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. Due to 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. Consistently with experimental results, the simulations predict that the experimental setup is unconditionally unstable, with small perturbations growing to a limit cycle whose shape is a first transverse acoustic mode of the chamber.
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