are normally selected as 45°, 90°,

Calculations are made in tabular form (table 5.4). 135°, 180°, 225°, 270°, 315° and 360°.

TABLE 5.4: Calculation of circular volute with Cur = constant

K= nOng co S.No.

eo

1

2

eo

Hm

r3 =

Q360

eo

2-r

-

K

K

3

J4

3

p

5

4

=

(3) + (5) 6

8° - selected uniformly at 45° interval

As mentioned earlier, final area at spiral outlet before entering the diffuser will be the sum of calculated area and the tongue area.

5.7 DESIGN OF CIRCULAR VOLUTE CROSS·SECTION WITH CONSTANT VELOCITY (C v) Flow velocity in spiral casing is taken as C v = 1. In order to maintain leak proof ax > Po' the pressure at the inner side of the casing and impeller shroud and very near to the shaft. Pressure ax must gradually reduce from the gland to the impeller side. Considering an elementary thickness 'dx' (Fig. 6.2) ofthe packing, equilibrium is maintained. When,

21t (R +r) fl ardx

=

-1t (R2 - r2) da x

... (6.6)

where III is the frictional coefficient of packing. Combining equations 6.5 and 6.6 and rearranging, we get

2fll ---'--"-dx. (R- r)K

Taking ax = Po and integrating 'x' up to length 'l'.

183

LOSSES IN PUMPS

ax =

or

... (6.7)

fl1

where

K It is evident that the pressure p gradually increases and is maximum when x I

2112--

P

max

= ax = 0 = poe

=

I. It will be

I

2/12-

(R - r) = poe

S

= poe2112Z

... (6.8)

where, S is the thickness = (R - r) and Z is the number of packing rolls inside stuffing box = Elementary friction force, dT

=

2n r dx III ax f~

f

T= 2nr ll 1Po oe

Power N s = T(f)r

l

S.

nr 2 s

fl

--

_1

2/12

poe

e/12 -I-x s

=nrS

II 1"'1

fl2

poe

i (

2112 S

1-e

- 2

l -I

~2s

)

~d1_e-2~2; I

l

)

... (6.9)

s watts. Coefficient fl is 0.02 to 0.1. About Const fl2 5 to 7 (= Z) packing rolls are used for normal pumps. Practically frictional coefficient Il considerably reduces due to the introduction of cooling water as mentioned earlier. =

(a) Normal

(d) With cooling

(b) With lantem ring at the middle

(e) Extemal cooling

(c) With cooling circulation

(I) Extemal and intemal cooling

Fig. 6.3. Different types of stuffing box arrangements and with cooling systems

184

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Fig. 6.4. Stuffing box with the classic cooling water jacket, cooling the outer diameter of the gland

Fig. 6.5. Stuffing box with unclear lantern ring for sealing water supply

Fig. 6.6. Stuffing box with externally cooled circuit to reduce the temperature of the pumped medium in the gland area

185

LOSSES IN PUMPS

_._.

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.~

Fig. 6.7. Stuffing box with lantern type end ring for cold water injection

Fig. 6.8. Stuffing box of special design with hollow shaft sleeve to cool the inner diameter of the gland

Fig. 6.9. Stuffing box with double cooling effect and duplicate cooling feed, cooling inner and diameter of gland

186

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Fig. 6.10. Stuffing box with double cooling effect and single cooling feed, cooling inner and outer diameter of gland

Fig. 6.11. Stuffing box with double cooling effect and single cooling feed and also introducing cooling liquid upstream of the packing end ring for cooling inner and outer diameter of gland

Fig. 6.12. Gland area of feed pump with injection type shaft, intensive cooling and differential type balancing device absorbing pressure fluctuations of feed pump suction pressure sealing water pressure

187

LOSSES IN PUMPS

6.2 (D) BEARING LOSSES (L1 NB ) Bearing losses depend upon the type of bearing used such as ball, roller, angular contact, thrust bearing. Based on the hydrodynamic theory of lubrication in bearings, power loss in bearings can be calculated. One such fonnula is given below. Power loss fiN

=

(J) rT Constant

=

1l-2nrl

B

T

where torque

fiNB

in bearing will be

2n 11 r (mr?-l Constant 0

... (6.10)

u

o

Coefficient of viscosity of the lubricating oil used. u = ror

Velocity of ball or roller centre.

r and I -

Radius and length of the ball or roller.

8 -

Radial clearance in the bearing.

6.3 (A) LEAKAGE FLOW THROUGH THE CLEARANCE BETWEEN STATIONARY AND ROTATORY WEARING RINGS Leakage flow is controlled by the clearances' b'. b

=

O.003r, for smaller pumps and b

=

0.2

+ (D) - 100) 0.001 mm for larger pumps. 'b' nonnally lies between 0.15 and 0.25 mm. Larger clearance leads to higher volumetric losses and corresponding lower volumetric as well as overall efficiencies. Figures 6.13 and 6.14 indicate the change in the perfonnance due to increased clearance. 2 600

120

E

g

a E 100 0

500

C

OJ

[2

.2 '0

'0 .~

300

60

0~

.~ OJ

>=" I"

C

OJ

'2 ~ 80 0~

Qj

-0

[2

40

200

.2

co

~ 20

100

0

20

40

60 Q in

80

100

120

140

% of Qnorm

Fig. 6.13. Effect of clearance at shaft between 2 stages H, 11 and axial thrust (1) Axial thrust under normal clearance 0.2 mm and (2) Under increased clearance 1.5 mm

188

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Average flow is 6.6 gpm/hole 26.4 gpm for all 4 holes

Quantity of flow in Ips.

Fig. 6.14. Effect of wearing ring clearance and balancing holes

189

LOSSES IN PUMPS

Referring Fig. 6.15, the flow through the clearance QL can be detennined from one dimensional theory Q

=

I

KAV = KA ~2gH.

(a)

(b)

(c)

(d)

