Dissertations / Theses on the topic 'Solid Rocket Motors'

Particle size distribution measurements were made with a Malvern 2600c forward laser light diffraction system across the exhaust nozzle entrance and exhaust plume of a small two-dimensional rocket motor. The solid propellants tested were GAP propellants containing 2.0% and 4.69% aluminum. Surface agglomeration of the aluminum, indicated by the in-motor results, was found to decrease as the motor chamber pressures were increased. At low pressures, increasing the aluminum loading with fixed total solids decreased the mean particle size at the nozzle entrance. Exhaust plume particle size was practically independent of nozzle inlet particle diameters, supporting the critical Weber number particle breakup theory. Initial validation of the Malvern 2600c measurements was accomplished by favorable comparison to exhaust plume particle distribution results obtained using a particle collection probe. Particle sizing
Solid propellant rocket engines
Light scattering
Theses

Solid propellant rocket motors are the most widely used propulsion systems for military applications that require high thrust to weight ratio for relatively short time intervals. Very wide range of magnitude and duration of the thrust can be obtained from solid propellant rocket motors by making some small changes at the design of the rocket motor. The most effective of these design criteria is the geometry of the solid propellant grain. So the most important step in designing the solid propellant rocket motor is determination of the geometry of the solid propellant grain. The performance prediction of the solid rocket motor can be achieved easily if the burnback steps of the rocket motor are known. In this study, grain burnback analysis for some 3-D grain geometries is investigated. The method used is solid modeling of the propellant grain for some predefined intervals of burnback. In this method, the initial grain geometry is modeled parametrically using commercial software. For every burn step, the parameters are adapted. So the new grain geometry for every burnback step is modeled. By analyzing these geometries, burn area change of the grain geometry is obtained. Using this data and internal ballistics parameters, the performance of the solid propellant rocket motor is achieved. To verify the outputs obtained from this study, rocket motor tests are performed. The results obtained from this study shows that, the procedure that was developed, can be successfully used for the preliminary design of a solid propellant rocket motor where a lot of different geometries are examined.

The simulation tool ROBOOST, in use at the Alma Propulsion Lab of the University of Bologna – Forlì Campus, exploits a hybrid ballistic model 0D-1D. The need of a complete Q1D model for the entire combustion time, from motor start-up to burn out arised. The present work is devoted to the development and test of a Q1D unsteady ballistic model for solid rocket motors performance prediction. The newly developed code, called SOL1D, is written in Matlab environment and is capable of predicting the time and space evolution of all the main thermodynamic variables during the solid rocket motor combustion process. The model has been tested and validated on a BARIA motor, thus demonstrating its adherence to experimental data. SOL1D paves the way for future works aimed at simulating performances of actual launchers.

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An investigation was conducted using a subscale solid rocket motor to measure the effect of nozzle residence time on the behavior of Al203 particles to assess the applicability of subscale motor data to full-scale motors and to measure the effects of nozzle entrance particle size distribution on the slag accumulated with submerged nozzles. Although particles as large as 140 micrometers were present at the nozzle entrance, most of the particulate mass was contained in much smaller particles. This observation is in good agreement with the small mass that accumulated above the submerged nozzle. It was found that both particle breakup and collision coalescence occurred across the exhaust nozzle, with a significant increase in the mass fraction of small (<2 micrometers) particles. Increasing the nozzle residence time enhanced particle breakup but did not affect the maximum plume particle size. Thus, full-scale motors are expected to have a higher percentage of mass in particles less than 2 micrometers than subscale motors but with similar diameters of the largest particles.

In solid rocket motors, the absence of combustion controllability and the large amount of financial resources involved in full-scale firing tests, increase the importance of numerical simulations in order to asses stringent mission thrust requirements and evaluate the influence of thrust chamber phenomena affecting the grain combustion. Among those phenomena, grain local defects (propellant casting inclusions and debondings), combustion heat accumulation involving pressure peaks (Friedman Curl effect), and case-insulating thermal protection material ablation affect thrust prediction in terms of not negligible deviations with respect to the nominal expected trace. Most of the recent models have proposed a simplified treatment to the problem using empirical corrective functions, with the disadvantages of not fully understanding the physical dynamics and thus of not obtaining predictive results for different configurations of solid rocket motors in a boundary conditions-varied scenario. This work is aimed to introduce different mathematical approaches to model, analyze, and predict the abovementioned phenomena, presenting a detailed physical interpretation based on existing SRMs configurations. Internal ballistics predictions are obtained with an in-house simulation software, where the adoption of a dynamic three-dimensional triangular mesh together with advanced computer graphics methods, allows the previous target to be reached. Numerical procedures are explained in detail. Simulation results are carried out and discussed based on experimental data.

Solid propellant rocket motor is the primary propulsion technology used for short and medium range missiles. It is also commonly used as boost motor in many di_erent applications. Its wide spread usage gives rise to diversity of environments in which it is handled and stored. Ability to predict the storage life of solid propellants plays an important role in the design and selection of correct protective environments. In this study a methodology for the prediction of solid propellant storage life using cumulative damage concepts is introduced. Finite element mesh of the solid propellant grain is created with the developed parametric grain geometry generator. Finite element analyses are carried out to obtain the temperature and stress response of the propellant to the environmental thermal loads. Daily thermal cycles are assumed to be sinusoidal cycles represented by their means and amplitudes. With the cumulative damage analyses, daily damage accumulated in the critical locations of the solid propellant grain are investigated. Meta-models relating the daily damage amount with the daily temperature cycles are constructed in order to compute probability of failure. The results obtained in this study imply that it is possible to make numerical predictions for the storage life of solid propellants even in the early design phases. The methodology presented in this study provides a basis for storage life predictions.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 281-289).
Small, uncrewed aerial vehicles (UAVs) are expanding the capabilities of aircraft systems. However, a gap exists in the size and capability of aircraft: no small aircraft are capable of sustained fast flight. A small, fast aircraft requires a propulsion system which is both miniature and high-power, requirements which current UAV propulsion technologies do not meet. Solid propellant rocket motors could be used, but must be re-engineered to operate at much lower thrust and for much longer burn times than conventional small solid rocket motors. This imposes unique demands on the motor and propellant. This work investigates technological challenges of small, low-thrust solid rocket motors: slow-burn solid propellants, motors which have low thrust relative to their size (and thus have low chamber pressure), thermal protection for the motor case, and small nozzles which can withstand long burn times.
Slow-burn propellants were developed using ammonium perchlorate oxidizer and the burn rate suppressant oxamide. By varying the amount of oxamide (from 0-20%), burn rates from 4mms⁻¹ to 1mms⁻¹ (at 1MPa) were achieved. Using these propellants, a low-thrust motor successfully operated at a (thrust / burn area) ratio 10 times less than that of typical solid rocket motors. This motor can provide 5-10N of thrust for 1-3 minutes. An ablative thermal protection liner was tested in these firings. Despite the long burn time, only a few millimeters of ablative are needed. A new ceramic-insulated nozzle was demonstrated on this motor. The nozzle has a small throat diameter (only a few millimeters) and can operate in thermal steady-state. Models were developed for the propellant burn rate, motor design, heat transfer within the motor and nozzle, and for thermal stresses in the nozzle insulation.
This work shows that small, low-thrust solid motors are feasible, by demonstrating these key technologies in a prototype motor. Further, the experimental results and models will enable engineers to design and predict the performance of solid rocket motors for small, fast aircraft. By providing insight into the physics of these motors, this thesis may help to enable a new option for aircraft propulsion.
by Matthew T. Vernacchia.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Aeronautics and Astronautics

The solid rocket propulsion is a simple and reliable system, it is less complex than liquid propulsion because it does not require tanks, pumps and the propellant is already stored into the combustion chamber. The main issues are the lower propulsive performance and the lack of controllability. The solid rocket motor thrust can be controlled only moving the nozzle direction of few degrees while its magnitude can not be controlled, therefore it is very important to well know the thrust profile because there is no possibility to control its magnitude during the flight. The thrust shape can be obtained experimentally or performing simulations. The first way is quite expensive therefore the second one is preferable. The tool ROBOOST (ROcket BOOst Simulation Tool), developed by the university of Bologna propulsion laboratory in collaboration with Avio S.p.A., already achieves the goal to predict the thrust profile during the ignition phase and the combustion one. But it fails to follow the experimental curve in the tail-off, underestimating the residual thrust. This discrepancy can be due to different phenomena that are not considered in the this simulation: heat coming from the nozzle, heat coming from slugs and the mass flow rate due to the thermal protection pyrolysis and ablation. This thesis focuses on simulate thermal protection pyrolysis and ablation obtaining their behavior when they are exposed to the hot gases of the combustion chamber.

