WSPH and ISPH Calculations of a Counter-Rotating Vortex Dipole

Abstract

Viscosity and vorticity are magnitudes playing an important role in many engineering physical phenomena such as: boundary layer separation, transition flows, shear flows, etc., demonstrating the importance of the vortical viscous flows commonly used among the SPH community. The simulation presented here, describes the physics of a pair of counter-rotating vortices in which the strain field felt by each vortex is due to the other one. Different from the evolution of a single isolated vortex, in this case each vortex is subjected to an external stationary strain field generated by the other, making the streamlines deform elliptically. To avoid the boundary influence, a large computational domain has been used ensuring insignificant effect of the boundary conditions on the solution. The performance of the most commonly used viscous models in simulating laminar flows, Takeda’s (TVT), Morris’ (MVT) and Monaghan-Cleary’s (MCGVT) has been discussed comparing their results. These viscous models have been used under two different compressibility hypotheses. Two cases have been numerically analyzed in this presentation. In the first case, a 2D system of two counter-rotating Lamb O seen vortices is considered. At first, the system goes through a rapid relaxation process in which both vortices equilibrate each other. This quasi-steady state is obtained after the relaxation phase is advected at a constant speed and slowly evolves owing to viscous diffusion. The results of the different Lamb-O seen numerical solutions have been validated with good agreement by comparison with the numerical results of a finite element code (ADFC) solution. A second case, somewhat more complex than the previous one, is a 3D Batchelor vortex dipole obtained by adding an axial flow to the system of the first case. The Batchelor vortex model considered here is a classical option normally used to model the structure of trailing vortices in the far-wake of an aircraft.