Time-Dependent Free Convection in Low Prandtl Number Fluids.

摘要

A numerical analysis is given for time-dependent free convection in a fluid with small Prandtl number. Consideration is given to a long two-dimensional cavity with vertical walls maintained at different temperatures. The results are relevant to the electron beam vaporization of liquid metals. The spatial problem is solved with the Galerkin finite element method, and a backward Euler method with step-size control is used to perform the time integration. For cases involving large convection and numerical instabilities, streamwise diffusion is introduced with an approach sharing some features in common with the Taylor-Galerkin and Petrov-Galerkin methods. Solutions are given for a Prandtl number of 0.015 and Grashof numbers between 10(sup 4) and 10(sup 7), corresponding to the transition region between steady-state laminar and turbulent flow. The results reveal the effects of added streamwise diffusion along with mesh and time-step refinement. 17 figs.