A method for developing an erosive burning model for use in solid propellant design-and-analysis interior ballistics codes is described and evaluated. Using Direct Numerical Simulation, the primary mechanisms controlling erosive burning (turbulent heat transfer, and finite rate reactions) have been studied independently through the development of models using finite rate chemistry, and infinite rate chemistry. Both approaches are calibrated to strand burn rate data by modeling the propellant burning in an environment with no cross-flow, and adjusting thermophysical properties until the predicted regression rate matches test data. Subsequent runs are conducted where the cross-flow is increased from M=0.0 up to M=0.8. The resulting relationship of burn rate increase versus Mach Number is used in an interior ballistics analysis to compute the chamber pressure of an existing solid rocket motor. The resulting predictions are compared to static test data. Both the infinite rate model and the finite rate model show good agreement when compared to test data. The propellant considered is an AP/HTPB with an average AP particle size of 37 microns. The finite rate model shows that as the cross-flow increases, near wall vorticity increases due to the lifting of the boundary caused by the side injection of gases from the burning propellant surface. The point of maximum vorticity corresponds to the outer edge of the APd-binder flame. As the cross-flow increases, the APd-binder flame thickness becomes thinner; however, the point of highest reaction rate moves only slightly closer to the propellant surface. As such, the net increase of heat transfer to the propellant surface due to finite rate chemistry affects is small. This leads to the conclusion that augmentation of thermal transport properties and the resulting heat transfer increase due to turbulence dominates over combustion chemistry in the erosive burning problem. This conclusion is advantageous in the development of future models that can be calibrated to heat transfer conditions without the necessity for finite rate chemistry. These results are considered applicable for propellants with small, evenly distributed AP particles where the assumption of premixed APd-binder gases is reasonable.

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-60).
Currently, a void exists in the development of small, unmanned aerial vehicles (UAVs) that can fly at speeds faster than 100 meters per second while maximizing endurance. Operating in such a regime requires the use of a slow-burning solid rocket motor. To achieve long burn times, an end-burning grain configuration is required in addition to a burn rate suppressant. Such a propulsion system presents unique thermal challenges due to the long exposure times and the close proximity of temperature sensitive vehicle components to the combustion reactions. This thesis presents the development of a thermal management system appropriate for small, slow burning solid rocket motors. Thermal protection is provided primarily by a thermally ablative liner with additional layers of fibrous insulation to protect the motor casing and avionics. Due to the complex nature of thermochemical ablation and scarcity of previous research in slow, end burning solid rockets, this problem is approached through both experimental and computational means. Experimental tests are performed on a full-scale model of an end-burning motor. Experimental results are used to validate a computational model of ablation. The ultimate goal is to provide an adequate amount of thermal insulation to protect the vehicle casing and avionics while maximizing propellant volume and hence endurance. Building such thermal management schemes requires innovative materials and machining methods to incorporate thermal protection in a tight space. This thesis adds to the greater body of knowledge of thermal protection design in slow-burning solid rockets, especially as it applies to a new class of small, fast UAVs.
by Jonathan R. Spirnak.
S.M.

Solid rocket motors consist of a thin metallic or composite shell filled with a soft rubbery propellant. Such motors are vulnerable and prone to buckling due to sudden external pressures produced by nearby detonation. The stability conditions of rocket motors subjected toaxisymmetric, external pressure loading are examined. The outer cases of motors are considered as isotropic (metallic) or anisotropic (composite), thin and high-strength shells, which are the main structures of interest in the stability analyses. The inner, low-strength elastic cores are modeled as linear and nonlinear elastic foundations. A general, refined, Sanders' nonlinear shell theory, which accounts for geometric nonlinearity in the form of von Karman type of nonlinear strain-displacement relations, is used to model thin-walled, laminated,composite cylindrical shells. The first order shear deformable concept is adopted in the analyses to include the transverse shear flexibility of composites. A winkler-type of linear and nonlinear elastic foundation is applied to model the internal foundations. Pasternak-foundation constants are also chosen tomodify the proposed elastic foundation model for the purpose of shear interactions. A set of displacement-based finite element codes have been formulated to determine critical buckling loads and mode shapes. The effect of initial imperfections on the structural responses are also incorporated in the formulations. A variety of numerical examples are investigated to demonstrate the validity and efficiency of the purposed theory under various boundary condiitions and loading cases. First, linear eigenvalue analysis is used to examine approximate buckling loads and buckling modes as well as symmetric conditions. An iterative solution procedure, either Newton-Raphson or Riks-Wempner method is employed to trace the nonlinear equilibrium paths for the cases of stress, buckling and post-buckling analyses. Both ring and shell-type models are applied for the structural analyses with different internal elastic foundations and initial imperfections.
Ph. D.

The aim of this thesis work is the study the solid particles migration phenomenon in concentrated suspension and the development of an OpenFOAM solver able to successfully predict the behaviour of such event. It is, in fact, common knowledge how the solid particles will tend to spread into an heterogeneous arrangement when the fluid is subjected to a non-uniform shear flow. As a consequence, the viscosity field will become uneven as well, giving rise to a non-Newtonian behaviour of the flow. In order to approach the problem, the OpenFOAM transient solver pimpleFoam has been modified, changing the implementation of the equation of motion to make it suitable for a variable viscosity field. Additionally, an iterative cycle for the resolution of the partial differential equation describing the particle migration process has been included in the algorithm. The model chosen to describe the viscosity field is the Krieger’s correlation, which consists of a power law linking the local volume fraction to the dynamic viscosity of the fluid. For the validation of the solver a bidimensional channel flow has been selected; the results of the simulation will be compared to experimental measurements and data provided by a 1D and a 2D finite volume implementations of the model from literature. Following the global trend deduced from the experiment, the distribution profile predicted via OpenFOAM also proved to follow in a quite satisfactory way the results of the 2D model. Subsequently a mesh sensitivity analysis is going to be performed in order to understand how is the solution affected by employing coarser discretizations.

Dans un moteur à propergol solide, l’écoulement dépend fortement des gouttes d’alumine en suspension, dont la fraction massique est élevée. La distribution en taille des gouttes, qui s’élargit avec la coalescence, joue un rôle clef. Or résoudre des écoulements diphasiques polydisperses instationnaires avec une bonne précision sur la taille est un défi à la fois sur le plan de la modélisation et du calcul scientifique: (1) de très petites gouttes, par exemple résultant de la combustion de nanoparticules d’aluminium, subissent mouvement brownien et coalescence, (2) de petites gouttes ont leur vitesse conditionnée par leur taille de sorte qu’elles coalescent lorsqu’elles ont des tailles différentes, (3) des gouttes plus grosses peuvent se croiser par effet d’inertie et (4) toutes les gouttes interagissent de manière fortement couplée avec la phase porteuse. En complément des approches lagrangiennes, des modèles eulériens ont été développés pour décrire la phase dispersée à un coût raisonnable, et ils permettent un couplage aisé avec la phase porteuse ainsi que la parallélisation massive des codes: les approches eulériennes sont bien adaptées aux calculs industriels. Le modèle Multi-Fluide permet la description détaillée de la polydispersion, des coreélations taille/vitesse et de la coalescence, en résolvant séparément des “fluides” de gouttes triées par taille, appelés sections. Un ensemble de modèles est évalué dans cette thèse et une stratégie numérique est développée pour effectuer des calculs industriels de moteurs à propergol solide. (1) La physique des nanoparticules est évalué et incluse dans un modèle de coalescence complet. Des méthodes de moments d’ordre élevé sont ensuite développées: (2) une méthode à deux moments en taille est étendue à la coalescence pour traiter la physique de la polydispersion et les développements numériques connexes permettent d’effectuer des calculs applicatifs dans le code industriel CEDRE; (3) une méthode basée sur les moments en vitesse du deuxième ordre, un schéma de transport à l’ordre deux sur maillages structurés ainsi qu’un modèle de coalescence sont développés. Des validations académiques de la stratégie pour gouttes d’inertie modérée sont effectuées sur des écoulements complexes puis avec de la coalescence; (4) une stratégie d’intégration en temps est développée et mise en œuvre dans CEDRE pour traiter efficacement le couplage fort, dans des cas instationnaires et polydisperses incluant de très petites particules. L’ensemble des développements est soigneusement validé: soit par des formules analytiques ad hoc pour la coalescence et pour le couplage fort d’une onde acoustique; soit par des comparaisons numériques croisées avec une DPS pour la coalescence et avec des simulations lagrangiennes de cas applicatifs, coalescents et fortement couplés; soit par des résultats expérimentaux disponibles sur une configuration académique de coalescence et sur un tir de moteur à échelle réduite. La stratégie complète permet des calculs applicatifs à un coût raisonnable. En particulier, un cal- cul de moteur avec des nanoparticules permet d’évaluer la faisabilité de l’approche et d’orienter les efforts de recherche sur les propergols chargés de nanoparticules
In solid rocket motors, the internal flow depends strongly on the alumina droplets, which have a high mass fraction. The droplet size distribution, which is wide and spreads up with coalescence, plays a key role. Solving for unsteady polydisperse two- phase flows with high accuracy on the droplet sizes is a challenge for both modeling and scientific computing: (1) very small droplets, e.g. resulting from the combustion of nanoparticles of aluminum fuel, encounter Brownian motion and coalescence, (2) small droplets have their velocity conditioned by size so they coalesce when having different sizes, (3) bigger droplets have an inertial behavior and may cross each other’s trajectory, and (4) all droplets interact in a two-way coupled manner with the carrier phase. As an alternative to Lagrangian approaches, some Eulerian models can describe the disperse phase at a moderate cost, with an easy coupling to the carrier phase and with massively parallel codes: they are well-suited for industrial computations. The Multi- Fluid model allows the detailed description of polydispersity, size/velocity correlations and coalescence by separately solving “fluids” of size-sorted droplets, the so-called sections. In the present work, we assess an ensemble of models and we develop a numerical strategy to perform industrial computations of solid rocket motor flows. (1) The physics of nanoparticles is assessed and included in a polydisperse coalescing model. High order moment methods are then developed: (2) a Two-Size moment method is ex- tended to coalescence to treat accurately the physics of polydispersity and coalescence and the related numerical developments allow to perform applicative computations in the industrial code CEDRE; (3) a second order velocity moment method is developed, together with a second order transport scheme, to evaluate a strategy for a moderately inertial disperse phase, and academic validations are performed on complex flow fields; (4) a time integration strategy is developed and implemented in CEDRE to treat efficiently two-way coupling, in unsteady polydisperse cases including very small particles. The developments are carefully validated, either through purposely derived analytical formulae (for coalescence and two-way acoustic coupling), through numerical cross-comparisons (for coalescence with a Point-Particle DNS, for applicative cases featuring coalescence and two-way coupling with a Lagrangian method), or through available experimental results (for coalescence with an academic experiment, for the overall physics with a sub-scale motor firing). The whole strategy allows to perform applicative computations in a cost effective way. In particular, a solid rocket motor with nanoparticles is computed as a feasibility case and to guide the research effort on motors with nanoparticle fuel propellants

