A numerical study of thermally-driven convective wave phenomenon

The subject of this study is the numerical modeling of a thermoacoustic convection (TAG) process. This investigation is carried out in two parts : (a) a review of earlier numerical models and the accuracy of their results, and (b) the development of a new numerical scheme for the solution of one and two-dimensional TAG processes. The problem of determining the transient flow velocity, temperature, pressure, and density in a fluid confined between two large parallel plates with specified boundary and initial conditions (e.g., constant temperature at the walls, initially isothermal) has been addressed by earlier numerical studies. These previous models predicted very rapid transient behavior with temperature fields rapidly approaching steady state. The first part of the present investigation shows that these results may be in error due to selection of improperly large grid sizes. The rapid transient behavior reported in these earlier studies is shown to behave in a more physically reasonable way when a systematic grid refinement study is carried out and a more appropriate mesh size is selected. A numerical model based on the SIMPLER algorithm, modified for flow compressibility , was developed for the solution of one and two-dimensional TAG processes. This model is shown to predict a much slower transient process than those predicted by other studies. That is, although the resulting thermally-induced fluid motion is shown to enhance heat transfer above that predicted by a rigid conduction model, the present model shows significantly lower transient temperature solutions and smaller velocity amplitudes than seen in previous numerical models. Also, the solution of the one-dimensional TAG problem is shown to agree reasonably well with a solution developed by perturbation methods. The results of the one and two-dimensional models are also compared with available experimental data and discrepancies are discussed.