Turbulence Generation from a Sweeping-Based Stochastic Model

Stochastic methods are widely used because they constitute a low-cost computational-fluid-dynamics approach to synthesize a turbulent velocity field from time-averaged variables of a flowfield. A new combined stochastic method based on the sweeping hypothesis is introduced in this paper. This phenomenon, stating that inertial range structures are advected by the energy containing eddies, is known to be an important mechanism of the turbulent velocity field decorrelation process. The proposed method presents the advantage of being easily implementable and applicable to any three-dimensional configuration as long as a steadyReynolds-averagedNavier–Stokes computation of the flow is available and assuming that the considered turbulence physics is compatible with the hypotheses made to build the current numerical model. The developed method is applied on a subsonic round cold free jet. The validation study shows that the synthesized turbulent velocity fields reproduce statistical features of the flow, such as two-point two-time velocity correlation functions, comparable to those found experimentally and integrates shear effects of themean flow. The mean convection velocity of the turbulent structures is also correctly modeled. In addition, the turbulent kinetic energy spatial distribution is preserved by the stochastic method. Nomenclature An = amplitude of the nth mode CK = Kolmogorov constant D = nozzle diameter D1∕2 = half-velocity diameter E = von Kármán-Pao energy spectrum k = wave number kc = cutoff wave number ke = wave number for which themaximum of energy occurs kmin = minimum wave number kmax = maximum wave number kn = wave number of the nth mode kt = turbulent kinetic energy kt max = maximum turbulent kinetic energy L = integral length scale Lη = Kolmogorov length scale N = number of modes Rij = velocity correlation function r = ξ2