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The linear high frequency stability of DLR's cryogenic H 2 /O 2 BKD test chamber is assessed using a hybrid computational fluid dynamic/computational aeroacoustic methodology, which is based on single flame simulations for the generation of an adequate mean flow and for the calibration of feedback models as well as on frequency space transformed linearized Euler equations. The application of a realistic mean flow field including combustion explains the spatial separation of transverse modes into a near face plate mode, which is found linearly unstable under certain operation conditions for the first transverse and a rear part mode. The axial mode shape length as well as eigenfrequencies is affected by propellant injection specifications and, in consequence, decisively influence pressure and transverse velocity sensitive dynamic flame response. The stability assessment procedure is finally applied to four operation conditions and the linear stability is predicted for the first transverse mode.

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Deutsches Zentrum für Luft-und Raumfahrt (DLR), Institute für Raumfahrtantriebe, Lampoldshausen C ombustion instabilities represent a challenging problem affecting a large number of rocket engine combustion chambers. Aim of the present study is to test a numerical procedure to predict the linear stability of an acoustic mode in a three dimensional configuration. The reference configuration is the BKD combustion chamber operated at the "Deutsches Zentrum für Luft-und Raumfahrt Lampoldshausen", which shows self-excited combustion instabilities for the first transverse mode for certain operation conditions. Here, four given load points are numerically investigated in terms of their stability behavior. For each load point, a flame transfer function around the first transverse mode frequency is determined from numerical simulations of a single flame configuration. Moreover, a three dimensional mean flow in the combustion chamber is computed considering equilibrium conditions in the chamber. Finally, mean flow and response function are incorporated into the linearized Euler code PIANO to analyze the thermoacoustic feedback. Results show that the methodology is able to perform a complete stability analysis from the knowledge of the load point conditions only by predicting the damping and growth rates.

Quantitative Stahility Analysis Using Real-Valued Frequency Response DataModels for the analysis of thermoacoustic instabilities are conveniently formulated in the frequency domain. In this case one often faces the difficulty that the response behavior of some elements of the system is only known at real-valued frequencies, although the transfer behavior at complex-valued frequencies is required for the quantification of the growth rates of instabilities. The present paper discusses various methods for extrapolation of frequency response data at real-valued frequencies into the complex plane. Some methods have been used previously in thermoacoustic stability analysis; others are newly proposed. First the pertinent mathematical background is reviewed, then the sensitivity of predicted growth rates on the extrapolation scheme is explored. This is done by applying different methods to a simple thermoacoustic system, i.e., a ducted premixed flame, for which an analytical solution is known. A short analysis determining the region of confidence of the extrapolated transfer function is carried out to link the present study to practical applications. The present study can be seen as a practical guideline for using frequency response data collected for a set of real-valued frequencies in quantitative linear stability analysis.