Smoothed particle hydrodynamics simulations of flow separation at bends

The separated flow in two-dimensional bends is numerically simulated for a right-angled bend with different ratios of the channel widths and for a symmetric bend with different turning angles. Unlike the potential flow solutions that have several restrictive assumptions, the Euler equations are directly solved herein by the smoothed particle hydrodynamics (SPH) method, which is a Lagrangian approach without a mesh. The coefficient of flow contraction is obtained in terms of the ratio of the channel widths and the turning angle. The velocity field and pressure distribution in a right-angled bend are calculated. The shape of the free streamlines for a symmetric bend with several turning angles is obtained. The numerical steady-state results are validated against available theoretical solutions. The computed velocity on the free streamline is consistent with Kirchhoff's theory.