Universit´ e Libre de Bruxelles Facult´ e des Sciences Appliqu´ ees
von Karman Institute for Fluid Dynamics Environmental and Applied Fluid Dynamics Department
Experimental and Numerical Study of Aeroacoustic Phenomena in Large Solid Propellant Boosters
J´ erˆ ome Anthoine
Thesis presented in order to obtain the degree of Docteur en Sciences Appliqu´ ees
September 2000
“The dream of yesterday is the hope of today and the reality of tomorrow”
Robert H. Goddard (1882–1945)
Contents
Abstract v
R´ esum´ e vii
Acknowledgements ix
List of tables xi
List of figures xiii
1 Introduction 1
1.1 ASSM program . . . . 3
1.2 Objectives and methodology of the present work . . . . 4
1.3 Chapters overview . . . . 5
2 Propulsion systems and Ariane 5launcher 7 2.1 History of the launchers . . . . 7
2.1.1 Rockets, from the East to the West . . . . 7
2.1.2 Pioneers . . . . 9
2.1.3 Post–war years . . . . 12
2.2 Propulsion . . . . 14
2.2.1 Rocket motor . . . . 14
2.2.1.1 Thrust . . . . 14
2.2.1.2 Exhaust velocity . . . . 16
2.2.1.3 Specific impulse . . . . 16
2.2.2 Propellant . . . . 17
2.2.3 Solid propellant . . . . 18
2.3 Ariane 5 launcher . . . . 18
2.3.1 Ariane 5 architecture . . . . 19
2.3.1.1 Fairing . . . . 21
2.3.1.2 Speltra . . . . 21
2.3.1.3 Vehicle equipment bay . . . . 21
2.3.1.4 L9/EPS storable propellant stage . . . . 21
2.3.1.5 H155/EPC main cryogenic stage . . . . 22
2.3.2 P230/MPS solid boosters . . . . 23
2.3.2.1 Propellant grains . . . . 24
2.3.2.2 Nozzle . . . . 27
2.5 Conclusions . . . . 32
3 Theoretical modeling 33 3.1 Theoretical background . . . . 33
3.1.1 Fundamentals of acoustics . . . . 33
3.1.1.1 Equations of linear acoustics . . . . 34
3.1.1.2 Acoustic energy, intensity and source power . . . . 34
3.1.1.3 The wave equation . . . . 35
3.1.1.4 Plane waves . . . . 36
3.1.1.5Standing plane waves in pipe . . . . 37
3.1.2 Fundamentals of hydrodynamics . . . . 39
3.1.2.1 The Taylor flow . . . . 39
3.1.2.2 Hydrodynamic instabilities . . . . 42
3.1.2.2.1 Vortex shedding from a backward facing step 43 3.1.2.2.2 Obstacle vortex shedding . . . . 43
3.1.2.2.3 Surface vortex shedding . . . . 44
3.1.3 Flow–acoustic coupling . . . . 45
3.1.3.1 The Mach number . . . . 45
3.1.3.2 Physical interpretation of flow–acoustic coupling . . . 46
3.1.4 Vortex–sound theory . . . . 47
3.2 Theoretical modeling . . . . 49
3.2.1 Theoretical model of the flow–acoustic coupling in presence of an inhibitor . . . . 49
3.2.2 Theoretical model of the effect of the nozzle cavity volume on the resonance level . . . . 5 2 3.2.3 Modeling of a resonant design in radial injected flow . . . . 55
3.2.3.1 Stability criterion for the SVS . . . . 56
3.2.3.2 Receptivity criterion . . . . 56
3.2.3.3 Stability criterion for the OVS . . . . 57
3.2.3.4 Vortex advection and resonance . . . . 58
3.3 Conclusions . . . . 60
4 Experimental acoustic investigation 61 4.1 Axial injected flow configuration . . . . 62
4.1.1 Experimental set-up . . . . 62
4.1.1.1 Sub–scale model in axial injected flow . . . . 63
4.1.1.2 Nozzle geometry and needle system . . . . 64
4.1.1.3 Instrumentation . . . . 71
4.1.2 Static pressure evolution . . . . 75
4.1.3 Acoustic insulation of the test section . . . . 76
4.1.4 Example of flow–acoustic coupling . . . . 80
4.1.5Influence of the inhibitor parameters . . . . 82
4.1.5.1 Influence of the inhibitor–nozzle distance . . . . 83
4.1.5.2 Influence of the internal diameter of the inhibitor . . 86
4.1.6 Influence of the test section length . . . . 88
4.1.7 Influence of the nozzle geometry . . . . 90
4.1.7.1 Pressure fluctuations at the forward end of the test
section . . . . 90
4.1.7.2 Pressure fluctuations at the backward end of the test section . . . . 95
4.1.8 Conclusion . . . . 98
4.2 Radial injected flow configuration . . . . 99
4.2.1 Experimental set-up . . . . 99
4.2.1.1 Experimental set-up . . . . 99
4.2.1.2 The instrumentation . . . 105
4.2.2 Flow field investigation . . . 106
4.2.3 Acoustic insulation of the test section . . . 111
4.2.4 Aeroacoustic investigation . . . 113
4.2.4.1 Investigation of the SVS instability . . . 114
4.2.4.2 Investigation of the OVS/SVS instability . . . 115
4.2.4.2.1 Inhibitor at 1/2 of the test section . . . 115
4.2.4.2.2 Inhibitor at 3/4 of the test section . . . 116
4.2.4.3 Interpretation . . . 118
4.3 Conclusions of the experimental acoustic investigation . . . 121
5Investigation of the flow by PIV 123 5.1 Characterization and Identification of Vortices . . . 124
5 .1.1 Characteristics of a Vortex . . . 124
5 .1.2 Identification of a Vortex . . . 125
5 .1.3 Eduction of a Vortex . . . 126
5 .2 Experimental Set-up . . . 127
5.2.1 The Sub-scale Model . . . 127
5.2.2 The PIV Instrumentation and Post-processing . . . 128
5 .2.3 The Adaptive Control System . . . 131
5 .3 The operating conditions . . . 132
5 .4 Analysis of the PIV Results . . . 135
5 .4.1 Mean Flow Field . . . 135
5 .4.2 Vortex Characteristics . . . 139
5 .5 Discussion and Conclusions . . . 146
6 Numerical investigation 149 6.1 Description of the CPS code . . . 15 0 6.2 Methodology of the numerical approach . . . 151
6.3 Axial injected flow configuration . . . 15 5 6.3.1 Simulation with the submerged nozzle . . . 15 5 6.3.1.1 The mesh and boundary conditions . . . 156
6.3.1.2 The grid dependency . . . 15 7 6.3.1.3 The unsteady simulation . . . 157
6.3.1.4 The averaged solution . . . 162
6.3.1.5The Fourier coefficient analysis . . . 167
6.3.1.6 The influence of the injected flow boundary condition 171 6.3.1.7 Comparison to the experimental data . . . 173
6.3.2 Influence of the nozzle geometry . . . 178
6.3.2.1 The unsteady simulation . . . 178
6.3.2.3 The Fourier coefficient analysis . . . 185
6.3.2.4 Comparison to the experimental data . . . 187
6.3.3 Conclusion of the axial injected flow configuration . . . 188
6.4 Radial injected flow configuration . . . 189
6.4.1 Investigation of the SVS instability . . . 189
6.4.1.1 The mesh and boundary conditions . . . 189
6.4.1.2 The unsteady simulation . . . 190
6.4.1.3 The averaged solution . . . 191
6.4.2 Investigation of the OVS/SVS instability . . . 195
6.4.2.1 The unsteady simulation . . . 196
6.4.2.2 The averaged simulation . . . 198
6.4.2.3 Comparison to the experimental data . . . 199
6.5Conclusions of the numerical acoustic investigation . . . 200
7 Conclusions and perspectives 203 7.1 Conclusions . . . 203
7.1.1 In axial injected flow . . . 205
7.1.2 In radial injected flow . . . 206
7.1.2.1 Without inhibitor . . . 206
7.1.2.2 With inhibitor . . . 207
7.2 Perspectives . . . 208
Bibliography 209 A The Wavelet analysis 217 A.1 Principle of 1D wavelet analysis . . . 217
A.2 Continuous wavelet transform . . . 218
A.3 2D continuous wavelet transform of the λ field . . . 220
B The PIV technique 223 B.1 Principle . . . 223
B.2 Recording techniques . . . 225
B.3 Tracer particles . . . 225
B.4 Image processing . . . 227
C Numerical investigation 231 C.1 The CPS code . . . 231
C.1.1 Basic Equations . . . 231
C.1.2 Spatial discretization of the inviscid part . . . 232
C.1.3 Spatial discretization of the diffusive parts . . . 233
C.1.4 Time integration . . . 233
C.1.5Boundary conditions . . . 234
C.2 The Mesh analysis . . . 234
Abstract
The present research is an experimental and numerical study of aeroacoustic phe- nomena occurring in large solid rocket motors (SRM) as the Ariane 5boosters. The emphasis is given to aeroacoustic instabilities that may lead to pressure and thrust oscillations which reduce the rocket motor performance and could damage the pay- load. The study is carried out within the framework of a CNES (Centre National d’Etudes Spatiales) research program.
