Liquid Particles Tracing in Three-dimensional Buoyancy-driven Flows

Buoyancy-driven convective flows are numerically analyzed in a cubic enclosure, containing a liquid subjected to a temperature difference between opposite lateral walls; all other walls are thermally insulated. The stationary gravity vector is perpendicular to the applied temperature gradient. The steady flow patterns are investigated within the framework of a liquid particles tracing technique. Three tracing techniques are compared: the first, based on a trilinear interpolation of the liquid velocity defined on the computational grid and an eighth order in time Runge-Kutta method; the second and the third, using a resampling the velocity field on a new approximately twice finer grid by cubic spline interpolation and then a combination of trilinear interpolation of velocity on the new grid, integrating in time with (2-nd method) a single forward time marching method; (3-rd method) a fourth order Runge-Kutta algorithm. Comparison of the results shows that for obtaining a precise tracing on a long time scale it is more important to have a good spatial velocity accuracy than precise integration in time. Unlike one vortex 2D pattern where the particles follow thin and closed circle trajectories staying in vertical cross-sections, it is shown that,the 3D flow consists of two sets of spiral-type motions identical in both halves of the cell with respect to the mid-plane. In the 3D flow even in the central vertical cross-section the particles follow spiral non-closed trajectories drifting outward the cube’s walls. It demonstrates that two-dimensional approach does not provide a clear picture of 3D convection. keyword: Particle tracing, convective flow, buoyancy.