Transverse Combustion Instability in a Rectangular Rocket Motor

A computational analysis of transverse acoustic instability is presented for an experimental combustion chamber with rectangular cross section. The analysis is shown to be efficient and accurate. The governing equations are solved on multiple, coupled grids, which are two-dimensional in the combustion chamber and nozzle and one-dimensional in the injector port. Thus, they allow for a fast simulation, even in a serial run. Because of the lengthscale difference, the jet flame behavior at the injectors (including effects of turbulence) can be decoupled from the acoustic effects and solved on a local grid for each jet flame emerging from an injector. Wave propagation through the injector feed ports is evaluated on additional, one-dimensional grids for each injector port. The overall algorithm is used to simulate the Purdue seven-injector rocket engine; good quantitative agreement between simulations and experiment is achieved. All simulations that are predicted to be unconditionally unstable are confirmed by the Purdue experiment. Small perturbations grow to a limit cycle for which the shape is a first transverse acoustic mode of the chamber. Only one result differs from experiment, albeit very slightly.