Parametric system identification of rocket combustion instability using the Fokker-Planck equation

Abstract

This project seeks to advance understanding of thermo-acoustic instabilities in liquid-propellant rocket engines (LPREs). Unstable thermo-acoustic coupling between combustion and acoustic modes in a rocket engine thrust chamber can lead to high pressure oscillations and subsequent structural damage. Since the mechanisms involved are not yet fully understood, engine stability cannot be assured at the design stage. Consequently, costly ground testing is required such as that undertaken at the German Aerospace Centre (DLR) site in Lampoldshausen for Ariane engines. A deeper understanding of instabilities would reduce ground testing requirements, and allow for more economical rocket engine development. This project, conducted in conjunction with the DLR, aims to extract key parameters governing thermo-acoustic behaviour in rocket combustors from dynamic pressure measurements using stochastic signal processing techniques. These system-defining parameters are the linear thermo-acoustic growth rate, the noise intensity of turbulence-induced stochastic heat release, and the coefficient of non-linear acoustic damping. In particular, knowledge of the growth rate would allow the efficient design of retrofitted acoustic dampers and the validation of linear thermo-acoustic models. Current parameter extraction methods in rocket literature are limited to stable (linear) conditions. In these conditions, a Lorentzian fit to the power spectral density of dynamic (acoustic) pressure is commonly used to find the growth rate. For unstable (non-linear) cases, the initially linear growth of instability is not directly observed by wall sensors due to time scale differences between localised thermo-acoustic effects and the response of acoustic chamber modes. The noise intensity and non-linearity coefficient are also not readily observable at non-linear conditions. In gas turbine literature, signal processing techniques based on the Fokker-Planck equation have been developed to extract system parameters from the statistics of unstable combustor data. The project focuses on applying these techniques to rocket engine conditions. Fokker-Planck parameter extraction techniques have been applied to experimental data from two rocket combustors named 'BKH' and 'BKD', both operated at the DLR Lampoldshausen test site. These are representative of real rocket engine conditions; operating at sufficiently high pressures and flow rates with liquid oxygen/hydrogen propellants. While BKH is a rectangular and stable combustor, BKD is cylindrical and naturally unstable at some load points. Acoustic modes in BKH are purely standing, while in BKD they exhibited rotational characteristics, as occurs in real engines. This is significant since the parameter extraction techniques have different formulations for standing and rotational mode behaviour. This project has tested the two formulations of the Fokker-Planck techniques on BKH and BKD experimental data. The Fokker-Planck parameter extraction techniques have been validated for stable BKH and BKD load points using Lorentzian fits, while positive indications of their applicability to an unstable BKD load point have been obtained. These indications consist of comparing the statistical phase behaviour of the unstable BKD load point to that of a stable load point, and observing differences which support the non-linear dynamical model assumed in the techniques.