Combustion instabilities are a major problem in the development of rocket engines. Since the resulting oscillations may even lead to the failure of engine operation, methods to prevent them have always been a field of interest in the design of rocket engines. As an example the application of baffles and acoustic absorbers might be mentioned. These devices are supposed to damp the acoustic eigenfrequencies and to avoid oscillations. But up to now, no reliable tool exists to predict the incidence of combustion oscillations.
The aim of this project is the realisation of a simulation tool that can be used for the design of the absorber ring of a rocket engine. This simulation tool should be able to describe the interactions of the resonators with the acoustics and the combustion in the engine. Validation data for the acoustic behaviour of the rocket combustor will be obtained by experiments on a model combustion chamber operated by cold flow. In the end, the tool will be validated against data obtained by bomb tests.
The modelling of the thermo-acoustic behaviour of the rocket combustor is based on the method for time domain simulation of combustion instabilities in annular combustors. This approach relies on the numerical solution of the wave equation for the corresponding combustor geometry. To consider the influence of the unsteady heat release on the acoustics, a source term is added to the wave equation. A flame model is needed to link heat release fluctuations and flow field conditions. The resulting equation is solved by the finite element code FEMLAB.
In a first step, the rocket combustion chamber was modelled as a closed cylinder. To take into account the influence of the nozzle on the oscillatory conditions in the chamber an appropriate boundary condition developed by Marble & Candel was used. The application of this condition results in an acoustically closed end at the combustor exit.
The heat release fluctuations were calculated by applying the classical Crocco-Model as combustion model. This model links the local heat release fluctuations to the local pressure fluctuations in the combustion zone, involving two parameters: the interaction index and the time-delay.
To obtain a more realistic model, including reflection of acoustic waves by the nozzle, the geometry of the model was extended to the nozzle throat. Instead of the wave equation, acoustic perturbation equations (APEs) are solved now. These describe the propagation of acoustic waves in non-homogenous mean flows and therefore take into account reflection and refraction of the acoustic waves in the convergent part of the nozzle. The Crocco-Model is still maintained as a heat release model. Aditionally the numerical tool FEMLAB was replaced by the computational aeroacoustics code PIANO. PIANO is developed at the Institute of Aerodynamics and Flow Technology of the DRL Braunschweig and is designed to simulate aeroacoustic noise generation and acoustic wave propagation in non-uniform flows.
Results obtained by using the Wave Equation
First calculations show that by this first approach different oscillation modes can be obtained depending on the parameters used in the combustion model. The first six possible eigenmodes calculated by an eigenmode analysis are shown below:
In the following movie you can observe the onset of the first transversal mode (T1); the simulation starts from random perturbations from which a self-sustained oscillation with growing amplitude develops.
Without any damping devices self induced oscillations are obtained for almost all parameter sets of the heat release model. Often even several unstable modes are obtained.
Results of the extended Modelling Approach using APEs
For the basic approach as well as for extended approach the onset of self-excited combustion instabilities can be simulated. Including the convergent part of the rocket nozzle, acoustic losses occur across the nozzle throat with sonic conditions. Therefore unstable behaviour occurs less frequently and oscillation amplitudes remain lower. Nevertheless, by choosing certain parameters of the heat release model, various unstable modes can be obtained. The shape of the first tangential mode obtained by a time dependent simulation is shown below:
Further steps in the modelling of the behaviour of the rocket engine will be:
Various activities for the validation of the model will follow.