Velocity decomposition approach for steady incompressible flow around multiple bodies

Abstract

The CFD simulations for external flow problems can request high computational costs. To reduce these costs, viscous/inviscid interaction methodology based in the domains decomposition and the Helmholtz velocity decomposition has been developed. The calculation of viscous flow by the Navier–Stokes equations is made on a computational reduced domain. In this work, an interactive methodology is presented, which consists of: calculate the potential flow outside the rotational region, impose the potential flow velocity field as a boundary condition in the reduced domain boundary, calculate the transpiration velocity to correct the potential flow, recalculate the potential flow velocity field outside the rotational region, and update the boundary conditions on the reduced domain. To formulate the transpiration velocity, the velocity decomposition approach was used, but to calculate the transpiration, it is necessary determine the boundary of the rotational region, called rotational boundary, where the vorticity is negligible. For this, negligible vorticity criteria were developed to find that boundary; however, determining it can be a complex task, as is the case of flow around multiple bodies. Some techniques, which may include the use of an auxiliary surface, have been developed to facilitate the determination of the rotational boundary. Thus, two proposals were made in this work, first: the use of an auxiliary surface to determine the rotational boundary to multiple bodies cases; and second: a new negligible vorticity criterion based on the total pressure field. Calculations were performed in the viscous reduced domain for two-dimensional incompressible flow, around a single body and multiple bodies. The use of the present methodology allowed reducing the computational costs. The aerodynamic coefficients and viscous flow fields obtained in the reduced domain were satisfactory for such engineering problems.