Application of the Time-Domain Impedance Boundary Condition to Large-Eddy Simulation of Combustion Instability in a Shear-Coaxial High Pressure Combustor

The time-domain impedance boundary condition (TDIBC) is used within a large-eddy simulation (LES) framework to investigate self-sustained longitudinal combustion instability in the Continuously Variable Resonance Combustor (CVRC) rig, a high-pressure, shear-coaxial injector combustor studied experimentally at Purdue University. A modified version of the constant mass characteristic boundary condition is used to account for the impedance at the oxidizer inlet, which is truncated and therefore becomes an approximation of the full inlet. Both linear and non-linear models for the inlet reflection coefficients are developed and compared against the full injector LES. The CVRC rig exhibits different amplitude levels of the pressure oscillation depending on the length of the oxidizer injector, and thus, offers a range of conditions to evaluate the use of the TDIBC. The combustor with a truncated oxidizer injector length of 2.05 cm is used to simulate conditions equivalent of three different oxidizer injector lengths of 9 cm, 12 cm and 14 cm, which are known to exhibit semi-stable, unstable and highly unstable behavior, respectively. The results are compared with LES that explicitly resolve the full oxidizer post without impedance. It is shown that the prediction by the non-linear reflection coefficient model is much better than the linear model. Further analysis is carried out to highlight the strengths and the limitations of the model.