Large SRM are composed of a submerged nozzle and segmented propellant grains separated by inhibitors. During propellant combustion, a cavity appears around the nozzle. Vortical flow structures may be formed from the inhibitor (Obstacle Vor- tex Shedding – OVS) or from natural instability of the radial flow resulting from the propellant combustion (Surface Vortex Shedding – SVS). Such hydrodynamic manifestations drive pressure oscillations in the confined flow established in the mo- tor. When the vortex shedding frequency synchronizes acoustic modes of the motor chamber, resonance may occur and sound pressure can be amplified by vortex-nozzle interaction.
Original analytical models, in particular based on vortex–sound theory, point out the parameters controlling the flow–acoustic coupling and the effect of the nozzle design on sound production. They allow the appropriate definition of experimental tests.
The experiments are conducted on axisymmetric cold flow models respecting the Mach number similarity with the Ariane 5SRM. The test section includes only one inhibitor and a submerged nozzle. The flow is either created by an axial air injection at the forward end or by a radial injection uniformly distributed along chamber porous walls. The internal Mach number can be varied continuously by means of a movable needle placed in the nozzle throat. Acoustic pressure measurements are taken by means of PCB piezoelectric transducers. A particle image velocimetry technique (PIV) is used to analyze the effect of the acoustic resonance on the mean flow field and vortex properties. An active control loop is exploited to obtain resonant and non-resonant conditions for the same operating point.
Finally, numerical simulations are performed using a time dependent Navier-Stokes solver. The analysis of the unsteady simulations provides pressure spectra, sequence of vorticity fields and average flow field. Comparison to experimental data is conducted.
The OVS and SVS instabilities are identified. The inhibitor parameters, the cham- ber Mach number and length, and the nozzle geometry are varied to analyze their effect on the flow–acoustic coupling.
The conclusions state that flow-acoustic coupling is mainly observed for nozzles in-
cluding cavity. The nozzle geometry has an effect on the pressure oscillations through
vortices travelling in front of the cavity entrance. When resonance occurs, the sound
pressure level increases linearly with the chamber Mach number, the frequency and
the cavity volume. In absence of cavity, the pressure fluctuations are damped.
R´ esum´ e
La pr´ esente recherche est une ´ etude exp´ erimentale et num´ erique des ph´ enom` enes a´ eroacoustiques se produisant dans les moteurs ` a propergol solide de grandes di- mensions (MPS), tels les acc´ el´ erateurs ` a poudre d’Ariane 5. L’accent est mis sur les instabilit´ es a´ eroacoustiques qui peuvent entraˆiner des oscillations de pression et de pouss´ ee r´ eduisant les performances de la fus´ ee et endommageant la charge embarqu´ ee.
Cette ´ etude est men´ ee dans le cadre d’un programme de recherche du Centre National d’Etudes Spatiales (CNES).
Les MPS sont compos´ es d’une tuy` ere int´ egr´ ee et de blocs de propergol segment´ es, s´ epar´ es par des protections thermiques (PT). Au cours de la combustion, une cavit´ e apparaˆit autour de la tuy` ere int´ egr´ ee. Des structures tourbillonnaires peuvent ˆ etre en- gendr´ ees par la PT (D´ etachement Tourbillonnaire d’Obstacle - DTO) ou par l’instabilit´ e naturelle de l’´ ecoulement radial, issu de la combustion du propergol (D´ etachement Tourbillonnaire de Surface - DTS). De tels ph´ enom` enes hydrodynamiques provoquent des oscillations au sein de l’´ ecoulement interne au moteur. Lorsque la fr´ equence de d´ etachement tourbillonnaire co¨ıncide avec l’un des modes acoustiques de la cham- bre de combustion, une r´ esonance peut se produire et la pression sonore peut ˆ etre amplifi´ ee par l’interaction tourbillon-tuy` ere.
Des mod` eles analytiques originaux, bas´ es en particulier sur la th´ eorie de Powell- Howe, mettent en ´ evidence les param` etres contrˆ olant le couplage a´ eroacoustique et l’effet de la g´ eom´ etrie de la tuy` ere sur la production sonore. Ils permettent de d´ efinir les conditions exp´ erimentales.
Les exp´ eriences ont ´ et´ e effectu´ ees dans des mod` eles axisym´ etriques en gaz froid respectant la similitude du nombre de Mach avec celui du MPS d’Ariane 5. La veine d’essai comporte seulement une PT et une tuy` ere int´ egr´ ee. L’´ ecoulement est cr´ e´ e, soit par injection axiale au fond avant, soit par injection radiale uniform´ ement r´ epartie le long de cylindres poreux. Le nombre de Mach interne peut ˆ etre modifi´ e de fa¸con continue grˆ ace ` a une aiguille mobile plac´ ee dans le col de la tuy` ere. Les mesures de pression acoustique sont prises au moyen de capteurs pi´ ezo-´ electriques. La technique de v´ elocim´ etrie par image de particules (en anglais, PIV) est utilis´ ee pour analyser l’effet de la r´ esonance acoustique sur l’´ ecoulement moyen et sur les propri´ et´ es des tourbillons. Une boucle de contrˆ ole adaptatif est exploit´ ee pour obtenir des conditions r´ esonante et non-r´ esonante pour le mˆ eme point de fonctionnement.
Finalement, des simulations num´ eriques sont obtenues au moyen d’un code de
calcul des ´ equations temporelles de Navier-Stokes. L’analyse des simulations non-
stationnaires fournit les spectres de pression, la s´ equence des champs de vorticit´ e et
l’´ ecoulement moyen. Ces r´ esultats num´ eriques sont compar´ es ` a la base de donn´ ees
exp´ erimentales.
la PT, le nombre de Mach et la longueur de la chambre, ainsi que la g´ eom´ etrie de la tuy` ere sont modifi´ es de mani` ere ` a analyser leur effet sur le couplage a´ eroacoustique.
Les conclusions indiquent que le couplage a´ eroacoustique est principalement ob-
serv´ e pour les tuy` eres avec cavit´ e. La g´ eom´ etrie de la tuy` ere a un effet important
dans l’amplification des oscillations de pression dues au couplage entre les fluctua-
tions acoustiques induites par le volume de la cavit´ e et les tourbillons se d´ epla¸cant
en face de l’entr´ ee de la cavit´ e. Quand une r´ esonance apparaˆit, le niveau de pression
acoustique augmente lin´ eairement en relation avec le nombre de Mach, la fr´ equence
et le volume de la cavit´ e. En l’absence de cavit´ e, les fluctuations de pression sont
amorties.