X

y

~~~ (f)

(e)

(g)

Fig. 6.15. Different types of wearing rings

Applying this principle to the flow through the clearance 'QL 'or called as leakage flow, we have I

QL

where,

Ai Di b Pi PI -

~

-

I

=~A~2gPi-PI=WTrDb~2gH r Pi I

I

... (6.11)

Area of the clearance Clearance diameter Clearance width Pressure before clearance Pressure after clearance at suction side of the impeller Pi - PI head loss in clearance y

Flow coefficient 0.003 r and should never be less than 0.15 mm for any type of wearing ring

N onnally b = construction. The pressure drop across the wearing ring [Fig. 6.15 (a)] between any point inside wearing ring and inlet H

=

Pi

Substituting the value for

P -po 2

I

y

H .= H PI

P2 - Pi y

Pi - PI Y

P

=

H _ P2 - Pi P y

... (6.12)

from equation (3.89)

yu~ [1 -(!....r )2] for nonnal wearing ring 8g

... (6.13)

2

... (6.14) Referring Fig. [6.15 (a)], the losses through the wearing ring consist ofloss at entry, loss in the passage and loss at exit.

190

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

he

=

Loss at entry, due to sudden entry

he

=

Loss at exit, due to sudden exit

=

=

2 VL 0.5 2g

2 V 1.00 2Lg

Loss in the passage having length 'l' and clearance 'b' and diameter 'D'. hf

=

lV2 L A, 8gR

where, VL is the velocity in the clearance R

=

Hydraulic Radius

=

Area Perimeter

= ----

QLb nD; ;

nD;b;

b;

2nD;

2

AlVL_ 2 __

So,

h

Total loss

h L =he +h+h =HPi f e

=

f

H

4gb[

=

Pi

Al;) vL ( 0.5+1.00+- 2b;

(

~+ 15 2b;

.

) (

1

QL j

=

!d!:L

2g 2

nD;b; )

----;==~l=== nDb I I

~+1.5 2b;

2

_1_ 2g

f2iH

'\j....,b~.L

Pi

... (6.15)

where Hpo is calculated as per equation (6.13) or (6.14). Comparing equations (6.15) and (6.12), fl will be gi~en as fl

1 = --;====

~+1.5 2b;

For high pressure pumps, Hpo will be higher due higher delivery pressure. The clearance cannot be altered since efficiency has to be maintained at high level as well as for ease in manufacture. So the leakage flow QL will be higher. Correspondingly, the volumetric efficiency and overall efficiency reduce. To maintain effibiency at higher level, QL has to be reduced. This is achieved by increasing the length of leakage path. Correspondingly, for the fixed value of area, /l value is changed. Different wearing ring forms are shown in Fig. 6.15.

191

LOSSES IN PUMPS

Px

-

Py

Y

QL~ 2g

y

1

[

(IlIAI)

2+

1 (1l2 A2)

2+

1 (1l3A3)

2]

~~! ~2 [~ +15+(~ +15)( ~r +( ~+15)( ~ J] 1

... (6.16)

In the similar manner, /l can be calculated for other configurations. The value for A, is calculated similar to the procedure followed for pipes. Equivalent pipe diameter' d' for the clearance b will be d

=

4R

2b.

=

Reynold's number for the clearance b is determined as

... (6.17) since the velocity of the fluid, ui

=

u "2.

Normal value of A, will be 0.04 to 0.08. For low viscous fluids, A, For pumps of Di > 100 mm, li the length of clearance passage

=

l

D

=

0.4. 0.12 to 0.15 and /l

=

0.5 to

I

0.6. When Di < 100 mm,

l r;= 0.2 to 0.25. Model analysis is not carried out for clearances. For prototypes, 1

keeping clearance width 'b / same, the length 'l/ is increased. Increase in length li increases the losses and reduces the leakage QL

. 1

When

.!:L> 0.25, D;

/l reduces only to a smaller extent, but I increases 1

considerably. The type of wearing ring construction used depends upon pump construction. li should always be;:::: 20 mm and /l S 0.65 considering techno-economical condition.

192

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Prof. A.A. Lomakin

1691 recommends that volumetric efficiency (ll vol) can be calculated as

(~~ ) ~ 1 + 0.68 "s-'" 6.3 (B) LEAKAGE FLOW THROUGH THE CLEARANCE BETWEEN TWO STAGES OF A MULTISTAGE PUMP p' - p' H

=

----=-1_-'-

P3

where p; = P 1 + yHi , H1

=

total head, and P'1

pressure at the hub of the impeller.

=

2

H

=

H1 -

P2 - P1

TTl - TT, +

~ ":i' + ;~ Since,

H 1-Hp

=

H dy

QL3

=

fl ndh b

+

Y

P3

2

U 2 -Uh

8g

;H ;:J1 I- (

-

H;:J]

~2gHP:3

... (6.18)

--~ -.-.-.-.-.-.-.-~.-.-.-::.-::.-::.-::.-~.-.-

--+-~------~~/~~~====~l

.

I

Fig. 6.16. Vortex formation at bend

Fig. 6.18. Flow in divergent passage

Fig. 6.17. Vortex formation due to sudden contraction

Fig. 6.19. Flow separation at imepller outlet due to shroud

193

LOSSES IN PUMPS

Fig. 6.20. Velocity distribution at

Fig. 6.21. Flow separation and return flow at the outlet

outlet of impeller

edge of impeller due to break effect

q=O,15

Fig. 6.22. Secondary flow at q = QQ

PI> Ps)·

Fig. 7.11. Balancing drum (another form)

Fig. 7.12. Axial thrust balancing by balancing drum

Pressure (P4) in the chamber (KI ) induces a force at the bottom ofthe disc clearance passage. If this pressure (P4) is larger than total axial thrust 'L F z' the moving disc moves away from the stationary ring. The disc clearance (b l ) now increases. This in turn increases the leakage flow (q3) and also the losses in the clearance. As a result of this, the pressure (P4) drops down and the disc moves towards the stationary ring which in turn reduces the clearance (b l ) and losses in the disc. This process repeats and the clearance (b l ) goes on changing, until the pressure (P4) equalises the axial thrust 'LFz- At this stage, the clearance b i remains constant. The leakage quantity (q3) flows through the tube to the impeller eye of the first stage of the impeller. The pressure drop (P4 - P5) at the disc clearance, the leakage flow (q3)' the dimensions of the clearance, the connecting pipe dimensions to carry the leakage quantity q3 back to the inlet of the 1st stage impeller are to be determined as follows: The pressure drop, L1 P thrust will be

=

(P4

-

P 5) across the disc clearance, to get complete balancing of axial

... (7.20)

207

AXIAL AND RADIAL THRUSTS

where, \f is the coefficient depending upon the pressure distribution across the disc \f < 1, Ra is outer diameter of disc and Rh is the outer diameter of the shaft sleeve. Taking an unifonn change of pressure across the clearance 'bl', the coefficient \f depends upon the dimensions of the disc only

(1-~{1+-t)+(1+2~{-tJ -3(tJ

3(1- ;J2

... (7.21)

where, ~ the coefficient depends upon the pressure drop at the entry to and exit from disc clearance and the losses in the clearance and is taken as ~ = 0.18 to 0.25. The leakage quantity (q3 ) will be q3

The flow coefficient

~

=2nrebl~~2gL1:

... (7.22)

will be 1 ~

=

... (7.23)

The pressure P4 before the disc can be detennined from the pressure drop across the axial clearance b. i.e., ... (7.24) Head developed per stage. Z Number of stages. Ps Suction pressure at impeller eye of 1st stage. Ps - The pressure in the balancing chamber outlet (not more than 5 to 8 kg/cm2 so that the stuffing box can work without any trouble). The pressure drop (P3 - P4) across the axial clearance (b) will be

where,

H

q

3

=

~s

A

s

~2g P3 -y P4

... (7.25)

Knowing q3 from equation (7.22) and the pressure drop from equation (7.21), the area ... (7.26)

208

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

For better operation, the clearance b1= (0.0010 to 0.0012) Ra and will be 0.6 to 0.8 mm. Now, the length 'L' for the clearance can be determined. The radius Ra ofthe disc is selected slightly less than the outer radius ofthe impeller. The diameter Rb = (1.2 to 1.5) Rsh where Rsh = the shaft radius. The inner radius Re is fixed, based on the sufficient length (ld) ofthe disc. The pressure drop' \f fip' is taken as constant. The coefficient \jf is determined from the condition that the force F d determined from the actual pressure distribution is equal to the pressure distribution on the complete surface ofthe disc i.e., Ra

IFzi

=

Fd = \If /1p dn (R} - R; )

f fip 2n rdr

=

Rb

Re =

Ra

f /1pd 2n rdr + f fipd 2n rdr

... (7.27)

The pressure distribution on both sides of the disc and the pressure drop fip change according to radius. Pressure on the right side ofthe disc Ps is constant and approximately 4 to 8 kg/cm2, for trouble free operation of stuffing box. The pressure 'p4' at the left side of the disc is also constant. The pressure drops from p 4 to P s due to losses in the balancing disc clearance fip where the coefficient will be 1.5

-

------;;---

-

Ald Ra + ( Re)2 + 0.5 2bd Re Ra

... (7.28)

where ld = Ra - Re and P.., the coefficient of friction, depends upon the Reynold's number ofthe flow 'Re'

R2h,~ e

... (7.29)

v

where Ca is the flow velocity at entrance and v the kinematic viscosity ofthe fluid. Normally P.. = 0.4 to 0.8 and will be 0.15 to 0.25. The pressure drop (fip) in the disc clearance can be taken as proportional to radius of the disc. It can be expressed ... (7.30) Substituting this value of fip in equation (7.21)

[(l-< >< '0 :0 C C 0 ~ ~

co

:0

c '0

E

C

'E "0co

OJ ~ OJ OJ "0 "0 OJ

OJ

C

OJ

~

~

OJ

0..

hs

c2

_0

hfs

2g

c2

2g

\: \

..£ y

Cavitation

\ \ .,..,\;

Fig. 9.3. NPSH determination and cavitation inception at inlet

PI

-

y

+Z + 1

(

wl - ul ) 2g

Px =

-

Y

+Z

x

(w; -

u;)

2g

+ hf

(1 - x)

... (9.7)

Referring the inlet velocity triangle, we have ... (9.8) Combining equations (9.7 and 9.8) and rearranging, we obtain PI

-

y

+z + 1

C2 2g

CUp

_1 _ _

u_l_l_=

g

~ +Z + Y x

(2

2)

Wx-U x

2g

+h

f

(I-X)

... (9.9)

239

CAVITATION IN PUMPS

Combining equations (9.6 and 9.9) 2

C Po + Z + _0_ Y 0 2g

Px + Z + Y x

=

(w2x _u x2) + ~ UC + h 2g

g

f

... (9.10)

(0 - x)

For cavitation free operation, minimum pressure p x;:::: P vp the vapour pressure. At minimum pressure

Px = Px (min)' velocity

(

W2 _u2) (w2 _u 2) x2g x

x2g x

=

. Adding (- Pvp) on both sides of equation (9.10) and

max

rearranging, we get ... (9.11)

But

( ~-~ ) C02 + -y 2g

=

H

sv

and (Z - Zo) is taken as x

=

U C lu 0, since it is very small, _ _1 g

=

0 for

normal entry in pumps. Px min = Pvp . Under critical condition for cavitation free operation. Equation (9.11) will be ... (9.12) Since point (0) and point (x) are very near to each other at suction.

Po + Zo +

C5

y

2g

=

POst + Zo Y

=

Pxst + Zx Y

... (9.13)

Combining equations (9.10) and (9.13), we have

P ---E!... Y

(

+ Zx

=

Px + Z + Y x

(2Wx2g-ux2) + ~ uC + h g j{o-x)

Pxst -Px) =-=fih= fo.PO (W;-U;) + __ ul Cu1 +h Y Y 0 2g g f

(0 - x)

... (9.14)

... (9.15) Comparing equations (9.12) and (9.15), it can be written as (Hsv)cr

=

(fihO)max

where, (fiho) max is called as Maximum Dynamic Depression. It is evident that (Hsv)cr is a function of kinetic energy of the flow at suction. Hence, dynamic similarity law can be applied between model and prototype values of (Hs). hj(O-X) is neglected, since it is very small because of convergent flow pattern between points 0 and x.

240

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Dynamic depression can also be expressed in some other form. All functions, as far as cavitation is concerned, take place at suction side and on the inlet edge ofthe blade (from point 0 to point 'x' on the blade). Referring inlet velocity triangle under normal entry condition C = C = 0, Co = C , CI Cmi

= =

C ml ' u~ + C~o = KIC

mo

UI

Uo

w5 and ui

mo

+ C~I = wi· Due to vane thickness flow velocity increases

where, KI is the vane thickness coefficient

(11

wx2 hO)max =

2

u x2

_

(;:::

2

2g

C2

2g

WX)2 (( wI

~

2

-wI +C I

+~

2g

m

2

Wx

2g

2g W 2 _W 2 x I

Taking,

2

Wx -U I

-lJ wi

(C m))2 C;'o

+

Cm

2g

r

and n

°

2g

~ ~ J-1 ) ( (

... (9.16)

... (9.17)

Substituting this value in equation (9.16), we get 2

(l1h)

o max

2

wI Cm =n-+m-o-

2g

... (9.18)

2g

Experiments conducted on different pumps by different authors, indicate that m = 1.0 to 1.2 and n = 0.3 to 0.4. Since, m and n are velocity ratios; similarity laws can be applied. Values of m and n remain constant for pumps of same specific speed.

9.2 CAVITATION COEFFICIENT (cr) THOMA'S CONSTANT Prof. Thoma

1971 has defined cavitation coefficient (a) a

=

_H-,s,,-,vc;;...r_=_(_M---,,-o....:;)m""a.x:;;:..

... (9.19a)

H

which is a non-dimensional number. Substituting H

Hsv

H

=

as

C =

u;U

2 ,

[W;2~U; 1 C

U

2 _U2 _

g indicates that a represents velocity ratios, which is constant for model and prototype of same specific speed, i.e., am = a p . However, this coefficient has certain drawbacks. For example, two pumps having identical inlet conditions but different outer diameters, H sv will remain same but H will differ and hence the value a

241

CAVITATION IN PUMPS

changes. This is overcome by defining another non-dimensional expression, called Cavitation Specific Speed (C). Moscow Power Institute I 58 I recommends a relation between cr and ns as cr

(ns)4/3 ... (9.19b)

= ---"--

4700

Based on intensive experimental investigation on cavitation on axial flow pumps, Leningrad Polytechnic Institute 11051 recommends the following equation to determine cr:

4b

(1+~) ( l+;fW=

cr

=

)2

-u 2

~----------------~-

2gH

... (9.19c)

where, f)-curvature and bm-maximum thickness.

9.3 CAVITATION SPECIFIC SPEED (C) Professors Rudnoffl1041, Wislicenus 11331, Watson 11031 and Karrassik 1541 defined cavitation specific speed (C).

5.62nJQ C

=

(Hsv)3/4 , or Hsv

=

10

(nJQ ]4/3 C

... (9.20)

This expression is similar to that of specific speed and hence called cavitation specific speed (C). Normally, pump speed is selected based on cavitation specific speed. Increase in speed for the given head and discharge of a pump, reduces the size of the pump. Due to reduction in area, the flow velocity increases, which intum increase the main friction losses and increased secondary flow losses. The cavitational property reduces considerably. In order to improve cavitational property, flow passage especially suction side of the pump must be improved and well designed for better streamlined flow. This can be done only by proper construction and efficient manufacturing technology. Since improvement in manufacturing of pump has its own limitations, for example, surface roughness cannot be reduced below certain limit unless costlier manufacturing processes are adopted. That's why cavitation specific speed (C) has a narrow range of operation unlike normal specific speed which ranges theoretically from '0' to 00, practically from 10 to 2500. Cavitation specific speed (C) ranges from 800 to 1100. To improve C above 1100, improved manufacturing and construction techniques must be adopted. Pump cost also considerably increases. F or normal design, 'C' can be taken as 900 to 1100 depending upon the manufacturing process available and speed is determined. For special pumps, C is selected as 1200 to 1500.

9.4 CAVITATION DEVELOPMENT When pressure at the point 'x' (Figs. 9.3 and 9.10) on the leading side of the impeller blade of the pump, falls below vapour pressure of the liquid for the prevailing temperature of the pumping liquid, the pumping liquid becomes vapour, 1 cc of liquid in the form of water, when converted into vapour,

242

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

occupies approximately 1780 cc of water vapour. Since the space available in between impeller blades is very small, pressure instantaneously raises to a very high value. This pressure rise makes the vapour to condense to liquid. Now the pressure falls below the vapour pressure and the liquid changes into vapour. Likewise the pressure changes from high positive to high vacuum instantaneously, many times in a second. The pressure rise is approximately in the order of 100 to 300 atmospheres. This sudden high instantaneous fluctuating pressure rise gives a heavy hammer blow on impeller blades, like shock waves. When pressure exceeds elastic limit of the material of the blade, metal is gradually removed from the blade. This pressure fluctuation followed by metal erosion and subsequent corrosion is called cavitation. Due to cavitation, impeller blades, shrouds, especially at inlet leading edge as well as other parts of pump like suction side of casing get damaged. Flow does not follow streamlined or axisymmetric pattern. Hydraulic losses increase; hydraulic efficiency and overall efficiencies considerably decrease. Huge noise and heavy vibrations are produced. Life of the pump reduces. Under severe cavitation condition, pump fails to work. At high vacuum, oxygen present in the fluid is released from the liquid, gets reacted with the material of the impeller and other parts of the pump. The metal is converted into metal oxide. This metal oxide, in the form of powder being weak, is carried away by the flowing fluid. Thus, corrosion adds to the erosion in reducing the metal thickness increasing the roughness of the surface. No metal is resistant to cavitation. Low strength metals gets corroded at a faster rate, whereas high strength materials gets corroded at a slower rate. Phosphor bronze gun metals have more elastic and anticorrosive property but possess low strength and smooth surface. Cast iron, malleable iron possess high strength but gets corroded at a faster rate. Stainless steel SS304 and SS316, an anticorrosive and high strength material is also used for pumps having more cavitating characteristics. Carpenter, alloy 20, Ni hard, Ni resist materials possess still higher strength and high anticorrosive quality. Initial stage of cavitation does influence on parameters of pumps namely head, discharge, power, efficiency and speed. When cavitation increases the rate of drooping down property of H-Q curve is noticed. Entire system becomes unstable when pump runs under severe cavitation. Pump cannot be run at this condition. Rate offlow, total head, power, efficiency and speed drops down suddenly and fluctuates. Figure 9.4 (a) shows a typical performance characteristics of pump under normal and at cavitation operating conditions. (H-Q) and (ll-Q) curves start droping down suddenly at certain flow rate when 50 H,N,l1

.,·-.11 hs = ,.. '.,0.5 m

40

H

\

I

. ", ,

,

I

70 60

~ 30

Normal

80

OJ

I 50

20

I

(f)

0... Z

4

10

2 10

20

30

40

50

60

1ii

8""

70

Flow Q [US]

Fig. 9.4. (a) Pump performance under normal and cavitating condition

Fig. 9.4. (b) The effect of cavitation on a centrifugal pump performance (effect of suction lift hs and NPSH)

CAVITATION IN PUMPS

243

cavitation occurs. No further increase in flow is possible. When suction lift (h s ) increases or NPSH decreases (H-Q) and (T)-Q) curves drop down more and more at a lower flow rate (Q) than the previous value [Fig. 9.4 (b)]. So also power discharge (N-Q) curve also drops down. The point, where it starts droping down suddenly, indicates the inception of cavitation.

9.5 CAVITATION TEST ON PUMPS Cavitation test is the process ofthe determination ofthe point of oscillation in Q, H, N, T), n, when suction lift (h s) or NPSH (Hsv) or dynamic depression (or anticavitating reserve) fih is changed from maximum to minimum, when pump is running at one point of H-Q curve [Figs. 9.5(a) and 9.5(b)]. For every operating point of the pump, there is one value of H sv below which cavitation starts. Cavitation test ends, the moment (Hsvcr)' the critical value of Hsv or fih or hs is determined for all selected point of operation. A curve joining all Hsv or hs values, obtained for different operating points gives the complete characteristics (Hsv) = f (Q) or C or (J = f (KQ) (Fig. 9.11). In closed test rigs, cavitation test is conducted by reducing the pressure in the space above water level in the closed reservoir with the help of a vacuum pump. Figure 9.6 illustrates a schematic sketch of a cavitation test set up and Figs. 9.7 and 9.8 show the actual cavitation test rigs for centrifugal pumps and axial flow pumps. Essentially a cavitation test rig consists of a closed tank to which suction and delivery pipe lines are connected. The delivery pipe has a venturimeter to measure the flow through the pump, a gate valve to control the flow rate and a tapping point to measure the delivery head ofthe pump. The suction pipe has a tapping point to measure the suction head of the pump and another tapping point to measure the temperature of water. A mercury manometer is connected to the delivery and suction head measuring points to measure the total head of the pump. Another mercury manometer is connected to the venturimeter to measure the flow rate ofthe pump. All the measuring points are located with sufficient upstream and downstream straight pipes (3D to 6D where D is the diameter of the pipe) before and after all flow obstructions. A vacuum pump is connected to the closed tank to change the vacuum in the tank. A mercury manometer is connected to the suction tapping point to measure the vacuum at the inlet of the pump. Pump, to be tested is kept at the adjustable test bed. A variable speed DC dynamometer is connected to the pump through a flexible coupling. Speed is measured by a tachometer. Torque output from the DC dynamometer to the pump is measured by a dial indictator. Proper cooling arrangement is provided at the stuffing box to avoid air entry into the pump through stuffing box and at the same time keep the stuffing box at low temperature. Additional supply of water to the tank and removal of water from the tank are carried out by separate gate valves. This arrangement is essential to keep the water temperature constant as water gets heated due to constant circulation. The temperature of water is measured by a thermometer fitted at the suction pipe. Cavitation test is conducted as per the method suggested here. From the load test performance graph, (i.e., H-Q and T)-Q graphs) a few operating points are selected very near to maximum efficiency point for (NPSH)p determination value (points 1,2,3,4,5 in Fig. 11.3). Pump is started with gate valve in closed condition for radial flow centrifugal pumps, whereas gate valve in opened condition for mixed and axial flow pumps. Speed is adjusted to run always at constant speed. The gate valve is adjusted so that the pump runs at point 1. After attaining steady flow condition, suction head i. e., vacuum before the impeller, total head, quantity power, speed are taken and efficiency is calculated. All the readings are entered in a tabular form (Table 9.2).

244

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

TABLE 9.2: NPSH (Hsv) determination for H = ...., Q = ...., N = ...., 11 = ..... S.No.

Suction head hs

Total headH

Flow rate Q

Power N

EffY·11

Speed n

(NPSH)p Hsvp

Net positive suction head of the pump, H svp is calculated by the fonnula

Psu - Pvp _ (h + h ) s Is y

(p;u -hs-hjs )- P;P =

Vacuum manometer reading - Vapour pressure

Now, the suction head 'h/ is increased by operating the vacuum pump and the vacuum is kept constant at one level. All values, mentioned above, are measured and entered in Table 9.2. In the same manner, suction head 'h/ is increased further in step by step and experiment is conducted until unsteady condition is attained. Discharge, total head, power and efficiency remain same, up to critical value of (Hsvp ). At Hsvp critical, all readings suddenly drop down and fluctuate. Pump runs with noise and vibration. This indicates that the pump is running under severe cavitation. No further increase in vacuum is possible and no further test on pump could be conducted. The vacuum is reduced and the pump is brought to the nonnal operating condition. Now, by adjusting the flow control valve, point '2' is set in the test. The experiment is repeated as mentioned earlier until (Hsvp) critical point is reached. Likewise, the experiment is repeated for points 3, 4,5, i.e., for all selected points. A graph H, Q, n, 11 = f(Hsv) (or) hs (or) fih is drawn taking values from the conducted test results for all points from Table 9.2. One such graph is given for one operating point in Fig. 9.5 (a). Since exact point of the beginning of severe cavitation could not be detennined, 1 to 2% drop in the values ofnonnal flow rate, total head, power and efficiency i.e., 98 to 99% ofnonnal flow rate, total head, power and efficiency is taken as (Hsvp) critical and this is the value of (NPSH)p of the pump at operating point 1 in load test curve ofthe pump. In the same manner, from the tests conducted (NPSH)p at other selected points (points 2, 3, 4, 5) are detennined. All (NPSH)p values are now plotted on the load test graph to get Hsv = f(Q) curve. The minimum most point in this curve is the best point of operation ofthe pump for cavitation free operation, which corresponds to maximum value of 'hs'(Fig. 9.5). Best cavitation free operating point need not be the best efficiency point of operation. For long life of the pump, it is always better to run the pump at best cavitation free operating point, than at best efficiency point. In open test rigs, the cavitation test is conducted by closing the gate valve at suction line, keeping the delivery gate valve at one position constant throughout the test. The experiment is repeated for different positions of delivery gate valve. Critical values of Hsvcr or (fihcr or hsmaJ depends upon the type of impeller i.e., specific speed (ns) of the pumps. For low specific speed pumps, ns < 100, H, Q, 11, N curves remain constant with the decrease of Hsv (or increase of hs) until critical point is reached. At critical point i. e., when cavitation starts,

245

CAVITATION IN PUMPS

all these values suddenly drop, i.e., horizontal lines change to vertical lines in the graph. When ns is increased, i.e., ns = 100 to 350, these values H, Q, 11, N gradually reduce until critical point is reached and then suddenly drops. In axial flow pumps, ns > 450, there will not be a sudden drop after critical point instead it will be gradual. Correct critical point, infact, cannot be determined. 55 /'

50

H

I

l"tl

N, kW

~~~45

Q Q

H

N

40

30

I

I~

~g 35

H

~/s 25 20

1102%

:6

30

t

110 80'{

15

75

10

70

/' Q

I

11

I

I~ /'

Ii Hs(Cr) I ---I

65

HS\lmin

2

(a) Schematic diagram

I

5

Q

10 5

6

80

I

70 /

I

N

H,m 1,2

I

It;

1,1

Hsv(min)

~

60

~ I

-

5

170 11,%

I

US

o 15

/11

II

N;:W~10

4

Q. Us 190 180

I

20

3

(b) Centrifugal pump

H

11

::f;: 6J

-

I :

Q

3

IL

1

4

5

I'> Io-In. 7 r" ~ ~

1,0

jb10

crr

lh 1

I

2 2

4

6

8

10

12

3

4

5

Hsv

(c) Centrifugal pump

(d) Axial flow pump

Fig. 9.5. Actual cavitation characteristics of pump Pv

----

~sl-

- - - - 1 X•. - -

Fig. 9.6. Schematic diagram of cavitation test rig 1. Control valve and 2. Flow measurement

Control valve Orifice Manometer vacuum

I.

Manometer flow measurement

I I I·

I!

I I

" iI__\..

-_.

D.C. Dynamometer

:0

o --I o o -< z

» ~

o

----

-u c ~ -u (f)

om z

Fig. 9.7. Cavitation test rig for centrifugal pump

--I :0 ""Tl

C G)

» r » z o

» x 5>

.s

o
45°, which is mostly for diffusers and hub sections of impeller blades, L1 a value increases up to 15° and depends not only upon a and To, but also on 13. Following figures (Figs. 10.12 to 10.22) illustrate these variations for 13 changing from 20 to 40°, at the interval of 2 0. ",IX =

I(To, ~)~

/

0,75

1 =0,8

/ I

1=

I

I I

/

/

/

II /

1 = 0,85 1 =0,9

V V V I 1 = 0,95 / / / V/ / /1 = 1,0 I I VV/ 1 = 1,05 /1 = 1,1 / V V 1/ / / I' 1 = 1,15 '/ / / / I' I' /'/ I / / = 1,2

,

~

~ ~ 1'/

'/

"/"'/ " /. V V / / /. V

h

/

/

./V /

/

./ ./

V- I' V- I'

/ /1 = 1,25

" /~

1 = 1,3 /. ~./ ./ "/ = 1,35 / ' / /' = 1,4

:...::~

v: V ...-: ~ " v. V V -'/ r-l = 1,45 A /. ~ /"/ ./~ /' ./ /" / ~ ~ ./ Al = 1,5 16 Q ~ ~ I/. ;..' ~ ~ ~ '" v. ~ ~ ~ " , ....-< I'-11 == 1:7 A

V'/ :h /

'"

~ ~ r ~ ....:: ~ ~ V V ......: % ;..-: k:: V / / ~ 1 = 1,8 /.~ ~ A r ~ ~ :;;.- ~ ~ ~ ~ ~ ....... ~ ~ ::::;.. .,- Cxi' angle Lie >Li( Hydraulic losses consist of: (1) Profile losses, which purely depends upon boundary layer on the profile surface and the wake formation after the profile, (2) End losses which depend on boundary layer on walls, which enclose the cascade system (at periphery and at hub) and due to the clearance between casing and impeller and (3) Secondary losses, arising due to cross flow existing at the channel passage due to pressure difference prevailing between leading and trailing edges of the blades both in axial and in radial directions. Due to the presence of casing, the flow is brought to rest at the casing surface. Centrifugal force is developed and boundary layer is increased which complicates the flow further. Boundary layer at the hub is increased. In variable pitch axial flow units, the radial clearance is increased due to blade rotation, which increases the end losses or annular losses. It is essential to bring the diffuser inlet edge very close to the impeller outlet

287

AXIAL FLOW PUMP

edge, which will reduce the profile losses due to aerodynamic wake at the outlet of the impeller, as well as shock losses at the entry to the diffuser.