Lo scopo principale di questo scritto è indagare in dettaglio la combustione non isotropa nei motori a propellente solido, nota come fattore di Hump, che provoca un discostamento tra il profilo di pressione sperimentale e teorico. Sulla base di studi che tentano di legare tali variazioni a fenomeni fisici si sono sviluppati dei codici numerici in ambiente Matlab per generare delle mappe delle anisotropie del rateo di combustione. In seguito coi modelli realizzati sono state condotte delle simulazioni con ROBOOST, un software sviluppato dall'Università di Bologna in collaborazione con Avio S.p.A., per determinare il termine Hump. L'importanza di queste analisi è dovuta al fatto che le previsioni delle curve balistiche nei nuovi motori devono essere migliorate al fine di ridurre la quantità di prove sperimentali necessarie per la caratterizzazione del loro comportamento balistico e abbassare i costi dovuti ai tiri al banco delle motorizzazioni.

This thesis presents the results and analyses of computational studies on certain problems of combustion instability in solid propellants. Specifically, effects of relaxing certain assumptions made in previous models of unsteady burning of solid propellants are investigated. Knowledge of unsteady burning of solid propellants is essential in studying the phenomenon of combustion instability in solid propellant rocket motors. In Chapter 1, an introduction to different types of unsteady combustion investigated in this thesis, such as 1) intrinsic instability, 2) pressure-driven dynamic burning, 3) extinction by depressurization, and 4) L* -instability, is given. Also, a review of previous experimental and theoretical studies of these phenomena is presented. From this review it is concluded that all the previous studies, which investigated the unsteady combustion of solid propellants, made one or more of the following assumptions: 1) quasi-steady gas-phase (QSG), 2) quasi-steady condensed phase reaction zone (QSC), 3) small perturbations, and 4) unity Lewis number. These assumptions limit the validity of the results obtained with such models to: 1) relatively low frequencies (< 1 kHz) of pressure oscillations and 2) small deviations in pressure from its steady state or mean values. The objectives of the present thesis are formulated based on the above conclusions. These are: 1) to develop a nonlinear numerical model of unsteady solid propellant combustion, 2) to relax the assumptions of QSG and QSC, 3) to study the consequent effects on the intrinsic instability and pressure-driven dynamic burning, and 4) to investigate the L* -instability in solid propellant rocket motors. In Chapter 2, a nonlinear numerical model, which relaxes the QSG and QSC assumptions, is set up. The transformation and nondimensionalization of the governing equations are presented. The numerical technique based on the method of operator-splitting, used to solve the governing equations is described. In Chapter 3, the effect of relaxing the QSG assumption on the intrinsic instability is investigated. The stable and unstable solutions are obtained for parameters corresponding to a typical composite propellant. The stability boundary, in terms of the nondimensional parameters identified by Denison and Baum (1961), is predicted using the present model. This is compared with the stability boundary obtained by previous linear stability theories, based on activation energy asymptotics in the gas-phase, which employed QSC and/or QSG assumptions. It is found that in the limit of large activation energy and low frequencies, present result approaches the previous theoretical results. This serves as a validation of the present method of solution. It is confirmed that relaxing the QSG assumption widens the stable region. However, it is found that a distributed reaction in the gas-phase destabilizes the burning. The effect of non-unity Lewis number on the stability boundary is also investigated. It is found that at parametric values corresponding to low pressures and large flame stand-off distances, small amplitude, high frequency (at frequencies near the characteristic frequency of the gas-phase) oscillations in burning rate appear when the Lewis number is greater than one. In Chapter 4, the effect of relaxing the QSG assumption is further investigated with respect to the pressure-driven dynamic burning. Comparison of the pressure-driven frequency response function, Rp, obtained with the present model, both in the QSG and non-QSG framework, with those obtained with previous linear stability theories invoking QSG and QSC assumptions are made. As the frequency of pressure oscillations approaches zero, |RP| predicted using present models approached the value obtained by previous theoretical studies. Also, it is confirmed that the effect of relaxing QSG is to decrease the |Rp| at frequencies near the first resonant frequency. Moreover, relaxing QSG assumption produces a second resonant peak in |Rp| at a frequency near the characteristic frequency of the gas-phase. Further, Rp calculated using the present model is compared with that obtained by a previous linear theory which relaxed the QSG assumption. The two models predicted the same resonant frequencies in the limit of small amplitudes of pressure oscillations. Finally, it is found that the effect of large amplitude of pressure oscillations is to introduce higher harmonics in the burning rate and to reduce the mean burning rate. In Chapter 5, first the present non-QSC model is validated by comparing its results with that of a previous non-QSC model for radiation-driven burning. The model is further validated for steady burning results by comparing with experimental data for a double base propellant (DBP). Then, the effect of relaxing the QSC assumption on steady state solution is investigated. It is found that, even in the presence of a strong gas-phase heat feedback, QSC assumption is valid for moderately large values of condensed phase Zel'dovich number, as far as steady state solution is concerned. However, for pressure-driven dynamic burning, relaxing the QSC assumption is found to increase |RP| at all frequencies. The error due to QSC assumption is found to become significant, either when |Rp| is large or as the driving frequency approaches the characteristic frequency of the condensed phase reaction zone. The predicted real part of the response function is quantitatively compared with experimental data for DBP. The comparison seems to be better with a value of condensed phase activation energy higher than that suggested by Zenin (1992). In Chapter 6, burning rate transients for a DBP during exponential depressurization are computed using non-QSG and non-QSC models. Salient features of extinction and combustion recovery are predicted. The predicted critical initial depressurization rate, (dp/dt)i, is found to decrease markedly when the QSC assumption is relaxed. The effect of initial pressure level on critical (dp/dt)i is studied. It is found that the critical (dp/dt)i decreases with the initial pressure. Also, the overshoot of burning rate during combustion recovery is found to be relatively large with low initial pressures. However as the initial pressure approached the final pressure, the reduction in initial pressure causes a large increase in the critical (dp/dt)i. No extinction is found to occur when the initial pressure is very close to the final pressure. In Chapter 7, a numerical model is developed to simulate the L* -instability in solid propellant motors. This model includes a) the propellant burning model that takes into account nonlinear pressure oscillations and that takes into account an unsteady gas- and condensed phase, and b) a combustor model that allows pressure and temperature oscillations of finite amplitude. Various regimes of L* -burning of a motor, with a typical composite propellant, namely 1) steady burning, 2) oscillatory burning leading to steady state, 3) oscillatory burning leading to extinction, 4) reignition and 5) chuffing are predicted. The predicted dependence of frequency of L* -oscillations on mean pressure is compared with one set of available experimental data. It is found that proper modeling of the radiation heat flux from the chamber walls to the burning surface may be important to predict the re-ignition. In Chapter 8, the main conclusions of the present study are summarized. Certain suggestions for possible future studies to enhance the understanding of dynamic combustion of solid propellants are also given.

