Boundary Layer Theory: New Analytical Approximations with Error and Lambert Functions for Flat Plate without/with Suction

In this work, we investigated the problem of the boundary layer suction on a flat plate with null incidence and without pressure gradient. There is an analytical resolution using the Bianchini approximate integral method. This approximation has been achieved by Lambert or Error functions for boundary layer profiles with uniform suction, even in the case without suction. Based on these new laws, we brought out analytical expressions of several boundary layer features. This gives a necessary data to suction effect modeling for boundary layer control. To recommend our theoretical results, we numerically studied the boundary layer suction on a porous flat plate equipped with trailing edge flap deflected to 40°. We showed that this flap moves the stagnation point on the upper surface, resulting to avoid the formation of the laminar bulb of separation. Good agreement was obtained between the new analytical laws, the numerical results (CFD Fluent), and the literature results.