Heterogeneous Combustion [1st Edition] 9781483276830

Table of contents :
Content:
Progress in Astronautics and AeronauticsPages ii-iii
Front MatterPage v
Copyright pagePage vi
The Propellants and Combustion Committee of the American Institute of Aeronautics and AstronauticsPage vii
PrefacePages ix-xiIrvin Glassman, Leon Green Jr., Hans G. Wolfhard
Techniques for the Study of Combustion of Beryllium and Aluminum ParticlesPages 3-16A. Maček, R. Friedman, J.M. Semple
Study of Quenched Aluminum Particle CombustionPages 17-39Charles M. Drew, Alvin S. Gordon, R.H. Knipe
Spectroscopic Investigation of Metal CombustionPages 41-73Thomas A. Brzustowski, Irvin Glassman
Vapor-Phase Diffusion Flames in the Combustion of Magnesium and Aluminum: I. Analytical DevelopmentsPages 75-115Thomas A. Brzustowski, Irvin Glassman
Vapor-Phase Diffusion Flames in the Combustion of Magnesium and Aluminum: II. Experimental Observations in Oxygen AtmospheresPages 117-158Thomas A. Brzustowski, Irvin Glassman
Vapor-Phase Diffusion Flames in the Combustion of Magnesium and Aluminum: III. Experimental Observations in Carbon Dioxide AtmospheresPages 159-176Arthur M. Mellor, Irvin Glassman
Analysis of a Dilute Diffusion Flame Maintained by Heterogeneous ReactionPages 177-202George H. Markstein
Combustion of Elemental Boron with FluorinePages 203-226U.V. Henderson Jr., Harry P. Woods, Genevieve Poplin
Oxidation of Graphite, Molybdenum, and Tungsten at 1000°TO 1600°CPages 227-250E.A. Gulbransen, K.F. Andrew, F.A. Brassart
Combustion of Pyrolytic Boron NitridePages 251-278M.D. Bowen, C.W. Gorton
Combustion and Disintegration of Zirconium Hydride-Uranium Fuel Rods During Atmospheric Re-EntryPages 279-307F.E. Littman, A.E. Levy-Pascal, N.A. Tiner
A Brief Review on the Combustion of Boron HydridesPages 311-326W.G. Berl
Characteristics of Diborane FlamesPages 327-343H.G. Wolfhard, A.H. Clark, M. Vanpee
Mechanism and Chemical Inhibition of the Diborane-Oxygen ReactionPages 345-374Gordon B. Skinner, Arthur D. Snyder
Oxidation of DiethyldiboranePages 375-390Walter H. Bauer, Stephen E. Wiberley, Erik I. Sandvik
Reaction of Pentaborane and Hydrazine and the Structure of the AdductPages 391-401H.V. Seklemian, R.W. Lawrence, G.A. Guter
Mechanism of Pyrolysis of Aluminum AlkylsPages 403-418Y.A. Tajima, C.J. Marsel
Inhibition of Afterburning by Metal CompoundsPages 419-448M. Vanpee, R.H. Tromans, D. Burgess
Introductory Considerations on Hybrid Rocket CombustionPages 451-484Leon Green Jr.
Fundamentals of Hybrid Boundary-Layer CombustionPages 485-522G.A. Marxman, C.E. Wooldridge, R.J. Muzzy
Combustion During Perpendicular FlowPages 523-558Welby G. Courtney, William R. Kineyko, Bruce E. Dawson
Research in Hybrid CombustionPages 559-581T.J. Houser, M.V. Peck
A Porous Plug Burner Technique for the Study of Composite Solid Propellant Deflagration on a Fundamental level and its Application to Hybrid Rocket PropulsionPages 583-608Robert F. McAlevy III, Suh Yong Lee
Production of Trace Species in Boundary LayersPages 609-642F.A. Williams
Laminar Boundary - Layer Wedge Flows with Evaporation and CombustionPages 643-664Tze-Ning Chen, Tau-Yi Toong
Homogeneous Nucleation in CondensationPages 667-675J. Feder, J. Lothe, K.C. Russell, J.P. Hirth, G.M. Pound
Homogeneous Nucleation from Simple and Complex SystemsPages 677-699Welby G. Courtney
Condensation Phenomena in NozzlesPages 701-724Peter P. Wegener
Water Vapor Condensation as an Explanation for the Great Apparent Radiance of Sun-Lit High-Altitude Rocket Exhaust PlumesPages 725-738J.M. Bowyer Jr.
Experimental Methods for the Study of Nucleation and CondensationPages 739-761W.J. Dunning
Contributors to Volume 15Pages 763-765

Citation preview

Progress

in ASTRONAUTICS and AERONAUTICS

(a continuation of Progress in Astronautics

and Rocketry)

A series of volumes sponsored by A m e r i c a n I n s t i t u t e of A e r o n a u t i c s a n d A s t r o n a u t i c s 1290 Avenue of the Americas, New York, New York 10019 Progress Seizes Editor Martin Summerfield Princeton University, Princeton, New Jersey

Titles in the Series Volume 1. SOLID PROPELLANT ROCKET RESEARCH. 1960 Editor .-MARTIN SUMMERFIELD, Princeton University, Princeton, New Jersey Volume 2. LIQUID ROCKETS AND PROPELLANTS. 1960 Editors: LOREN E. BOLLINGER, The Ohio State University, Columbus, Ohio; MARTIN GOLDSMITH, The RAND Corporation, Santa Monica, California; AND ALEXIS W. LEMMON JR., Battelle Memorial Institute, Columbus, Ohio Volume 3. ENERGY CONVERSION FOR SPACE POWER. 1961 Editor: NATHAN W. SNYDER, Institute for Defense Analyses, ton, D. C.

