Turbulence modelling of statistically periodic flows: Synthetic jet into quiescent air

Computations of a 2D synthetic jet are performed with usual RANS equations solved in time-accurate mode (URANS), with the standard k–ε model and the Rotta + IP second moment closure. The purpose of the present work is to investigate the ability of these standard turbulence models to close the phase-averaged Navier–Stokes equations. Results are compared with recent experiments by Yao et al. made available to the CFD Validation of Synthetic Jets and Turbulent Separation Control workshop held in Williamsburg in 2004. Comparisons of the performance of the models with experimental data show that the evolution of the vortex dipole generated by inviscid mechanisms is not correctly reproduced by the k–ε model. The Reynolds-stress model gives much more realistic predictions. However, several characteristics are not well predicted, as for instance the convection velocity. A detailed analysis shows that the vortex dipole dynamics is essentially inviscid during the early blowing phase, when the flow is more transitional than fully turbulent. Turbulence develops and influences the dynamics of the vortices only at a later stage of the blowing phase. Consequently, it is of importance that the turbulence models do not predict erroneously high levels of turbulence. In particular, the present study shows that the correct prediction of the region of negative production that appears during the deceleration of the blowing velocity, due to the misalignment of the strain and anisotropy tensors, is crucial. Therefore, linear eddy-viscosity models must be discarded for this type of pulsed flows, in particular for flow control using synthetic jets.