10.9 (8) DESIGN OF AXIAL FLOW PUMP AS PER JOWKOVSKI'S LIFT METHOD-ANOTHER METHOD (i) For the given value of Q, Hand hs the speed 'n' is determined as

where,

[~~

r 4

... (10.31)

nQ

=

II"

~ (II", - II,p) -

(h' + hft +

~~ )

The suction head hsand frictional loss are equal to zero (i.e., hs = 0, hft = 0), since axial flow pumps work under submerged condition. Hat = barometric pressure 10.336 MWC, Hvp vapour pressure for water at 15°C = 0.336 MWC and C)s the eye velocity = Cl' the absolute velocity ofthe liquid at entry. Undernormal entry condition, C I = Cml = Cm ,where Cml is the meridional or flow velocity at entry. (ii) Suction specific speed C is selected as C = 800 to 1200 for preliminary calculation. Correct value is obtained after the design. The speed (n) is calculated as per equation (10.31), which gives a relation between (Hsv) and specific speed (ns). Prof. Suhanoff I 108 I recommends that, for cavitations free operation, the dynamic depression (fih) can be expressed as fih

where

CI

=

m(

~~) + n ( ~; )

Average absolute velocity at inlet

-

Average relative velocity at inlet m - The experimential coefficient, which is defined as the ratio of actual velocity (C I ) to average velocity (C lav ) at inlet = 1.02. n - The experimental coefficient, which is defined as the ratio of actual velocity (wI) to average of relative velocity (w lav ) at inlet = 0.2. The value of 'n' should not be less than 0.2 and it depends upon the specific speed (nJ Dynamic depression (fih) depends upon the impeller inlet diameter, the velocity on the blade to inlet, and suction conditions. This equation is applicable only when flow is a non-separated flow or near to that. Under separated flow condition the coefficients 'm' and 'n' depend upon the angle of attack. In axial flow pumps, flow separation on the blade at inlet is due to pressure drop below vapour pressure. Writting down the equation between points (1) and (X) at inlet. wI -

P ---1... y

Since hl (1-x)

=

+Z + I

2

2

_W..:....!_-_u..:....! =

2g

0, Zx = Zz and u l

P

~ + Zx +

Y

= Ux for

Px Y

w2 x

_ U 2

2g

x

axial flow pumps

PI

Y

+

2

2

WI -Wx

2g

+

1h f(1 - x)

288

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Cavitation starts when Wx = w max i.e·,px = P min ' P ' . can b e wntten as -min H ence tea h bove equatIOn y

P1

= -

y

+

W12 - W;'ax

2g

The coefficient 'fih' is a characteristic coefficient of dynamic depression on the profile, which depends upon the flow conditions, the fonn of profile and its geometrical parameters

,f}

(8~ , ~m

which depend upon the location ofthe profile in the blade system. That's why

cavitational characteristics depend upon the pump construction to a considerable extent especially for axial flow pumps of high specific speed. n4/3

Thoma's cavitation coefficient 'cr' is detennined from the equation as cr = 4;00 and Hsv = crH from which the speed 'n' can be calculated.

0,8

1 ,0

9° 1 ,5

t [ 0,5

~,6 ~,~ 0,8 0,9

,1,0 1,2 1

•

°

0,01

Fig. 10.36.

usle

= f

(fm

0,02

0,03

0,04

0,05

0,06

0,07

0,08

t) for the profile of a cascade system-for shockless entry

l/' I

(us Ie

+ 1°)

289

AXIAL FLOW PUMP

Cavitation calculation also depends upon the relation between the average force to the maximum force on the impeller.

K=~

i.e. ,

Pvmax

Pv max

=

Pj - Pmin , the maximum pressure depression on the profile, when compared to the pressure on the profile.

p"~= ~

PI

-/"P ~ ~ -h,-(~ ) ~II,,- (~ ) andp= ~yCy (~D

Knowing the lift force of the blade, the area of the blade for cavitation free operation can be calculated as A Zj

=

!1r P av

K is a function of profile form. As per Suhanoff, K = 0.65, and as per Rudinoff, K = 0.55. K", 0.9 for low specific speed pumps and K = 1.67 for profiles developed by Moscow Power Institute, Russia.

The value of K > 1 indicates that the load on the pressure side (concave side) of the profile is more. (iii) Impeller diameter D = K ~Q/n , where K

=

4.5 to 5.4 and sometimes up to 6. For axial flow

pumps, higher value is selected. Value 6 is selected under special circumstances. If the value K is small, cavitation effect will be earlier due to smaller eye diameter which leads to higher flow velocity at inlet. Outer diameter is always selected for economical flow velocity i. e., as minimum flow velocity as possible to reduce the profile losses and cavitation. At the same time, higher value of outer diameter increases the overall size of the pump. (iv) Hub diameter d h is taken as d h = 0.35 to 0.6 Di for ns = 1100 to 800. However, hub diameter should be selected to accommodate the impeller blade turning mechanism. Although cylindrical hub is normally used for pumps of higher specific speed, sometimes conical hub is adopted to get a better control on total head. Mostly the area ratio (A/Aj) = 0.85 to 0.9.

(v) For better efficiency, flow velocity em is selected as em = 0.74 .J2gH or em = (0.25 ± 0.05) (0 R . The value 0.25 is for periphery and Ri is the selected radius. i Hydraulic efficiency, 11h = 0.86 to 0.89 and impeller efficiency, 11i

=

0.92 to 0.94.

H.

Head developed by the impeller is calculated as Hm

=

-'

11h

and H

=

11· H . Therefore,

11m

H=Hh=H~ m

h

1

111

(vi) Calculations are carried out as per Euler's and 10wkovski's formulae. A relation between hydraulic efficiency 11h and impeller effiency 11i is given by

290

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

1

... (10.32a)

where Sd is the coefficient of friction for the diffuser and So is the coefficient of friction for the outlet channel. A3 is the area of the diffuser inlet and A2 is the area of the impeller outlet. Sd = 0.36 and So = 0.17 are the experimental coefficients. Another expression is 1 4

-4

2

4

:3

11i

... (10.32b)

1 + 2240 11dn; KJ + So x 00014n; Ka

where Ka is the coefficient, Ka = 0.25 to 0.37; 0.25 is for 11h = 0.94 and 0.37 for 11h = 0.9l. (vii) Based on the experimental results, the angle subtended by the vane in plan should be approximately 85° for peripheral profile and 115° for hub profile.

(viii) Number of blades Z = 3 to 6 for ns = 1500 to 450. (ix) Ifthe blade curvature is too much, which normally occurs at hub sections, a flow separation takes place, especially for a diffuser passage at an early stage. At the same time, the blade should have a minimum curvature and should not be a straight blade. Minimum curvature occurs at peripheral section of the blade. Blade curvature must always be selected, so that correct value of Cy is attained without any flow separation. Based on the experimental results, the empirical value ofthe relative maximum blade curvature recommended is

f8

~m

=

7% for hub and 2% for periphery. Relative maximum thickness

will be 10% at hub and 3 % at periphery. The change of maximum blade curvature and

maximum blade thickness for other sections are selected such that smaller variation at the top half of the blade and larger variation at the lower half of the blade is attained. Blade thickness

f8

at hub is selected based on the strength requirements and at periphery as low

value as possible to avoid undue vibration as well as facility to cast in foundry. However, the danger of cavitation is more at the periphery, especially very near to axial clearance between impeller and casing. If the blade thickness is reduced to low, the forces on the profile and cavitation increase steeply to a maximum and steeply decrease on both sides of the blade. If the blade thickness is increased, the suction effect (h s ) reduces for a narrow range of angle of attack. If it is decreased, suction effect reduces for a wide range of angle of attack. That's why, the blade thickness must be properly selected. (x) All profiles of different sections are linked in such a way that their centre of gravity is in a

radial line and passes through the axis ofthe rod connecting the blade and turning mechanism. This point will be mostly the centre point of maximum thickness and is usually at O.4l to 0.5l depending upon the profile.

291

AXIAL FLOW PUMP

Force calculations, detennination of Cy and selection of profile are carried out by the following method: Axial velocity, Cm = 0.74 ~2gH or C m = (0.25 ± 0.05) the selected radius. Tangential velocity, C

U2

(0

Ri' 0.25 is for periphery and Riis

=gHm ,H =: and =0.85 to 0.87. m

U

1Jh

'Ih

Pressure difference between the blade inlet and outlet is given as fih

=

C2

P2-Pl =H- ~ andH = H .

Y

•

2g

•

11.

m

fiR fir

=

Axial component of the total hydrodynamic force will be __z

(P2 - Pl)(2nR), where R.

••

is the radius of the streamline selected. Tangential force acting on the blade is

Resultant force, ... (10.33)

The geometrical average relative velocity, w = is

Cm sin 13= The deviation angle, A,

=

(8 -

13=).

Nonnal force acting on the blade is dY =

cos A, --- (H"I; h, f4

(xi) The mean line of the profile is an arc of a circle. The radius of this arc

R

[21m

=

-+81m

... (10.34)

2

(xii) The radial clearance is 0.001 Di (should be 0.1 to 0.15 and should not exceed 0.25 rom). (xiii) Distance between blade outlet and diffuser blade inlet is 0.15 Dr

Diffuser Calculations (i) Absolute angle u 2, tangential component of absolute velocity Cu2' thickness coefficient K2 and meridional velocity C at the outlet of the impeller are known, from which the inlet m2 conditions of the diffuser can be determined. Taking C = K 2 C in order to account for m2

profile thickness of diffuser blade, and since, C

U3

(ii) In order to get complete conversion of C

~

=

C ,tan u 3 U2

m3

C

~

=

C

into pressure, the value

U3

(~) is always selected t

[

as - > 1.5. t

(iii) From the experimental analysis, I 131 I it has been established that an additional angle (L1) must be added over and above 90° for the diffuser blade angle at oulet in order to make the flow tangential to the mean line and the flow can be purely axial at the outlet of the diffuser. Table (10.1) gives the value of (L1) for the selected lit value. TABLE 10.1 [

-

0.7

1.0

1.5

2.0

2.5

3.0

L1 0

20.5

19.5

16.9

11.5

12.5

10.5

t

(iv) The mean line ofthe profile is an arc of a circle. (v) The blade curvature

~m

and vane solidity

~

are selected to get proper angle of divergence

2£ for the flow passage between two diffuser blades and also to get constant axial velocity at all sections between inlet and outlet as well as desired velocity distribution of C along m3

the radius before and after the diffuser. About 2£ = 6° at periphery and 8° at hub are recommended which provide constant height (lI) along the meridional plane. Further, the curvature

~m

should be selected so as to get sufficient value of Cy under non-separated

flow condition.

295

AXIAL FLOW PUMP

(vi) Selection of number of diffuser blades is normally (Zi + 1), where Zi is the number of impeller blades. However, number of diffuser blades should be selected such that the inlet l

l

flow passage is a square. The - for diffuser is determined as t

t

=

1- sina3 2 . Length ofthe tan £

blade M

I

... (10.35)

2

firZC y WI

2g

From the known coefficient of lift (C), the profile and its characteristics can be obtained. From the profile characteristics, the pressure P min can be found out. An approximate value of C y is 1.65 Pmin. The distance between impeller outlet edge and diffuser inlet edge is recommended as 0.15Di, where Di is the impeller diameter. Angle subtended by the diffuser blade in plan is found to increase 1.6 times at periphery and 2 times at hub than that of impeller blade for ns = 450 to 750.

10.10 FLOW WITH ANGLE OF ATTACK Indirect method suggested by Prof. Lisohen I 65 I , inspite of complicated and tedious process, gives a very good agreement between theory and experiment. Hence, this method is used only when there is an absolute necessity to improve cavitational characteristics of pumps for which entire process has to be repeated again with corrections applied to the velocity distribution and the shape of the profile already available from I set of calculation. The direct method suggested as per lift method as well as by Prof N. E. Voznisenski and Prof. Pekin gives a flow on thin profile for shockless entry without any angle of attack [v(O) = 0]. For a flow with angle of attack these processes do not give good results especially for cavitational characteristics. For axial flow pumps, Ux = up Zx = ZI h!(1-x) = o. Px

y

=.!i+

wI2 _wx2

2g

y

2

Then,

Pmin

y

=.!i+

WI

y

2

-W max

2g

Circulation r for a flow over a cylinder can be written as r = 4naV= sin a, where a is the radius of cylinder, a is the angle of attack i.e., angle between the direction ofthe velocity vector V= and the horizontal line passing through the centre of the cylinder which is the profile or cascade axis (= direction of blade velocity 'u'), V= is the infinite velocity or undisturbed velocity before and after the blade. The above equation can be written for a curved plate as r* = nlw = sin a, where I = 4a, the chord length of the profile, w~ is the new infinite velocity of flowing fluid before and after the blade with an angle of attack a. Normally a is very small « ±5°), so sin a'" a and hence, r*= nlw ~a. Taking L as the ratio of circulation of profile in cascade to isolated profile

r;

=

Ln lw~a

... (10.36)

296

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Value of 'L' can be found from the graph (Fig 10.8). Referring to the combined velocity triangle, (Fig. 10.5),13= is the angle of flow over profile for no circulation. With 'a' as the angle of attack, the flow will be at an angle l3' = = (13= + a). The new w' = and w~= are reduced, since blade velocity u and meridional velocity Cmremain same. The procedure for the calculation of flow over a thin profile with angle of attack is as follows: Circulation rb for a flow with angle of attack 'a' can be written as

rb

2ngHm =

-----'-"-

11h zO)

... (10.37a)

K~. ~~

~:

Fig. 10.38. Velocity triangle for a flow with angle of attack

For the selected value of angle of attack a s ±5°, circulation r* with angle of attack is r* = Lnlw~a ... (10.37b) Values 13~ and w~ are determined from the combined velocity triangle. Value L is determined from the graph (Fig. 10.8) for the given value of a. Hence, circulation r without any angle of attack is ... (10.38) r = rb -r* Geometrical average velocity from the velocity triangle (Fig. 10.38) w' = = w =cos a. Geometrical average angle 13= for a flow without angle of attack is ... (10.39) 13= = 13~ - a From the known values of w =' rand 13=, lift method or Prof. Voznisenski's method can be applied for design of axial flow pump.

10.11 CORRECTION IN PROFILE CURVATURE DUE TO THE CHANGE FROM THIN TO THICK PROFILE Methods suggested in lift method and by Prof. Voznisenski for the design of axial flow pumps, give a thin profile in the form of an arc of circle. In real practice, blade system has thick profiles with definite thickness instead of thin profile which is called camberline in profiles. Due to this additional thickness, flow area in between two blades in the cascade system reduces, which results in change in relative velocity from inlet edge to the outlet edge of the profile. Flow velocity and the quantity of flow also change. Correction factors are applied on blade curvature ofthe thin profile, designed by lift method or Prof. Voznisenski's method, in order to overcome this drawback, and the performance of pump remains unaltered.