Washi?ig-

Volume 4. SPACE POWER SYSTEMS. 1961 Editor: NATHAN W. SNYDER, Institute for Defense Analyses, ton, D. C.

Washing-

Volume 5. ELECTROSTATIC PROPULSION. 1961 Editors: DAVID B. LANGMUIR, Space Technology Laboratories, Inc., Canoga Park, California; ERNST STUHLINGER, NASA George C. Marshall Space Flight Center, Huntsville, Alabama; AND J. M. SELLEN JR., Space Technology Laboratories, Inc., Canoga Park, California Volume 6. DETONATION AND TWO-PHASE FLOW. 1962 Editors: S. S. PENNER, California Institute of Technology, Pasadena, California; AND F . A. WILLIAMS, Harvard University, Cambridge, Massachusetts Volume 7. HYPERSONIC FLOW RESEARCH. 1962 Editor: FREDERICK R. RIDDELL, Avco Corporation, Wilmington, chusetts

Massa-

Volume 8. GUIDANCE AND CONTROL. 1962 Editors: ROBERT E. ROBERSON, Consultant, Fullerton, California; AND JAMES S. FARRIOR, Lockheed Missiles and Space Company, Sunnyvale, California

ACADEMIC PRESS • NEW YORK AND LONDON

P r o g r e s s in ASTRONAUTICS i d AERONAUTICS (a continuation of Progress in Astronautics

and Rocketry)

Titles in the Series (continued) Volume 9. ELECTRIC PROPULSION DEVELOPMENT. 1963 Editor: ERNST STUHLINGER, NASA George C. Marshall Space Center, Huntsville, Alabama

Flight

Volume 10. TECHNOLOGY OF LUNAR EXPLORATION. 1963 Editors:

CLIFFORD I. CUMMINGS AND HAROLD R. LAWRENCE, Jet

sion Laboratory, California Institute

of Technology, Pasadena,

Propul-

California

Volume 11. POWER SYSTEMS FOR SPACE FLIGHT. 1963 Editors:

MORRIS A. ZIPKIN AND RUSSELL N. EDWARDS, Space Power and

Propulsion Section, Missiles and Space Division, General Electric Company, Cincinnati, Ohio

Volume 12. IONIZATION IN HIGH-TEMPERATURE GASES. 1963 Editor: KURT E. SUVLER,National Bureau of Standards, Washington,B.C. Associate Editor: JOHN B. F E N N , Princeton University, Princeton, New Jersey Volume 13. GUIDANCE AND CONTROL — I I . 1964 Editors: ROBERT C. LANGFORD, General Precision Inc., Little Falls, New Jersey; AND CHARLES J. MUNDO, Institute of Naval Studies, Cambridge, Massachusetts Volume 14. CELESTIAL MECHANICS AND ASTRODYNAMICS. 1964 Editor: VICTOR G. SZEBEHELY, Yale University Observatory, New Haven, Connecticut Volume 15. HETEROGENEOUS COMBUSTION. 1964 Editors: HANS G. WOLFHARD, Research and Engineering Support Division, Institute for Defense Analyses, Washington, D. C; IRVIN GLASSMAN, Guggenheim Laboratories for Aerospace Propulsion Sciences, Department of Aerospace and Mechanical Sciences, Princeton University, Princeton, New Jersey; AND LEON GREEN JR., Research and Technology Division, Air Force Systems Command, Washington, D. C.

(Other volumes are planned)

ACADEMIC PRESS • NEW YORK AND LONDON

Heterogeneous Combustion Edited by

Hans G. Wolfhard Research and Engineering Support Division, Institute for Defense Analyses, Washington, D. C. Irvin Glassman Guggenheim Laboratories for Aerospace Propulsion Sciences, Department of Aerospace and Mechanical Sciences, Princeton University, Princeton, New Jersey Leon Green Jr. Research and Technology Division, Air Force Systems Command, Washington, D. C.

