Analyses of liquid rocket instabilities using a computational testbed

Abstract

A synergistic hierarchy of numerical and analytical models is used to simulate three-dimensional combustioninstability in liquid rocket engines. Existing phenomenological models for vaporization and atomization are used in quasi-steady form to describe the liquid phase processes. In addition to a complete nonlinear numerical model, linearized numerical and closed-form analytical models are used to validate the numerical solution and to obtain intial estimates of stable and unstable operating regimes. All three models are fully three dimensional. The simultaneous application of these approaches permits computationally inexpensive surveys to be performed in rapid parametric fashion for a wide variety of operating conditions. Stability maps obtained from the computations indicate that, when droplet temperature fluctuations are present, vaporization and atomization can drive instability. The presence of droplet temperature fluctuations introduces areas of instability for smaller drop sizes and colder drop temperatures. The computational procedures are demonstrated to accurately capture the three-dimensional wave propagation within the combustion chamber. The validated results indicate excellent amplitude and phase agreement for properly selected grid resolution. The nonlinear model demonstrates limit cycle behavior for growing waves and wave steepening for large-amplitude disturbances. The current work represents a validated computational testbed upon which more comprehensive physical modeling may be incorporated.