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.

The present research is an experimental and numerical study of aeroacoustic phenomena occurring in large solid rocket motors (SRM) as the Ariane 5 boosters. 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 payload. The study is carried out within the framework of a CNES (Centre National d'Etudes Spatiales) research program. <p><p>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 Vortex 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 motor. 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.<p><p>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.<p><p>The experiments are conducted on axisymmetric cold flow models respecting the Mach number similarity with the Ariane 5 SRM. 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 analyse 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.<p><p>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.<p><p>The OVS and SVS instabilities are identified. The inhibitor parameters, the chamber Mach number and length, and the nozzle geometry are varied to analyse their effect on the flow acoustic coupling.<p><p>The conclusions state that flow acoustic coupling is mainly observed for nozzles including cavity. The nozzle geometry has an effect on the pressure oscillations through a coupling between the acoustic fluctuations induced by the cavity volume and the 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.<p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

The objective of this study was to design a launch vehicle capable of deploying a nanosatellite into a Sun-synchronous orbit at 500 km orbital altitude from the JAS 39E/F Gripen fighter aircraft. This was achieved by first performing theoretical calculations for the required nozzles and solid propellant grain configurations for the first two solid stages, followed by the necessary liquid propellant configuration for the third stage. Lastly, two methods were investigated in solving the trajectory ascent problem for the launch vehicle design. First, by stating the trajectory problem as an initial value problem while guessing a Sigmoidal steering law. Secondly, by stating the trajectory problem as a boundary value problem. The latter was solved by transcribing the trajectory problem into a nonlinear program where a parametric steering law was derived using a Sequential quadratic programming algorithm.Ultimately, resulting in a launch vehicle design with a gross lift-off mass of 1,289 kg, capable of launching an 8.4 kg payload into the targeted orbit, with suggested modifications to increase the possible payload mass to 12.9 kg. / Målet med den här studien var att designa en luftlanserad trestegsraket kapabel till att transportera en nanosatellit upp till en solsynkron omloppsbana på 500 km altitud från ett JAS 39E/F Gripen jaktflygplan. Det gjordes genom att först beräkna de nödvändiga dysorna och krutladdningsformerna för de två första stegen tillsammans med en flytande bränsledesign för det tredje steget. Två metoder undersöktes för bananalysen. Först genom att anta en Sigmoidal styrningsfunktion för pitchen, sedan genom att transkribera problemet till ett icke-linjärt program där en parametrisk styrlag togs fram genom att använda en Sequential quadratic programming algoritm. Slutligen presenterades en raketdesign med en total vikt på 1 289 kg, kapabel till att skjuta upp en nyttolast på 8,4 kg till den önskade omloppsbanan tillsammans med förslag som kan öka den möjliga nyttolasten till 12,9 kg.