A Selection of Technical Papers based mainly on the American Institute of Aeronautics and Astronautics Heterogeneous Combustion Conference held at Palm Beach, Florida December 11-13, 1963

@

ACADEMIC PRESS • NEW YORK • LONDON • 1964

COPYRIGHT© 1964 BY ACADEMIC PRESS INC. ALL RIGHTS RESERVED NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS

ACADEMIC PRESS INC. Ill

FIFTH AVENUE

N E W YORK, N E W YORK 10003

United Kingdom

Edition

Published by ACADEMIC PRESS INC. (LONDON) LTD. BERKELEY SQUARE HOUSE, LONDON W. 1

Library of Congress Catalog Card Number: 64-25708

PRINTED IN THE UNITED STATES OF AMERICA

THE PROPELLANTS AND COMBUSTION COMMITTEE OF THE AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS December 1963 Stanford S P e n n e r , C h a i r m a n Institute for Defense A n a l y s e s , Washington, D. C. William G. Dukek E s s o R e s e a r c h and Engineering Company, Linden, N. J. John B. Fenn P r i n c e t o n University, P r i n c e t o n , N. J. Raymond F r i e d m a n Atlantic R e s e a r c h Corporation, Alexandria, Va. Irvin G l a s s m a n P r i n c e t o n University, P r i n c e t o n , N. J. Leon Green J r . Air F o r c e S y s t e m s Command, Washington, D. C. Robert A. G r o s s Columbia University, New York, N. Y. Joseph F. Masi U. S. Air F o r c e Office of Scientific R e s e a r c h , Washington, D. C. William Nachbar Stanford University, Stanford, Calif. P e t e r L. Nichols J r . A e r o j e t - G e n e r a l Corporation, A z u s a , Calif. Antoni K. Oppenheim University of California, B e r k e l e y , Calif. Robert J. Thompson J r . Rocketdyne, Canoga P a r k , Calif. Tau-Yih Toong M a s s a c h u s e t t s Institute of Technology, C a m b r i d g e , M a s s . F o r m a n A. Williams University of California, San Diego, Calif. Hans G. Wolf h a r d Institute for Defense A n a l y s e s , Washington, D. C. Hideo Y o s h i h a r a General D y n a m i c s / A s t r o n a u t i c s , San Diego, Calif. Maurice J. Zucrow Purdue University, Lafayette, Ind. vii

PREFACE

In the strictest sense heterogeneous combustion is defined as combustion supported by heterogeneous chemical reaction. Examples of heterogeneous reactions include a gas reacting with another gas on a solid surface or reacting with the surface itself. In general use the subject of heterogeneous combustion is considered in a much broader context. If, in any aspect of the combustion process, more than one physical state exists, then the over-all process is considered hetero­ geneous. By this definition the burning of solid propellants which first gasify and then react homogeneously would be a heterogeneous problem, as would be the case of two liquid propellants reacting in the liquid phase and having gaseous products. However, in this book the primary concern is with certain condensed state diffusion flames which involve the combustion of solids and liquids in gaseous atmospheres. In e s ­ sence, droplet burning is considered as a heterogeneous phenomenon, even though the principal energy release may be the result of homo­ geneous gas-phase reactions. Any condensed-phase diffusion flame meets the requirement of this definition. Gas-phase diffusion flames, or for that matter gaseous premixed and decomposition flames, can take on heterogeneous characteristics as well, if they are supported by heterogeneous reactions or create a condensed phase. The paper by Markstein which is related to metal vapor-oxygen systems fits this classification, as do the papers which describe diborane-oxygen combustion. Not only do all papers in this volume fall within the general defi­ nition, but they also are related to three topics of great current interest to the combustion and chemical propulsion fields. In fact, these topics-combustion of metals, hybrid rockets, and condensation--bear a direct relationship to each other. The hybrid rocket motor is one in which both liquid and solid pro­ pellants are used. The solid component is usually a singly perforated cylinder but can take any shape similar to unrestricted solid propellant grains. The liquid is injected in the open port area of the grain at a position close to the forward end or, in some cases, in a chamber vol­ ume ahead of the forward end of the grain. After ignition, the liquid apparently is vaporized due to the heat release from the ignition phase, and further combustion between the vapor and gasifying solid proceeds

ix

by a diffusion flame. This diffusion mechanism is different from that mentioned earlier in that the stagnant conditions usually assumed for particles no longer exist, and fluid mechanical considerations become important. In addition to the feature of controllability, hybrid rocket motors gain a performance advantage over solid propellant rockets in their ability to contain conveniently large quantities of high-energy metals and metal compounds, such as Al, Mg, Be, Zr, BeH 2 , AlLiH 4 , etc. These materials are dispersed uniformly in the solid grain as in metal­ lized composite solid propellants. The performance advantage of hy­ brids can be realized only if the metals and metal compounds burn ef­ ficiently within the motor. Metal combustion leads to high boiling point products in which much of the available heat is obtained from the latent heat of condensation of these products. For efficient performance, then, not only must the metals burn completely, but the product oxide must condense within the motor as well. Thus, condensation phenomena are of great importance in metallized systems. In the initial section of the book are some of the first published works on the analytical determination of metal burning rates, the vari­ ous flame mechanisms of aluminum and magnesium, the combustion of aluminum in carbon dioxide atmospheres, and the ignition temperature of beryllium. Two other papers are concerned with the high-temperature oxidation of molybdenum, tungsten, graphite, and boron nitride, which are considered protective, high-temperature materials. Such know­ ledge of high-temperature surface oxidation contributes directly to the knowledge of the over-all combustion process of metals. For, as point­ ed out by two groups, Glassman and his co-workers and Friedman and Ma£ek, it is the initial oxidation of the particle surface which controls the ignition of the metal. This fact is particularly significant in prac­ tical propellant systems. Similarly, the study on the combustion of zirconium hydride-uranium fuel rods, which was motivated by the prob­ lem of dispersing radioactive materials during atmospheric re-entry, contributes information on the various models of metal combustion which have been proposed. The physical state in which the metal element is introduced into the combustion chamber does not affect the theoretical performance ob­ tainable in metallized propellant systems. Thus, if it is difficult to ob­ tain high efficiencies with metal particles, then, perhaps, the metal can be introduced in various other forms, such as a liquid alky 1-metal com­ pound, a polymeric substance containing a metallic element in the chain, etc. The possibilities of this approach lead to various studies which contribute both directly and indirectly to the understanding of metal combustion phenomena. The oxidation and flame studies with diborane and its alkyl derivatives are of particular interest, as are the reaction studies between boron and nitrogen compounds. A contribution to this latter problem is made here by Seklemian and Lawrence, who isolate the adduct formed between pentaborane and hydrazine by running the x