297

AXIAL FLOW PUMP

Blade thickness is always selected based on the strength and durability of hub section of impeller blade, where the thickness is higher and based on technology in manufacture for the peripheral section of impeller as well as for the diffusers, where the thickness is small. Prof. S. M. Beelosirkovski, Prof. A. C. Genevski, Prof. Polovski, Prof. E. L. Bloch I 9, 105 I developed method to overcome the drawback of change in performance due to the dressing of thin camberline with thick profiles. This work was reworked by Prof. A.N. Papir I 85, 86, 87, 105 I by the following procedure: Profiles in cascade system consist of: (i) diverging passage type used in mixed and axial flow pumps, where the relative and meridional flow velocities reduce from inlet to outlet and another and (ii) converging passage type used in mixed and axial flow turbines, where the relative and meridional flow velocities increase from inlet to outlet. Apart from that, hydrodynamic machines are classified as: (i) machines with high aspect ratio (lIt> 1.2 to 1.4) and (ii) machines with low aspect ratio (lit < 0.5 to 0.7). In high aspect ratio machines, fluid velocity on the blade is practically independent of the changes in fluid velocity before the blade system. The direction of fluid velocity is practically same as the blade angle at outlet, whatever may be the circulation. In low aspect ratio machines, the fluid velocity on the blade depends upon the fluid velocity before the blade system i.e., depends upon the circulation around the profile or the load on the blade 1105 I. This means that in high aspect ratio profile system, the fluid velocity direction at outlet is independent of change in angle of attack and lift of the profile, where in low aspect ratio units, it mostly depends upon the angle of attack and lift. Based on the above factors, the influence of profile dressing on a thin camberline on pump performance is found to be a function of two factors: (1) The change in the interactive force of thick profile, when compared to that ofthin profile, under ideal fluid flow conditions and (2) Effect of viscosity on velocity distribution along the profile. Prof. A. N. Papir has developed an expression

i f U' J =

B2

which is given in a graphical form (Fig. 10.39). A short description is given below.

Outlet blade angle of thin profile under real fluid flow condition is given as cot B2

=

... (10.40)

A cot Bl + B

where, Bl and B2 are the inlet and outlet flow angles measured with respect to the blade velocity' u' and A and B are constants and are a function of geometrical parameters and lift in a cascade system.

A=

and

B

1l l---C. 4 t yz cos

A 1-'0

1l 1 + - - C yi cos Bo 4t

Il C . A -2 t yz·sml-'o

= ---=::....::.....,-----

1l

1+--CyicosBo 4t

... (10.41)

... (10.42)

I\) (() (Xl

0,55

~Tr

II

0,45

f>

0,40

,,~ /",

0,35

~/ /

0,20

V ./" . / ,........ ,........

0,15 0,10

Lla= 10' +=10

Lla=20' { Lla= 30'

