Numerical study of the effective impedance of a thermoacoustic stack

The force balance in the neighborhood of an idealized thermoacoustic stack is analyzed using two-dimensional unsteady flow simulations. The numerical model is based on a small-Mach-number approximation to the compressible Navier-Stokes equations; it ignores acoustic wave propagation within the stack but retains bulk compressibility and the convective nonlinearity of the original conservation equations. The effects of long wave acoustic pulses which drive the stack flow are taken into account through suitable velocity boundary conditions. The computations are used to characterize the effective impedance of the stack and to analyze its dependence on operating conditions and stack configuration parameters. Results are compared to semi-heuristic explicit formulas based on the linear theory.