Les gouttes d’oxyde d’aluminium présentes en masse dans l’écoulement interne des moteurs-fusées à propergol solide ont tendance à influerde façon importante sur l’écoulement et sur le fonctionnement du moteur quel que soit le régime. L’objectif de la thèse est d’améliorerles modèles diphasiques eulériens présents dans le code de calcul semi-industriel pour l’énergétique de l’ONERA, CEDRE, en y incluant lapossibilité d’une dispersion locale des particules en vitesse en plus de la dispersion en taille déjà présente dans le code, tout en gardant unestructure mathématique bien posée du système d’équations à résoudre. Cette nouvelle caractéristique rend le modèle capable de traiter lescroisements de trajectoires anisotropes, principale difficulté des modèles eulériens classiques pour les gouttes d’inertie modérément grande.En plus de la conception et de l’analyse détaillée d’une classe de modèles basés sur des méthodes de moments, le travail se concentre sur larésolution des systèmes d’équations obtenus en configurations industrielles. Pour cela, de nouvelles classes de schémas précis et réalisables pourle transport des particules dans l’espace physique et l’espace des phases sont développées. Ces schémas assurent la robustesse de la simulationmalgré différentes singularités (dont des chocs, -chocs, zones de pression nulle et zones de vide...) tout en gardant une convergence d’ordredeux pour les solutions régulières. Ces développements sont conduits en deux et trois dimensions, en plus d’un référentiel bidimensionnelaxisymétrique, dans le cadre de maillages non structurés.La capacité des schémas numériques à maintenir un niveau de précision élevé tout en restant robuste dans toutes les conditions est un pointclé pour les simulations industrielles de l’écoulement interne des moteurs à propergol solide. Pour illustrer cela, le code de recherche SIERRA,originellement conçu durant les année 90 pour les problématiques d’instabilités de fonctionnement en propulsion solide, a été réécrit afin depouvoir comparer deux générations de modèles et de méthodes numériques et servir de banc d’essais avant une intégration dans CEDRE. Lesrésultats obtenus confirment l’efficacité de la stratégie numérique choisie ainsi que le besoin d’introduire, pour les simulations axisymétriques,une condition à la limite spécifique, développée dans le cadre de cette thèse. En particulier, les effets à la fois du modèle et de la méthodenumérique dans le contexte d’une simulation de l’écoulement interne instationnaire dans les moteurs-fusées à propergol solide sont détaillés.Par cette approche, les liens entre des aspects fondamentaux de modélisation et de schémas numériques ainsi que leurs conséquences pour lesapplications sont mis en avant
The massive amount of aluminum oxide particles carried in the internal flow of solid rocket motors significantly influences their behavior.The objective of this PhD thesis is to improve the two-phase flow Eulerian models available in the semi-industrial CFD code for energeticsCEDRE at ONERA by introducing the possibility of a local velocity dispersion in addition to the size dispersion already taken into accountin the code, while keeping the well-posed characteristics of the system of equations. Such a new feature enables the model to treat anisotropicparticle trajectory crossings, which is a key issue of Eulerian models for droplets of moderately large inertia.In addition to the design and detailed analysis of a class of models based on moment methods, the conducted work focuses on the resolution ofthe system of equations for industrial configurations. To do so, a new class of accurate and realizable numerical schemes for the transport ofthe particles in both the physical and the phase space is proposed. It ensures the robustness of the simulation despite the presence of varioussingularities (including shocks, -shocks, zero pressure area and vacuum...), while keeping a second order accuracy for regular solutions. Thesedevelopments are conducted in two and three dimensions, including the two dimensional axisymmetric framework, in the context of generalunstructured meshes.The ability of the numerical schemes to maintain a high level of accuracy in any condition is a key aspect in an industrial simulation of theinternal flow of solid rocket motors. In order to assess this, the in-house code SIERRA, originally designed at ONERA in the 90’s for solidrocket simulation purpose, has been rewritten, restructured and augmented in order to compare two generations of models and numericalschemes, to provide a basis for the integration of the features developed in CEDRE. The obtained results assess the efficiency of the chosennumerical strategy and confirm the need to introduce a new specific boundary condition in the context of axisymmetric simulations. Inparticular, it is shown that the model and numerical scheme can have an impact in the context of the simulation of the internal flow ofsolid rocket motors and their instabilities. Through our approach, the shed light on the links between fundamental aspects of modeling andnumerical schemes and their consequences on the applications

Les oscillations de pression sont un enjeu majeur dans le design des moteurs à propergol solide car de faibles oscillations de pression (ODP) dans la chambre entraînent de fortes oscillations de poussée ce qui conduit à des vibrations néfastes pour les structures et les satellites embarqués. Les ODP sont encore aujourd'hui un vaste sujet de recherche et la simulation numérique est un outil indispensable dans leur analyse. De nombreux travaux ont permis de mettre en évidence divers mécanismes générateurs d'oscillations, mais la conception des nouveaux moteurs favorise la formation d'une instabilité hydrodynamique, appelée VSA et caractérisée par des détachements tourbillonnaire au niveau des discontinuités de la surface débitante. Etudiée dans les travaux sur le C1x [Vuillot 1995, Dupays 1996], il reste cependant divers points à aborder afin d'avoir une vision complète des mécanismes qui pilotent et modifient cette instabilité. Pour cela, il a été choisi dans ces travaux d'isoler le VSA dans une configuration académique et d'étudier dans un premier temps, l'impact du soufflage latéral, généré par un dégagement gazeux du à la combustion d'un bloc de propergol en aval de l'angle. Les deux approches utilisées, à savoir la simulation numérique et la stabilité linéaire, démontrent que le soufflage latéral possède un fort effet stabilisant sur le VSA. Dans un deuxième temps, l'impact de la combustion des particules d'aluminium et des résidus, présents dans un moteur à propergol solide, est analysé. Ces travaux montrent que les particules, via des mécanismes complexes, peuvent jouer à la fois un rôle stabilisant et déstabilisant sur le VSA. Pour finir, l'impact de la mise à l'échelle sur l'instabilité est étudié. Si en gaz seul, les résultats obtenus à échelle réduite sont directement transposables vers l'échelle réelle, la mise à l'échelle modifie le comportement des particules dans les structures tourbillonnaires et donc leur rôle sur l'instabilité.

Star grain configuration design has been widely used in solid rocket applications for several decades. Although a large number of surface cracks are detected in the rocket motor propellants, the mechanism of these cracks is sull not well known due to the complex geometry of the grain. A stress-freezing photoelastic investigation has been performed to study the deep cracks which emanate from the fingertips of the star-shaped cutout cylinders. Using three-dimensional photoelasticity and proper algorithms in fracture mechanics, the stress intensity factors (SIF's) and the stress singularity orders along the crack front have been calculated. A surface effect on the dominant singularity order is observed and some analytical results are employed as a comparison. Meanwhile, three-dimensional finite element solution to the circular cylinder is used to find the “equivalent” inner radius for the internal star cylinder and the variation of SIF's along the crack border shows a very similar trend to the experimental results once the "equivalent" radius is adopted.
Master of Science

Design process of a solid rocket motor with the objective of meeting certain mission requirements can be specified as a search for a best set of design parameters within the overall design constraints. In order to ensure that the best possible design amongst all achievable designs is being achieved, optimization is required during the design process. In this thesis, an optimization tool for internal ballistic design of solid rocket motors was developed. A direct search method Complex algorithm is used in this study. The optimization algorithm changes the grain geometric parameters and nozzle throat diameter within the specified bounds, finally achieving the optimum results. Optimization tool developed in this study involves geometric modeling of the propellant grain, burnback analysis, a 0-dimensional ballistic performance prediction analysis of rocket motor and the mathematical optimization algorithm. The code developed is verified against pretested rocket motor performance.

In the design and development of solid propellant rocket motors, the use of numerical tools able to simulate, predict and reconstruct the behaviour of a given motor in all its operative conditions is particularly important in order to decrease all the planning and costs. This study is devoted to present an approach to the numerical simulation of a given SPRM internal ballistics, NAWC no. 13, during the quasi steady state by means of a commercial numerical tool, ANSYS FLUENT. The internal ballistics model constructed in this study is a 2-D axisymmetric model, based on several assumptions. Among them is the assumption that there is no contribution of the erosive burning and the dynamic burning in the burning rate model. The results of the internal ballistics simulation are compared with the results found in the bibliographical research, thus validating the model that has been set up. The validation of the results also allows us to conclude that the assumptions made in the construction of the model are reasonable. Suggestions and recommendations for further study are outlined.
Na concepção e desenvolvimento de motores foguete sólidos, o uso de ferramentas numéricas capazes de simular, prever e reconstruir o comportamento de um dado do motor em todas as condições operativas ´e particularmente importante, a fim de diminuir todos os custos e planeamento. Este estudo ´e dedicado a apresentar uma abordagem para a simulação numérica de balística interna de um determinado motor foguete de propelente sólido, Naval Air Warfare Center no. 13, durante a fase quasi steady state por meio de uma ferramenta numérica comercial, ANSYS FLUENT. O modelo de balística interna construído neste estudo é um modelo axissimétrico 2-D. Tem por base vários pressupostos. Entre eles, está o pressuposto de que não há contribuição da queima erosiva e da queima dinâmica no modelo da taxa de queima. Os resultados da simulação balística interna são comparados com os resultados encontrados na pesquisa bibliográfica, validando assim, o modelo que foi construído. A validação dos resultados também nos permite concluir que os pressupostos assumidos na construção do modelo são razoáveis. Sugestões e recomendações para um estudo mais aprofundado são delineadas.

