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

Abstract

Computations of a 2D synthetic jet are performed with usual RANS equations solved in time-accurate mode (URANS), with the standard k-e 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-e 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.

Successes and Challenges for Flow Control Simulations

“…But it is unclear at this point whether URANS methods are fully adequate for predicting mean-flow quantities, and if so, which models work and which do not. With high-fidelity boundary conditions, the simple linear SA and SST models appeared to do reasonably well for many features of interest in the near field, but the work of Carpy and Manceau 22 suggests that linear models are missing key physics and more advanced nonlinear models or even full Reynolds stress model may be required.…”

Revisiting URANS Computations of the Backward-facing Step Flow Using Second Moment Closures. Influence of the Numerics

“…As a consequence, the turbulent production is overestimated. For instance, in a 2D flow, as shown by Carpy and Manceau [5], the exact production can be written as…”

“…Moreover, even for non-stationary flows, like pulsed flows or flows around moving obstacles, for which the ensemble average is time-dependent, it is also worth pointing out that using standard RANS models in an unsteady computation is questionable. Indeed, although they sometimes provide satisfactory solutions, they are mainly formulated under the assumption of equilibrium, which can lead to a significant misrepresentations of the physical mechanisms present in unsteady flows: for instance, Carpy and Manceau [5] have shown that linear eddy-viscosity models give a completely wrong dynamics in a pulsed jet, due to the lack of representation of the stress-strain misalignment. On the contrary, second-moment closures (SMCs) are able to reproduce the global dynamics of this flow without any case-specific modification.…”

Unsteady Predictions of Mixing Enhancement with Steady and Pulsed Control Jets

“…a Reynolds Stress Transport (RST) model) could improve the absolute level of accuracy of URANS for this problem. Carpy and Manceau [31] have shown that this can improve the accuracy of isolated pulsed jet prediction, but it is not clear whether this would remove the absolute error in potential core length prediction; this is worthy of exploration.…”