Prediction of momentum and scalar transport in turbulent swirling flows with an objective Reynolds-stress transport closure
Published Web Locationhttps://doi.org/10.1007/s00231-009-0501-1
The accurate prediction of turbulent swirling flows requires the use of a differential Reynolds-stress transport model to close the time-averaged Navier–Stokes equations. The performance of such model is largely determined by the way in which the fluctuating pressure–strain correlations are approximated. A number of alternative approximations are available, all of which depend explicitly on the mean vorticity tensor. Such dependence renders a constitutive relation inconsistent with the principle of Material Frame Indifference (MFI). In this paper, an objective model (i.e. one which is consistent with MFI) for the pressure–strain correlations is presented. This model, which was developed using Tensor Representation Theory, has fewer terms than the conventional alternatives and is therefore easier to implement in computational codes. Moreover, the model was calibrated to correctly reproduce the relative stress levels in both free and wall-bounded flows without the need to employ wall-damping corrections. The performance of this model is assessed using experimental data from both weakly- and strongly-swirled jets. Comparisons are also made with results obtained using three widely-used alternative models for the pressure–strain correlations. It is found that the objective model, although simpler in formulation than the others, yields results that are generally in closer correspondence with the data. The paper also reports on the prediction of mass transfer in a swirling jet. The case considered was that of a co-axial, strongly-swirled flow with an outer annular air stream and an inner helium jet. Swirl was imparted to the outer stream only. The concentration of helium was predicted using a differential scalar-flux transport closure. Close agreement was obtained with the measured concentrations. Analysis of the predicted mass fluxes revealed that the turbulent diffusivity is strongly anisotropic in this flow.