10

~~~

-V ... :::-: ~ -"

~ ~V

--

...........:: ~

..'-:: ~

~

~~

~~

J -1

./

V V ~ ~V /~ ~

---

L/~

, ",

~

V'

"

.,../

0,05

60

/

/ /' r

0,25

I

"

f

/

/

0,30

50

I

i

Om

4°

,,

I

0,50

,

~V

70

80

60

:0

a' 2 40

50

20

30 I t

~

---

O ,10

I

I I = ° 5" Lla = 2O'

t

"

I - ° 5" Lla - 25'

t

"

1°,15 -1°,20

01,5;Lla

10 1O'

o --I o o -< z

» ~

o "U

C

~

"U (f)

om z

--I :0 ""Tl

C G)

Af

Fig. 10.39. ~

m

=f

(

(1.2'

t~)

» r » z to find the increase in profile curvature to take care of profile thickness

o

» x 5>

.s

299

AXIAL FLOW PUMP

130 is the flow angle under zero circulation n

130 ="2- a

13

+"2

C yi is the coefficient of lift under angle of attack i

=

0

The coefficients A and B for a thick profile will be different and can be obtained by an approximate formula

A =A+a

l) dm (-

... (10.43)

t t l

... (10.44)

and

~

Functions a ( ) and b (

~,a, ~ )

account for the thickness of profile

8~ = 8

m,

relative thickness

ratio which determines approximately the change in circulation in thick profile with respect to the circulation in thin profile. The result of Prof. Papir's analysis is given in graphical form (Fig. 10.39), with 8 2 = ~ -132 (132 is 2 the outlet blade angle) where 8 2 is designated as indirect blade angle in x-axis and t:.! in y-axis, where c

1m

=

1m l

is relative blade curvature of the camberline (thin profile) and

thickness. The function

i

=

~ = d m relative maximum l

~ tan %.In the graph, +ve direction is for pumps and -ve direction is for

turbines. From the graph, it is evident that for high aspect ratio lit> 1.2 to 1.4, correction factor

b.f c

is

independent of angle of attack i. e., not depending upon the angle of direction t:.13 but depends upon only the flow direction at outlet, whereas for low aspect ratio

(~< 0.5 to 0.7 ) the correction factor

t:.{ is

practically independent of outlet flow direction but mostly depends upon the angle of deviation t:.13 i.e., depends upon lift force and angle of attack. For turbine cascade system the dependence with t:.13 starts earlier than for pump cascade system i.e., already when lit = 1.

10.12 EFFECT OF VISCOSITY The result of viscous effect on flow is the development of boundary layer at the surface. Under non-separated flow condition the real fluid flow is on the surface of the thick profile instead of on the

300

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

surface ofthin profile. Nonnally, at inlet, the profile thickness is always more at the convex surface of the profile than at the concave side. As a result, the deviation in flow direction of viscous fluid, when compared to the flow direction of ideal fluid, will be always with lesser angle of curvature i. e., L113 is less in the cascade. Circulation in real fluid will be less than that in ideal fluid. This deviation will be larger in pump, (i.e., divergent flow) than that in turbines (i.e., convergent flow). As a result, boundary layer thickness at the convex surface will be higher in pumps than in turbines. Effect of viscosity and subsequent reduction in hydraulic efficiency can be accurately calculated from the boundary layer thickness in profile 1 32, 64, 78 I. With sufficient accuracy, the effect of viscosity on circulation can be taken as: 18, 16 I.

Kr

=

rr

=

0.86 to 0.93

th

take

Kr increases when lit increases, for pumps Kr '" 0.9 and for turbines Kr '" 0.95. It is essential to 1.1 r, where r is the circulation actual calculated as per equation (10.7).

r th =

10.13 SELECTION OF IMPELLER DIAMETER AND SPEED Flow velocity at suction eye under optimum condition is given as

For axial flow pump,

(0.06 to 0.08) as ~Qn2

Co

=

C

C

-

--::---=-'=::--

m -

mo

=

4Q

... (4.24) ... (10.45)

rrD2(1-d 2)

where, -;[ = ~ , dh is the hub diameter. Combining the above two equations and rearranging D

Q

n

=

-2 3/2

(0.06 to 0.08) 4(1- d)

nD3

... (10.46)

where, n is speed in rpm. Using non-dimensional parameter KQ = ~ (where n is in rps) in the above nD3 equation, we have

KQ

=

60 (0.06 to 0.08) ~ [

(1- -;[2) ]

3/2

... (10.47)

Taking an average of 0.066 for the coefficient, which is practically used for all pumps, KQ=

For axial flow pumps hub ratio condition, KQ

=

0.4 to 0.5.

0.7 (1- (p) 3/2

d = 0.4 to 0.6.

KQ is 0.32 to 0.54. Under maximum efficiency

301

AXIAL FLOW PUMP

Mostly, speed is detennined for better cavitational characteristics for which cavitational specific speed (C) is used as

c=

... (10.48)

Expressing C in tenns of K Q , we get

60~KQn3D3 C=

(~; f4

or

Constant

... (10.49)

C, K Q, Hsv are very nearly constant for pumps. Nonnal values of C = 1000,

Hsv 10 =

1 KQ = 0.45

for most of the pumps and KQ = 0.6 for very high specific speed pumps, nD '" 8.4 for nonnal units, nD '" 7.3 for very high specific speed units (n is in rev/s). Correspondingly, uperi (= rrDn) = 26 to

27 mls and '" 33 if C is higher and, uperi

=

23 mls for very high specific speed units.

10.14 SELECTION OF HUB RATIO Free vortex design is adopted while designing axial flow pumps. Circulation and total head developed at all radii are constant, i.e., CU r = constant. For potential flow and for nonnal entry, CUj = O. Blade curvature (13) and geometric average blade angle (13=) increase from periphery to hub. Blade becomes a twisted blade with more twist at hub angle 13= at hub and less at periphery. Karl pfliderer 1971 has suggested that outlet should not exceed 90°. Based on this, he gave an expression

UL-GL ~ (I;~~r t"~O" (;;5 J

... (10.50)

where, p is the head correction coefficient due to finite number of blades in impeller and 130a is the inlet blade angle at hub section. However, based on the experimental results on a number of axial flow pumps, Prof. Papir 184 1has developed an expression for hub ratio selection, which is given below: Specific speed,

n

3.65n(rpm)J(j s

=

H3/4

219n(rps)J(j =

H3/4

rr Flow rate through impeller, Q ="4 D2(1 - d 2) Cm. From velocity triangle, flow velocity Cm = ( U

C ---t u

)

ndhn

nd h

n

-

tg13=· Blade velocity at hub section, uh=~=D D 60 = nDnd (n in rps).

302

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Tangential velocity C at hub, C U2

h=

U2

_ 2:

. Combining all the above equations, flow rate

gH md llhnDn

3

-2

Q - 4 D n (1- d) Substituting the value of unit head, KH

=

(d _

gHm ) 21lh n 2n 2D2d tg13=

n~~2

and unit discharge, KQ

=

n;3

in the above

equation K

n2(1 -

=

-

Q

4

-2)(-

d

d -

gKH)

21lh n 2 d

tg13

... (10.51)

=

Substituting this in specific speed equation, we get

n

219n 2

... (10.52)

=-s

A graph KH = fens) (Fig. 10.40) is drawn based on the test results of different specific speeds (ns = 450 to 1600) having ll max ;:::: 85% taken from universal characteristics. The values KQ ranges from 0.4 to 0.6 in these pumps. However, KQ is taken as constant and = 0.5 for all pumps and 13= for hub is taken as 38°, although it ranges from 35° to 40°. These values are substituted in equation (10.51) and a graph dh = fens) is drawn (Fig. 10.41). Experimental results are also indicated in this graph. Dotted line indicates the recommendation given by K. pfliderer 1 97 I. Figure 10.42 gives the combination of above two graphs (Figs. 10.40 and 10.41). It gives a relation t

dh =

f(KH)opt.

"

'\\

\ 0,1

"- '\.

" ~

o

500

1000

......

.............

1500 (ns)opt

303

AXIAL FLOW PUMP

\

..

,

1\

0.8

\.

0.7

0.6

~ ~

\..

~

,

0.5

" r'-. ~

0.4 -

-

=(~)

.......

......... 1'"

as perl eqn.10.45

0.3

•

...... t'-..

min

....

r--...

...... r-....

...

1""-

-

-r- -r- --

I"- ......

~

0.2 0.1 200

400

600

800

1000

1200 1400

1600

~

o

0,6

2000

2200

-- - -. I-'

f.-

0,5

0,4 0,3

1800

......

...... " " ..

0,05

....

"...tJ

,.. .... f.-i""'"

-

--

0,10

~

2400

2600 2800

3000 (nJo

_f-'" ~

_.

P -

0,15

- - as per equation - - - - as per Ptliderer

10.15 SELECTION OF

(~leri-ASPECT RATIO AT PERIPHERY

A major part of losses occur in impeller due to high velocity of flow and the divergent passage. Profile loss is the sum of frictional losses and losses in divergent passage. Aspect ratio plays a very important role. Frictional losses increase when (lit) ratio increases but loss due divergence decreases. It is

304

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

necessary to find optimum value of (lIt) for which the sum of these two losses are minimum. Based on equation (10.1), we can write for a divergent passage as

w

U2

zr

-w

= -- =

2nr

Uj

r

... (10.53)

-

Bernoulli's equation for real fluid flow through impeller passage will be

L1n 'Y

p

2 (p j -p2 ) + -2 (wUj

=

w 2U2 )

-

=

yh f

... (10.54)

where, h is the combined losses in impeller passage. f

For constant head at all radii in impeller passage under optimum condition, we have

r

2ngH llh wZ

=

=

gt(H +hf )

... (10.55)

u

Since, H = Hm llh = (H + hf) llh From the cascade analysis, the force due to losses i.e., drag force 'X' will be

X

=

t sin

13= and L1p =

13=

yt hfsin

... (10.56)

and lift will be 2

Using coefficients X= Cx p

w;

w,:

l

and

2

I, Y = Cy P

w; l

I = p w=

r

w:,

w = w sin A h = C . = C --z = P=, f x t 2g sm~= x t 2gw z

C

and

=

y

:. For normal entry,

2r lw=

=

2(CU2 -Cu )

2Cu

w=(lIt)

w= (lit)

2gH

... (10.57)

CUj =0 L1CU = CU2 - C Uj = CU2 = CU hf w~ h =-=C f H x t 2gHwz

---=---

... (10.58)

Equation (10.58) shows that losses are the function of aspect ratio lit and the relative velocity The geometrical average relative velocity w = will be maximum at periphery. Hence, major percentage of losses in impeller of axial flow pump occurs at periphery of the impeller passage.

w 3=.

Losses in impeller consist of profile losses arising due to friction in impeller passages and subsequent wake formation at the outlet ofthe impeller cascade system and non-profile or secondary losses arising out of secondary flow in impeller passage due to pressure difference between leading side and trailing side of blades as well as due to clearance between casing and impeller blades. Since, flow in impeller passage is under fully developed turbulent region, where '/' is independent of Reynold's number, the losses depend upon Cy and CX' a relation between C x and Cy can be written as

Cy

=

a C 2x + bCx + C

... (10.59)

305

AXIAL FLOW PUMP

where a, b, c are constants, depend upon the geometry of blade system. Substituting the values of Cy and Cx from equation (10.12) and rearranging

h

=

I

_1_ wm

(a 2gHw= .!-+b Cuw,; llhu2 l gH

Using non-dimensional coefficient, KQ

w~

=

+C

w~ .~)

n;3 and KH

+-';) co:~~ ~

nD

... (10.60)

2gH t

=

n~2

(E- ~~:~ ) co:~~

... (10.61)

Substituting these values in equation (10.59)

h

I

-

4KQ

... (10.62)

In axial flow pumps, KQ is mostly constant for all ns values. Taking, KQ = constant

hI = f ( ~,KH ).

Differentiating equation (10.62) up to first approximation with respect KH and equating it to zero, we get

2gKlt

Taking,

L

~os3~=(n-~:~J(n+~:~)GJ

=0

... (10.63)

n -gKH -2mh gKH

M= n + - 1ITlh gKH

N= n - - 1ITlh S

g 2COS2~ = K2 H 2 1l~ n LM

T=

2 3 4g KJ cos ~=N a C 1l~ n 2L2M

b

C

... (10.64)

306

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Equation (10.63) can be written as

(~)

=

-

2

+ -JS +T

S

... (10.65)

opt I

Differentiating equation (10.63) up to second approximation and equating it to zero, we get

(tl)

2cos~= opt II =

(1(211h) _!

ra

... (10.66)

v-;:

2

gKH

Equations (10.65 and 10.66) are more or less found to be same. From the test results of pumps having 11 > 85% it is found

a

-

b

=

c

8.15 and -

= -

c

From fundamental equations u

=

15

1( Dn, where n is the speed in rps, we have gH

gnD

21( D n 11h

2 1( 11h

-~--=--K

tan

13

= =

C

__ z-

=

H

4KQ

----=----

... (10.67a)

gKH ) 1( I-dh2) (1(---

u u -C2

(

21( 11h

The value KQ for axial flow pumps ranges from 0.4 to 0.6. Hydraulic efficiency, (11h) is more or less constant for all pumps ('" 90%). Substituting these values in equation (1O.67a), to 34°, taking

13=

proportional to

(KH)opt

13= changes from 14° to 18°. At higher values 24°

constant for all ranges of KQ and K H , equation (10.66) leads to

(~)

opt

directly

i.e., a straight line variation. Practically, for each value of K H , there exists a

range of 13=, but this variation is negligible. A

relatiOn(~)

= !(KH)opt

is drawn in Fig. 10.43. Possible

opt

variations in angle

13= is also indicated with dotted line in this figure. It is seen that this graph coincides

with the values of lit of tested pumps.

(~) t

characteristics.

opt

can be selected from this graph to get better cavitational

307

AXIAL FLOW PUMP

Ht

ri

1,4 '/

~;

;

1,2

".

l..- t/"; ,~ V ...

1,0

%;

;

0,8

.~ ,;.-:;

..... ~ k;: ~

0,6

'l ~

..,

.~ ~

0,4 .;~

0,2

~

~

~

0.05

0.10

Fig. 10.43.

(nperi

0.15

f(KH )oPt' fl= at TJ max condition

Professor Wislicenus 133 has recommended the selection of vane, solidity 1

1

(~) as

Z r2 - - log ... (1O.67b) 2sin~= 'i Prof. A.J. Stepanoff 11121 has given a chart for the selection of hub ratio, aspect ratio and number of blades as a function of specific speed (ns) (Fig. 10.44). l

Hub ratio

1,1 1,0 0,9

l\~~~Mt-' ~~" o~~ \.

0,8

s

OJ

c

\. \

1\ \

0,7

\.'00'

\', _

I\.

\.

" r\ \

\

0,6

OJ

c

co

>

\ 0,5

5

0,4

495

T\'i- \

,I\.

'~~

'\.

I\.

~

~ ~t--r-

~ ~ 5 x 10 6

=

1.25; b = 4.8 if Re < 5 x 10 6

=

6.5;

=

Combining (10.90) and (10.91), we get **

R **

=w8 --

vG

V

e

Taking,

a

G1

=

G1

=

fs w

(b-1)

iV(b-2)

ds

... (10.92)

o

G R** e

... (10.93) S

~b

2)

viV -

f

w(b-1)

ds

... (10.94)

0

The expression for 8** can be obtained depending upon G 1 for each region of flow. (I) Laminar region: For laminar flow as per Prof. Loisanski I 67 I

G=R** e and hence,

... (10.95)

The above equation has been rewritten substituting its values to suit the present works I 105, 106 I

"8**

R** el

where,

-

=

f

Sz

0.44

[

-5.8 WI

-

WI

Rei

-4.8

W

-

dS

... (10.96)

0

"8** R el 1

... (10.97)

R:; is the Reynold's number based on 8;* at the end of laminar region.

(il) Transition region: Zincin and Mologen 1142 I has detennined a relation for G as

Correspondingly

G

=

1259 (R;*)-(lIlO)

8**

=

~

G _1_

w [ 1259

... (10.98)

](10/9)

... (10.99)

321

AXIAL FLOW PUMP

The above expression is transfonned into a convenient fonn for the present work as 1105, 106 1

-

{o.9 Sz w dS + C } Sft

=

Rei

[ 1259 Wtr 45

](10/9)

55

... (10.100)

tr

where, Ctr' the constant of integration, is detennined from the parameters at the end oflaminar region as per the condition 10.79 C

tr

=

_ G tr -

and

"8** G I tr

-55

WI

(

1259

... (10.101)

**)(-1110) Rei

... (10.102)

The value of "8;; will be ... (10.103)

"8;; If the flow starts from transition region directly, Ctr = O. (iir) Turbulent region: For turbulent region, Prof. Loisanski 67 For Re< 5 x 10 6 1

G

8**

and

=

1

suggested that

79.5 (R;*t4

v

G

1 =-W

... (10.104)

](4/5)

... (10.105)

[ 79.5

If Re > 5 x 10 6 , we have

and

G

=

153.2 (R!*)1I6

... (10.106)

8**

=

~ [~](617)

... (10.107)

153.2

W

Above expressions are rewritten to suit the present work: 1 105, 106 1 For

Re

>5

x

106 , Re**

=

R [ 8,u=1 38 79 5 -e1 2.8 1.25 _ w d

f

. wtu

Str

4/5

S + ctu ]

... (10.108)

where, C tu is the constant of integration, and is detennined from the condition [equation (10.85)] and calculated from the conditions at the end of transition region as

and

Ctu -- w· -38S:**G 0tr tr

... (10.109)

Gtu

... (10.110)

- **

8tu

=

=

79.5 (R**) 114 etr R** etu R Wei

tu

... (10.111)

322

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

m+ 1

0.9

0.8

Hp' M= Hsy- Hp> O. Pump supplies quantity at a lower pressure (Hp), whereas the system is at a higher pressure (Hsy). Pump cannot supply flow against high pressure ofthe system. The flow gradually reduces until pump pressure (Hp) is equal to system pressure (Hsy). Same situation occurs when flow is reduced by a small amount i.e., (- L1QA)' Now, Hp > Hsy' L1H= Hsy- Hp < O. Pump supplies water at a higher pressure than the system pressure. This difference in pressure causes an increase in quantity. This increase in quantity reduces the pump pressure (Hp) and increases the system pressure (Hsy), until both the pressures are equal i.e., until point A is attained. Entire process is automatically carried out. Pump can operate only at point A where the condition is Hp = H sy' Hence, point A is a stable operating point.

(b) Unstable Operation Normal head-discharge curve for a centrifugal pump will have a shape of gradually rising characteristics, when quantity of flow is reduced from maximum to zero flow condition (Fig. 11.20). In some of the pumps due to heavy secondary losses at very flow rates, head-discharge curve of the pump droops down instead of raising after attaining maximum head at certain quantity (point K) Fig. 11.20.

354

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Always shut off head (Q = 0) will be the highest head in (Hp- Q) curve for all pumps of good design. But due to high secondary flow at low flow rate, (Hp- Q) curve droops down and the shut off head will be lower than the normal value. In Fig. 11.20, point B is the meeting point of the (Hsy- Q) and (Hp- Q) curves. A small increase in quantity ( + Li Q B) moves the operating pointto the right hand side ofthe graph (+ Q direction). At this stage, system pressure H sy is lower than the pump pressure (Hp), LiH = H sy- Hp < 0 (negative value) as a result pump supplies more quantity to the system, which makes the point to move further to the right hand side (+ Q direction). Point B cannot be reached at all. Pump supplies more and more quantity to the systems until point A in attained. If the quantity is slightly reduced (-LiQ B)' it can be seen that pump pressure (Hp) is lower than system pressure (Hsy).

