Roman Gaydukov

The problem of flow of a non-Newtonian viscous fluid with power-law rheological properties along a semi-infinite plate with a small localized irregularity on the surface is considered for large Reynolds numbers. The asymptotic solution with double-deck structure of the boundary layer is constructed. The numerical simulation of the flow in the region near the surface was performed for different fluid indices. The results of investigations of the flow properties depending on the fluid index are presented. Namely, the boundary layer separation is investigated for different fluid indices, and the dynamics of vortex formation in this region is shown.

This study numerically investigates boundary layer separation criteria for flows over small surface irregularities on a flat plate at high Reynolds numbers using the double-deck model framework. By solving the Prandtl equations with self-induced pressure, critical amplitude values (i.e., the height of a hump or the depth of a pit) separating attached laminar flow from separated flow with a stationary vortex are determined for Gaussian-shaped irregularities. The results show that separation begins at points of zero curvature of the streamlined surface. Importantly, no geometric parameter (such as maximum curvature or tangent angle) remains invariant along the obtained critical amplitude values, refuting prior hypotheses of a universal critical curvature of the irregularity. Furthermore, the critical amplitude values differ for humps and pits of identical shape. Thus, a separation criterion based solely on the geometry of the irregularity is not attainable for arbitrary shapes.