The work presented in this thesis deals with the application of optimization tools to the design of solid rocket motor grains per internal ballistic requirements. Research concentrated on the development of an optimization strategy capable of efficiently and consistently optimizing virtually an unlimited range of radial burning solid rocket motor grain geometries. Optimization tools were applied to the design process of solid rocket motor grains through an optimization framework developed to interface optimization tools with the solid rocket motor design system. This was done within a programming architecture common to the grain design system, AML. This commonality in conjunction with the object-oriented dependency-tracking features of this programming architecture were used to reduce the computational time of the design optimization process. The optimization strategy developed for optimizing solid rocket motor grain geometries was called the internal ballistic optimization strategy. This strategy consists of a three stage optimization process; approximation, global optimization, and highfidelity optimization, and optimization methodologies employed include DOE, genetic algorithms, and the BFGS first-order gradient-based algorithm. This strategy was successfully applied to the design of three solid rocket motor grains of varying complexity. The contributions of this work was the development and application of an optimization strategy to the design process of solid rocket motor grains per internal ballistic requirements.
M.S.
Department of Mechanical, Materials and Aerospace Engineering;
Engineering and Computer Science
Mechanical Engineering

In this study, a detailed service life assessment procedure for solid propellant rockets under random environmental temperature and transportation loads is introduced. During storage and deployment of rocket motors, uncontrolled thermal environments and random vibratory loads due to transportation induce random stresses and strains in the propellant which provoke mechanical damage. In addition, structural capability degrades due to environmental conditions and induced stresses and strains as well as material capability parameters have inherent uncertainties. In this proposed probabilistic service life prediction, uncertainties along with degradation mechanisms are taken into consideration. Vibration loads are accounted by utilizing acceleration spectral density values which are induced during various deployment scenarios of ground, air and sea transportation. Furthermore, thermal loads are represented with a mathematical model being a harmonic function of time. Throughout the finite element analyses, a linear viscoelastic material model is to be used for the propellant. Change in the structural capability of the propellant with time is calculated using Laheru'
s cumulative damage model. Moreover, to include aging effect of the propellant, Layton model is used. To determine the effects of induced stress and strains under variations and uncertainties in the random loads and material constants, mathematical surrogate models are constructed using response surface method. Limit state functions are utilized to predict failure modes of the solid rocket motor. First order reliability method is used to calculate reliability and probability of failure of the propellant grain. With the proposed methodology, instantaneous reliability of the propellant grain is determined within a confidence interval.

Cette thèse vise à modéliser les instabilités hydrodynamiques générant des détachements tourbillonnaires pariétaux (ou VSP) responsables des Oscillations De Pression dans les moteurs à propergol solide longs et segmentés par interaction avec l’acoustique du moteur. Ces instabilités sont modélisées en tant que modes de stabilité linéaire globaux de l’écoulement d’un conduit à parois débitantes. En supposant que les structures pariétales émergent d’une perturbation de l’écoulement de base, des modes discrets et indépendants du maillage utilisé sont calculés. Dans ce but, une discrétisation par collocation spectrale multi-domaine est implémentée dans un solveur parallèle afin de s’affranchir de la croissance polynomiale des fonctions propres et de la présence de couches limites. Les valeurs propres ainsi calculées dépendent explicitement des frontières du domaine, à savoir la position de la perturbation et celle de la sortie, et sont ensuite validées par simulation numérique directe. On montre alors qu’elles permettent bien de décrire la réponse à une perturbation initiale de l’écoulement modifié par une rupture de débit pariétale. Ensuite, la simulation d’une réponse forcée par l’acoustique se fait sous forme de structures tourbillonnaires dont les fréquences discrètes sont en accord avec celles des modes de stabilité. Ces structures sont réfléchies en ondes de pression de même fréquences remontant l’écoulement. Finalement, la simulation numérique et la théorie de la stabilité permettent de montrer que le VSP, dont la réponse est linéaire vis-à-vis d’un forçage compressible comme l’acoustique, est le phénomène moteur des Oscillations De Pression
The current work deals with the modeling of the hydrodynamic instabilities that play a major role in the triggering of the Pressure Oscillations occurring in large segmented solid rocket motors. These instabilities are responsible for the emergence of Parietal Vortex Shedding (PVS) and they interact with the boosters acoustics. They are first modeled as eigenmodes of the internal steady flowfield of a cylindrical duct with sidewall injection within the global linear stability theory framework. Assuming that the related parietal structures emerge from a baseflow disturbance, discrete meshindependant eigenmodes are computed. In this purpose, a multi-domain spectral collocation technique is implemented in a parallel solver to tackle numerical issues such as the eigenfunctions polynomial axial amplification and the existence of boundary layers. The resulting eigenvalues explicitly depend on the location of the boundaries, namely those of the baseflow disturbance and the duct exit, and are then validated by performing Direct Numerical Simulations. First, they successfully describe flow response to an initial disturbance with sidewall velocity injection break. Then, the simulated forced response to acoustics consists in vortical structures wihich discrete frequencies that are in good agreement with those of the eigenmodes. These structures are reflected into upstream pressure waves with identical frequencies. Finally, the PVS, which response to a compressible forcing such as the acoustic one is linear, is understood as the driving phenomenon of the Pressure Oscillations thanks to both numerical simulation and stability theory

As advances in solid rocket technology push rocket motors to more extreme operating speeds and temperatures, it becomes increasingly important to have well-designed material systems capable of surviving these harsh conditions. One common component in these systems is the use of a fiber- and particle-reinforced EPDM insulation layer between the motor casing and the solid fuel to shield the casing from the temperatures of the burning fuel and from the high velocity of gas particles traveling within the motor. This work studies several insulation materials to determine which exhibits the highest shear strength after being charred. Double-notch shear test specimens of three materials, ARI-2718, ARI-2719, and ARI-2750, were charred and tested to measure the failure strength of each charred material. The ARI-2750 showed the highest shear strength when loaded along the material orientation, but the ARI-2719 was strongest when transversely loaded. The strength measurements for ARI-2750 were highly sensitive to loading direction, unlike ARI-2718 and ARI-2719. Extensive scanning electron microscopy to identify correlations between shear strength and microstructure revealed that the amount of fiber orientation and amount of residual matrix material may have significant impacts on charred shear strength in these materials.
Master of Science

Approved for public release, distribution is unlimited
Three propellants with aluminum/silicon weight percentages of 18/0%, 13.5/4.5%, and 12/6% were fired in a subscale motor to determine if the plume infrared signature could be reduced without a significant loss in specific impulse. Spectral measurements from 2.5 to 5.5 micrometers and thermal measurements from 3.5 to 5.0 micrometers were made. Plume particle size measurements showed that only particles with small diameters (less than 1.93 micrometers) were present with any significant volume. Replacing a portion of the aluminum in a highly metallized solid propellant with silicon was found to eliminate the Al2O3 in favor of SiO2 and Al6SiOl3, without any change in particulate mass concentration or any large change in particle size distribution. These particulates were found to have significantly lower absorptivity than Al2O3. An additional investigation was conducted to determine the particle size distribution at the nozzle entrance. Malvern ensemble scattering, phase-Doppler single particle scattering and laser transmittance measurements made through windows in the combustion chamber at the nozzle entrance indicated that large particles were present (to 250 micrometers). However, most of the mass of the particles was contained in particles with diameters smaller than 5 micrometers. Approximate calculations made with the measured data showed that if 100 micrometers particles are present with the smoke (particles with diameters less than 2 micrometers) they could account for only approximately 10% of the article volume

This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2019
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 97-100).
A gap exists in the design space for aircraft mass and speed: no flight vehicles with a mass of less than 10 kg and speed greater than 100 m/s are available. The small, fast "Firefly" flight vehicle is being developed to explore the capabilities and challenges for aircraft in this gap. The compact Firefly aircraft is configured around a long-endurance, end-burning solid rocket motor that provides 2-3 minutes of powered flight. Challenges exist for manufacturing solid rocket motors for small, fast aircraft such as Firefly. Achieving desired motor performance requires a void-free propellant grain and thermal liner and a strong propellant-to-liner bond. However, observations and tests following several motor manufacturing attempts have revealed voids in the propellant and liner and delamination at the propellant-to-liner interface. Manufacturing defects such as these have led to large increases in chamber pressure and thrust during a static fire test of a motor. This thesis describes the development and implementation of manufacturing methods for slow-burning, long-endurance motors used in small, fast aircraft. Innovative tooling and rigorous procedures have been developed to help ensure the consistent production of a long-endurance solid rocket motor. Successful static firings of a test motor validate the effectiveness of many of the developed manufacturing methods.
by Kelly J. Mathesius.
S.M.
S.M. Massachusetts Institute of Technology, Department of Aeronautics and Astronautics

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2017.
A framework for optimising a tactical solid rocket motor nozzle is established and investigated within the ANSYS Workbench environment. Simulated results are validated against thrust measurements from the static bench firing of a full-scale rocket. Grid independence is checked and achieved using inflation based meshing. A rocket nozzle contour is parametrized using multiple control points along a spline contour. The design of experiments table is populated by a central composite design method and the resulting response surfaces are used to find a thrust optimised rocket nozzle geometry. CFD results are based on Favre-mass averaged Navier-Stokes equations with turbulence closure implemented with the Menter SST model. Two optimisation algorithms (Shifted Hammersley Sampling and Nonlinear Programming by Quadratic Lagrangian) are used to establish viable candidates for maximum thrust. Comparisons are made with a circular arc, Rao parabolic approximation and conical nozzle geometries including the CFD simulation there-off. The effect of nozzle length on thrust is simulated and optimised within the framework. Results generally show increased thrust as well as demonstrating the framework's potential for further investigations into nozzle geometry optimisation and off-design point characterisation.