reaction in very dilute solutions of cyclohexane. Bauer et al. consider the oxidation of diethyldiborane under explosive and nonexplosive condi­ tions. Wolf hard et al. report flame speed data for diborane. Their observations on the BO spectra found in the flames leads one to believe that BO is present only as an intermediate. Pyrolysis of the alkyls is considered by Skinner and Snyder, who report experimental data on di­ borane, and by Takima and Marsel, who discuss the mechanisms for the decomposition of the aluminum alkyls. Papers in the third section of this volume deal with some aspects of the over-all hybrid combustion process, which from Green T s intro­ ductory review is seen to center about the problem of heat and mass addition at the fluid-solid interface. Refinement of the simplified theory employed in this review by introduction of boundary-layer growth con­ siderations is discussed by Marxman et a l . , and experimental results are compared. Courtney et al. report spectroscopic observations of hybrid burning. Their results give insight as to the thickness of the flame zone. Houser and Peck discuss the role of surface pyrolysis in determining solid phase regression rates. McAlevy discusses various modeling techniques that could prove valuable not only for hybrids, but also for composite solid propellants. Williams in a theoretical analysis considers the boundary-layer distribution of trace species, such as those found in an ablation or surf ace combustion process. In their paper Chen and Toong consider evaporation with combustion in a well-defined aerodynamic configuration. Fundamental to many of the studies previously mentioned is the formation and growth of the condensed particle (B 2 0 3 , B, BN, Al, MgO, etc.). Theoretical and experimental studies of nucleation and conden­ sation phenomena are reviewed in many of the papers in the last section. Most deal with compounds classically used in such investigations; how­ ever, one by Courtney reports some initial work on a metal oxide sys­ tem. This volume undoubtedly contains one of the largest and most in­ teresting collections of recent papers on metal and hybrid combustion. Most were presented at the AIAA Heterogeneous Combustion Conference in December 1963. Irvin Glassman Princeton University, Princeton, N. J. Leon Green Jr. Air Force Systems Command, Washington, D. C. Hans G. Wolfhard Institute for Defense Analyses, Washington, D. C. July 1964

XI

TECHNIQUES FOR THE STUDY OF COMBUSTION OF BERYLLIUM AND ALUMINUM PARTICLES A. Macek,* R. Friedman,** and J. M. Semple^ Atlantic Research Corporation, Alexandria, Va. Abstract Dilute streams of beryllium and aluminum powders, consist­ ing of particles 30 to 45u in diameter, were suddenly intro­ duced into hot gases of known composition and temperature, Two techniques of hot-gas generation were used. Beryllium particles, burned in a closed bomb at pressures ranging from 2.4 to 50 atm, were observed by standard photographic techni­ ques. Aluminum particles, burned in gases generated by a flat flame burner at atmospheric pressure, were photographed in flight by a specially developed magnification technique. The processes of ignition and combustion of these metals are cor­ related with the temperature and the composition of hot ambient gases. The gas temperature necessary for ignition of beryllium increases from 2380° to 2650°K as the partial pressure of oxygen decreases from 5 to 0.1 atm. The modes of combustion of aluminum vary with the chemical composition of ambient gases. Oxygen promotes vigorous combustion and fragmentation of burn­ ing particles. In virtual absence of water there is much dif­ fuse luminosity surrounding the burning aluminum particle, whereas in the presence of water in amounts larger than about 0.1 atm the luminous reaction is confined to a region closely adjacent to the particle. Magnified photographs, revealing fine details of particle combustion processes, are shown. Presented as Preprint 63-485 at the AIAA Heterogeneous Com­ bustion Conference, Palm Beach, Fla., December 11-13, 1963. Sponsored by Project SQUID, which is supported by the Office of Naval Research, Department of the Navy, under Contract Nonr 1858(25) NR-098-038. * Senior Scientist, Kinetics and Combustion Division. /Vice President, Research. /Research Engineer, Kinetics and Combustion Division.

