Prediction of growth of turbulence in a uniformly sheared flow using the vortex-in-cell method

Abstract

A mixed Lagrangian-Eulerian description of the evolution of the discretized vorticity field is used for the numerical prediction of incompressible, uniformly sheared turbulent fmows. In this new application a combination of several adjacent mixing layers simulates the initial condition used to generate the uniformly sheared flow as done in some of the experimental methods in wind tunnels. The two dimensional vortex dynamics method which has been extensively used for mixing layer analysis is adopted due to the similarities in the structure and the method of generating mixing layers and uniformly sheared flows. The governing equations are the vorticity and the continuity equations. The vorticity fleld is represented by a set of vortex elements which moves by the induced velocity field. To treat the large number of vortex elements at a reasonable computer cost, the velocity field is calculated by the vortex-in-cell (VIC) method, in which 48 000 vortices move through a fixed Eulerian mesh system with grid points. Statistical results were obtained by time averaging the unsteady solution. The flow field was calculated for the shear rate dU/dy = 67 s-1 and centerline velocity Uc = 425 cm/s.