3D vortex simulation of flow in an opposed-piston engine

Abstract
A 3-D Lagrangian random vortex-boundary element method is extended to the case of compressible flow at low Mach numbers. The simulations utilize the equation for the transport of (vorticity/density), which is identical in form to the vorticity transport equation for incompressible flow, but with two modifications. First, diffusion involves a time-varying, spatially homogeneous diffusivity. This is implemented by appropriately modifying the diffusion time scale, so that the diffusivity is time-invariant. Second, the continuity equation includes a spatially uniform, but time-dependent density. This effect is accounted for in the potential component of the velocity field via a Poisson equation with a spatially-uniform, time-dependent volumetric source term. The latter is converted to a source on the boundary of the domain, which allows the grid-free evaluation of the potential velocity field using the boundary element method. As a result, grid-free simulation of flow in the complex geometry of engines during the entire intake and compression strokes is made possible. In this paper, the formulation for the method and preliminary results from the simulation of the swirling flow inside a typical two-stroke opposed-piston engine are presented.