Acknowledgments
The European Space Agency (ESA) and the Centre National d’Etudes Spatiales (CNES) that supported in part this work are first gratefully acknowledged. In par- ticular, Mr. J. Gigou from ESA and Mr. R. Bec from the CNES.
My most sincere thanks to my supervisor and promoter, Professor Jean-Marie Buchlin, for his guidance and continuous support during the development of the work.
I appreciate his encouragements, his education in the art of presentation and his reading of the manuscript.
I wish to express my gratitude to my co-supervisor, Professor Domenico Olivari, for helping me to solve the crucial questions. I am also indebted to Philippe Plan- quart for providing me good advises throughout the thesis. I am equally thankful to the von Karman Institute for Fluid Dynamics and the Environmental and Applied Fluid Mechanics Department (EA) for offering me a unique opportunity to work in a stimulating international environment. Thank you Professors John Wendt, Mario Carbonaro and Michel Riethmuller.
I also would like to thank Serge Radulovic for getting me the fellowship and being my sponsor at the CNES. I express my gratitude and respect to Mico Hirschberg from the Technical University of Eindhoven for being a nice advisor and friend. You provided me a light through the darkness of acoustics by drawing my attention to the fundamental aspects.
This work is part of a research program coordinated by CNES and ONERA. I would like to thank all the participants for their interesting discussions during the many CNES meetings. Your collaboration and pertinent questions encouraged me to work harder. Thank you Frank Godfroy (SNPE), Fran¸ cois Vuillot and Michel Pr´ evost (ONERA), and many others.
I also express my gratitude to Jean-Fran¸cois Gu´ ery from SNPE for installing the CPS code at the VKI. I appreciate a lot your kindness and availability to solve the numerical problems and all my technical doubts during the thesis. Special thanks to S´ ebastien Candel and Manuel Mettenleiter (from Ecole Centrale Paris) for providing the adaptive control device and applying it to the VKI model. I am equally thankful to J´ erˆ ome Griffond and Gr´ egoire Casalis for the theoretical development related to the radial flow and its VKI application.
I am indebted to Olivier Repellin for assisting me during the PIV measurements, to Timo Deuschle, Val´ erie Chagras and Dilek Yildiz for their contributions to the acoustic part.
The experimental part of this work could not have been accomplished without the
assistance of the EA personnel. Thank you Pascal, Nils, Louis, Didier, Jacques, Karl,
Next, I would like to thank my Ph.D. colleagues and friends who I enjoyed to work with during my stay at VKI. Special thanks to Agnes for our long discussion and squash matches; to Ozgur for sharing the office, being so surprising and saving me during my Turkish trip; to Vincent and Olivier for your hospitality during the CNES meeting in Paris; to Patrick, Christophe, Thomas, Laurent, Jean-Baptiste, ...
for being so nice friends.
Finally a warm thank for my family for ever trusting me and supporting my
choices, and for their love through especially difficult moments.
List of Tables
1.1 Comparison of the vortex–induced oscillation data. . . . 2 2.1 The launch vehicles overview (operational or in development) . . . . . 14 2.2 Characteristics of propulsion system types. . . . . 17 2.3 Characteristics of the Ariane 5fairing, Speltra and vehicle equipment
bay (VEB). . . . 21 2.4 Characteristics of the Ariane 5 motor stages. . . . . 23 2.5 Characteristics of the solid propellant motors. . . . 30 4.1 Comparison between the experimental conditions (nominal and range)
of the axial injected flow set-up and the Ariane 5full–scale booster parameters. . . . 69 4.2 Specifications of the PCB piezoelectric transducers Mod. 106B50 and
of the amplifying power unit Mod. 483B08. . . . 72 4.3 Characteristics of sintered–bronze sphere Poral plates - Bronze 90/10. 78 4.4 Comparison between the predicted and the experimental Mach num-
bers for coupling occurrence in function of the total length variation. . 90 4.5Comparison between the nozzle cavity volumes and the maximum pres-
sure levels. . . . 93 4.6 Comparison between the experimental conditions (nominal and range)
of the radial injected flow set-up and the Ariane 5full–scale booster parameters. . . 104 4.7 Summary of the experimental acoustic results with radial injection flow.118 5.1 Parameters of the three PIV configurations. . . 135 5.2 Comparison of the position of the recirculation bubble center for the
three configurations. . . 136 5.3 Number of velocity fields recorded for the three configurations, and
number of vortices found. . . 141
6.1 Coordinates of the virtual sensors. . . 15 6
6.2 Position of the center of the recirculation bubble from CPS and PIV. . 176
6.3 Coordinates of the experimental piezoelectric probes. . . 177
List of Figures
1.1 Internal geometry of the Ariane 5 solid rocket motor. . . . 1
1.2 The Aerodynamics of Segmented Solid Motors (ASSM) program. . . . 4
1.3 Methodology of the research related to the Ariane 5P230/MPS. . . . 6
2.1 The first rockets originated in China at the 12th century. . . . . 8
2.2 The Congreve and Hale rockets. . . . 8
2.3 The Jules Verne capsule and the Tsiolkowski rockets. . . . 9
2.4 Goddard rockets. . . . 11
2.5 The Ariane launchers family. . . . . 13
2.6 The rocket motor. . . . . 15
2.7 The Ariane 5 launcher. . . . 20
2.8 The Ariane 5 elements. . . . 22
2.9 The internal geometry of the Ariane 5booster. . . . 24
2.10 The elements of a solid rocket motor. . . . 25
2.11 Grain configurations. . . . 26
2.12 Burning surface progression in a star grain. . . . 26
2.13 Photography of the real Ariane 5booster nozzle. . . . 27
2.14 Mean flow, velocity vectors and streamlines. . . . 28
2.15 Flexible bearing gimbaling nozzle. . . . . 28
2.16 The thrust vector control methods. . . . 29
2.17 SRM internal geometry. . . . 31
2.18 SRMU internal geometry during burn. . . . 31
2.19 RSRM internal geometry. . . . 31
3.1 Plane wave . . . . 37
3.2 Acoustic pressure and velocity shapes of the first acoustic mode of a closed–closed tube of length L. . . . 38
3.3 Description of the theoretical problem. . . . 40
3.4 Streamlines, and axial velocity magnitude of the Taylor flow. . . . 42
3.5 Vortex shedding from a backward facing step. . . . 43
3.6 Obstacle vortex shedding (OVS). . . . 43
3.7 Surface vortex shedding (SVS). . . . 44
3.8 Stability theory applied to the VKI model. . . . . 45
3.9 The flow–acoustic coupling. . . . 47
3.10 Axial evolution of the acoustic velocity. . . . . 51
3.11 Theoretical modeling of the vortex–nozzle interaction. . . . 53
4.2 The 1/30–scale modular axisymmetric set-up for fully axial injected flow. 63
4.3 Detailed drawing of the submerged nozzle. . . . 64
4.4 Photograph of the submerged nozzle. . . . 65
4.5Drawing of the needle in the submerged nozzle. . . . 66
4.6 Expected vortex path and interaction with the needle system. . . . 66
4.7 Linear evolution of the Mach number with the needle position. . . . . 67
4.8 Technical drawing of the needle system. . . . 68
4.9 Photograph of the needle head inside the submerged nozzle. . . . 69
4.10 Photographs of the 1/30-scale axisymmetric set-up for fully axial in- jected flow. . . . 70
4.11 Drawings of the different exhaust nozzle geometry’s. . . . 71
4.12 Drawing of the nozzle 9 with a larger cavity volume. . . . 72
4.13 Positions of the PCB transducers and hot wire probe in the axial model. 73 4.14 Comparison of the mass flow rates computed from the sonic condition at the nozzle throat and measured by the orifice plate flow meter. . . . 74