LiH

H sy -Hp >

=

Unstable

o.

Stable

H

llH llH

= =

Hsy - Hp< 0 Hsy - Hp > 0

o

II

Q

Fig. 11.22. Stable and unstable operations in pumping system

The quantity of flow is reduced further until pump reaches the point (Q = 0). At this stage pump runs with regulating valve in opened condition, but there will not be any flow in the system. Here again point B cannot be reached. Point B is the unstable point. This region is called unstable region curve OBK in Fig. 11.20. This unstable effect will exist in all pumps if (Hp-Q) curve droops down at lower flow rates. The pump should not be operated in this region. However, pumps can be operated at stable condition even when drooping down characteristics prevails at low flow rates. In Fig. 11.19, the shut off head of pump (at Q = 0) is lower than the shut off head of the system. In Fig. 11.23 pump shut off head is at a higher level than system shut off head. System curve and pump curve meet at point B, which is located at

H

I

o

0

I

v

Fig. 11.23. Condition for stable operation at unstable region Ho > HSYO

355

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

unstable region of pump characteristics. The condition of point B in Fig. 11.24 is same as the condition of point A in Fig. 11.20. Any small increase in + fiQB increases Hsy and decreases Hp i.e., /1H= Hsy - Hp > o (+ve). Due to higher resistance in system, quantity reduces. This reduction continues until point B is reached. Any small decrease in flow rate (-fiQB ) makes Hp > H sy or fiH = H sy - Hp < O. Higher pressure in pump increases the flow to the system until point B is reached. Therefore, point B is a stable point although it lies on the drooping down side of pump characteristics. Mathematically, stable condition will ..

dHsy

H (Curve OS)

C

I

o

Q

dH p

Fig. 11.24. Condition for stable operation in eXIst If - - > - - . dQ dQ unstable region An example of this condition is illustrated in Fig. 11.25.

Fig. 11.25. Change of unstable operation into stable operation due to (a) static head change and (b) due to system resistance change

Referring to Fig. 11.25, point '1' is the stable operating point of the system. When delivery tank water level raises, the operating point, due to static head, change to point '2' and '2". Point '2' is the stable operating point, whereas point ' 2' , is the unstable operating point. This unstable region starts from point '5' and above. Maximum height of water level in the tank can be up to point 'K'. Further increase in water level leads to reverse flow (Refer section 11.7).

11.7 REVERSE FLOW IN PUMP

S

-Q

Q

Fig. 11.26. Reverse flow in pump

356

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

In Fig. 11.26 a pumping system is illustrated wherein the systems i. e., suction and delivery pipes, remain same. A closed delivery tank (condenser, accumulator) is attached to the system. Quantity Qp enters the tank from pump, whereas quantity Q1leaves the tank to another system. Quantities Qp and Q 1 are independent of each other. If Qp > Q l' water level in the tank gradually raises. Correspondingly, pressure P2 also increases. Since system remains same, the pattern of dynamic part of system curve remains same, whatever be the quantity Q2' increase in pressure P2 and raise in level Z2 in the tank. Change is only in the static head i.e., 2

H

=

.IJ!

where, H

st

=

P2 - PI

Y

2

P2 - PI + (Z _ Z ) + C2 - C1 = H + H Y 2 1 2g st dy

+(Z2 -Zl) and H dy =

2 C 2 -C12

2

g Due to this, (H.IJ! -Q) curve raises parallel to the previous (H.IJ! -Q) curve (Figs. 11.21 and 11.26). Point A moves towards left and point B towards right along (Hp -Q) curve. Still QA > QB. However, at one condition, the increase in static head makes (H.IJ!-Q) curve to be tangent to (Hp-Q) curve at point K (Fig. 11.26). Any further increase in pressure P2 or level Z2 raises (H.IJ!-Q) curve above (Hp-Q) curve. Operating point K moves to point R, where only further increase in Hsy is possible, i.e., to the area of reversible flow. Flow moves from the tank to the pipe. This induces a reversible water wave. Pressure P2 reduces. Operating point R moves to point N Because flow reduction is possible only along the curve R.N, any further reduction in pressure moves the operating point from N to A and then gradually to S, because only at point A, further reduction in pressure is possible. Thus, a cycle is completed. This cycle repeats so long as there is no change in the system. Pressure fluctuates at a faster rate. Ifthe flow fluctuation is large, the unstable condition starts even earlier when operating point is at A. Even a small disturbance in pressure can induce unstable condition, if operating point is very near to point K. Reverse flow prevails until Hst = Ho (at Q = 0) i.e., shut off head. When Hst < H o' pump starts pumping with operating point at A or below point A under stable condition. When QA < QK' stable operation of the pump is not possible. dHsy dH p dQ < dQ from Q

=

0 to Q

=

QK· Hence unsteady flow prevails between these two points.

Quantity 'Q' passing through the system will be either Q = 0 or Q = QK" At this region, reverse flow takes place. Drooping down characteristics at low flow rate is the unstable region so long Hst > Ho. It becomes stable when Hst < H o' and stable operations starts from the condition Hst < Ho to the condition Hst = Ho. The same thing will happen even if pumps are running in parallel or in series. The only difference is that combined characteristics must be studied. However, a raising characteristics of H-Q curve from Qmax to Qo i.e., up to shut off head is the best H-Q curve for stable operation. Such pressure fluctuations quite frequently occurs in boiler feed water storage drums, condensers, accumulators and in pipes with elastic properties. This effect is more predominant in pumping compressible fluids such as gas and air especially pumping to storage cylinders.

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

357

A series of sudden and high intensity fluctuations can create oscillations in the system. Constant fluctuations of low intensity quite frequently appears in the delivery line. Disturbances created by aerodynamic wake after the impeller blades flow over volute tongue, flow over diffuser blades, uneven angular velocity of the rotor (in case of gas and air pumping) are a few instances of creation of disturbances. If the frequency of the disturbance does not coincide with the frequency of the system, the amplitude of such oscillations gives a very low effect on performance even when the pump works near maximum head point (10 and under stable condition. Ifthe disturbance frequency is very nearly or exactly equal to system frequency, resonance effect is created and the pump will work in the unstable operation, even when pump is working far away (point A) from maximum head point K. The frequency of operation of the system depends on dimensions of the delivery pipe and does not depend upon the speed of rotation. A reduction in accumulator energy increases the frequency of oscillation which inturn increases the amplitude of pressure fluctuations. The energy waves developed due to pressure fluctuations, either direct or indirect, combined together, can create high intensity shock waves. However, increase in frequency of the amplitude of fluctuations increases a self breaking effect. A change in quantity of flow is created by the change in circulation, provided sufficient time is available. When total, combined self oscillating frequency of the system is reduced or in other words, when oscillating frequency increases, circulation time almost reaches the condition for one cycle of oscillation. This almost stops further increase in the amplitude of the oscillation, with the result, energy is dissipated under low accumulator energy. Circulation is inversely proportional to speed or tangential velocity of the blade. As a result, any pump working in the unstable region, when speed is reduced up to certain limit, will work in stable condition at all flow rates. The limited speed will be higher where system conditions are low. Boiler feed pumps, compressors working under high speed have a very little time to adjust, will undergo unstable operation even when accumulator energy is small. Stable operation in boiler feed pumps can be obtained by having continuous raising characteristics from full open to full close i.e., without any drooping down characteristics at partial flow. Experimental investigation shows that reduction in number of impeller blades and low outlet blade angle 132 will provide a stable raising pump (H-Q) curve. Better results are also found when the impeller blades are extended into impeller eye at suction i.e., increasing length of the blade at suction side (Fig. 9.10). High specific speed pumps have raising characteristics. Diverting part of fluid from delivery line to suction line is also one of the reasons for unstable operation for pump.

11.8 PUMP REGULATION The process of changing the characteristics of system and that of pump to meet the output demand is called regulation of pumps. By this, the operating point of (Hsy-Q) and (Hp -Q) curves will meet the required output head and discharge. Regulation is done by several methods namely (1) By valve control system; (2) By transfer line control system; (3) By speed control ofthe pump; (4) By diameter control ofthe impeller ofthe pump; (5) By impeller and diffuser blade adjustments and (6) By changing the static height in suction and delivery tanks.

358

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

11.8.1. Regulation by Delivery Valve Control This method is simple, but with heavy hydraulic losses in the control valve. Regulation is done by a regulating valve fitted at the delivery pipe. Figure 11.27 shows the performance by delivery valve regulation process. By adjusting the valve, either closing or opening, the (Hsy-Q) curve changes (curves CA ,CA ,CA ). Each curve is for one position of gate valve opening. Xl x x3 2

Fig. 11.27. Regulation by delivery control valve

Due to the adjustment in valve, the system resistance is changed by which the operating point moves either upwards or downwards along the (Hp -Q) curve. Hydraulic losses are higher due to obstruction created by the valve and pump efficiency reduces considerably. However, due to simplicity, this regulation is widely used. Flow regulation by suction valve, although possible, is not carried out for incompressible fluids like water, oil, etc. due cavitation problem, since regulation of suction valve increases total suction head. However, for compressible fluid, suction valve control is carried out since density increases due to fall in pressure, which reduces the flow quantity. Moreover, unstable condition area moves toward left hand side of H-Q curve, more for air and less for gas. Figure 11.28 illustrates the graph for valve regulation by suction control valve and by delivery valve control. In Fig. (11.27), A is the operating point when the delivery control valve is at full open condition. Points A Xl ,A x2 ,A X3 are the operating points when control valve is gradually closed. Dotted lines

corresponds to the (Hsy-Q) curves for different opening positions of the suction valve.

11.8.2. Regulation by Transfer Line Method In low specific speed pumps, the power of the pump reduces when control valve is gradually closed. Maximum power occurs when control valve is at full opened condition. But in axial flow pumps, power of the pump increases when flow rate is reduced or the control valve is gradually closed. In such installations, a transfer line is always provided. The flow from the transfer line is sent back to the suction sump. When the control valve in the main line is gradually closed, part ofthe flow from the main line is transferred to transfer line. But pump has constant flow rate, thereby power is kept constant and below overloading capacity.

359

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

>f!. 0 0 0

0 N

~

0

(J)

0 00 LO ~

E 0 I"-

~ ""0 !\l Q)

I

]i 0

0 -

()

C

LO

~

.~

-()

~J

-

C'J~

50

H= D2~ .".

40

...... ~

"..... OJ

I

I

~

~~

~N

\,-0

Efficiency %

,.....-

?Y

J,~'\

~~

:[

N

T~~ V"

GL D3

~ c

~

...

./

.... ' . /

~/ ~

/'

~ead

,/"

30 200

220 Diameter (D 2)

240 mm

Fig. 11.35. Effect of impeller outer diameter (D 2) reduction on pump performance

366

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

H Ar---~

B

Fig. 11.36. For the calculation of probable diameter reduction

1,21--+-+--+-+--+---'-T""""""1

0,42OL..-...L..-.....40-L..-60-'--...L..-.....OO-'---1.L.OO---'-----L120----JL....-140-'--....I1l,;

Fig. 11.37. Experimental coefficient k for turning impeller diameter with respect to 115 as per "RUTSCHI"II

Qnl

nl11vl

Qn2

n211 v2

H nl ,

H n2

=

ni

11hl

2

n 2 11h2

and

Nnl

N

n2

=

ni 11m2 3

... (11.9)

n 2 11mi

In Fig. 11.32.(a), (Hp -Q) curves for three different speeds are drawn, over which the (Hsy-Q) curve C B3 B2 Bl is overlapped. The operating points are B 3, B2 and Bl on each speed curve. It can be seen that although by model analysis points are obtained, efficiencies are not equal. At point' B l' efficiency is maximum. But efficiencies at other two points B2 and B3 are less than maximum efficiency. The (Hsy -Q) curve must be altered in order make the pump to work at maximum efficiency at all speeds. However, the loss in efficiency due to speed change is negligible when compared to other methods i.e., regulation by delivery valve control method, as well as changing the impeller diameter keeping speed constant. This method of regulation is economical. There is no limit, provided prime mover capacity is sufficient to run the pump at such speed. Danger of cavitation is avoided completely. This method is adopted only for a single stage units. For pumps in series or parallel, valve control method is always carried out keeping pump speed constant for all pumps.

11.8.4. Regulation by Diameter Control (Outer diameter trimming to meet the desired head and discharge) Instead of change in speed, which requires a prime mover with speed changing facilities to a greater extent, which involves huge cost, a change in diameter of impeller at constant speed is carried out in chemical industries. As per model analysis,

367

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

-

QI

Q2

D{

11vj

HI

D2 11v2

H2

= -3 - , -

~2 11kj

NI and D2 11hz N2

= -2 -

D~

11m2

D2

11mj

= -5- - -

... (11.10)

Here also, the (Hp -Q) curve for other diameters changes parallely with respect to original (Hp-Q) curves. Loss of efficiency in changing the diameter is very high when compared to the loss of efficiency in changing the speed. Maximum efficiency also reduces for other diameters. This is due to the fact that flow at outlet is not streamlined flow when outer diameter is trimmed. There will be fully developed separated flow at outlet edge of the impeller followed by an aerodynamic wake. Secondary flow increases considerably. Because of this, flows in diffuser and in outlet element are also fully developed separated flows. As a result, hydraulic efficiency reduces to a greater extent, volumetric efficiency also reduces to a smaller extent. Mechanical efficiency very slightly decreases due to reduced disc friction loss. Overall efficiency reduces to a greater extent. However, in some impellers when impeller diameter is reduced very slightly, the efficiency improves slightly due to improved, better, flow pattern at the outlet of impeller at the passage between impeller, and diffuser, at the diffuser and at outlet elements. Figures (11.33 (a) and (b), 11.34) show the performance of pump with different diameters but with the same speed. The system curve is also shown in the same graph. Comparing the curves [Figs. 11.32 (a) and (b), 11.33 (a) and (b), and 11.34], it is evident that efficiency drop in changing diameter is high when compared to the efficiency drop in changing speed. In Fig. 11.3 7, the experimental results give the limit up to which the diameter of impeller can be safely reduced to get better performance i.e., without sacrifice in efficiency. If the same impeller with different trimmed outer diameters is tested in the same spiral casing or diffuser, it is found, that llmax for each trimmed diameter lies on the corresponding point, such that ... (11.11) The change of Q in proportion to D3 is due to the change of Cm and the flow area 'A2' perpendicular in direct proportion to the impeller diameter. 2 m2 Referring to Fig. 11.36, the H-Q curve for the original diameter is curve AB. The required values of H and Q are given by point 'C'. A line is drawn from the origin '0' to pass through 'C' and then to meet the original H-Q curve AB at point 'D'. This indicates that

to C

D2C [ D2d

J2 ""[~J",,[Hc J Q d

... (11.12)

Hd

This method has been suggested by Beljourn of France 11761 and later accepted by other countries. Although theoretically Hoc D2 and Q oc D3 practically, the outer diameter 'D2' must be trimmed to a value slightly higher than the value calculated as per the law H oc ~, in order to compensate for the quantity which follows Q oc D3. However, it is found that this correction is not necessary if the law suggested by Beljourn is applied.

11.8.5. Regulation by Static Head Change (1) Static Head Fluctuation in Delivery Reservoir In Figs. 11.38 and 11.39, pump (H-Q) curve with a drooping down characteristics regulation by static head change is shown. Water level in the suction tank is taken as (origin, 0-0, i.e., x-axis-

368

