Simulation of high re boundary layer flows using vorticity confinement

Abstract

Abstract. We describe how Vorticity Confinement (VC) can be regarded as a new pde formulation of the slightly viscous incompressible flow equations. These equations, when discretized and solved, generate nonlinear solitary waves that can be used to efficiently approximate a large class of external flow problems, including the effects of separating turbulent boundary layers. These problems can involve subsonic flow over complex structures such as ships, buildings, and realistic topography such as hills. These problems typically involve the simulation of a large ensemble of flow conditions for each configuration to be designed or analyzed. One of the most difficult aspects of these simulations is that often the main effects of the dynamics of thin evolving vortical structures must be solved for.The VC method appears to be effective for many of these problems, since it requires much less computing and setup time than current Navier Stokes "RANS" approximations. The method involves treating the flow over a solid body as a two-scale problem: The first component is an "outer" smoothly varying, mainly irrotational flow with perhaps large scale vortical components where standard CFD techniques can be used. The second component is composed of thin vortical regions. These vortical parts consist of mostly thin attached boundary layers, thin separating vortex sheets, which roll up and thin vortex filaments, which result from roll up. The VC method involves treating these regions with a single equation that has three equilibrium states corresponding to these regions. The equation allows transition between these equilibrium states so that for example, boundary layers can separate and roll up into vortex filaments, and vortex filaments can join and reconnect with other filaments. These properties survive discretization and require no extra logic.VC can be used to treat the entire flow in a locally-Cartesian computational grid with the solid surfaces "immersed" in the grid so that they can be quickly generated for many configurations. Adaptive or conforming fine scale grid cells are then not required to approximate the thin vortical boundary layers, or thin separating vortex sheets. Instead, vortical structures created with Vorticity Confinement, which are essentially thin, non-diffusing, or confined "Nonlinear Solitary Waves" (NSW's) are used to "carry" the vorticity in these regions. The VC method has the efficiency of panel methods, but the generality and ease of use of fixed grid Euler equation methods. In this paper we concentrate on attached and separating boundary layers; there are already in the literature a large number of papers describing the use of VC for free, convecting vortices.