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Numerical simulation is performed and compared with a firing test of an H 2 O 2 ∕polyethylene hybrid rocket engine equipped with a catalyzer. The simulation is performed assuming an axisymmetric flow, unsteady Reynolds-averaged Navier-Stokes equations are solved based on a single-phase flow. Stable pressure oscillations are observed during the firing test and could be explained by the simulation with the formation of large-scale vortices at the end of the fuel grain and in the postcombustion chamber. These vortices transport unburnt fuel to the nozzle and play a major role in the mixing process in the postchamber. Two semi-empirical approaches are applied and provide a good order of magnitude for the frequency and frequency shift during the firing test. Another simulation has been performed with an added oxidizer postchamber injection. It revealed that small-scale vortices along the fuel grain in the baseline case are probably generated by the oscillatory motion of the flow due to pressure fluctuations in the engine. Nomenclature C μ = turbulence model constant c = speed of sound, m · s −1 c th = theoretical characteristic velocity, m · s −1 D = fuel port diameter, m D t = nozzle throat diameter, m f = frequency, Hz k = turbulence kinetic energy, m 2 · s −2 k Ross = ratio of vortex transport velocity to freestream velocity L = total combustion chamber length, m L f = fuel grain length, m L pre ch = length of the prechamber, m L Ross = distance between shear layer initiation and impingement point, m l = exhaust nozzle length, m M = Mach number m = stage number (number of coherent structures) _ m = mass flow rate, kg · s −1 O∕F= oxidizer-to-fuel mixture ratio p = pressure, Pa Q = Q criterion, rad 2 · s −2 R = specific gas constant, J · kg −1 · K −1 R f = fuel port radius, m r = distance from wall, m S = symmetric part of velocity gradient tensor S D = Strouhal number based on end-port diameter T = temperature, K T Ross = period, s U = freestream velocity, m · s −1 U vortex = vortex transport velocity, m · s −1 V = combustion port total volume, m 3 V x = axial velocity, m · s −1 x = axial position, m Y = mass fraction y = radial position, where y equal to zero is the axis, m α = empirical constant Δt = correction factor, s η c = combustion efficiency κ = von Kármán constant ρ = density, kg · m −3 τ bl = boundary-layer delay time, s ψ = function of isentropic coefficient Ω = skew-symmetric part of velocity gradient tensor ω = turbulence specific dissipation rate, s −1 Subscripts 1L = first longitudinal acoustic mode end = end of firing test H = Helmholtz mode hy = hybrid intrinsic instability ini = beginning of firing test ox = oxidizer

Table des matières Liste des figures xii Liste des tableaux xiii Nomenclature xv A Récapitulatif du modèle d'instabilités hydrodynamiques Bibliographie viii Modélisation des instabilités hydrodynamiques dans les moteurs-fusées hybrides xviii Modélisation des instabilités hydrodynamiques dans les moteurs-fusées hybrides 1. Une partie de ce chapitre a fait l'objet d'un article dans le Journal of Propulsion and Power : « Vortex shedding influence on hybrid rocket pressure oscillations and combustion efficiency » [62]. Modélisation des instabilités hydrodynamiques dans les moteurs-fusées hybrides

Despite the fact that hybrid propulsion offers significant benefits, it still suffers from some limitations such as the natural oxidizer to fuel ratio shift which induces variations of the engines’ performances while operating. To overcome that issue, Japan Aerospace Exploration Agency (JAXA) has been studying an innovative concept for several years based on the combination of controlled axial and radial oxidizer injections, called altering-intensity swirling-oxidizer-flow-type engine. This type of motor is theoretically capable of managing both the thrust and the oxidizer to fuel ratio independently and instantaneously by using a feedback control loop. To be effective, such engines would require in-flight instantaneous and precise thrust and an oxidizer to fuel ratio measurements as well as an adapted feedback control law. The purpose of this study is to investigate the effect of measurement errors on the engine control and to propose a regulation law suitable for these motors. Error propagation analysis and regulation law are developed from fundamental equations of hybrid motors and applied in a case where resistor-based sensors are used for fuel regression rate measurement. This study proves the theoretical feasibility of hybrid engines feedback control while providing some methods to design the engine and regression rate sensors depending on the mission requirements.

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Burning tests of a laboratory-scale hybrid rocket engine were carried out with gaseous oxygen and a microcrystallinewax based fuel to look into the feasibility of using an intrusive resistor-based sensor for measuring the fuel regression rate.This initial screening was driven by the need for real-time control of the oxidizer-to-fuel ratio in altering-intensity swirlingflow-type hybrid rocket engines aiming at performance optimization. To build up a framework for comparison with the measured data, a traditional ballistic reconstruction technique was critically revised; with the measured aft-chamber pressure and oxygen mass flow rate time histories, the fuel regression-rate and port diameter were reconstructed over the firing, by estimating the combustion efficiency with the constraint that calculated and measured fuel mass consumed are equal. This technique invariably suffers from the issue of presenting multiple solutions for the fuel mass flow rate in the proximity of the optimum mixture ratio, for which a novel variable-efficiency approach is proposed. Reconstructed data show that regression rate is nearly constant in each firing, yielding dependence upon the port diameter other than the mass flux.Resistor-sensor raw data displayed large deviation from the ballistic results for the slower burning rate of the sensor support.A detailed analysis is presented.

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