Cold-flow tests were conducted in mediums of air and water to investigate the internal flow field about the nozzle region of a proposed solid rocket motor (SRM) configuration that would potentially replace the current external boosters on NASA's Space Shuttle. One-eighth-scale clear acrylic models of the proposed submerged aft-dome and aft finned grain elements were constructed to simulate the aft segment of the SRM at ignition and 35 seconds into the firing sequence. Pressure, velocity, and turbulence profiles were obtained during cold air testing, while air bubbles and dye were used for flow visualization during water tunnel testing.

The flow visualization experiments indicated the presence of strong inlet vortices, alternating vortex shedding from both grain models' fins, circumferential flow in the aft-dome and around the nozzle, and recirculatory flow in the aft-dome and near an upstream portion of the 35-second grain model. Data acquired during cold air testing showed a turbulent low-velocity flow field in the aft-dome for both grain models. With respect to pressure and mean velocity virtually the entire nozzle/aft-dome region exhibited a minimal sensitivity to nozzle vectoring.

Master of Science

In this thesis, Initial Value Problem of Level-set Method is applied to solid propellant combustion to find the grain burnback. For the performance prediction of the rocket motor, 0-D, 1-D or 3-D flow models are used depending on the type of thre grain configuration.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1993.
Includes bibliographical references (leaves 119-124).
by Jackson H. Jung.
M.S.

Control of vortex-driven instabilities was demonstrated via a scaled-down, cold-flow simulation that modeled closed-end acoustics. When vortex shedding frequencies couple with the natural acoustic modes of a choked chamber, potentially damaging low-frequency instabilities may arise. Although passive solutions can be effective, an active control solution is preferable. An experiment was performed to demonstrate an active control scheme for the reduction of vortex-driven oscillations. A non-reacting experiment using a primary flow of air, where both the duct exit and inlet are choked, simulated the closed-end acoustics. Two plates, separated by 1.27 cm, produced the vortex shedding phenomenon at the chamber's first longitudinal mode. Two active control schemes, closed-loop and open-loop, were studied via a cold-flow simulation for validating the effects of reducing vortex shedding instabilities in the system. Actuation for both control schemes was produced by using a secondary injection method. The actuation system consisted of pulsing compressed air from a modifed, 2-stroke model airplane engine, controlled and powered by a DC motor. The use of open-loop only active control was not highly effective in reducing the amplitude of the first longitudinal acoustic mode, near 93 Hz, when the secondary injection was pulsed at the same modal frequency. This was due to the uncontrolled phasing of the secondary injection system. A Pulse Width Modulated (PWM) signal was added to the open-loop control scheme to correct for improper phasing of the secondary injection flow relative to the primary flow. This addition allowed the motor speed to be intermittently increased to a higher RPM before returning to the desired open-loop control state. This proved to be effective in reducing the pressure disturbance by approximately 46%. A closed-loop control scheme was then test for its effectiveness in controlling the phase of the secondary injection. Feedback of the system's state was determined by placing a dynamic pressure transducer near the chamber exit. Closed-loop active control, using the designed secondary injection system, was proven as an effective means of reducing the problematic instabilities. A 50% reduction in the FFT RMS amplitude was realized by utilizing a Proportional-Derivative controller to modify the phase of the secondary injection.
M.S.A.E.
Department of Mechanical, Materials and Aerospace Engineering;
Engineering and Computer Science
Aerospace Engineering

Thesis (MScIng)--University of Stellenbosch, 2003.
ENGLISH ABSTRACT: The emission spectrum measured in the middle infrared (IR) band from the plume of a rocket can be used to identify rockets and track inbound missiles. It is useful to test the stealth properties of the IR fingerprint of a rocket during its design phase without needing to spend excessive amounts of money on field trials. The modelled predictions of the IR spectra from selected rocket motor design parameters therefore bear significant benefits in reducing the development costs. In a recent doctorate study it was found that a fundamental approach including quantum-mechanical and computational fluid dynamics (CFD) models was not feasible. This is first of all due to the complexity of the systems and secondly due to the inadequate calculation speeds of even the most sophisticated modern computers. A solution was subsequently investigated by use of the ‘black-box’ model of a multi-layer perceptron feed-forward neural network with a single hidden layer consisting of 146 nodes. The input layer of the neural network consists of 18 rocket motor design parameters and the output layer consists of 146 IR absorbance variables in the range from 2 to 5 μm wavelengths. The results appeared promising for future investigations. The available data consist of only 18 different types of rocket motors due to the high costs of generating the data. The 18 rocket motor types fall into two different design classes, the double base (DB) and composite (C) propellant types. The sparseness of the data is a constraint in building adequate models of such a multivariate nature. The IR irradiance spectra data set consists of numerous repeat measurements made per rocket motor type. The repeat measurements form the pure error component of the data, which adds stability to training and provides lack-of-fit ANOVA capabilities. The emphasis in this dissertation is on comparing the feed-forward neural network model to the linear and neural network partial least squares (PLS) modelling techniques. The objective is to find a possibly more intuitive and more accurate model that effectively generalises the input-output relationships of the data. PLS models are known to be robust due to the exclusion of redundant information from projections made to primary latent variables, similarly to principal components (PCA) regression. The neural network PLS techniques include feed-forward sigmoidal neural network PLS (NNPLS) and radial-basis functions PLS (RBFPLS). The NNPLS and RBFPLS algorithms make use of neural networks to find non-linear functional relationships for the inner PLS models of the NIPALS algorithm. Error-based neural network PLS (EBNNPLS) and radial-basis function network PLS (EBRBFPLS) are also briefly investigated, as these techniques make use of non-linear projections to latent variables. A modification to the orthogonal least squares (OLS) training algorithm of radial-basis functions is developed and applied. The adaptive spread OLS algorithm (ASOLS) allows for the iterative adaptation of the Gaussian spread parameters found in the radial-basis transfer functions. Over-fitting from over-parameterisation is controlled by making use of leaveone- out cross-validation and the calculation of pseudo-degrees of freedom. After cross-validation the overall model is built by training on the entire data set. This is done by making use of the optimum parameterisation obtained from cross-validation. Cross-validation also gives an indication of how well a model can predict data unseen during training. The reverse problem of modelling the rocket propellant chemical compositions and the rocket physical design parameters from the IR irradiance spectra is also investigated. This problem bears familiarity to the field of spectral multivariate calibration. The applications in this field readily make use of PLS and neural network modelling. The reverse problem is investigated with the same modelling techniques applied to the forward modelling problem. The forward modelling results (IR spectrum predictions) show that the feedforward neural network complexity can be reduced to two hidden nodes in a single hidden layer. The NNPLS model with eleven latent dimensions outperforms all the other models with a maximum average R2-value of 0.75 across all output variables for unseen data from cross-validation. The explained variance for the output data of the overall model is 94.34%. The corresponding explained variance of the input data is 99.8%. The RBFPLS models built using the ASOLS training algorithm for the training of the radialbasis function inner models outperforms those using K-means and OLS training algorithms. The lack-of-fit ANOVA tests show that there is reason to doubt the adequacy of the NNPLS model. The modelling results however show promise for future development on larger, more representative data sets. The reverse modelling results show that the feed-forward neural network model, NNPLS and RBFPLS models produce similar results superior to the linear PLS model. The RBFPLS model with ASOLS inner model training and 5 latent dimensions stands out slightly as the best model. It is found that it is feasible to separately find the optimum model complexity (number of latent dimensions) for each output variable. The average R2-value across all output variables for unseen data is 0.43. The average R2-value for the overall model is 0.68. There are output variables with R2-values of over 0.8. The forward and reverse modelling results further show that dimensional reduction in the case of PLS does produce the best models. It is found that the input-output relationships are not highly non-linear. The non-linearities are largely responsible for the compensation of both the DB- and C-class rocket motor designs predictions within the overall model predictions. For this reason it is suggested that future models can be developed by making use of a simpler, more linear model for each rocket class after a class identification step. This approach however requires additional data that must be acquired.
AFRIKAANSE OPSOMMING: Die emissiespektra van die uitlaatpluime van vuurpyle in die middel-infrarooi (IR) band kan gebruik word om die vuurpyle te herken en om inkomende vuurpyle op te spoor. Dit is nuttig om die uitstralingseienskappe van ‘n vuurpyl se IR afdruk te toets, sonder om groot bedrae geld op veldtoetse te spandeer. Die gemodelleerde IR spektrale voorspellings vir ‘n bepaalde stel vuurpylmotor ontwerpsparameters kan dus grootliks bydra om motorontwikkelingskostes te bemoei. In ‘n onlangse doktorale studie is gevind dat ‘n fundamentele benadering van kwantum-meganiese en vloeidinamika-modelle nie lewensvatbaar is nie. Dit is hoofsaaklik as gevolg van die onvoldoende vermoë van selfs die mees gesofistikeerde moderne rekenaars. ‘n Moontlike oplossing tot die probleem is ondersoek deur gebruik te maak van ‘n multilaag perseptron voorwaartse neurale netwerk met 146 nodes in ‘n enkele versteekte laag. Die laag van invoer veranderlikes bestaan uit agtien vuurpylmotor ontwerpsparameters en die uitvoerlaag bestaan uit 146 IR-absorbansie veranderlikes in die reeks golflengtes vanaf 2 tot 5 μm. Dit het voorgekom dat die resultate belowend lyk vir toekomstige ondersoeke. Weens die hoë kostes om die data te genereer bestaan die beskikbare data uit slegs agtien verskillende tipes vuurpylmotors. Die agtien vuurpyl tipes val verder binne twee ontwerpsklasse, naamlik die dubbelbasis (DB) en saamgestelde (C) dryfmiddeltipes. Die yl data bemoeilik die bou van doeltreffende multiveranderlike modelle. Die datastel van IR uitstralingspektra bestaan uit herhaalde metings per vuurpyltipe. Die herhaalde metings vorm die suiwer fout komponent van die data. Dit verskaf stabilitieit tot die opleiding op die data en verder die vermoë om ‘n analise van variansie (ANOVA) op die data uit te voer. In hierdie tesis lê die klem op die vergelyking tussen die voorwaartse neurale netwerk en die lineêre en neurale netwerk parsiële kleinste kwadrate (PLS) modelleringstegnieke. Die doel is om ‘n moontlik meer insiggewende en akkurate model te vind wat effektief die in- en uitvoer verhoudings kan veralgemeen. Dit is bekend dat PLS modelle meer robuus kan wees weens die weglating van oortollige inligting deur projeksies op hoof latente veranderlikes. Dit is analoog aan hoofkomponente (PCA) regressie. Die neurale netwerk PLS-tegnieke sluit in voorwaartse sigmoïdale neurale netwerk PLS (NNPLS) en radiale-basis funksies PLS (RBFPLS). Die NNPLS en RBFPLS algoritmes maak gebruik van die neurale netwerke om nie-lineêre funksionele verbande te kry vir die binne PLS-modelle van die nie-lineêre iteratiewe parsiële kleinste kwadrate (NIPALS) algoritme. Die fout-gebaseerde neurale netwerk PLS (EBNNPLS) en radiale-basis funksies PLS (EBRBFPLS) is ook weens hulle nie-lineêre projeksies na latente veranderlikes kortiliks ondersoek. ‘n Aanpassing tot die ortogonale kleinste kwadrate (OLS) opleidingsalgoritme vir radiale-basis funksies is ontwikkel en toegepas. Die aangepaste algoritme (ASOLS) behels die iteratiewe aanpassing van die verspreidingsparameters binne die Gauss-funksies van die radiale-basis transformasie funksies. Die oormatige parameterisering van ‘n model word beheer deur kruisvalidering met enkele weglatings en die berekening van pseudo-vryheidsgrade. Na kruisvalidering word die algehele model gebou deur opleiding op die volledige datastel. Dit word gedoen deur van die optimale parameterisering gebruik te maak wat deur kruisvalidering bepaal is. Kruisvalidering gee ook ‘n goeie aanduiding van hoe goed ‘n model ongesiende data kan voorspel. Die modellering van die vuurpyle se chemiese en fisiese ontwerpsparameters (omgekeerde probleem) is ook ondersoek. Hierdie probleem is verwant aan die veld van spektrale multiveranderlike kalibrasie. Die toepassings in die veld maak gebruik van PLS en neurale netwerk modelle. Die omgekeerde probleem word dus ondersoek met dieselfde modelleringstegnieke wat gebruik is vir die voorwaartse probleem. Die voorwaartse modelleringsresultate (IR voorspellings) toon dat die kompleksiteit van die voorwaartse neurale netwerk tot twee versteekte nodes in ‘n enkele versteekte laag gereduseer kan word. Die NNPLS model met elf latente dimensies vaar die beste van alle modelle, met ‘n maksimum R2-waarde van 0.75 oor alle uitvoer veranderlikes vir die ongesiende data (kruisvalidering). Die verklaarde variansie vir die uitvoer data vanaf die algehele model is 94.34%. Die verklaarde variansie van die ooreenstemmende invoer data is 99.8%. Die RBFPLS modelle wat gebou is deur van die ASOLS algoritme gebruik te maak om die PLS binne modelle op te lei, vaar beter in vergelyking met die K-gemiddeldes en OLS opleidingsalgoritmes. Die toetse wat ‘n ‘tekort-aan-passing’ ANOVA behels, toon dat daar rede is om die geskiktheid van die NNPLS model te wantrou. Die modelleringsresultate lyk egter belowend vir die toekomstige ontwikkeling van modelle op groter, meer verteenwoordigde datastelle. Die omgekeerde modellering toon dat die voorwaartse neurale netwerk, NNPLS en RBFPLS modelle soortgelyke resultate produseer wat die lineêre PLS model s’n oortref. Die RBFPLS model met ASOLS opleiding van die PLS binne modelle word beskou as die beste model. Dit is lewensvatbaar om die optimale modelkompleksiteite van elke uitvoerveranderlike individueel te bepaal. Die gemiddelde R2-waarde oor alle uitvoerveranderlikes vir ongesiende data is 0.43. Die gemiddelde R2-waarde vir die algehele model is 0.68. Daar is van die uitvoer veranderlikes wat R2-waardes van 0.8 oortref. Die voor- en terugwaartse modelleringsresultate toon verder dat dimensionele reduksie in die geval van PLS die beste modelle lewer. Daar is ook gevind dat die nie-lineêriteite grootliks vergoed vir die voorspellings van beide DB- en Ctipe vuurpylmotors binne die algehele model. Om die rede word voorgestel dat toekomstige modelle ontwikkel kan word deur gebruik te maak van eenvoudiger, meer lineêre modelle vir elke vuurpylklas nadat ‘n klasidentifikasiestap uitgevoer is. Die benadering benodig egter addisionele praktiese data wat verkry moet word.