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Q-axis) reference line. Pump 1 supplies water through the delivery pipe 2 to the reservoir 3. Water level in the delivery reservoir corresponds to the static heights H, HI' H2 and H3 which are obtained by the meeting point of system curves AE, A IE2, A2E2 and A3E3 ' with pump (H-Q) curve. Points B, BI' B2 and C are the corresponding operating points. Pump operation will be stable between heads Hand H2 i.e., between points Band B2. For further increase in height H2 to H3 by reducing the flow rate QB to QB ' the system curve AIEl raises parallel to x-axis and will meet the pump (H-Q) curve at two poiAts. (se~ Fig. 11.39). This corresponding to the level in the reservoirs a2 b2 and above. The flow rate is 0 < Q < QB2' the pump operation becomes unstable in this region. When the pump head is raised H further, the system curve A2 E2 goes up and will touch the H-Q curve at one point C. The moment pump operating point reaches point C, the operating point momentarily shifts to point 0r---_~_A A2 and there will not be any flow. Since the system head is higher, the operating point further shifts towards left side (Fig.11.26) and will be co CI"""'=----r operated at point A (Fig. 11.26), where the flow will be reversed. This sudden change creates huge noise vibration and water hammer which depends upon the flow rate and length of the C pipe. Flow in positive direction will start only when the water level goes below a!, b l which Fig. 11.38. Regulation by static head change corresponds to the head HI. Pump operation will be always unstable between H2 and H3 and above. N

~~_L_L_

_ _ _ _ __L~Q~

E3

C

1.£

3

l.--' --::::: f'E, I::l,

.... ~

A

E1 ~

V

B1

I-- I-"

--

""~

-

--

--

a ========

- --------

IF

~( 0 "-I\..\-

= __

--------

- - - a 1=_=_

=-=_=-=_=-=_=-=_:-1

=-::..---==-::..--

I

co

N

I

::f

I

o Q

Fig. 11.39. Static head fluctuation in delivery reserve

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

369

In order to avoid such unstable operation, pump (H-Q) curve must be a gradual raising characteristics up to Q = 0, i.e., without any drooping characteristics at low flow rate or other arise the curve A 2-C will be a raising curve as a continuous curve of C B2-B1 . This fluctuation of water level in delivery tank normally exists in systems, where condensers and accumulators are fitted in the delivery line.

(2) Regulation with Two Different (H-Q) Curves of the Pump In Fig. 11.40, a system operation with two different Q-H (H-Q) curves, one with less drooping characteristics indicated by (H-Q) B continuous line and another with higher max drooping characteristics (H-Q) A indicated by dotted line are shown. It is evident that the higher drooping (H-Q) A curve (dotted line) is recommended and accepted for automatic regulated operation by a pressure control relay, if the fluctuations are large and quite frequent, because of smaller difference between Qa max and Qa min for the given Hmax to H min . These values are also very close to the regular flow rate. But the range between Qb max and Q b min is large for the same head valuation Hmax to H min for the curve of B [continuous line curve (H-Q)B]. It is necessary to bring Fig. 11.40. Regulation by two different down the value (Hmax - H min ) in order to get safe automatic (H-Q) curves of the pump regulation. Ifthe operating point (Hmin) is at the right side of maximum efficiency point, the pump may be overloaded due to power increase or pump may be unsteady due to cavitation. Hence, necessary care should be taken in fixing the normal regular operating point (Hmi), especially when automatic relay is fitted. Pump automatically starts at (Hmi) and automatically stops at (Hmax)' Normally, this pressure difference will be 2 to 3 kg/cm2.

(3) Static Head Change in Suction Reservoir In Fig. 11.41(a), two different (H-Q) curves of pump are (H-Q)a and (H-Q)b' Curve CE is the system curve. Static height Hs corresponds to low water level in the suction reservoir, and Hs corresponds to the high water livel in the suction reservoir. Taking the low water level in the suctiori tank as the normal operating condition, the operating point is B with parameters H B, QB and N B. When water level reaches the higher level, the head will be HA and the parameters are QA' HA, N A, corresponding to point A. The power increase is fiN = NA - N B . Prime mover must be capable of taking this excessive power, if not, regulation is carried out by operating the control valve until QA reduces to Q~ and N~. The difference in head H A-HB = h3 is the loss created by the control valve. The control valve system is simple but not efficient. The efficiency loss will be more. That's why when any system operates under larger and frequent suction or delivery reservoir level variations, system will be operated with another H-Q curve with larger drooping characteristics by this the change in Q, N, will be considerably small than in the lesser drooping characteristic of (H-Q). However, best and efficient method always changes the speed of the pump. The same system is adopted when delivery tank fluctuations take place. Delivery tank fluctuations take place. This is applicable for smaller changes in the level of water in the suction sump.

370

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

In Fig. 11.41 (b), the operating system (HSY-Q) with the pump curve (Hp-Q) is given for larger changes in the level of water in the suction reservoir. When the suction head increases, the head discharge curve of the pump (Hp-Q) droops down at earlier stage with respect to original, the curves OB,OC,OD,OE and OF. The required specification, marked as X, is met, when the suction head is approximately 2 m. When the suction head increases or if the level of water in the suction reservoir goes down further, the pump curve (Hp-Q) droops down earlier, and the required specification (the point X) is not met with. Hence for this pump, the required suction head should not be more than 2 m and the level of water in suction reservoir should not go down below this level. Figure 11.33(b) shows that pump is operating with large suction depth conditions.

Fig. 11.41 (a). Static head change in suction reservoir 50r-~----r---~---r--~----~--'---'

"-.11 hs = ,.' ' .....0.5 m \

40

I

\

", ,

~ 30 I

80 0~

>c

()

70

OJ

·0

-= 60 W

~

OJ

50

20

I

(f)

0.. Z

4

10

2 10

20

30

40

50

60

co

()

"" (5

70

Flow Q [Us]

Fig. 11.41(b). Larger static head change in suction reservoir

371

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

(4) Regulation by Impeller Blades and Inlet Guide Blade Rotation A small rotation of inlet guide blades before impeller blades, to some extent, changes the input energy to the impeller, which in tum changes the total head of the pump for the same quantity of flow. Efficiency almost remains same in this process. However, regulation can be done only to a very small range. Efficiency and head drop very much for further changes. Hence this method is not adopted in pumps. But the blade rotation is widely used with variable pitch adjustable impeller blade axial flow pumps. It is not possible in fixed impeller blade propeller pumps.

cS'" II

J

Fig. 11.42. Regulation by impeller blade pitch control

When impeller blade is rotated with respect to its own axis, the angle of attack is changed. If angle of attack is increased, area between two blades, axial velocity, tangential velocity, total head, circulation, lift and quantity of flow increase. The geometrical average velocity w = absolute and blade angles also change. In Fig. 11.42, continuous line is for the original value and dotted line is for increased angle of attack. Reducing angle of attack by rotating the impeller blade in opposite direction reduces all values mentioned above including efficiency. At maximum efficiency, total head increases slightly because total head depends upon the curvature of the profile. As already explained in Chapter 10, it was shown that hydraulic efficiency llh is given as ... (11.13) Relative velocity w = reduces only a little for a larger value of reduction in angle of attack. Value sin (13= + A,) reduces to a greater extent, with the result, hydraulic efficiency drops when angle of attack is reduced or when impeller blade is rotated in the opposite direction (-L113= ). Up to a reduction of 13= = 23 ° to 25°, efficiency drop is only very little. Futher reduction in angle of attack reduces efficiency significantly.

11.9

EFFECT OF THE PUMP PERFORMANCE WHEN SMALL CHANGES ARE MADE IN PUMP PARTS 1. Filing the trailing side ofthe outlet edge ofthe impeller blade raises (H-Q) curve (Figs. 11.43, 11.44, 11.45 and 11.46) to a certain extent. Efficiency may remain same or may increase. But normally decreases.

372

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

2. Filing the leading side ofthe outlet edge ofthe impeller blade drops (H-Q) curve. Efficiency also drops (Figs. 11.47 and 11.48). 3. Instability in (H-Q) curve at low Q can be removed shifting the inlet edge ofthe impeller blade towards eye. 4. Thinning the inlet edge by filing both sides of the blade especially more on the leading side, less on the trailing side and rounding off the inlet edge reduces drooping nature at unstable region. 5. Increasing the eye diameter Do near inlet edge of the impeller blade and sometimes shifting the inlet edge inside improve NPSH. 6. Increasing the blade length at hub and decreasing the blade length at periphery ofthe inlet edge, in other words, increasing the inclination of inlet edge with respect to outer shroud improves NPSH. 7. Filing the volute tongue removes the unstable nature at low Q, but Q reduces at higher flow rate. 8. Increase in volute area may increase the overall efficiency but optimum efficiency shifts to higher Q. Reduction in volute area will reduce overall efficiency and the optimum 11 shifts to lower Q. Original vane

removed

Fig. 11.43. Underfiling of outlet tip of pump blade (Filing the training ride of outlet of impeller blades)

373

TESTING, PERFORMANCE EVALUATION AND REGULATION OF PUMPS

?ft 60 ~

~.~

N

J" f/

.>2

::a5 40 ""0

1----(a) OF

~

U2 ----~

~;

"='

" '\

I

C

coco ""0

NCO

.---

~OJ

.s:: 60

]i

--

0

a-

{jo

()

t) ~.

1.1' (: II<

E E

E E

"cO

"

Section I : Type AFP 450

TABLE D6.4: a = 32° 43' . , -3

K

m -3

0

0.016

z z

0.025

0.064

0.241

0.200

0.089

0.076

0.073

0.072

0.831

0

0.172

0.251

0.092

0.079

0.075

0.075

0.633

0

0.212

0.172

0.095

0.087

0.085

0.016

0

0.186

0.182

0.159

0.153

-0.198

0

0.132

0.156

0.161

-0.179

0

0.036

0.048

-0.556

0

-0.677

-2

-0.064

-0.047

-1

-0.241

-0.222

-0.172

0

-0.200

-0.215

-0.251

-0.212

1

-0.089

-0.089

-0.092

-0.172

-0.186

2

-0.076

-0.076

-0.079

-0.095

-0.182

-0.132

3

-0.072

-0.072

-0.075

-0.085

-0.153

-0.161

-0.048

-0.011

--I

Section I : Type AFP 450 TABLE D6.6: Values !J.aki and !J.bki

-pt

P

C1 = -Z = -0.03343; C2 = - - . C1 = 0.00114 1l 6 -3

K

1.

C I cos

2.

C I sin

3.

C2 cos

4.

C2 sin

UK UK UK UK

-5/2

-2

-1

0

1

2

+5/2

3

L

-0.03120

-0.03112

-0.03086

-0.02982

-0.02813

-0.02614

-0.02452

-0.02405

-0.02389

-

-0.01201

-0.01223

-0.01286

-0.01512

-0.01807

-0.02083

-0.02272

-0.02322

-0.02338

-

0.00106

0.00106

0.00105

0.00102

0.00096

0.00089

0.00084

0.00082

0.00082

-

0.00041

0.00042

0.00044

0.00052

0.00062

0.00071

0.00078

0.00079

0.00080

-

LiaKi

(1) -[(4) (Sk - s) 1

=

-3

-0.031

-0.031

-0.031

-0.030

-0.029

-0.027

-0.026

-0.026

-0.025

-0.256

-2

-0.031

-0.031

-0.031

-0.030

-0.029

-0.027

-0.026

-0.026

-0.025

-0.256

-1

-0.031

-0.031

-0.031

-0.030

-0.028

-0.027

-0.025

-0.025

-0.025

-0.253

0

-0.031

-0.031

-0.030

-0.030

-0.028

-0.027

-0.025

-0.025

-0.024

-0.251

1

-0.031

-0.031

-0.030

-0.029

-0.028

-0.026

-0.025

-0.025

-0.024

-0.249

2

-0.030

-0.030

-0.030

-0.029

-0.028

-0.026

-0.025

-0.025

-0.024

-0.247

3

-0.030

-0.030

-0.030

-0.029

-0.028

-0.026

-0.024

-0.024

-0.024

-0.245

LibKi

=

:0

o --I o o -< z

» ~

o -0 C ~

(2) + [(3) (Sk - s) 1

-0

(f)

-3

-0.012

-0.013

-0.013

-0.015

-0.017

-0.21

-0.021

-0.022

-0.022

-0.156

om

-2

-0.013

-0.013

-0.013

-0.015

-0.017

-0.21

-0.021

-0.022

-0.022

-0.156

--I :0

-1

-0.013

-0.013

-0.013

-0.015

-0.017

-0.21

-0.022

-0.022

-0.022

-0.158

"C

0

-0.013

-0.014

-0.014

-0.016

-0.018

-0.021

-0.022

-0.023

-0.023

-0.164

1

-0.014

-0.014

-0.014

-0.016

-0.019

-0.021

-0.023

-0.023

-0.024

-0.167

2

-0.014

-0.015

-0.015

-0.017

-0.019

-0.021

-0.023

-0.023

-0.023

-0.170

» r » z

3

-0.014

-0.015

-0.015

-0.017

-0.019

-0.021

-0.023

-0.023

-0.023

-0.170

z

G)

o

» x 5>

.s

o

Section I : Type AFP 450

m (f)

G)

TABLE D6.7: Calculation of the values

.s

o

Section I : Vari. A-AFP 450/2

m (f)

TABLED6.19

G)

z

o

-3

K

-2

-1

+2

+1

0

+3

L

"-0 C

I - Ao = 5.3094

t

~

I

P IO

t

0.0009

Ao

0.2621

0.5999

0.6920

0.2621

0.5999

0.0009

2.4178

-0

o o

~

I - Al = 18.4300

t

P II

I - A 1=-15.5200

PI

PI

L

t

-

-0

I

t Al I

I -

t

--0.0085

--0.0317

0.0196

0.1378

0.1482

0.5095

-0.0049

0.7680

o z z

m --I

(f)

A

-I

0.0041

-0.1231

-0.4291

--0.1160

0.0267

--0.0165

0.0072

-0.6467

--0.0035

0.1586

0.1391

0.7138

1.1361

0.3918

0.0032

2.5391

0.22825

0.17166

-0.11431

-0.29545

-0.22122

-0.05968

};

I - Bo =-0.8680

t

I - BI = --4.0872

t

I - B2 = 1.2591

t

I - B* = 1.0321

t

I - B** = -0.1358

t

ql

QK

L

LQKO Bo + ...

0.29068

-3

-5/2

-2

-1

0

1

2

5/2

3

L

0.1330

0.3044

0.4057

0.6439

0.6772

0.4472

0.1587

0.0672

0.0175

2.8548

()1

o w

()1

Section I : Vari. A-AFP 450/2

o

-l'>

TABLE D6.20: Calculation of velocity components (wx + K

i

-3

-5/2

-2

-1

qj

0

1

v~')

2

5/2

3

L

qj Cf>Ki

-3

-0.0035

-0.016

-2

0.1586

0.674

-1

0.1391

0.392

0

0.7138

-0.413

1

1.1361

-3.559

2

0.3918

-1.823

3

0.0032 Lj

-2.1692

-2.1417

-2.0536

-1.6047

-0.6055

0.3490

1.0175

1.1955

1.2503

--4.762

P j \11K

:0

o --I o o -< z

» ~

-3

-0.0035

0.0053

o

-2

0.1586

-0.1762

-0 C

-1

0.1391

0.0175

(f)

0

0.7138

0.3997

om

1

1.1361

0.5965

--I :0

2

0.3918

0.5023

"C

3

0.0032

0.0049

~

-0

z

G)

L2

0.6695

0.6816

0.7137

0.7563

0.4760

-0.1842

-0.5532

-0.5990

-0.6107

1.3500

» r » z

1.3500

» x

o

5>

.s

o

Section I : Vari. A-AFP 450/2

m (f)

G)

TABLE D6.21: Calculation of values of

.s

o

Section I : Vari. A-AFP 450/2

m (f)

TABLE D6.23: Calculation of velocity K

-3

nK=nK/(//2)

j

0.Ql

0.02

-0.1390 -0.0006 0.0261 -0.1135

-1

0

1

2

5/2

3

0

0

0

0

0

0

0

0.01

-0.1863 -0.0012 0.0412 -0.1463

-0.5930 0 0.1316 -0.4614

-1.0405 0 0.4641 -0.5764

v'x

-1.3577 0 1.0000 -0.3577 B

- 0.4474 -2.1068 0.6490 0.5320 -0.0700 IBb IBb+ LAa IBb-LAa

* **

z

-2

B. J

0 1 2

G)

o

"-u 0.02

0.4485 -1.4439 -0.4456 0 0.0056 -1.435 -1.5485 -1.3211

0.3991 -1.2114 -0.3756 0 0.0056 -1.185 -1.3313 -1.0387

0.2888 -0.6428 -0.1913 2.4849 0.0057 1.945 1.4836 2.4064

0.1876 -0.0942 -0.0251 0.6320 0.0060 0.7063 0.1299 1.2827

j

U

c ~ -u

o o

Aju yj

2.7368 9.5000 -8.0000 LAa

j

(up to 4 digits)

-5/2

A. J

0 1 -1

(v~)

-1.3684 0 0 -1.3684

-1.3577 -1.1875 0 -2.5452

-1.0405 -0.5511 0 -1.5916

-0.5930 -0.1563 0 - 0.7493

-0.1390 -0.0310 0.0004 - 0.1696

-0.1863 -0.0489 0.0010 - 0.2342

0 0.6706 0 0.0847 0.0111 0.766 -0.6024 2.1344

-0.0782 0.4864 -0.0749 0.0564 0.0223 0.412 -2.1332 2.9572

-0.1876 -0.0942 0.0251 0.0454 0.0832 0.128 -1.7196 1.4636

- 0.2888 -0.6428 0.1913 0.0431 0.3270 -0.370 -1.1193 0.3793

- 0.4485 -1.4439 0.4456 0.0423 0 -1.404 -1.5736 -1.2344

- 0.3991 -1.2141 0.3756 0.0423 0 -1.195 -1.4292 - 0.9608

~

-u

o z z

m --I

(f)

qj

0.0782 0.4864 0.0749 0.1693 0.0074 0.816 0.4583 1.1737

Section I : Vari. A-AFP 450/2 TABLE D6.24: Calculation of velocities and thicknesses K

IiK

=

-3

0.01

nK /(//2)

wx +v" x w=

Wx

+ v~' + v;

{

QK dey)

0.02

1

K

Q

-[w(O) +w(y)J

2

{

-2

-1

0

1

2

5/2

0

0

0

0

0

0

0

3

0.Ql

0.02

11.4356

11.4201

11.3379

10.7821

9.7638

8.8494

7 .8712

7.6069

I

10.1043

12.9037

11.4678

11.2404

9.1614

6.7162

6.1516

6.4876

5.9544

10.3969

13.8265

12.6206

11.9558

11.8982

11.8066

9.3348

7.9862

6.2936

0.3044

0.4057

0.6439

0.6772

0.4472

0.1587

0.0672

9.8871 10.1145

0.1330 =

-5/2

7.5280 6.0988

I

6.5672

0.0175

0.0135

0.0132

0.0242

0.0354

0.0577

0.0740

0.0652

0.0256

0.0104

0.0029

0.0029

0.0131

0.0128

0.0227

0.0323

0.0539

0.0571

0.0383

0.Ql71

0.0084

0.0027

0.0027

()1

o

-....J

()1

Section I : Vari. A-AFP 450/2

o

TABLE D6.25: Calculation of velocities -5/2

K

-n

K

j

=

0.02

nJ!(l/2)

-2

0.03

-1

0.04

0.03

0.05

0.05

1 -1

2.7368 9.5000 -8.0000 LAa

j

0 1 2

* **

v;-

B

+1

0

+1

0.06

0.07

0.08

0.03

0.04

0.06

0.07

Ajll yj

Aj

0

(v~)

0

0.06

co

-0.5324

-0.5254

-0.9569

-0.9333

-1.2851

-1.2711

-13197

-13099

-13003

-1.2906

-13137

-1.2993

-1.2711

-1.2572

-00025 0.1602 -D.3747

-00036 0.1735 -0.3555

-00043 0.4430 -0.5182

-00056 + 0.4372 -0.5017

-00142 0.8822 -0.4171

-0.0170 0.8609 -0.4272

0.1502 0.1320 -13379

-0.1656 0.1456 -13299

-0.1791 0.1574 -13220

-0.1909 0.1678 -13137

-1.0546 0.0075 -2.3608

-1.0287 0.0100 -2.3180

-0.9793 0.0150 -2.2354

-0.9557 00174 -2.1955

0 0.6098 0 0.0844 0.0111

0 0.6002 0 0.0843 0.0111

0 0.5906 0 0.0841 0.0111

0.0781 0.4559 -0.0656 0.0564 0.0222

-0.0780 0.4462 -0.0626 0.0564 0.0221

-0.0778 0.4275 -00570 0.0564 0.0220

-0.0776 0.4185 -00543 0.0563 0.0219

0.6956 -D.6264

0.6858 -0.6279

0.3711 -1.8643

0.3648 -1.8307

Bjll qj

j

-0.4474 -2.1068

0.2782 -0.6123

0.2683 -0.5741

0.1858 -0.1164

0.1845 -0.1200

0.6490 0.5320 -D.0700

-0.1872 1.8482 0.0057 13326 0.9579

