Numerical simulations of Sakiadis boundary-layer flow

Abstract

When a static fluid encounters a moving boundary, it experiences a large shear and forms a boundary layer. A self-similar solution of the boundary-layer equations for such flow was first revealed by Sakiadis in 1961. Despite the ubiquity of this type of flow, there are so far no published numerical simulations. In this article, we use OpenFOAM, a widely used open source software, to conduct a numerical simulation of the isothermal Sakiadis flow. The results are in good accord with the theoretical solution except near the leading edge, where the boundary-layer approximations are not fulfilled. We present that the boundary layer thickness is not zero at the beginning of the boundary-layer flow, although this condition has been extensively used. Currently, in boundary-layer research different definitions of boundary layer thickness are being employed. We also show that depending on the definition used, self-similarity appears at different stream-wise positions. The widest range of self-similarity can be obtained by using the definition of momentum thickness. Finally, we also present a new self-similar solution in wall normal direction near the leading edge. These results obtained from the simulation might well be applicable to many other boundary-layer flows, such as the Blasius flow.