The present research project is carried out at the von Karman Institute for Fluid Dynamics (Rhode-Saint-Genèse, Belgium) with the financial support of the European Space Agency.

The first stage of spacecrafts (e.g. Ariane 5, Vega, Shuttle) generally consists of large solid propellant rocket motors (SRM), which often consist of segmented structure and incorporate a submerged nozzle. During the combustion, the regression of the solid propellant surrounding the nozzle integration part leads to the formation of a cavity around the nozzle lip. The propellant combustion generates liquefied alumina droplets coming from chemical reaction of the aluminum composing the propellant grain. The alumina droplets being carried away by the hot burnt gases are flowing towards the nozzle. Meanwhile the droplets may interact with the internal flow. As a consequence, some of the droplets are entrapped in the cavity forming an alumina puddle (slag) instead of being exhausted through the throat. This slag reduces the performances.

The aim of the present study is to characterize the slag accumulation process in a simplified model of the MPS P230 motor using primarily optical experimental techniques. Therefore, a 2D-like cold-gas model is designed, which represents the main geometrical features of the real motor (presence of an inhibitor, nozzle and cavity) and allows to approximate non-dimensional parameters of the internal two-phase flow (e.g. Stokes number, volume fraction). The model is attached to a wind-tunnel that provides quasi-axial flow (air) injection. A water spray device in the stagnation chamber realizes the models of the alumina droplets, which are accumulating in the aft-end cavity of the motor.

To be able to carry out experimental investigation, at first the the VKI Level Detection and Recording(LeDaR) and Particle Image Velocimetry (PIV) measurement techniques had to be adapted to the two-phase flow condition of the facility.

A parametric liquid accumulation assessment is performed experimentally using the LeDaR technique to identify the influence of various parameters on the liquid deposition rate. The obstacle tip to nozzle tip distance (OT2NT) is identified to be the most relevant, which indicates how much a droplet passing just at the inhibitor tip should deviate transversally to leave through the nozzle and not to be entrapped in the cavity.

As LeDaR gives no indication of the driving mechanisms, the flow field is analysed experimentally, which is supported by numerical simulations to understand the main driving forces of the accumulation process. A single-phase PIV measurement campaign provides detailed information about the statistical and instantaneous flow structures. The flow quantities are successfully compared to an equivalent 3D unsteady LES numerical model.

Two-phase flow CFD simulations suggest the importance of the droplet diameter on the accumulation rate. This observation is confirmed by two-phase flow PIV experiments as well. Accordingly, the droplet entrapment process is described by two mechanisms. The smaller droplets (representing a short characteristic time) appear to follow closely the air-phase. Thus, they may mix with the air-phase of the recirculation region downstream the inhibitor and can be carried into the cavity. On the other hand, the large droplets (representing a long characteristic time) are not able to follow the air-phase motion. Consequently, a large mean velocity difference is found between the droplets and the air-phase using the two-phase flow measurement data. Therefore, due to the inertia of the large droplets, they may fall into the cavity in function of the OT2NT and their velocity vector at the level of the inhibitor tip.

