Flat Plate: Laminar Boundary Layer (TOP)
For this case, an unstructured grid has been generated using a standalone suite of structured-to-unstructured grid generator programs. Initially, an H-topology 49x41 (stream wise x normal) structured grid was constructed that consisted of approximately 16 points across the boundary layer (for a Reynolds number=10,000). Next, the two-dimensional grid was extruded twice in a spanwise direction by a distance of 0.02L to form a three-dimensional dual-channel structured 49x41x3 H-H grid. Finally, from this grid an unstructured tetrahedral grid was constructed by dividing each hexahedral cell in two prismatic cells and further subdividing each of the prismatic cells in three tetrahedra. The unstructured grid consists of 23040 tetrahedral cells and 8384 boundary faces.
The flowfield analysis for this case has been performed considering a parallel moving freestream at a Mach number of 0.5 and a Reynolds number per unit plate length (L) of 10,000. The computations have been performed for 3000 iterations that reduces the flow residue by more than five-and-a-half order of magnitude. Figures 1 and 2 compare the distributions across the boundary layer of the computed tangential velocity and normal velocity respectively, with the corresponding analytical distributions obtained from Blasius solution. The computed solution correctly exhibits the self-similar nature of the flow and compares fairly well with the theoretical solution.
Fig. 1: Comparison of computed and theoretical tangential velocity distributions across a boundary layer.
Fig. 2: Comparison of computed and theoretical normal velocity distributions across a boundary layer.
