A computational method for a thermoacoustic boundary layer in a gas-filled tube

This paper demonstrates a computational method to solve equations for a thermoacoustic boundary layer in a gas-filled tube subjected to a temperature gradient axially. With applications to numerical simulations of thermoacoustic systems, the purpose is to establish a method to evaluate numerically a velocity v(b) at the edge of a boundary layer directed into a core region in the outside of the layer. The computational method exploits a series expansion in terms of Chebyshev polynomials. Solved is a benchmark example for which analytical solutions are available. Assuming that a quiescent gas is started by an impulse and an acoustic field in the core region is given, an axial velocity and a temperature disturbance in the boundary layer are sought, from which v(b) is derived. Comparing the numerical solutions obtained against the analytical ones, it is found that the acoustic field and ultimately v(b) are well obtained with good accuracy. It is thus concluded that the present computational method will apply to numerical simulations based on the boundary-layer theory.