3

MACEK, FRIEDMAN, AND SEMPLE

Introduction The work described herein deals with a fundamental investi­ gation of ignition and combustion of single metal particles of diameters ranging from 30 to 45u. Although different experi­ mental procedures have been used, the essence of this study has always been the same, and it is quite simple. Metal particles of known sizes and shapes are suddenly plunged into hot gases of known physical and chemical characteristics, and their be­ havior is observed photographically. Techniques needed for this work were to a large extent de­ veloped and used previously in a study of combustion of alu­ minum particles, and much of this development and application has been described in earlier publications.-U 2 The purpose of this paper is 1) to present the application of a previously de­ veloped technique to the study of beryllium particle ignition, and 2) to describe a recently developed technique for observa­ tion of fine details of metal particle burning which has so far been applied to aluminum only. Efforts are now being made to extend this technique to combustion of beryllium. 1.

Ignition of Beryllium

a. Background The main experimental problems in the study of beryllium ignition and combustion are the high ignition temperature of the metal and the high toxicity of both the metal and its com­ bustion products. The combustion characteristics of the metal are largely determined by the thermodynamic properties of the metal and its oxide (BeO), listed in Table 1. Since BeO forms a protective layer, one might expect, in analogy to the results previously obtained with aluminum,^ that the ignition process will be influenced by the melting of beryllia. It is inter­ esting to .note that the normal boiling point of the metal is quite near the melting point of the oxide, and this may also be a determining factor in ignition. Indeed, as will be seen below, techniques necessary for quantitative study of beryllium combustion must allow generation of controllable ambient tem­ peratures approaching these high values. The boiling point of beryllia, about 4100°K, presumably determines the metal flame temperature. b. Experimental Procedure The procedure was to admix small amounts of the metal powder to a combustible mixture consisting of a fuel and an oxidizer, 4

HETEROGENEOUS COMBUSTION which was then burned in loosely tamped powder form (about 1 gm/ cm^) in a pressurized bomb. The oxidizer was ammonium per­ ch lor ate. The fuel was trioxymethylene, a volatile compound, which makes even quite fuel-lean, relatively cool mixtures flammable at atmospheric pressure. The amount of beryllium added, 0.05 wt %, was so small that it did not perturb the thermodynamic properties of the oxidizer-fuel mixture to any appreciable extent. A dilute stream of metal particles thus ignited and burned in the combustion product gases consisting of known proportions of H2O, CO2, N2, HCl, 02> and free atoms and radicals. Temperature of the gases for several constant pressures was computed by an IBM 7090 program with the usual assumption of equilibrium adiabatic conditions, and it was also measured, at atmospheric pressure, by the spectral line reversal method. The measured temperatures were 60° to 70°K below the computed ones. Safe handling of beryllium and its combustion products pre­ sents a major problem. An apparatus conforming to stringent industrial hygiene requirements, shown in Fig. 1, has therefore been constructed which allows the beryllium-containing powder to be ignited in sealed capsules. Dilution required for dis­ posal of combustion products is 1 ppm of beryllium in water or 25 jig of beryllium in 1 m^ of air. The combustion products contained in the air-tight burner are therefore flushed first with a stream of nitrogen through a dry filter, and then with generous amounts of water, all without opening the burner. Frequent analytical safety checks are necessary. The procedure of determing the ignition limit as a function of ambient gas temperature and oxygen content can be illustra­ ted by reference to Fig. 2, which describes these ambient con­ ditions corresponding to mixtures of ammonium perchlorate and trioxymethylene at three pressures; the percentage of free oxy­ gen in the ambient gas is virtually independent of the total pressure, so that a single oxygen-content curve suffices for all pressures. As long as the mixture is fuel-lean, progres­ sive addition of fuel to oxidizer increases the temperature and decreases the oxygen content of the product gas. The pro­ cedure is continued up to the temperature at which a signifi­ cant fraction of the metal particles ignites. This tempera­ ture and the corresponding partial pressure of oxygen are the ambient conditions that define the ignition limit of the metal. c. Results The results of ignition of beryllium particles, size range 30-45u, are shown in Fig. 3. The total pressure in the forementioned experimental procedure is not an independently 5

MACEK, FRIEDMAN, AND SEMPLE

variable parameter, and it varies from point to point in the figure from 2.4 to 50 atm. It can be seen that the metal ig­ nites at temperatures as low as 2380°K when the partial pres­ sure of oxygen is several atmospheres, and only above 2650°K when it is down to about 0.1 atm; this means that in fuel-rich mixtures the temperature limit for ignition of beryllium ap­ proaches the melting point of BeO (2820°K). Thus it appears possible that, in a close analogy to the case of aluminum, the temperature of the beryllium particle rises by self-heating above the ambient temperature to the melting point of the oxide, at which point ignition occurs. Since the normal boiling point of beryllium is slightly below the melting point of oxide, boiling of the metal introduces an additional process to reckon with at low pressures. Further work, which is in progress now, may give basis for firmer judgment. The mode of combustion of beryllium particles was also found to be affected by the ambient conditions. Large excess of oxy­ gen appears to accelerate the burning. At low oxygen content, low pressures, and high temperatures, metal particle tracks are sharp and straight on photographic exposures, a character­ istic of surface combustion of metals. At high oxygen content, high pressures, and low temperatures, the light from the burn­ ing particle is often intermittent and fairly diffuse, charact­ eristic of gaseous combustion. These trends are illustrated by photographs taken through the window of the closed bomb (Fig. 4 ) . 2.