4.15Evolution of different pressures with the Mach number in the segments. 75 4.16 Comparison between VKI experiments and the theoretical modeling of the pressure drop through stacked porous plates. . . . 78
4.17 Contours of pressure fluctuation spectrum on both sides of the porous plates. . . . 79
4.18 Pressure fluctuation spectrum on both sides of the porous plate for a Mach number of 0.09. . . . 79
4.19 Contour of pressure fluctuations. L = 393 mm ; l = 71 mm ; d = 5 8 mm ; nozzle 1. . . . 80
4.20 Contour of velocity fluctuations. . . . . 81
4.21 Contours of pressure fluctuations and evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude. L = 393 mm ; l = 71 mm ; d = 5 8 mm ; nozzle 1. . . . . 82
4.22 Contours of pressure fluctuations. L = 393 mm ; d = 5 8 mm ; l = 46 mm & 71 mm ; nozzle 1. . . . 83
4.23 Evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude for different inhibitor–nozzle distances. L = 393 mm ; d = 5 8 mm ; nozzle 1. . . . 84
4.24 Evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude for different inhibitor–nozzle distances. L = 393 mm ; d = 5 8 mm ; nozzle 7. . . . 85
4.25Evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude for different inhibitor heights. L = 393 mm ; l = 71 mm ; nozzle 7. . . . . 86
4.26 Evolution of the maximum amplitude of the pressure fluctuation for different ratios l/h. . . . 87
4.27 Evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude for different total lengths. l = 71 mm ; d = 5 8 mm ; nozzle 7. . . . 89
4.28 Acoustic velocity fluctuation shapes. l = 71 mm ; L = 393 mm &
188 mm. . . . 89
4.29 Evolution of the maximum of the pressure fluctuation, in terms of Strouhal number and amplitude for different nozzle geometries at low Mach number. l = 71 mm ; d = 5 8 mm ; nozzles 1 to 6. . . . 91 4.30 Evolution of the maximum of the pressure fluctuation for different noz-
zle geometries at low Mach number. l = 71 mm ; d = 58 mm ; nozzles 1 to 6. . . . 92 4.31 Evolution of the maximum of the pressure fluctuation, in terms of
Strouhal number and amplitude for different nozzle geometries at high Mach number. l = 71 mm & 46 mm ; d = 58 mm ; nozzles 7 & 8. . . 93 4.32 Evolution of the maximum of the pressure fluctuation, in terms of
Strouhal number and amplitude for nozzles 7 and 9. l = 71 mm ; d = 5 8 mm. . . . 94 4.33 Evolution of the maximum sound pressure level versus the nozzle cavity
volume. l = 71 mm ; d = 5 8 mm. . . . 95 4.34 Comparison of the evolution of the maximum of the pressure fluctu-
ation at different locations along the test section wall and for noz- zles 1 & 7. L = 393 mm ; l = 71 mm ; d = 5 8 mm. . . . 96 4.35Evolution of the Strouhal number of the pressure and velocity fluctu-
ations. . . . 97 4.36 The 1/30–scale modular axisymmetric set-up for radial injected flow. . 100 4.37 Photographs of the 1/30-scale axisymmetric set-up for radial injected
flow. . . 101 4.38 The porous cylinders and their settling chambers. . . 102 4.39 Drawing of the nozzle 10 for larger Mach numbers. . . 103 4.40 Instrumentation of the 1/30–scale axisymmetric set-up for radial in-
jected flow. . . 105 4.41 Hot wire anemometer for flow field characterization. . . 106 4.42 Detailed photograph of the hot wire and the test section for flow field
characterization. . . 107 4.43 Evolution of the axial velocity along the symmetry axis. M 0 = 0.09. . 108 4.44 Radial profiles of absolute velocity at different axial positions. . . 108 4.45Ratio of axial to radial velocity components. . . 109 4.46 Spectrum of the velocity fluctuation at 3 mm from the injection wall.
M 0 = 0.09. . . 110 4.47 Axial evolution of the velocity fluctuation at 3 mm from the injection
wall. M 0 = 0.09. . . 111 4.48 Contours of pressure fluctuations and evolution of the maximum of the
pressure fluctuation, in terms of Strouhal number and amplitude on both sides of the porous cylinders. . . 112 4.49 Pressure fluctuation spectrum measured on both sides of the porous
cylinders for a Mach number of 0.09. . . 113 4.50 Evolution of the pressure fluctuations for the SVS instability mode -
without inhibitor. . . 114 4.51 Evolution of the pressure fluctuations for the OVS/SVS instability
mode - with inhibitor at 1/2 of the test section. . . 116 4.52 Evolution of the pressure fluctuations for the OVS/SVS instability
mode - with inhibitor at 3/4 of the test section. . . 117
4.53 Interpretation of the configuration without inhibitor. . . 119
section. . . . 120
4.55 Interpretation of the configuration with inhibitor at 3/4 of the test section. . . . 120
5 .1 The Oseen vortex. . . 125
5.2 Comparison between the λ field and the Mexican Hat (r 2 = x 2 + y 2 ). . 126
5.3 Sketch and photography of the experimental facility. . . 128
5.4 Instrumentation for PIV measurements. . . 129
5 .5 Adaptive control system. . . 131
5.6 Contour of pressure fluctuations with respect to the frequency and the mean flow velocity. . . 133
5.7 Application of the adaptive control system. . . 134
5.8 Spectrum of the pressure fluctuations. . . 135
5.9 Statistical convergence of the velocity and turbulent fluctuation. . . . 136
5.10 Mean flow, velocity vectors and streamlines. . . 137
5.11 Schematic of the recirculation bubble in the non–resonant and resonant cases at U 0 =20 m/s. . . 138
5.12 Velocity profiles in the non–resonant and resonant cases at U 0 =20 m/s. 138 5.13 Contours of turbulent fluctuations. . . 139
5.14 Example of wavelet analysis on the vorticity and the λ fields. . . 140
5.15 Spatial distribution of the vortices for U 0 =20 m/s. . . 142
5.16 Convergence for the average diameter for U 0 =20 m/s, resonant. . . 142
5.17 Group averages of the vortex characteristics in non dimensional vari- ables for the three configurations. . . 144
5.18 Evolution of the tangential velocity and vorticity distributions for the generic Oseen vortex with increasing position from the inhibitor. . . . 145
5.19 Evolution of the tangential velocity and vorticity distributions for the generic Oseen vortex under resonant and non resonant conditions. . . 146
5.20 Two scenarios for aeroacoustic coupling. . . 146
6.1 Methodology of the CPS code simulations. . . 152
6.2 Example of convergence of a pressure signal. . . 153
6.3 Contours of pressure fluctuation spectrum measured on both sides of the porous plate. . . 15 4 6.4 The axial injected flow simulation with the submerged nozzle. . . 155
6.5 Meshing of the numerical domain. . . . 15 7 6.6 Comparison between time and frequency signals for the three grids. . . 158
6.7 Waveband amplitude of the pressure spectrum for grid convergence. . 158
6.8 Axial and Radial mean velocity profiles along the radius for different grids. . . 15 8 6.9 Pressure spectra at different sensors for the axial injected flow with submerged nozzle. . . . 160
6.10 Sequence of vorticity fields. . . 162
6.11 Mean flow field for the axial injected flow with submerged nozzle. . . . 163
6.12 Axial and Radial mean velocity profiles along the radius at different axial coordinates. . . 164
6.13 Axial mean velocity profile along the radius at the inhibitor edge. . . . 165
6.14 Mappings of velocity fluctuations for the axial injected flow with sub- merged nozzle. . . 166 6.15Axial and Radial velocity fluctuation profiles along the radius at dif-
ferent axial coordinates. . . 166 6.16 Mean velocity and velocity fluctuation profiles along the symmetry axis.167 6.17 Spatial distribution of the Fourier coefficient modulus and argument
of the pressure, axial velocity and radial velocity for the first acoustic mode. . . 168 6.18 Spatial distribution of the Fourier coefficient modulus and argument of
the pressure, axial velocity and radial velocity for the second acoustic mode. . . 169 6.19 Profiles of the Fourier coefficient modulus and argument of the pressure,
