NUMERICAL SIMULATIONS OF RESONANT OSCILLATIONS IN A TUBE

Abstract

The article concerns a genuinely two-dimensional numerical study of resonant oscillation phenomena in a gas-filled tube with an isothermal wall or an adiabatic wall. The time-dependent, axisymmetric, compressible Navier-Stokes equations in two dimensions are solved by a new finite volume method with the second-order kinetic flux-vector splitting (KFVS) scheme for convective terms, and a third-order Runge-Kutta method for the time evolution. The oscillatory motion of the fluid in a closed tube is generated by a piston at one end, and reflected by the other closed end. Weak shock waves propagating within the tube at the resonant frequency and slightly off-resonance frequencies are numerically captured, which are consistent with both experimental observation and previous theoretical analyses. The interesting results of the sudden change in axial velocity near the piston and the closed end are also presented.