Rng-based viscoelastic turbulence model and numerical applications

摘要

A Reynolds stress model being quadratic in the mean strain rate and additionally containing its Oldroyd derivative has been shown to arise naturally from the mode reduction process, when renormalization group theory (RNG) is applied up to second order in the " epsilon expansion" to the suitably stochastically forced Navier Stokes equations. The resoluting anisotropic turbulence model fulfills the principles of Galileian invariance and material objectivity from continuum mechanics. Its mathematical structure is similar to the two-scale DIA model of Yoshizawa, but our model coefficients have been explicitly calculated from theory and they depend smoothly on the local turbulence Reynolds number. Therefore the model may be used over a wide range of different flow regimes. In the high Reynolds number limit, our model becomes identical with the constitutive equation of a viscoelastic fluid (second order fluid). So the proposal of Rivlin, who conjectured more than fourty years ago, that a turbulent Newtonian fluid could be regarded as a non-Newtonian fluid, seems to have received some support. In the high Reynold-snumber case our model is similar to Speziale's, which was established on a purely constitutive basis with empirically adjusted coefficients. The closure of our Reynolds stress model is up to now achieved by means of the RNG K - epsilon model of Yakhot, Orszag, Thangam, Speziale, Gatski. Their modeling of the additional production term present in their dissipation rate transport equation and constituting the main difference between their model and the standard K - epsilon model, may be motivated for small shear rates by means of our Reynolds stress model. From a methodological point of rivew, there are some similarities between our work and the work of Rubinstein and Barton, so our result may be compared with theirs. Our model does contain convective transport terms of the strain rate tensor, which are absent from the model of Rubinstein and Barton, but which they state to be essential in the model of Speziale (surely, they are important in the low-Reynoldsnumber regime); their model fails to fulfill the requirement of material objectivity, ours does. With the aid of the commercial codes FIDAP and STARCD, a first version of our turbulence model has been applied with encouraging results to some turbulent separated flow situations.