axial velocity and radial velocity for the two first acoustic modes. . . . 170 6.20 Injection velocity response to variation of static pressure. . . . 172 6.21 Pressure spectra for constant and variable flow injection. . . 173 6.22 Axial and Radial mean velocity profiles along the radius for constant
and variable mass flow injection. . . 173 6.23 Comparison of pressure spectra between numerical simulation and cold
flow experiment. . . 174 6.24 Comparison of streamlines between numerical simulation and cold flow
experiment. . . 175 6.25Comparison of velocity profiles between numerical simulation and cold
flow experiment (PIV). . . 176 6.26 Comparison of the numerical and experimental profiles of the relative
modulus of the Fourier coefficient for the pressure. . . 178 6.27 The axial injected flow simulation with the convergent–divergent sec-
tion nozzle without cavity. . . 179 6.28 Pressure spectra at different sensors for the axial injected flow with
and without cavity at the nozzle. . . 180 6.29 Mean flow field for the axial injected flow with nozzle without cavity. . 181 6.30 Axial and Radial mean velocity profiles along the radius at different
axial coordinates. . . 182 6.31 Vortex path for the nozzles with and without cavity. . . 183 6.32 Mappings of velocity fluctuations for the axial injected flow with nozzle
without cavity. . . 183 6.33 Axial and Radial velocity fluctuation profiles along the radius at dif-
ferent axial coordinates. . . 184 6.34 Mean velocity and velocity fluctuation profiles along the symmetry axis.184 6.35Axial evolution of the Fourier coefficient modulus and argument of the
pressure, axial velocity and radial velocity. . . 185 6.36 Axial evolution of the Fourier coefficient modulus of the pressure, axial
velocity and radial velocity for the nozzles with and without cavity. . . 186 6.37 Comparison of pressure spectrum between numerical simulation and
cold flow experiment. . . 187 6.38 Comparison of velocity profiles between numerical simulation and cold
flow experiment (hot wire). . . 188 6.39 The radial injected flow simulation with the submerged nozzle and
without inhibitor. . . 189
submerged nozzle and without inhibitor. . . 191 6.41 Instantaneous vorticity field for the radial injected flow with submerged
nozzle and without inhibitor. . . 191 6.42 Mean flow field for the radial injected flow without inhibitor. . . 192 6.43 Mean velocity magnitude profiles along the radius at different axial
positions. . . 193 6.44 Comparison of the numerical, experimental and theoretical velocity
magnitude profiles along the radius at x = 0.35m from the forward end.193 6.45Mappings of velocity fluctuations for the radial injected flow with sub-
merged nozzle and without inhibitor. . . 194 6.46 Evolution of the velocity fluctuation along the axial position at 3 mm
from the injection wall. . . 194 6.47 Comparison of the numerical and experimental evolution of the velocity
fluctuation amplitude along the axial position at 3 mm from the side wall. . . 195 6.48 The radial injected flow simulation with the submerged nozzle and with
inhibitor. . . . 195 6.49 Pressure spectra at different sensors for the radial injected flow with
submerged nozzle and with inhibitor. . . 197 6.50 Instantaneous vorticity field for the radial injected flow with submerged
nozzle and with inhibitor. . . 197 6.51 Mean flow field for the radial injected flow with inhibitor. . . 199 6.52 Comparison of the experimental and computed pressure spectra. . . . 199 A.1 Period doubling sinusoid and its Fourier transform. . . 218 A.2 Influence of the dilatation l and translation x parameters of the Morlet
wavelet ψ l,x . . . 219 A.3 Modulus of the wavelet transform of the signal. . . 219 A.4 2D Marr (Mexican Hat) wavelet. . . 221 B.1 Basic set-up of two dimensional PIV system. . . . 224 B.2 Two theoretical pictures with the tracers displacements. . . 224 B.3 Cross-correlation functionvof 64 × 64 pixels window. . . 228 B.4 Cross-correlation processing flow-chart. . . 229 C.1 Control cell for the diffusive terms. . . 233 C.2 Mesh density analysis for the numerical domain of the axial injected
flow configuration with the submerged nozzle. . . 235 C.3 Mesh density analysis for the numerical domain of the radial injected
flow configuration with the submerged nozzle and without inhibitor. . 236 C.4 Mesh density analysis for the numerical domain of the radial injected
flow configuration with the submerged nozzle and with inhibitor. . . . 237
Chapter 1
Introduction
The present research is an experimental and numerical investigation of the aeroa- coustic instabilities occurring in a sub-scaled cold flow model of the Ariane 5 solid rocket motor. The phenomenon develops in the confined flow established in the motor and involves a coupling between hydrodynamic instabilities and longitudinal acoustic modes.
Aeroacoustic instabilities occur in a wide range of technical applications. The re- sulting oscillations are sometimes wanted in systems designed to produce the periodic motion efficiently as in musical instruments. Nevertheless, in most cases aeroacoustic instabilities perturb the operation, as for the Ariane 5 launcher. Then, that research finds its interest knowing that these aeroacoustic instabilities lead to pressure and thrust oscillations which reduce the rocket motor performances and could damage the payload.
For technological reasons, large solid propellant boosters, such as the Ariane 5 accelerator, are made of segmented propellant grains and a submerged nozzle (fig- ure 1.1). Two inhibitor rings ensuring thermal protection separate the propellant grains.
Inhibitors
Nozzle
Propellant grains
Figure 1.1: Internal geometry of the Ariane 5 solid rocket motor.
The hot burnt gas flow originates radially from the burning surface of the com- bustion chamber and then develops longitudinally before reaching the exhaust nozzle.
Propellant is consumed during the flight at a rate which exceeds that of the inhibitor
rings. Then, regression of the burning surface is faster than the consumption of the inhibitors. These protrude in the flow after a certain time producing regions of high shear where vortex shedding may be generated. This hydrodynamic instability is called OVS (Obstacle Vortex Shedding). On the other hand, the bending flow re- sulting from the propellant combustion also features a natural instability potentially capable of generating vortices and called SVS (Surface Vortex Shedding). These two mechanisms drive pressure oscillation if the shedding is coupled to one of the acoustic resonant modes of the motor chamber.
These oscillations have received considerable attention in the past twenty years in relation with developments of large solid propellant motors. Although these motors were predicted stable by classical stability assessment methods (Lovine & Waugh, 1975; Brown et al., 1981), such grain segmentation conducted to low amplitude, but sustained, pressure and thrust oscillations, on first longitudinal acoustic mode frequen- cies. These pressure oscillations have been reported for the Space Shuttle RSRM, the Titan–34D SRM, the Titan–IV SRMU and the Ariane 5 MPS (Mason et al., 1979;
Blomshield & Mathes, 1993; Brown et al., 1981; Dotson et al., 1997; Scippa et al., 1994). All these boosters have a length over diameter ratio (L/D) in the range 9 − 12 and demonstrated similar pressure oscillations, whatever the number of segments. Ta- ble 1.1 yields a comparison of the published vortex–induced oscillation data. Values are not reported in the literature for the Titan–34D SRM. Zero-peak relative ampli- tudes are typically less than 0.5% for pressure oscillations and less than 5% for thrust oscillations.