Photographic Study of Particle Combustion

a. Experimental Technique In this technique metal particles are injected into lamin­ ar ly flowing hot gases, generated by a flat-flame burner. The burner and the properties of the gases that it generates were described in detail before.-^^ Briefly, the hot gases consist of known proportions of tUO, COo, No, and 0^, which are inde­ pendently variable to a significant extent; the temperature can be varied from 1900° to 2900°K; the total pressure is restrict­ ed to 1 atm, The diagnostic technique for studying fine details of par­ ticle combustion consists of still photography through a mag­ nifying lens system. The optical system has a standard 48-mm focal-length objective lens and a 1QK magnifying eyepiece. Photographs are taken by a Reflex Leitz Microscope camera using 35-mrn TRI X film. The depth of focus is 0.5 mm and the field of view 4.5 mm. The optical system is mounted on a cathetometer at a slight angle off the horizontal so that the

6

HETEROGENEOUS COMBUSTION vertically rising particles cross the focal plane at a shallow angle. This system gives a magnification on film of 8 X. Sat­ isfactory prints have been obtained with magnification factors up to 50. Positioning of the lens at various heights above the burner plate thus allows observation of the entire history of the particle from ignition to burnout. b. Results The photographic technique has been applied to combustion of spherical aluminum particles, size range of 30-35|i, and has revealed many complex features of the process. It has been found previously2 that there are distinct effects on combustion of aluminum particles of both oxygen and water vapor in the hot ambient gases. Oxygen promotes vigorous combustion, and, if its concentration is sufficiently high, there is fragmentation of burning particles. It has also been found that in virtual absence of water vapor there is much diffuse luminosity sur­ rounding the burning particle, suggesting extensive vapor phase reaction, whereas in the presence of water in amounts larger than about 0.1 atm the luminous reaction is confined to a region closely adjacent to the particle. These effects have now been observed in close detail, as illustrated by Figs, 5-9. Figures 5 and 6 show successive stages of particle combust­ ion in low-moisture and high-moisture gases, respectively. The oxygen content in both cases is relatively low, so that burning is smooth (no fragmentation). It can be seen that the stages in the two figures are qualitatively similar. In the early stages following ignition, frames a and b in both figures, the burning appears to be even. The central intensely luminous core -- 30-50ji wide, corresponding approximately to the par­ ticle diameter --is surrounded by a less luminous region. The striking difference between Figs. 5 and 6 is the appearance of the outer region, which is much wider and more diffuse in the absence of water. This difference in appearance persists into the later stages (Figs. 5c and 6c) in which the particles ro­ tate. Figure 2d records a particle at or near burnout; rota­ tion has ceased, there is no outer region, and luminosity of the central core is dwindling. These progressive stages are typical of burning aluminum particles in hot gases whose oxy­ gen content is too low to cause fragmentation. Figures 7-9 show comparable phenomena in high-moisture and low-moisture gases, side by side. The temperature in these figures is about 2400°K, and there is sufficient oxygen to cause some particles to undergo fragmentation (Fig. 9). The difference in the amount of diffuse luminosity between the 7

MACEK, FRIEDMAN, AND SEMPLE

adjacent photographs differing in amounts of water vapor is quite pronounced in all three figures. There does not seem to be a ready explanation for these com­ plex processes. However, we found in our earlier work^ that, although in the presence of appreciable amounts of water vapor combustion of aluminum particles is accompanied by formation of hollow bubbles (reported earlier by Fassell et al.3), there is no evidence of such a process in low-moisture gases. This fact and the fact that in the presence of water vapor the outer, less luminous region is sharply delineated on the outside (e.g., Figs. 6b and 7b) suggest that the outer layer luminosity may represent different things. In the presence of water, where combustion is confined to a region close to the surface and takes place asymmetrically with formation of bubbles, the dim outer layer is perhaps a relatively cool condensed phase portion of the burning system. In the absence of water the burning is probably true vapor phase reaction, which indeed one should ex­ pect for aluminum on the basis of the relative volatilities of the metal and the oxide. ^ Work is now in progress to apply the gas-burner photographic techniques to combustion of beryllium particles. References Friedman, R. and MaSek, A., "Ignition and combustion of aluminum particles in hot ambient gases," Combustion and Flame

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DIFFUSION FLAME ABOVE POROUS OXIDE LAYER H/T BACK TO LIQUID

METAL BOILS OXIDE SHATTERS HOT DROPLETS OF METAL BURN IN DIFFUSION FLAMES

Combustion of volatile metal particles in a hot oxidizing atmosphere.

