3D simulations with k-epsilon realizable turbulence model

Simulations with finer mesh

Hypothesis and Goals

The preliminary 3D simulations using k-epsilon realizable (RKE) turbulence model failed to converge to a satisfactory level. Based on the results and discussion of previous models , a finer mesh in z-direction should the first attempt to resolve the convergence issue.

Methods and Procedures

The mesh of 2D models is swept in the z-direction with a width of 0.1m (lengthxheightxwidth(x*y*z) = 0.2*1*0.1), and a mesh interval size of 0.002m (#intervals=50), which is in the same order of magnitude as that of x and y directions.

Results and Discussion

Since the finer mesh contains 1,500,000 cells, which is 50 times as many as that of the 2D mesh and 70 times as big as the 2D mesh in terms of the file size, the iteration takes about 30 seconds per step. After about 3000 iterations for 30 hours, the residual plots started to oscillating with no further trend of convergence. The residual of continuity stays a little above e-5 and the others between e-6 and e-5.

Shown below are the residual plot, energy dissipation contour of various rendering surface and the pathline in mid-width plane and the whole domain.



The solution were not converged enough for the flow to be fully developed. As demonstrated in a simulation later this semester, the contour of energy dissipation rate is quite sensitive to the convergence rate, thus nothing conclusive could be drawn from the solution.

To improve convergence, we can try modifying the mesh to reduce the number of cells in stagnation region.