Here, rarefied thermally driven flow is investigated in two-dimensional equilateral triangular cavities with different uniform wall temperatures. We used three different solvers, i.e., the direct simulation Monte Carlo solver, discrete unified gas kinetic scheme solver, and continuum set of equations of a slow non-isothermal flow solver. Two main cases were considered; in the first case, the cavity's base is considered hot, and the other sides were set cold. In the second case, the right half of the bottom wall was regarded as a diffuse reflector with high temperature, while the left half of the bottom border was set as a specular reflector. The adjacent side walls were set cold with diffuse reflector boundary conditions. The imposed temperature difference/wall boundary condition induces various vortices in the geometry. In case 1, we observe that principal vortices appearing in the triangle are due to nonlinear thermal stress effects, and the thermal creep effects cause other smaller, confined ones. In case 2, a thermal edge flow is set up from the specular wall on the way to the diffusive hot wall, creating a large vortex in the geometry. As the Knudsen number decreases, another small vortex appears near the left cold border.
This study examined rarefied thermally-driven flow in a square cavity (Case 1) and rectangular bend (Case 2), with various uniform wall temperatures in two dimensions. We employed the direct simulation Monte Carlo (DSMC) to solve problems with a wide range of Knudsen numbers Kn = 0.01 to 10, and the discrete unified gas kinetic scheme (DUGKS) solver was used at Kn = 0.01. The scenario was that, in case 1, the bottom side and its opposite were set hot, and the other sides were set cold. Diffuse reflector boundary conditions were set for all walls. The imposed temperature differences created four primary vortices. The results of the continuum set of equations of the slow non-isothermal flow (SNIT) solver proved that the primary vortices in the square cavity were caused by nonlinear thermal stress effects, and other smaller vortices appearing at Kn = 0.01, 0.1 were brought about by thermal creep processes. As the Kn increased, vortices generated by thermal creep disappeared, and eddies created by nonlinear thermal stress occupied the cavity. In case 2, i.e., a rectangular bend, two sides were set cold, and the others were hot. Two primary vortices were formed, which were caused by nonlinear thermal stress effects. The direction of streamlines in the two main vortices was opposite, from the warm to the cold zone, as some eddies on the left were counterclockwise, and others were clockwise.
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