BURNING BEHAVIOUR OF CALCIUM LITHIUM SODIUM POTASSIUM MAGNESIUM

LARGE PARTICLE

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BURNING

COMBUSTION

METAL ALWAYS SOLID, OXIDE STATE DEPENDS ON HEAT LOSSES

AND SURFACE

OXIDATION

H/T

STEADY

A. 9URFACE TEMP.

O

70

o z

c

O O

c/>

o rn z m o c

VAPOR-PHASE DIFFUSION FLAMES IN THE COMBUSTION OF MAGNESIUM AND ALUMINUM: I. ANALYTICAL DEVELOPMENTS Thomas A. Brzustowski* and Irvin Glassman/"' Princeton University, Princeton, N. J. Abstract High heats of vaporization or dissociation of metal oxides upon vaporization generally limit the temperatures of metal-oxygen flames to the boiling points of the respective oxides. Aluminum and magne­ sium can burn in the vapor phase because their boil­ ing points are lower than those of their oxides. The combustion of single magnesium and aluminum drop­ lets is described by an extension of the quasi-steady vapor-phase diffusion flame theory previously used to describe the combustion of hydrocarbon droplets. The theory is modified to consider flame radiation, transport of condensed oxide products, and evapora­ tion of the metal. The fraction of oxide vaporized in the reaction zone varies with the ambient oxygen content. High flame emissivities, resulting from the presence of condensed oxide in the reaction zone, render the metal flames nonadiabatic. Droplet sur­ face temperatures can be hundreds of degrees lower Presented as Preprint 63-489 at the AIAA Heteroge­ neous Combustion Conference, Palm Beach, Fla., Dec. 11-13, 1963. This research was supported by the Allegany Ballistics Laboratory, Hercules Powder Co. under its Subcontract No. 41 to Princeton University. This paper was abstracted from the recent Ph.D. Thesis of the junior author. *Research Aide, Guggenheim Laboratories for the Aerospace Propulsion Sciences, Department of Aero­ nautical Engineering; now Assistant Professor of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada. ~/~ Professor, Guggenheim Laboratories for the Aero­ space Propulsion Sciences, Department of Aero. Eng. 75

T. A. BRZUSTOWSKI AND I. GLASSMAN

than the metal boiling points. The flame zones lie very close to the droplets. Calculated evaporation constants of magnesium and aluminum droplets are in the range of values observed with hydrocarbons. Good results for the burning rate and flame radius are obtained with very little computation. A o£f °L B /? C D 3D ^ H k k . st

= = = = = = = = = = = =

L Le M m

= = = =

n

=

p p p r R R R

= = = = = = =

C

=

0^ = T ' = T^p = BP

u W XA^* X

^ Nomenclature area, cm fraction of product vaporized evaporation coefficient transfer number ratio of diffusivities specific heat at constant pressure, ca]/9-mole K binary diffusion coefficient, cm^/sec dimensionless molar flux emissivity enthalpy, cal/g-mole thermal conductivity, cal/sec-cm-°K stoichiometric coefficient, moles condensed product per mole oxidizer latent heat of evaporation, cal/g-mole Lewis number molecular weight g/g-mole stoichiometric coefficient, moles vaporized produce per mole oxidizer stoichiometric coefficient, moles fuel per mole oxidizer total pressure, atm partial pressure, atm vapor pressure, atm radial co-ordinate, cm characteristic distance in heat transfer, cm universal gas constant, 82.06 atm cmyg-mole-°K universal gas constant, 8.317 x 10? ergs/g-mole-°K _, ~ Stefan-Boltzmann constant, 1.354 x 10 cal/cm 2 -sec-°K" 4 radiant heat-transfer parameter absolute temperature, °K boiling point of metal, °K

= boilinq point of metal oxide, °K ^ r = mass velocity, cm/sec = molar flux, g-moles/sec = dimensionless burning rate = mole fraction 76

HETEROGENEOUS COMBUSTION

Identifying A B C f fc i o p pc [ ] =

= = = = = = = = = = = =

Symbols

droplet surface flame zone surrounding atmosphere fuel condensed fuel inert diluent oxidizer vaporized products condensed products chemical specie average in AB average in BC Introduction

The necessity for an understanding of the burning mechanism of metals arose from the need to explain first the discrepancy often observed between pre­ dicted and measured performance, and second, various features of combustion instability found in rocket motors using metallized propellants. Thermo­ dynamics predicts that the flame temperature of a metal burning in oxygen is generally limited to the boiling point of the oxide by its endothermic dissociation on vaporization.2>3 This fact sug­ gests that a necessary condition for the vaporphase combustion of a metal droplet, and similarly for a hydrocarbon droplet, is that the boiling point of the oxide exceed the boiling point of the metal, thus assuring the possibility of heat transfer to the droplet from a surrounding vapor-phase reaction zone. This criterion for vapor-phase combustion was stated by Glassman^ who used it to conclude that Li, Na, Mg, Al, Ca, K, Be, and Ba could burn in the vapor phase. Brzustowski and Glassman 4 later presented a qualitative description of the necessity but not sufficiency of Glassman's criterion by discussing the pre-ignition oxidation reactions of metal particles that sometimes inhibit vapor-phase combustion. The vapor-phase combustion mechanism is the fastest possible mode of burning. Because its existence has often been observed,5^ it is important that it be understood as fully as possible.

