Simulating the nonlinear acoustic oscillations in a resonator by gas-kinetic scheme

The nonlinear oscillation in a compressible air-filled two-dimensional cylindrical resonator driven by a loudspeaker is simulated by using the gas-kinetic scheme. The influences of shock wave and higher harmonic on the time and space distribution of acoustic variables are investigated numerically for the practical applications of high-intensity acoustic devices. The validation of the developed model is verified by comparing the numerical results of pressure distribution with the theoretical ones for the finite-amplitude case. And then, the verified gas-kinetic scheme is used to simulate the acoustic field of highly nonlinear standing wave. Some interesting physical phenomena have been revealed for the highly nonlinear case. Sharp velocity spikes accompanied by the saw-tooth pressure waveforms appear at the end of the resonator. Moreover, the pressure at the position of theoretical pressure node is not zero and its frequency is about twice of the resonance frequency. Furthermore, the second harmonic is predominant at the location of pressure node. And nonlinear saturation can be found in tandem as the shock wave appears. Additionally, quasi-one-dimensional distribution accompanied changing flow direction and annular effect is observed for the spatial distribution of x-velocity. In addition, the y-velocity is in an irregular two-dimensional distribution and the y-velocity is not any more negligible relative to the x-velocity. Meanwhile, the important impacts as well as the causes of these nonlinear phenomena are analyzed. The results demonstrate the gas-kinetic scheme is an efficient and appropriate method for simulation of highly nonlinear acoustic oscillation and concerned problems.