Finally, a third mechanism, dripping is identified as a contributor to the accumulation process. In the current quasi axial 2D-like set-up large drops are dripping from the inhibitor. In this configuration they are the main source of the accumulation process. Therefore, additional numerical simulations are performed to estimate the importance of dripping in more realistic configurations. The preliminary results suggest that dripping is not the main mechanism in the real slag accumulation process. However, it may still lead to a considerable contribution to the final amount of slag.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Dans un moteur à propergol solide, des instabilités thermoacoustiques auto-entretenues, induites par le couplage de la dynamique de la combustion des gouttes d’aluminium, libérées par la combustion du propergol, avec le champ acoustique peuvent induire des oscillations de pression.L’analyse menée tout au long de ce manuscrit repose sur un ensemble d’hypothèses simplificatrices: (i) la réponse de la combustion de gouttes d’aluminium aux perturbations acoustiques est contrôlée par l’écoulement local autour de la goutte, (ii) le processus de combustion peut être supposé quasi stationnaire pour la gamme de fréquences et les amplitudes acoustiques étudiées et (iii) la combustion de l’aluminium est brusquement arrêtée lorsque le diamètre de la goutte d’aluminium diminue en dessous d’un diamètre résiduel.L’instabilité thermoacoustique est étudiée au moyen de simulations numériques de l’écoulement dans un moteur générique et d’analyses théoriques. Le diamètre résiduel des gouttes d’aluminium après la combustion, l’amplitude de la perturbation acoustique et la durée de la combustion des gouttes d’aluminium figurent parmi les principaux paramètres modifiant l’instabilité. En outre, trois comportements de réponse de la combustion à l’acoustique sont identifiés : un comportement linéaire pour les faibles niveaux de pression acoustique puis un comportement quadratique (faiblement non-linéaire) et enfin un comportement fortement non-linéaire quand l’amplitude des oscillations augmente.Ensuite, deux aspects importants de la réponse des gouttes d’aluminium sont identifiés. Ils sont associés aux oscillations de la durée du temps de combustion des gouttes, identifiables à la frontière du nuage de gouttes, et aux fluctuations du taux d’évaporation contrôlées par la convection de l’écoulement gazeux autour de chaque goutte. Tenant compte de ces dynamiques,des expressions analytiques sont obtenues permettant de reproduire avec précision les résultats numériques des simulations de l’écoulement. Quatre nombres sans dimension qui régissent la dynamique de ces instabilités sont également identifiés. Inspiré de l’analyse théorique précédente, un modèle numérique d’ordre réduit faiblement non linéaire est finalement développé pour prédire des cycles limites
In a solid rocket motor, self-sustained thermo-acoustic instabilities, induced by the coupling of the combustion dynamics of aluminum droplets released by the burning propellant with the acoustic field can induce pressure oscillations.The analysis conducted throughout this manuscript relies thus on a set of simplifying hypothesis by assuming (i) that the response of the combustion of aluminum droplets to acoustic perturbations is controlled by the oscillating drag exerted by the local flow around the droplet, (ii) that this unsteady combustion process can be assumed quasi-steady for the range of frequencies and acoustic amplitudes studied and (iii) that aluminum combustion is abruptly quenched when the aluminum droplet diameter falls below a residual diameter.The thermo-acoustic instability is studied first by numerical flow simulations in a generic solid rocket motor and theoretical analyses. The post-combustion residual diameter of the aluminum particles, the amplitude of acoustic perturbation and the lifetime of the burning aluminum droplets are among the main parameters altering the instability. Also, three combustion response behaviors to acoustics are identified : a linear behavior for small acoustic pressure levels followed by a quadratic behavior then a highly non-linear behavior when the pressure amplitude increases in the motor chamber. Moreover, two important features of the response of aluminum droplets are identified. They are associated to oscillations of the droplet lifetime at the boundary of the droplet cloud and to fluctuations of the droplet evaporation rate, controlled by convection. The dynamics of the droplets highly depends on gas and droplet velocity fields and on droplet diameter. Taking these features into account, yields analytical expressions that allow to reproduce with accuracy the numerical results from the flow simulations. Four dimension less numbers are then identified. They govern the dynamics of these instabilities. Inspired from the previous theoretical analysis, a weakly nonlinear low-order numerical model is finally developed to predict limit cycles

Les lanceurs ont un impact sur la composition de l'atmosphere, et en particulier sur l'ozone stratospherique. Parmi tous les types de propulsion, les moteurs à propergol solide ont fait l'objet d'une attention particulière car leurs émissions sont responsables d'un appauvrissement significatif d'ozone dans le panache des lanceurs lors des premières heures suivant le lancement. Ce phénomène est principalement dû à la conversion de l'acide chlorhydrique, un composé chimique présent en grandes quantités dans les émissions de ce type de moteur, en chlore actif qui réagit par la suite avec l'ozone dans un cycle catalytique similaire à celui responsable du "trou de la couche d'ozone", cette diminution périodique de l'ozone en Antarctique. Cette conversion se produit dans le panache supersonique, où les hautes températures favorisent une seconde combustion entre certaines espèces chimiques du panache et l'air ambiant. L'objectif de cette étude est d'évaluer la concentration de chlore actif dans le panache d'un moteur à propergol solide en utilisant la technique des Simulations aux Grandes Echelles (SGE). Le gaz est injecté à travers la tuyère d'un moteur et une méthode de couplage entre deux instances du solveur de mécanique des fluides est utilisée pour étendre autant que possible le domaine de calcul derrière la tuyère (jusqu'à l'équivalent de 400 diamètres de sortie de la tuyère). Cette méthodologie est validée par une première SGE sans chimie, en analysant les caractéristiques de l'écoulement supersonique avec co-écoulement obtenu par ce calcul. Ensuite, le chimie mettant en jeu la conversion des espèces chlorées a été étudiée au moyen d'un modèle "hors-ligne" permettant de résoudre une chimie complexe le long de lignes de courant extraites d'un écoulement moyenné dans le temps résultant du calcul précédent (non réactif). Enfin, une SGE multi-espèces est réalisée, incluant un schéma chimique auparavant réduit afin de limiter le coût de calcul. Cette simulation représente une des toutes premières SGE d'un jet supersonique réactif, incluant la tuyère, effectuée sur un domaine de calcul aussi long. En capturant avec précision le mélange du panache avec l'air ambiant ainsi que les interactions entre turbulence et combustion, la technique des simulations aux grandes échelles offre une évaluation des concentrations des espèces chimiques dans le jet d'une precision inédite. Ces résultats peuvent être utilisés pour initialiser des calculs atmosphériques sur de plus larges domaines, afin de modéliser les réactions entre chlore actif et ozone et de quantifier l'appauvrissement en ozone dans le panache
Rockets have an impact on the chemical composition of the atmosphere, and particularly on stratospheric ozone. Among all types of propulsion, Solid-Rocket Motors (SRMs) have given rise to concerns since their emissions are responsible for a severe decrease in ozone concentration in the rocket plume during the first hours after a launch. The main source of ozone depletion is due to the conversion of hydrogen chloride, a chemical compound emitted in large quantities by ammonium perchlorate based propellants, into active chlorine compounds, which then react with ozone in a destructive catalytic cycle, similar to those responsible for the Antartic "Ozone hole". This conversion occurs in the hot, supersonic exhaust plume, as part of a strong second combustion between chemical species of the plume and air. The objective of this study is to evaluate the active chlorine concentration in the far-field plume of a solid-rocket motor using large-eddy simulations (LES). The gas is injected through the entire nozzle of the SRM and a local time-stepping method based on coupling multi-instances of the fluid solver is used to extend the computational domain up to 400 nozzle exit diameters downstream of the nozzle exit. The methodology is validated for a non-reactive case by analyzing the flow characteristics of the resulting supersonic co-flowing under-expanded jet. Then the chemistry of chlorine is studied off-line using a complex chemistry solver applied on trajectories extracted from the LES time-averaged flow-field. Finally, the online chemistry is analyzed by means of the multi-species version of the LES solver using a reduced chemical scheme. To the best of our knowledge, this represents one of the first LES of a reactive supersonic jet, including nozzle geometry, performed over such a long computational domain. By capturing the effect of mixing of the exhaust plume with ambient air and the interactions between turbulence and combustion, LES offers an evaluation of chemical species distribution in the SRM plume with an unprecedented accuracy. These results can be used to initialize atmospheric simulations on larger domains, in order to model the chemical reactions between active chlorine and ozone and to quantify the ozone loss in SRM plumes

The ability of a propulsion system is very crucial for the capability of a missile or a rocket system. Unlike liquid propellant rocket motors, the only control mechanism of the thrust value is the propellant geometry in solid propellant rocket motors. When the operation of solid propellant rocket motor has started, it cannot be stopped anymore. For this main reason the advance of dual pulse motor technology has started. The aim of this study is to investigate the geometrical effects of design parameters on the flow behavior of a dual pulse solid propellant rocket motor by using commercial Computational Fluid Dynamics (CFD) methods. For the CFD analysis, a generic dual pulse rocket motor model is constituted. Within this model, initially four different geometry alternatives of Pulse Separation Device (PSD) are analyzed. To begin PSD analyses, mesh sensitivity analyses are performed on one PSD geometry alternative. By defined grid size, the analyses of PSD geometry alternatives are performed. Computed results were compared in terms of flow behavior (flow streamlines, velocity distribution, turbulent kinetic energy&hellip
etc.) with each other. With the selected PSD geometry alternative the effects of L/D ratio (Length/Diameter ratio) of first pulse chamber, Achamb/APSD ratio (Chamber area/PSD opening area) and APSD/Ath ratio (PSD opening area/Throat area) on the flow behavior is investigated. Flow analyses are performed by simulating the unsteady flow of second pulse operation. With the performed analyses, it is aimed to identify generic geometric definitions for a dual pulse rocket motor.