RSRM SRMU MPS
First acoustic mode
MPO (0-to-peak) [kPa] − 16.2 25.5
MPO (0-to-peak) / mean pressure 0.0025 0.005 0.0027 Time of occurrence of MPO 70 − 75 57 − 64 90 − 95
Second acoustic mode
MPO (0-to-peak) [kPa] − No −
MPO (0-to-peak) / mean pressure − No 0.002
Time of occurrence of MPO − No 65 − 70
Table 1.1: Comparison of the vortex–induced oscillation data. MPO stands for “max- imum pressure oscillation”. From Dotson et al. (1997).
Vortex driven acoustically coupled oscillations were later observed on sub–scaled model rockets (see Vuillot et al., 1993; Pr´ evost et al., 1996; Traineau et al., 1997).
These various studies point out that the frequency of oscillation increases as the grain
surface rises. This observation typifies processes which depend on the velocity of
the flow. Then, the oscillations could be attributed to a periodic vortex shedding
resulting from a strong coupling between the vortices and the acoustic properties of
the combustion chamber.
1.1. ASSM program
1.1 ASSM program
Stability prevision of large solid propellant rocket motors has been an active sub- ject, both in the USA and in Europe. To support the development of the Ariane 5 P230/MPS solid motors, the CNES 1 initiated, in 1989, the ASSM 2 research pro- gram. This multi collaborative project is supported by the CNES and the Industrials:
Snecma, SNPE 3 and AML 4 . The CNES is the program manager while the scientific coordination is carried out by ONERA 5 . Most of the scientific projects are executed by the Industrials or by Research Laboratories and Universities, such as the VKI.
The scientific methodology of the ASSM program is based on the understanding of the physical aspects, on their modeling and on the development of stability assessment tools. The objective, as defined in 1990, was to predict the pressure oscillation levels and frequencies. That ambitious objective needed to develop direct numerical simu- lation codes and to design cold flow experiments and static firing tests. Of course, the program is not limited to the investigation of the aeroacoustic instabilities. It is also addressed to the combustion instabilities, the flow–structure coupling, the two-phase flow coupling, among others.
Between 1989 and 1998, the program was divided into three research themes:
• The SF theme (Flow Stability). This theme was oriented to the understanding and the modeling of the vortex shedding which is expected to be responsible of the pressure and thrust oscillations. The objective was to predict the levels and frequencies of the instability modes and/or to evaluate the stability margin for naturally stable motors.
• The PTI theme (Internal Thermal Protection). This theme was axed on the 3D characterization of the steady aerodynamic and on the determination of the thermal flux in order to predict the removal of the material used for the thermal protections.
• The PhC theme (Condensed Phase). The alumni deposit observed during static firing tests of the Ariane 5 MPS was very important. It was explained by the sizing of the alumni particles. The objective of the theme was then to predict the size of the alumni particles generated by the propellant combustion.
Since 1998, the structure has changed to give place to 6 research projects, as indicated in figure 1.2. Projects 1, 2 and 4 are the continuity of the three themes initiated in 1989. Project 3 is oriented to the flow–structure coupling and to the development of physical models for the computational codes. An active control project aims to investigate the possibilities of applying such adaptive techniques to reduce the pressure and thrust oscillations. Finally, the 5 th project called DAME (Development and Improvement of Experimental Facilities) groups all the experimental aspects of the project. It is split into two sub-projects oriented to the cold flow experiments and firing tests, respectively. The aim of that project is to quantify the pressure and thrust levels (firing tests), to model fundamental aspects of the problem by isolating
1
Centre National d’Etudes Spatiales
2
Aerodynamics of Segmented Solid Motors
3
Soci´ et´ e Nationale des Poudres et Explosifs
4
A´ erospatiale Matra Lanceurs
5
Office National d’Etudes et de Recherches A´ erospatiales
Figure 1.2: The Aerodynamics of Segmented Solid Motors (ASSM) program.
them (cold flow experiments) and to validate the physical models to be implemented in numerical computations. The cold flow experiments have the advantage to allow parametrical investigations in a cheaper way than the firing tests. Nevertheless, they are far to take into account all the parameters and should then be considered only for investigation of fundamental aspects.
1.2 Objectives and methodology of the present work
This research has been carried out at the von Karman Institute (VKI) within the framework of the ASSM research program, through the “DAME/cold flow experi- ments” project. It offers to the VKI the opportunity to work in partnership with TUE 1 , SNPE, ONERA and ENSMA 2 . Moreover, the VKI has also collaborated with the Ecole Centrale Paris through the Active Control project.
The specific objectives of the present study are the following:
• To carry out an experimental investigation of the flow–acoustic coupling phe- nomenon, using a sub-scaled axisymmetric cold flow model representative of the geometry of the real booster. The test section includes only one inhibitor where the vortices are generated and a submerged nozzle where the vortices collide to generate sound. The emphasis is particularly given to the effect of parameters such as the total length of the test section, the inhibitor–nozzle distance, the inhibitor diameter and the injected flow velocity ;
• To analyze the effect of the acoustic resonance on the mean flow field and on the vortex properties ;
• To investigate the effect of the nozzle design on the pressure oscillations by car- rying out cold flow experiments and using numerical approach ;
• To validate the numerical computations by the cold flow experiments.
1
Technical University of Eindhoven
2
Ecole Nationale Sup´ erieure de M´ ecanique et d’A´ erotechnique
1.3. Chapters overview In both experimental and numerical approaches, the flow is injected axially through the forward end in a first investigation. In a second investigation, the hot burnt gas flow from the combustion is simulated by radially injected flow. The reason for using first an axial injection is the resulting better acoustic insulation of the test section from the air supply (see chapter 4 for more details). That appropriate insulation is necessary as the research deals with acoustic measurements in the test section. How- ever, such a methodology allows to emphasize the OVS (Obstacle Vortex Shedding) and SVS (Surface Vortex Shedding) hydrodynamic instabilities separately. Indeed, the SVS comes from the natural instability of the bending flow resulting from the propellant combustion and is therefore simulated only through the radial injection.
Consequently, the axial injected flow configuration mimickes the OVS instability while the radial configuration may simulate both SVS/OVS instability or the SVS alone de- pending if the inhibitor is used or not.
In fulfilling these objectives, it is intended to establish modeling of the occurrence of flow–acoustic coupling and a physical interpretation of the nozzle design effect on the pressure oscillations.
The complete methodology of the thesis is summarized in the flowchart shown in figure 1.3.
1.3 Chapters overview
A review of the rocket history and of the propulsion systems is given in chapter 2.
Then, the Ariane 5 launcher architecture is reported followed by a detailed description of the Ariane 5 booster and of other large solid rocket motors.
The objective of chapter 3 is twofold: the first part deals with the theoretical background reviewed from literature. In particular, the fundamentals of acoustics and hydrodynamics and a physical interpretation of the flow–acoustic coupling are proposed. The second part is devoted to present original models of the flow–acoustic coupling developed in the frame of this thesis.
In chapter 4 the experimental acoustic investigation is presented. Acoustic pres- sure measurements are carried out to investigate the flow–acoustic coupling and to characterize the influence of the nozzle design and other parameters on the pressure fluctuation levels. The acoustic measurements performed by means of PCB piezoelec- tric transducers are taken in a 1/30–scale axisymmetric cold flow model of the Ariane 5 SRM with either axial or radial injected flows. The experimental database allows the validation of the theoretical modeling developed in chapter 3.
A particle image velocimetry technique (PIV) is used to analyze the effect of the
acoustic resonance on the mean flow field and on the vortex properties. The PIV
measurements are taken in a transparent 1/15–scale axisymmetric cold flow model of
the Ariane 5 SRM with axial injected flow. An active noise control device is exploited
to obtain resonant and non-resonant conditions for the same operating point. The
resonance effect is analyzed in terms of mean flow field and vortex properties. This
approach is presented in chapter 5.