0.1777 1.3998 0.0057 0.9220 0.5670

-00386 0.6018 0.0060 0.6386 0.1204

-00417 0.5803 0.0060 0.6091 0.1074

1.7073

1.2770

11568

LBb LBb + LAa LBb -LAa

1.1108

0.0779 0.4367 0.0598 0.1677 0.0074 0.7495 0.3324

0.0778 0.4275 0.0570 0.1669 0.0074 0.7366 0.3094

1.1666

1.1638

0 0.6106 0 0.0845 0.0111 0.7152

0.7053

-

-

2.0531

2.0352

-

-

+ 2

0.3908

0.3841

-

-

2.7516

1.7021

-

:0

o --I o o -< z

+ 5/2

» ~

0.01

0.02

0.03

0.01

0.02

o

-1.0105 -0.5192 0.0013 -1.5284 -0.1874 -0.1037 0.0304 0.0454 0.0827 -0.1326

-0.9827 -0.5112 0.0025 -1.4914 -0.1868 -0.1111 0.0349 0.0454 0.0813 -0.1363 -1.6277 1.3551

-0.9569 -0.5040 0.0038 -1.4571 -0.1858 -0.1164 0.0386 0.0454 0.0792 -0.1390 -1.5961

-0.5492 -0.1662 0.0013 -0.7141 -0.2858 -0.6390 0.1929 0.0431 0.3010 -0.3878 -1.1019 0.3263

-0.5324 -0.1823 0.0025 -0.7122 -0.2782 -0.6122 0.1872 0.0431 0.2432 -0.4169 -1.1291 0.2953

-u c ~ -u (f)

-

+ 1.3958

-

om z

--I :0 "'Tl

C G)

» r » z o

» x 5>

.s

o

Section I : Vari. A-AFP 450/2

m (f)

G)

z

o

TABLE D6.26: Calculations of velocities and thicknesses

nK

=

K

-3

nJ!(l/2)

0.02

-5/2 0.03

-2

0.03

0.04

-1 0.05

0.06

1

0

0.07

0.08

"'Tl

0.06

0.02

0.07

2.5

2 0.01

0.03

+3

-u c ~ -u

o o

0.02

~

-u 0.05

0.06

0.03

0.04

0.01

0.02

0.00

o

0.01

z z

m --I

Wx

+v~

11.4201

v"

w

= Wx

+ v~+ v~

QK QK

10.7821

9.7638

8.8494

7.8712

0.1204

0.1074

0.3324 0.3094 -0.6294 -0.6275 -1.8643 -1.8307 -1.6277 -1.5961 -1.1019 f-1.1291

1.7073 1.2770

1.1568

1.1108

1.1666 1.1638 2.0531

2.053

2.7516 1.7021 +1.3958 1.3551

9.1359

6.9851

0.3263 0.2953

12.372

11.9871 11.4583 11.4453 11.1145 11.0915

7.0187

6.2435

6.2751

6.5050

6.4780

13.127

12.6970 12.4947 12.4487 11.9487 11.9459 11.8169 11.7990 11.6010 11.5515

9.2670

9.2263

7.9860

7.9330

0.4057

0.6439

9.1370

0.6772

0.4472

0.1587

0.0672

0.0239

0.0245

0.0354

0.0354

0.0576

0.0577

0.0740

0.0740

0.0653

0.0651

0.0256

0.0255

0.0103

0.0102

0.0225

0.0231

0.0323

0.0324

0.0539

0.0539

0.0571

0.0572

0.0382

0.0383

0.0171

0.0172

0.0084

0.0084

EW(O)+W(y)]

(f)

7.6069

0.9579 0.5670

0.3044

d(y)=

11.3379

w

9.99

12.22

11.45

11.10

9.14

7.00

6.26

6.50

603

(Final Value)

10.26

13.01

12.48

11.95

11.81

11.56

9.24

7.94

6.43

()1

o

.s

o

Section I : Pump-AFP 450

m (f)

G)

z

TABLE D6.30: Theoretical pressure and velocity distribution on the profile

o

"-0 r= 122.8mm;

u2 = 105.9512;

u = 10.2918 m/s;

C

u2

~

-0

- - =1.1309 2gH

o o

~

-3

-5/2

-2

-1

0

+1

+2

+5/2

+3

-0

o z z

m

w w2 u

p

2

2

w

2gH

{ { {

9.99

12.22

11.45

11.10

9.14

7.00

6.26

6.50

6.03

10.26

13.01

12.48

11.95

11.81

11.56

9.24

7.94

6.43

99.8840

149.3284

131.1025

123.2100

83.5396

49.0000

89.1876

42.2500

36.3199

105.1794

169.2601

155.7504

142.8085

139.4761

133.6336

85.3776

63.0436

40.9651

0.0648

-0.4630

-0.2685

-0.1842

0.2499

0.6079

0.7126

0.6799

0.7432

0.0082

-0.6757

-0.5315

-0.3933

-0.3578

-0.2955

0.2196

0.4580

0.6936

+5/2

+3

2

(J=

wmax-u

--I

(f)

2

2gH = 93.6880

=0.5315

2gH

SECTION III r= 145.4mm;

K

w w

2

{ {

u2 2gH = 1.5850

u2 = 148.4937;

u = 12.1858 mls;

-3

-5/2

-2

-1

0

+1

+2

11.75

13.77

12.84

12.42

10.35

8.85

8.50

8.93

8.48

12.05

14.73

14.14

13.50

13.37

13.27

11.52

10.46

8.92

189.6129

164.8656

154.2564

107.1225

78.3225

72.2500

79.7449

176.0929

132.7104

136.1002 142.4729

---------- ----

178.7569 216.9729 199.9396 182.2500 ---- ---- ---- ---

1....- _ _ _ _ _ _ _

72.0139

109.4116 79.5180 --- ----

()1

w

---------- ---u

p

2

W

2

2gH

{

---- ---- ----

---

r---- ----

--- ----

0.1323

-0.4289

-0.1747

-0.0615

0.4416

0.7490

0.8138

0.7338

0.8163

0.0643

-0.7309

-0.5491

-0.3603

-0.3230

-0.2946

0.1685

0.4172

0.7342

w2

(J=

max

_u 2 = 0.5491

2gH

SECTION V r = 168.00mm;

W

w2

p

u2

w2

2gH

{ { {

u2

u2 = 198.2436;

u = 14.0799 m/s;

- - =2.1160 2gH

+2

-3

-5/2

-2

-1

13.77

15.16

14.20

13.62

12.05

10.73

10.76

11.46

11.14

14.07

16.16

15.70

15.12

14.99

15.05

13.67

12.91

11.55

189.6129

229.8256

201.6400

185.5044

145.2025

115.1329

115.7776

131.3316

124.0996

197.9649

261.1456

246.4900

228.6144

224.7001

226.5025

186.8689

166.6681

133.402

0.0921

-0.3371

-0.0363

0.1360

0.5661

0.8871

0.8802

0.7142

0.7914

o --I o o -


.s

DESIGN OF PUMP COMPONENTS

529

TABLE D7.2: Computer programme in C++ for profile loss calculation for impeller # include < stdio. h> # include < math. h> # include < Conio. h> # define Z 7.0 # define pi 2217

char hip; yoidmainO } int i ; float xy [10], xy 2 [10], hfl [10], B1_inf [10]; eff [10], eff [10], effy = 0 effy = 1 = 0, efft, efft 1; float float CxCtu [10], CyCtu [10], CxRetust 2 [10], CyRetust 2 [10], CyBtu [10], CxUtu [10], CyUtu [10]; float Cxde1 tatust_ tr [10], Cyde1 tatust_2 [10], Cyde1 tatist 2 [10], Cxde1 tatust2 [10] ; float CyCtr [10], CxCtr [10], CyRetrst 2 [10], CxRetrst 2 [10] ; float CxB_1 [10], CxU_1 [10], CXPU_1 [10], CxUR_1 [10], Cxthetal [10], CxRe1 [10], Cxdeltast 2_1 [10], Cxde1 tast 21 [10] ; float CYB_1 [10], CyU_1 [10], CyUR_1 [10], CyX1 [10], CxRe1 st 2 [10], Cyde1 tast2_1 [10], Cyde1 tast 21 [10]; Nu = 1 1.07 e-9 = 9.81 ; float float Cz, HS, P1J, H,W1Jnf [10], t [10] ; U [10], r [10], B2_inf[1O] ; float float Wt; float W2_inf [10], deU_xx, hw ; float Wu2_ inf [10], Ret_xx, U_t, ReI [10], U_tl,B, Ce ; WI ,max U1_max, PI_max; float float PI P1m, PI_min; float b, Bb, U_1, d_s, U1-t; float U l_b, Reb_xx, del_b_xx; Ull, Cb, Ree_ xx, del_e, del_e ; float float x, n del_xx, dell_e_xx ; float s [10], s_min [10], sl [10] ; float 1b, ub B_b, Q Xb, ReH_xx; float dell_bxx, dell_e_xx;

530

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

float

Ct, k, Gt, T ;

float float

StI, UtI, B_t, sbl ; X_t, Ge, dell_t xx, Xe ;

float float

del_e_xx, dell_cv ; del_ t_xx_cv ;

float float float

Ret_xx_cV, Ul_max_cv, Pl_max_cv ; Wl_max_cv, Ul_max_cv.Pl_max_cv ; Pl_cv, Plm_cv, Pl_t_cv :

float float

B_b_cv, Reb_xx_cv, del_b_xx_cv ; Ul_b_cv, Reb_xx_cv, del_b_xx_ cv ;

float float

Ull_cv, Cb_cv, Ree_xx_cv, Be_cv, Ul_e_cv, del_e_cv ; del_xx_cv, U_cv, Ibl,ibl ;

float float

Q_cv, Xb_ cv, Reh,xx_ cv ; dell_b_xx_cv, dell_e_xx_cv ;

float float

Ct_cv, k_cv, Gt_cv ; Srl_cv, UtI_cv, B_t_cv ;

float int ch ;

X_t_cv, Ge_cv, dell_t_xx_c, Xe_cv ;

fflush (stdin) ; clrscr 0 ; I * data available * I printf (" In this program calculates the profile losses in axial flow Ipumps Inln") ; printf (" this is impleted in c language It/tlnln") ; printf (" In give input parameters In") ; printf (" In ******** general detailss ******** ") ; printf (" In give the values for Cz, Hs, n, PI r, H/n") ; scanf ("%f %f %f %f f", & Cz, & Hs, & n, & Pl_ r, & H) ; for (i = 1 ; i < = 3 ; i ++ )

{ printf (" enter the value of r %d", i) ; scanf ("%f" & r [i]) ; U [i] = (( 2.0* pi * r [i]* n) 160.0) ; Wl_inf [i] = sqrt (( Cz* Cz) +(U [i] * U [i] )) ; Bl_ inf [i] = atan (CzI U [i] ) ; printf (" B l_inf [%d] = %f In " , i, B 1_ inf [i]) ; printf (" I nU [%d] = %f In Wl_inf [%d] = %f In ", i U [i], i, wl_ inf [i] ; printf (" I ngive the value ofwu2_inf [i] :", i) ; scanf ("%f", & Wu2_inf[i]) ; B2 _inf [i] = atan (CzlWu2 _inf [i]) ;

DESIGN OF PUMP COMPONENTS

531

printf(" InB2_inf(%d] = %f", i, (B2Jnf[i])); printf (" In sin (B2_ inf [%d] = %f ", i, sin (B2_inf[i] * (I80/pi ))) ; printf (" I ngive the value for 1%d", i); scanf ("%f ", & 1 [i] ) ; t [i] = (2* pi *r [i] ) IZ ; printf (" In value of 1%dl T%d : %fl n", i, i, 11 [i] It [i] )) ; printf(" In value ofWl_inf[%d] ** 2/2g is: %f", i, (Wl_inf[i] * Wl_inf[i] I (2*g ))); W2_inf [i] = CzI sin (B2_inf [i] * (I80 Ipi)) ; printf(" In the value ofW2_ inf[%d] is: %f", i, W2_inf[i] ; printf (" In the value of W2 _ inf [%d] square is : %f", i, W2 _ inf [i] * W2 _ inf [i] ; printf (" In sthe value of W2_ inf [%d] I Wl_ inf [%d] is : % f ", i,i, W2 _ inf [i] I Wl_inf [i] ; ReI [i] = ((Wl_inf[i] * 1 [i] ))/Nu; printf (" In The value of Re 1 %d = = %e ", Re 1 [i] ; getch 0 ; clrscr 0 ; } printf (" In ******** laminar region ********* ") ; printf (" In Give the values or s 1, s2, s3 : In") ; scanf ("%f %f %f ", & s [1], & s_min [2], & s_ min [3] ) ; for (i = 1 ; i < = 3 ; i ++ ) } sl [i] = s [i] + s_min [i]; printf (" In The value of sl [%d] = %f ", i, sl [i] ) ; } for (i = 1 ; i < = 3 ; i ++) { { printf (" I n CONVEX IN") ; printf (" I n Enter the values for CxB _1 and CxU_lin) ; scanf ("%ff ", & CxB_ [i], & CxU_l [i] ; CXPU _1 [i] = pow (CxU_l [i], 3.8) ; CxUR_l [i] = CxU_l [i] * ReI [i] ; Cxthetal [i] = 0.44 * CxB _ 1 [i] ; Cxxl [i] = Re 1 [i] * Cx thta [i] ; CxRel st2 [i] = sqrt 9Cxxl [i] ; Cxdel tast 2_1 [i] = CxRel st 2 [i] I CxUR_l [i] ; Cxdel tast 21 [i] = Cxde 1 tast 2_1 [i] * 1 [i] ; Cxtr [i] = 1259 * pow (Cxrel st 2 [i], -0.2) * Cxde tast2_1 [i] * pow (CxU-l [i], 5.5) ;

532

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

printf (" Enter the value for CxBtr and CxUtr/n") ; scanf ("%f %f ", & Cx Btr [i], & CxUtr [i] ; CxRetrst 2 [i] = pow (((( 0.9 * CxBtr [i] + CxCtr [i]) * ReI [i]) I (1259 * pow (CxUtr [i], 4.5 ))), 1.1111) ; Cxdel tast2_tr [i] = CxRetrst2 [i] I ReI [i] * CxUtr [i] ; Cxde 1 tast 2tr [i] = Cxde 1 tast 2_tr [i] * 1 [i] ; CxCtu [i] = 153.2 * pow (CxRetrst 2 [i], 0.167) * Cxdel tast2_tr [i] * pow (CxUtr [i] = 3.8) ; printf (" Enter the value for CxUtku and CxBtu In") ; scanf("% £010 f", & CxUtu [i], & CxBtu [i]); CxRetust2 [i] = pow ((((1.17 * CxBtu [i] * CxUtu [i] ) ; Cxdel tatust2 [i] = Cxde tatust _2 [i] * 1 [i] ; } printf(" CONCAVE/n",); scanf("%f%f", & CvB_l [i], & CvU_l [i] ; CvPU_l [i] = pow (CvU_l [i], 3.8) ; CvUR_l[i] = CvU_l [i] * ReI [i] ; Cvtheta [i] = 0.44 * CvB_l [i] ICvUR_l [i] ; CvRel st2 [i] = CvRel st 2 [i] I CvUR_l [i] ; Cvdel tast2_1 [i] = Cvdell tast 2_1 [i] * 1 [i] ; CvCtr [i] = 1259 * pow (CvRelst2 [i], -0.1 * Cvdel tast 2_1 [i] * ow (CVU_l [i], 5.5) ; printf (" Enter the values for CvBtr and CvUtr In") ; scanf ("%f %f ", & CvBtr [i], & CvUtr [i]) ; CvRetrst 2 [i] = pow (((( 0.9 * CvBtr [i] + CvCtr [i] * ReI [i] 1(1259 * pow (CvUtr [i], 4.5)), 1.1111) ; Cvdel tast2_tr [i] = CvRetrst2 [i] * CvUtr [i] ; Cvde 1 tast 2tr [i] = Cvde 1 tast 2_tr [i] * 1 [i] ; CvCtu [i] = 153.2 * pow (CvRetrst 2 [i], 0.167 * Cvdel tast 2_tr [i] * pow (CvUtr [i], 3.8) ; printf (" Enter the value for CvUtu and CvBtul n") ; scanf ("%f %f ", & CvUtu [i], & CvBtu [i]) ; CvRetust 2 [i] = pow (((( 1.17 * CvBtu [i] + CvCtu [i] * ReI [i] ) I (153.2 * pow (CvUtu [i], 2.8)), 0.8571) ; Cvde 1 tatust_2 [i] = Cv Retust 2 [i] I ( CvUtu [i] * ReI [i] ) ; Cvdel tatust 2 [i] = Cvdel tatust_2 [i] * 1 [i] ; } } for (i = 1 ; i < 3 ; 1 ++) { printf (" CONVEX/n") ; printf (" CxRelst2 [%d]

%f In", ", i, CxRelst2 [i] :

DESIGN OF PUMP COMPONENTS

533

printf (" Cxdel tast 2_1 [%d] = %f1n"; i, Cxdel tast 2_1 [i] ; printf (" Cxde 1 tast 21 [%d] = %f In", i, Cxdel tast 21 [i] ; printf (" CxCtr [%d] = %f In", i, CxCtr [i] ; printf (" CxRetrst 2 [%d] = %f In", i, CxRetrst2 [i]) ; printf (" Cxdel tast2_tr [%d] = %f In", i, Cxdeltast 2_tr [i] ; printf (" Cxdel tast2 tr [%d] = %f In", i Cxdeltast 2tr [i] ; printf (" CxCtu [%d] % fin", i, CxCtu [i] ; printf (" CxRetust 2 [%d] = %f In", i, CxRetust 2 [i] ; printf (" Cxde ltatust_2 [%d] = %f In", i, Cxdel tatust_2 [i] ; printf (" Cxde 1 tatust 2 [%d] = %f In", i, Cxdeltatust2 [i] ; = %f In", i, CyRelst2 [i] ; printf (" In CONCAVE In") ; printf (" CyRe 1st 2 [%d] %f/n", i, Cydel taust2_1 [i] ; printf (" Cyde ltast 21 [id] = %f In", i, Cydeltast 21 [i] ; printf (" CyCtr [%d] = %f In", i, CyCtr [i] ; printf (" CyRetrst 2 [%d] = %f In", i, CyRetrst2 [i] ; printf (" Cydeltast2_tr [%d) = %f In", i, Cydeltast2_tr [i] ; = %f In", i, Cydeltast2tr [i] ; printf (" Cyde ltast 2tr [%d] printf (" CyCtu [%d] = %f In", i, CyCtu [i] ; printf (" CyRetust 2 [%d] = %f In", i, CyRetust 2 [i] ; printf (" Cyde ltatust_2 [%d] = %f In", i, CYdeltatust_2 [i] ; printf (" Cydel tatust2 [%d] = %f In", i, Cydeltatust 2 [i] ; } Clrscr 0 ; gpt i = 1 ; i < = 3 ; i ++ ) { xyl [i] = pow (CxUtu [i] * Wl_inf [i] IW2 inf [i], 3.2) * Cxdel tatust 2 [i] ; xy2 [i] = pow (CyUtu [i] * Wl_inf [i] IW2 inf [i], 3.2) * Cydel tatust 2 [i] ; hfl [i] = (pow (W2_inf [i], 2) * (xyl [i] + xy2 [i] )) I (g* t [i] * sin (B2_inf [i] * (180 Ipi))) ; printf ("hfl [%d] = %f In", i, hfl [i] ; eff [i] = (H-hfl [i]) I H ; eff [i] = H I (H+hfl [i] ; printf ("eff [%d] = %f It/teffl [%d] = %f In", i, eff [i], i effl [i] ; effy = efty + eff [i] ; eftyl = effyl + effl [i] ; } efft = effy I 3. efftl = efty 1/3 ; printf ("efficiency = % f It/t, Efficiency 1 = %f ", eff, efftl) ; PROGRAM END In") ; printf ("Inlnln

534

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

Design No. D8 D8.1

DESIGN OF AXIAL FLOW PUMP-AS PER METHOD SUGGESTED BY PROF. N.E. JOWKOVSKI

Given, H = 3 m; Q = 0.27 m3/s; n = 900 rpm. Based on the experimental results already available, hydraulic efficiency, llh is assumed = 0.87. Impeller efficiency ll i = 0.94, K = (5.03 to 5.25) selected 5.24 afterwards. No. of impeller blades Zi = 4. Suction specific speed, C = 1150.

(1)

Impeller Design

H 3 Hm = - = - - = 3.4483 11h 0.87 Hi = ll i · Hm = 0.94 x 3.4483 = 3.2414 m. (0 =

Impeller outer diameter, Di = K

Hub diameter,

2nn 60

=

2xnx900 60

3{Q v-;; = 5.24

d =

d

Dh

= 0.5;

1

(2)

=

94.2478 rad/s.

~0.27

900 = 0.350 m.

dh = 0.5Di = 0.175 m.

Suction Conditions C

=

C

m

_--:--4Q_~

=

4xO.27 n (0.35 2 -0.175 2 )

n(Dl -d~)

0

Hsv

Hsv

MVmax

y

=

=

4.167 mls.

3.0128 m.

Hat - Hvp - hs or hs = Hat - Hvp - Hsv = 10.336 - 0.336 - 3.0128 = 6.9872 m.

=

= H

_

sv

C~

= 3.0128 _

2g

4.167 = 2.1278 m. 2x9.81

Selecting the anticavitating profile developed by Moscow Power Institute for Hydraulic Machines, Moscow K = 1.6 taken from its characteristics

Pav = K L1PVmax = 1.6 y y

x

2.1278 = 3.4045 m.

535

DESIGN OF PUMP COMPONENTS

Change of the relative curvature ({}n the radial direction is made such that the load on the outer half of the blade (middle to periphery) is low and the load between hub and middle is high. The impeller design and diffuser design are given in the following tabular form for hub suction only. The procedure for other sections will be same. However, the details for all other sections are given wherever necessary. TABLE D8.1: Impeller design DetailslSection

S.No.

I

1.

Radius rr = 94 rum, rrr = 118, rIll = 143, rN = 168

2.

u=

60

3*.

c

=

m

nDn

Cm

l

2

constant at all sectIOns

.

nDI (I-d)

~I

5.

wI =

6.

(w 2I /2g) m

7**.

8.

C

tan- I

u2

=

U2 =

(~m ) (deg)

(C m Isin

~I )

m/s

9.8232 4.9182

(gHm) mls -U

tan- I

[

~:

)

deg

3.8183

47.5°

C'"2

9.

C'"2

10.

W

11.

(w~/2g) m

12.

4.167

=

4Q

4.

C0 m/s

Cm

=

2

=

8.8592

mls n = 900 rpm. 2

94

2

= --

sinP2

m/s.

6.5373 2.1782

~~ ~ ton-' (u~(~ )d,g (Cm/sin ~=) mls

13.

w=

14.

(w:j2g) m

=

8.1024 3.346

---------------------------------

536

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

15.

2498.3

16.

1475.56

17.

dRu

y

-C Cm 2nrz g u

dr

957.8

2

18.

0=

19.

A=O-~=

20.

Lift force, Y

21.

Length, 1=

22.

t=-

23.

Relative pitch, T

2.05

deg =

dy dr

COSA

dR z

1758.27

cos 0 dr

dP dr Z -y[dY]/( av

)

129.28 (130)

mm.

2nr

147.66

Z

=

(f)

1.1421

24.

7.0

Curvature selected for other Sections II = 6.4, III = 5.5, IV = 3.0 25.

Relative profile thickness

8m = (o~

)

X

100

10.0

For other sections II-7.8, III-5.5, IV-3.0

1.01

26.

(0 in Fig.) from Fig. 10.36 angle of attack deg

27.

U

28.

~1= ~= + u.

29.

m1=

30.

m 2 = (U OCa - ( 01 )

rca) from Fig.. 10.37 (G from Fig. 10.37

0.7675 -0.6

537

DESIGN OF PUMP COMPONENTS

31. 32.

35.4 4.4°

33.

237

34.

0.429

Pmin

7

35.

36.

n-Jv (check) C = (

Hsv

900x.JQ.27

)3/4

(0.3)3/4

1153

10

TABLE D8.2: Design of diffuser z=7 Details/Section

S.No. 1. 2. 3.

Radius r z mm. same as for impeller Cm3 = 1.065 Cm 2 (constant for all other sections) r a =CU r mls 2 (constant for all sections)

4.

P av 1 K =1+ -'--

5.

ct3

I

y

tsin~2

I

94 4.4379 4.4379

1.036

Cm3

= tan

-Ie

(deg)

6.

Angle of divergence (2£)°

7.

-

I

t

C-Sina3 ) 2tanc:

8.

2nr t= -mmZ=7 Z

9.

[=

----

49.3°

U2

U)

x

tmm

8° 1.73

84.37

146

-----------------------------

538

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

i)

10.

Blade Height, H

11.

~

12.

~=45- 2(a3-~)

28.2

14.

8 = (a3 +~)

77.5°

15.

R=--

238.2

16.

(Ozm ) (Tin figure and text)

0.055

17.

8 (h)mm.

12.5

=

I cos ( 45° -

136.9

from Table deg

1

13.

Z

2sin~

The mean line (or) the camber line is an arc of a circle of radius 'R'. The mean line is dressed with the thick profile for which the entire characteristics are known (from the Wind Tunnel Test).

APPENDIX I

EQUATIONS RELATING Cy ' Y~ax, 80 FOR DIFFERENT PROFILES

max

s:

1. For Profiles 428, 682, 364, 480, C y

=

Y 4.8 -Z-+ 0.092

2. For Profiles 408,490,436,387, C y

=

Ymax 4.4 -Z+ 0.092

s:

... (2)

3. For Profiles 622, 623, 624, 384, C y

=

4.0 -Z- + 0.092 8°

... (3)

... (1)

UO

UO

Ymax

4. For Profiles (Camber line is arc of a circle) 608, 609, 610, C y

=

5.0

Y~ax + 0.092 8° ... (4)

5. For Profile Munk - 6 (260), C y

=

dmax 1.3 -Z- + 0.106 8°

... (5)

6. For NACA Profile 23012, C y

d max 1.08 1.3 -Z- + 0.106 8°

... (6)

=

where, dmax = Maximum Thickness 7. For Symmetrical Profile No. 443, C y

=

0.095 8°

... (7)

-·~·-·-·-·-·-·-1·6·5.O-9-·-·-·-.l~·' _. --=:=. _. _. _. _. _. -1·6·5,0-6· _. _. _. _. _.

539

-~.,

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

540

Cl1,1 I.~

~~

-~\; I

O,f

-/--

II, 0,6

q ~4 ~;

~2 ~I

Polar Curves

~Z8

4.08

f2Z

!!I~ 0,0", .. =

I

.36'4

68Z1

4.9°1, I

436

23

7°~1

...:z~I~

J

f ::~91

~ 2,H JI",.,= ~,C697 0

---;§J

H.J!

3§7 -"

6' 1

60B\: t=z.e Yn~D':U.I~//i.

~e8

-~

!

N~C,4 230(21

Man/