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Solid propellant combustion is source of instabilities in rocket motors. Each energy fluctuations, whatever the origin (turbulences, heterogeneity of propellant, ), can be amplified and coupled with the chamber acoustic resulting in injected mass flow and burned gas temperature fluctuations; this coupling happening in a specific frequency range. In addition, some motor tests have shown instabilities during transient shutdown when there is a significant pressure variation. Therefore, the response function of solid-propellant must be studied and it is necessary to build unsteady models to anticipate the appearance of those instabilities. Based on the important work done before the 2000s at ONERA, the subject of the combustion response of solid propellant has been reinvested through the integration of a non-linear model [1] in the ONERA multi-physics CFD code CEDRE. This research and technology program is done in the frame of an ONERA/CNES cooperation on solid propulsion. We first describe the one-dimensional model and the numerical approach of the problem. Recent experiments have shown level of instabilities that couldnt be explained by linear models that is why the thermal behaviour of the propellant is numerically resolved avoiding any linearization. An intrinsic validation of both the response model and numerical developments is performed by eliminating any interaction with the combustion chamber. Linear and non-linear domains are investigated for a large range of frequencies by introducing small and larger pressure oscillations. These simulations are compared to the known [2] linear model behaviour. More realistic simulation cases are then studied. The TEP motor is a simplified rocket motor test-case that is simulated with CEDRE. This motor has been largely studied as its a simple configuration, allowing easy and rapid simulations to validate numerical and physical models. A perturbation has been introduced in the rocket chamber and the propellant response to pressure oscillation observed. The simulations have been compared to the impulsive method based on the linear pressure coupled response function, used by Vuillot et al. [3] with the same propellant and test data. This allows to validate the model in a theoretical motor. Then a real rocket motor is simulated but to adjust the response model parameters to realistic propellant some experimental data are necessary. ONERA put in place a dedicated test set up allowing to characterise the propellant combustion response by means of a modulated exhaust jet technique. The geometry of the experimental apparatus has been meshed and simulated to reproduce experimental configuration. Simulation data and experimental data have been compared with the non-linear model. A theoretical response function given by an experimental apparatus geometry can be obtained by these simulations which was not possible before the integration of the model in the CFD software [5]. The model being adjust for a real propellant the simulation of an unstable rocket burning this propellant is possible. Finally, the C1x motor configuration is simulated to observe the influence of the response on the level of instabilities. The studied motor being intrinsically unstable, the pressure oscillation appears naturally due to a vortex shedding phenomenon. The application of the response function model at the burning surface is studied and compared to the instabilities observed in Dupays et al. [4].

This work presents the experimental investigation of heat fluxes through the walls of a reduced-scale rocket motor using hydrogen and oxygen as propellants. The engine is water cooled so that it ca...