Prior literature largely assumes zero streamwise pressure gradient (or unspecified). A systematic domain study for a finite plate under more general pressure-gradient conditions is yet to be published.
Using the Galerkin finite-element Navier-Stokes solver (FEM3D) on UH’s Sabine/Carya clusters, a full controlled numerical experiment with a graded mesh (dense to transition to sparse) is run. The graded mesh is opted for to make the process economical. This mesh design still allows for a one to one ratio of element size at each point of interest ensuring smooth results close to the wall.
A central focus is the Blasius paradox and reports of negative velocity at the trailing edge. We find the results indicated complete agreement in streamwise profiles with Blasius-type expectations under appropriate conditions. But transverse velocity is sensitive to domain/pressure-gradient effects and turns negative at x/L > 0.9 up to the trailing edge. We also examine skin-friction trends and asymptotic behavior. We quantify deviation vs Reynolds number to get key metrics.
We run laminar flows up to 720 000 Re. Skin friction coefficient approaches the Blasius solution, however there is a minimum of 2% deviation occurring at the highest Reynolds number. The streamwise velocity component agrees with Blasius results but transverse results do not.
The main result of this analysis is that the drag coefficient is correctly predicted by the Blasius theory up to 2% accuracy. However, the transverse velocity component is not predicted correctly. Still, this inaccuracy has no influence on the fanning friction factor (simply an academic issue).