Journal of Theoretical
and Applied Mechanics

35, 2, pp. 285-303, Warsaw 1997

Vortex cloud modelling of separated flows

Eustachy S. Burka, Piotr Lampart
A method for numerical simulation of 2D incompressible high Reynolds number flows with laminar separation and big recirculation zones – regions of vortex formation and wake building – is presented. The paper is concerned with the case of separation from the surface, not from sharp edges. The calculation method draws on viscous splitting of the vorticity transport equation. At. each time step, this equation is solved in three separate substeps – convection (of point vortices and vortex sheet elements with their local velocities), diffusion (by means of the random walk technique) and generation (by means of Martensen's concept of vortex sheet extended by Lewis). The method does not assume any separation criterion. Locations of the separation points can be roughly estimated by means of computer flow visualisation as the stations at which the calculation elements – particles of fluid – leave the vicinity of the profile and the fluid begins to recirculate. This method of modelling has been called the cloud vorticity method. The aerodynamic force and its moment are calculated from the balance of momentum and moment of momentum equations in the flow domain. The flow patterns for a circular cylinder and NACA profile operating under separating conditions are presented to illustrate the calculation method. The occurrence of secondary phenomena in separated flows is also considered in the paper.
Keywords: vorticity transport equation; viscous splitting; random walk; vortex cloud