Ariane 5 P230/MPS aeroacoustics research
Inhibitors
Nozzle
Propellant grains
Axial injected flow
OVS instability
Radial injected flow
SVS/OVS instability or SVS alone
Experimental Numerical Experimental
BOOSTER 1/15 BOOSTER 1/30 CPS (SNPE) BOOSTER 1/30
Fluid dynamic (PIV)
Acoustic (PCB)
Acoustic and fluid dynamic
Acoustic (PCB) Comparison experimental − numerical
Comparison axial − radial injected flow configurations Analytical model of occurrence of flow–acoustic
coupling –Interpretation of nozzle effect on pressure oscillations
Resonance effect on vortices
Figure 1.3: Methodology of the research related to the Ariane 5 P230/MPS.
Numerical simulations, performed using the CPS code developed at SNPE and Bertin Technologies, under CNES and SNPE support, are reported in chapter 6. The numerical simulations are performed with either axial or radial injected flows and for two different nozzle geometries. The computations provide flow field characteristics not available from the experimental approach, allowing a better understanding of the nozzle design effect on the pressure oscillations. The validation of the numerical simulations by cold flow experiments is also the subject of chapter 6.
Finally, chapter 7 draws the general conclusions and proposes future work.
Chapter 2
Propulsion systems and Ariane 5 launcher
2.1 History of the launchers
From time immemorial, we have wanted to leave the Earth and explore space. The discovery of the action–reaction principle by Newton as the key to the space explo- ration remains a major event in the thought history. Its consequence, the development of modern launchers, led to open the Universe to the man exploration.
However, this intellectual breakthrough does not guarantee an easy transition from the theory to its application. Although the rocket has been used from time to time duringone millennium, its application was limited to weapons until the early 20th century. Prodigious efforts, stimulated by both World Wars, were necessary for the astronautics to go from the dream to the reality.
2.1.1 Rockets, from the East to the West
The first rocket may have originated in China as early as the 12th or 13th centuries (National Air and Space Museum, 1991). These were propelled by gunpowder and were probably used as weapons (figure 2.1). The Mongols propagated the Chinese discovery by attackingpeople who copied and improved the rockets, such as the Japanese, the Indians, the Arab.
Europe realized, only at the end of the 18th century, that rockets could be formidable
weapons. The decisive event did not happen in Europe but in India. The son of the
Mysore Rajah equipped its army with 5000 rocket throwers and used his rockets
against the British at the battles of Seringapatam in 1792 and 1799 (Encyclopae-
dia Universalis, 1989). The success was such that British soldier William Congreve
designed a much improved version for British forces (Brown, 1996). Congreve built
rockets of 15 different sizes but the most commonly used was a 14.5 kgblack powder
(a) (b)
Figure 2.1: The first rockets originated in China at the 12th century. (a) from Ency- clopaedia Universalis (1989). (b) from National Air and Space Museum (1991).
rocket with a range of 2700 m (figure 2.2a). Congreve rockets were used effectively in attacks against Boulogne in 1806, Copenhagen in 1807, during the War of 1812, at the battle of Waterloo and at the battle of Fort McHenry in 1814. England and other countries used Congreve rockets until the mid-19th century, although they were often unpredictable. In the mid-1800s, William Hale improved the Congreve rocket.
He eliminated the cumbersome wooden guidestisks, used previously, by designing his rocket to rotate which improved its stability and performance (figure 2.2b). The British began to use Hale rockets during the Crimean War (1853–1856). Both Union and Confederate troops used them duringthe Civil War and by the end of it, Hale’s
(a) The Congreve rocket (b) The Hale rocket
Figure 2.2: The Congreve rocket (a) with its wooden guidestisks (cut on the photo)
and the Hale rocket (b) with spin stabilization. From Encyclopaedia Universalis
(1989).
2.1.2. Pioneers rockets had superseded Congrese’s. Improvements in cannon surpassed rockets and, except for use by the French in World War I, rockets were virtually extinct by the twentieth century.
2.1.2 Pioneers
In the late 19th century, French novelist Jules Verne (1828–1905) wrote two books entitled “From the Earth to the Moon” (1865) and “Around the Moon” (1867). These works inspired scientists to take the first steps toward space travel. Verne’s heroes, three artillerists, journey to the Moon in a space capsule that was shot from a cannon (figure 2.3a).
Konstantin Eduardovich Tsiolkowski (1857–1935), a Russian mathematics profes- sor,was the first to observe that rockets were prerequisites for space exploration. He is considered like the father of the Astronautics. As early as 1883, Tsiolkowski noted that gas expulsion could create thrust. Therefore, a rocket would operate even in a
(a) Verne Capsule (b) Tsiolkowski rockets
Figure 2.3: The Jules Verne capsule and the Tsiolkowski rockets. (a) From National Air and Space Museum (1991). (b) The top drawingis the first representation of a liquid propellant rocket. The two tanks are on the left. The ergols are mixed at “A”
and the hot gas are ejected at “B”. On the right, in the cockpit, is indicated the word
“man” (from Encyclopaedia Universalis, 1989).
vacuum. Figure 2.3b provides drawings of the Tsiolkowski rockets. In 1903, he pub- lished a milestone paper describingin detail how space flight could be accomplished with rockets. He advocated liquid oxygen and liquid hydrogen as propellants. He described staged rockets and showed mathematically that space exploration would require staging.
Dr. Robert H. Goddard (1882–1945), professor of physics at Clark University, was the first to design, build and make flying a liquid–propelled rocket, which was poten- tially more powerful than solid–fuel types (National Air and Space Museum, 1991).
That feat required more than 200 patentable inventions. Goddard recognized that the first step into upper atmospheric and spacecraft exploration was to device liquid rockets that worked reliably. In 1919, he published his milestone paper, “A Method of ReachingExtreme Altitudes”. On March 16, 1926, near Worchester, Massachusetts, he experienced the world’s first successful liquid rocket (figure 2.4a). Propelled by liquid oxygen and gasoline, it flew for 2.5 s, reaching an altitude of 12.5 m and a speed of 28 m/s. On May 4, 1926, Goddard launched an improved version of the first rocket (figure 2.4b, right). On the left of figure 2.4b, one can see the Goddard “Hoopskirt”
rocket developed in 1928. A small rocket engine is mounted in the nose. Fuel tanks and the alcohol burners that were used to maintain fuel pressure are placed on two legs. The rocket made its most successful flight on December 26, 1928, when it flew a distance of 62.3 m in 3.2 s. These early Goddard rockets may have inspired the development of modern liquid–fuel rockets.
By 1929, Dr. Goddard had tested four rockets, each one better that the last. With this success and the assistance of Charles Lindbergh, he was able to gain a substantial grant from the Guggenheim Fund. With this backing, Goddard moved his work to the isolation of the desert near Roswell, New Mexico. There he developed pump-fed stages, clustered stages, and pressurization systems, worked on gyro control systems and developed the idea of soundingrockets. He worked his rockets up to a size of 230 kg, altitudes of 2000 m and speed of 300 m/s. When Goddard died in 1945, he had developed the first version of every piece of equipment that would be needed for a vehicle like Saturn V. His work would not be fully appreciated for another 10 years – at least, in the United States.
However, enthusiasm for rocketry was more vigorous in Russia and Germany, and Dr. Goddard’s work was followed more carefully there than at home. In Russia, the government funded research as early as 1930 through two research groups: the Leningrad Gas Dynamics Laboratory (GDI) and the Group for the Study of Jet Propulsion (GIRD). It was the latter group, under the leadership of Sergei Korolyev (1907–1966), that was effective in producingthe series of Russian successes in propul- sion that led to the launch of Sputnik.
