Addressing The Blasius Paradox In the Flow Around A Flat Plate With A Numerical Experiment

The Blasius paradox in the laminar flow around a flat plate is the fact that the transverse component of velocity reaches a final positive value. As a consequence, the boundary layer thickness increases indefinitely. This paradox is due to the fact that the flat plate is semi infinite in the original solution to this flow problem. However, we are interested in the solution to this flow problem with a flat plate of finite length. In this case, it is impossible to verify the Blasius' solution for the transverse component of the velocity. This issue has been discussed by some researchers in the last thirty years. However, there is no consensus so far. In this work, we address this problem by performing a numerical experiment in the flow around a flat plate. We choose appropriate size of the flow domain, in order to ensure undisturbed flow conditions upstream of the leading edge of the flat plate and far away from the flat plate plate in the transverse direction of the flow. The full Navier Stokes equations are solved in the flow domain with Galerkin finite elements. Appropriate boundary conditions are formulated in the flow domain where the flat plate (with finite length) is placed. The result of this research is that the transverse component of the velocity is negative only close to the lfat plate and gradually tends to zero. In addition, the transverse velocity component is negative close to the trailing edge of the flat plate. As a consequence, the boundary layer thicknes becomes flat. In other words, the Blasius paradox disappears if we study this flow with a flat plate of finite length. The results of this work are independent of the magnitude of the Reynods (Re) number. Results are presented in the range 0.1 ≤ Re ≤ 1·10⁶.