A numerical investigation of the response of an enclosed compressible gas to varying boundary conditions

Thermally-driven convection heat transfer has been studied experimentally, numerically, and analytically. Numerical modeling of thermoacoustic convection heat transfer (TAC) can incorporate fast acoustic time scales for detailed kinematic studies or consider slow expansion conduction time scales for bulk motion studies. In the expansion conduction model the acoustic velocity is filtered out with the bulk fluid motion remaining as the only motion of interest. The numerical modeling can also include or exclude the effect of gravity for either earth-bound or space applications.

The purpose of this study is to develop a working numerical model for use in the thermal and kinematic analysis of the response of an enclosed compressible gas to various mechanical and thermal stimuli at its boundary. For this study a compressible fluid enclosed between two large parallel walls with varying thermal or velocity wall conditions is considered. The compressible fluid is assumed to be an ideal gas with properties similar to air or helium. The governing equations are solved using SIMPLER algorithm.

Three types of thermal boundary conditions. considered: (1) A step change in boundary temperature are relative to the initial gas temperature (2) A transient ramp profile (linear function of time), and (3) An oscillating temperature on one boundary in conjunction with uniform temperature on the opposing boundary. In addition a fourth case is considered where an isothermal fluid is enclosed between one rigid wall and one wall with oscillating velocity boundary condition simulating resonator in a thermoacoustic refrigeration process. a

The unsteady temperature and velocity profiles are computed and presented for all cases. The Nusselt number at the heated wall is also computed and the results are presented and discussed.