In Germany, the government instituted vigorous research in rocketry in order to
circumvent the armament restrictions that resulted from World War I. The work was
carried out under the sponsorship of Karl Becker, head of ballistics and armament for
the German army. He appointed Walter Dornberger to develop the rockets. Dorn-
berger was joined by a young scientist, Werner von Braun (1912–1977). In 1932,
Dornberger led the construction of the test site and von Braun produced and suc-
cessfully fired their first liquid rocket, the A–1. The group had started their work in
a suburb of Berlin that clearly was not suitable for continued firings. In 1935, they
2.1.2. Pioneers
(a) (b)
Figure 2.4: Goddard rockets. (a) Schematic of the first liquid rocket launched on March 16, 1926 (from Encyclopaedia Universalis, 1989). (b) An improved version of the first liquid rocket launched on May 4, 1926 (on the right) and the Goddard
“Hoopskirt” rocket developed in 1928 (on the left) (from National Air and Space Museum, 1991).
moved to an isolated peninsula near the Baltic Sea called Peenemunde. It was at Peenemunde that the second von Braun design, the A–2, was built and successfully launched, followed by the A–3 and, in 1942, by the A–4. The A–4 was renamed the Vengeance–2, or V–2, by the army and placed in production. The V–2 was 14 m high, single-stage, weighted 11300 kg and capable of carrying a 900 kg payload to 200 km.
It was the first vehicle of any kind to kreak the sound barrier. The propellants were liquid oxygen and alcohol 1 . Six thousands V–2s were made ; 2000 fell on England.
1
The fuel was changed from the gasoline that Goddard used to alcohol because the Germans had
more potatoes than petroleum.
Much more details about the works of Goddard, Korolyev and von Braun are given in Encyclopaedia Universalis (1989).
2.1.3 Post–war years
In 1945, it was clear to the team at Peenemunde that the war was lost. With their facility in the path of the Russian army, von Braun and over 100 members of his staff decided that the United States was a preferable captor. They left Peenemunde and moved tons of equipment and documents to the Hartz mountains, where they were certain to be captured by U.S. troops. Germany defeated, the Paperclip operation organized the repartition of the remaining German rockets and scientific documents between the Allies.
von Braun and his staff were moved to Redstone Arsenal in Huntsville, Alabama, which later became Marshal Space Flight Center. Under control of the U.S. Army, von Braun continued to improve the V–2 which was launched for the first time from the U.S. in April 1946. In parallel to the U.S. Army, the U.S. Air force investigated a missile project, which became the Titan rocket, while the U.S. Navy developed the Vikingrocket. The Vikingwas launched 14 times between 1949 and 1957. In 1956, the U.S. Navy created the Army Ballistic Missile Agency, with the help of von Braun, to realized the Jupiter missile. Duringits first launch on September 20, 1956, the Jupiter reached an altitude of 1100 km and covered a distance of 5475 km from Cape Canaveral. Because the Americans did not want to be left behind the Soviets, they investigated 9 missiles programs between 1955 and 1958, such as for example the Jupiter, the Atlas and the Titan. Most of them were transformed into launchers since the United States decided in 1955 to send satellites into space. The Saturn launcher is the unique launcher family that was developed by the U.S. in a perspective of civil applications. Saturne V, used between 1967 and 1973, remains in mind as the launcher of the manned mission to the Moon.
At the end of the second war, the Soviets followed another methodology than the Americans. In place of developingnew technology launchers, the Soviets adapted the ballistic missiles. The German V–2 factory was taken down and moved to the U.R.S.S.
and Korolev started to improve the V–2 rocket. He built and tested 5 rockets, named R–1 to R–5, between 1948 and 1953. The R–7, or Zemiorka, rocket was developed in 3 years only. On October 4, 1957, that rocket launched the first artificial satellite, Spoutnik–1, from Baikonour. The Zemiorka rocket provides a thrust of 4400 kN at liftoff while the U.S. Thor missile, operational in 1958, provides only 765 kN. The concept of the Korolev rocket was so judicious that it is still in use today. Later, the U.R.S.S. developed the Proton and the Soyuz rockets. Proton was mainly used for the Mir deployment while Soyuz was devoted to the manned missions.
The other countries started much later their space programs and with less financial support than the U.S. or U.R.S.S. The first Chinese launch success dated from April 1970 with a two–staged rocket, the CZ–1. At the same period, the Japanese tested a four–staged launcher, the Lambda–4S, which after improvements became the M–III.
India launched its first rocket, the SLV–3, in July 1980 while the first flight of the
Brazilian rocket, the VLS–1, ended in failure in 1997. The European developments
2.1.3. Post–war years lead to different vehicles such as the Black Arrow (1969–1971), the Diamant (1962–
1975), the Europa (1962–1972). All these European programs were stopped at the early 1970s because of the start of the Ariane program. In July 1973, the European ministers decided to develop a heavy launcher to replace the Europa program. The objective is to be competitive for the satellites launches. The prime contractor is the CNES 1 and the first successful launch was made on December 24, 1979. In 1977, ESA 2 approved a development program aiming to improve the performance of the Ariane launcher. It resulted in a complete family of launchers with Ariane 5 as the latest one (figure 2.5).
Table 2.1 gives an overview of all the operational and in development rockets worlwide. The Ariane 5, the Titan–34D, the Titan–IV and the Space Shuttle are the only vehicles to be lifted thanks to huge solid propellant motors. The other vehicles involve small solid rockets or liquid propellants motors. As the thesis is devoted to the instabilities occurringin large solid propellant motors, only the solid rockets used by the Ariane 5, the Titan–34D, the Titan–IV and the Space Shuttle vehicles will be detailed in sections 2.3 & 2.4.
Figure 2.5: The Ariane launchers family.
1
Centre National d’Etudes Spatiales
2
European Space Agency
Countries Rockets
Brazil VLS, VLM
China LM–2*, LM–3*, LM–4*
Europe Ariane–4*, Ariane 5
India PSLV, GSLV
Israel Shavit–1, Leolink–1, Leolink–2 Japan H-II*, J-I, M-V
Russia Angara family, Kosmos–3M, Proton family, Rockot, Shtil–1, Shtil–2, Start, Strela, Soyuz U, Soyuz ST, Molniya
Ukraine Dnepr–1, Dnepr–M, Tsiklon–2, Tsiklon–3, Zenit–2, Zenit–3SL United States Athena–I, Athena–II, Atlas–II*, Atlas–III*, Atlas–V*, BA–2,
Delta–II, Delta–III, Delta–IV*, K–1, Minotaur, Pegasus XL, SSLV & Commercial Taurus, Titan–II, Titan–IVB, Space Shuttle Table 2.1: The launch vehicles overview (operational or in development). From Isakowitz et al. (1999).
2.2 Propulsion
2.2.1 Rocket motor
Although the use of black powder started in China at the 12th century and in Europe at the end of the Middle Ages, the understanding of the phenomenon involved in the propulsion is recent.
The rocket motor is a jet propulsion system for which the propulsive force comes from a momentum variation of the system itself 1 . There is no mass sample from outside but an ejection, at a certain relative speed, of a mass fraction of the system.
As shown in figure 2.6, a rocket consists of a chamber, a throat and a nozzle. The rocket generates thrust by accelerating a high-pressure gas to supersonic velocities in a converging–diverging nozzle, called Laval nozzle. In most cases, the high-pressure gas is generated by high-temperature decomposition of propellants. The application of the momentum conservation leads to look for the highest exhaust velocity.
2.2.1.1 Thrust
Rocket thrust is generated by momentum exchange between the exhaust and the vehicle and by the pressure imbalance at the nozzle exit (Brown, 1996). The thrust due to momentum exchange F m can be derived from Newton’s second law,
F m = Q m U e (2.1)
where Q m is the mass flow rate of the propellant and U e is the average velocity of the exhaust gas. Equation 2.1 assumes that the velocity of the exhaust gas acts along the nozzle centerline.
1
