Finite amplitude standing wave in closed ducts with cross sectional area change

A linear theory was developed to estimate the resonant frequency and the standing wave mode in closed ducts with variable cross sectional area. The finite amplitude standing wave in closed ducts with area contraction was numerically studied. The effect of area contraction ratio and the gas properties on nonlinear standing wave was investigated. One-dimensional numerical simulation was conducted using fundamental fluid dynamics equations taking the effects of viscosity and frictions into consideration. Finite difference MacCormack scheme was used by preserving the computational accuracy within second-order in time and fourth-order in space, respectively. The dependences of the pressure waveform on the area contraction ratio, the limit of area contraction ratio to obtain shockless high amplitude pressure waveform with the variation of gas properties and the amplitude of pressure waveform with the variation of duct geometries were investigated. In addition, the compression ratios at the closed end of the duct with different area contraction ratios for different duct geometries were presented. This study suggests that changes in duct geometry can have a significant impact on overall performance of acoustic compressors.