77

T. A. BRZUSTOWSKI AND I. GLASSMAN

A knowledge of the influence of gas pressure, composition and temperature, and of the size and concentration of the metal particles on the burning rate of a single metal particle is a necessary first step in the explanation of the observed effects of metal additives on the combustion of rocket propellants. An analysis of vapor-phase combustion of metal droplets is presented here. It is based on the familiar theory developed to describe the combustion of hydrocarbon droplets.- However, the following characteristics peculiar to the combustion of metals have necessitated the revision of some of the accepted assumptions and approximations. 1) The thermodynamics of metal oxides indicates that, at the highest range of burning rates, the flame temperature will be fixed at the boiling point of the oxide and the state of the oxide pro­ duced will be variable, with some oxide always forming in the condensed phase. 2) The diffusion of oxygen towards the flame zone is affected by the condensed product. More impor­ tant, the condensed products of combustion cannot diffuse, they must be convected with the bulk gas motion. 3) The existence of condensed species in the flame zone at the high temperature level makes thermal radiation important both in the rate of heat feedback from the flame to the evaporating surface and in the rate of heat loss from the flame to the surroundings. 4) The evaporation of metal from the droplet surface may not be very fast in comparison with the diffusion processes occurring in the gas phase. The Model The same model is used here as in the familiar droplet burning theory. A spherical droplet A is surrounded by a concentric thin flame zone B. The shell AB is a stagnant film of gas through which fuel vapor diffuses from the droplet surface A to the reaction zone B. Concentric with the drop and outside the flame zone lies another stagnant gas film BC whose outer boundary is generally taken to 78

HETEROGENEOUS COMBUSTION

be at infinity, Oxidizer from the surroundings diffuses towards the flame zone through the film BC. Fuel and oxidizer are assumed to diffuse into the flame zone in stoichiometric proportions but maintain no concentration at B. Heat is transferred from B toward the droplet to provide the latent heat of vaporization of the fuel and to heat the vapor to the flame temperature. The transport of combustion products to the surroundings through the film BC opposes the inward diffusion of oxidizer. Heat is transferred from the flame to the surroundings through the film BC. The entire system is at a uniform pressure and remains invariant with time. The analysis was developed in terms of the rates of five physical processes occurring in the model. These were: 1) The diffusion of oxidizer to the flame zone through BC # 2) the diffusion of fuel vapor from the droplet surface to the flame zone through AB, 3) the transfer of heat from the flame zone to the droplet surface by conduction and radiation, 4) the loss of heat from the flame zone to the surroundings by conduction and radiation, and 5) the evaporation of fuel from the droplet. The diffusion of oxide from the flame zone to the droplet surface was not considered. The inclusion of this process would have introduced great math­ ematical difficulties into the analysis, even if there had been enough physical data available to allow a realistic description of the phenomenon. The main justification for the omission of this mechanism lies in the experimental observation that the oxide which diffused back to the metal surface did not seem to influence the burning mechanism to any great extent. Nevertheless, the insignificance of the transport of oxide to the droplet surface must be considered as one of the approximations of the analysis. The suggestion that Mg burns in the vapor phase and a diffusion analysis of the combustion of Mg ribbon were first presented by Coffin. The analysis of Ref. 6 did not take into account the four characteristics of metal combustion listed in the introduction. The thick flame zone used in the model of Ref. 6 predicted a flame structure notably different from what has been observed. The 79

T. A. BRZUSTOWSKI AND I. GLASSMAN

apparent quantitative agreement between the pre­ dicted and observed burning rates resulted from the incorrect consideration of flame-spreading time in the determination of experimental steady burning rates. ^ .The contribution made by Coffin was the indication of the gross similarity between the dif­ fusion flames of hydrocarbons and of metals. The present work is an outgrowth of that idea. Governing Equations The derivation of the governing equations is straightforward. However, because their signifi­ cance and limitations may not be readily apparent, the assumptions involved in the derivations are emphasized. Stoichiometry The overall stoichiometry, based on one mole of oxidizer, is shown in realtion (1): The species denoted by [f],[o],[pc], and [p] are fuel vapor, oxidizer, condensed products, and vapor­ ized products, respectively. Additional species appearing below are [fc] , condensed fuel, and [i], the inert diluent gas. The same letters are used as subscripts to identify the properties of these species. The stoichiometric coefficients n ., k St

, and Su

m s t are defined in relation (1). k s ^. Heat-Transfer Equations The two heat-transfer equations arise from the application of the equation of continuity of total enthalpy at the boundaries of the stagnant films. It is assumed that thermal radiation is neither absorbed nor emitted in the stagnant films. Accord­ ingly, the radiation terms appear only in the boundary conditions of the equation of coupled heat and mass transfer. 80

HETEROGENEOUS COMBUSTION

The equation of c o n t i n u i t y of t o t a l enthalpy takes the following form: U) fc H f c (TA) = U f H(\

(24)

^

~

I ~(rrt/rB)

UJ

—

fB

(26)

r

*

p£c

where t h e unknowns a r e Lir,