Estimating Resolution Lengths of Hybrid Turbulence Models

A two-stage procedure has been devised for estimating the spatial resolution achievable in the simulation of a given flow on a given computational grid by a computational fluid dynamics (CFD) code that incorporates a hybrid model of turbulence. The hybrid models to which this procedure is especially relevant are those of the Reynolds-averaged Navier-Stokes (RANS) and the partial-averaged Navier-Stokes (PANS) approaches. This procedure represents the first step toward adding variable-resolution turbulence-modeling capabilities to CFD codes as part of a continuing effort to increase the accuracy and robustness of CFD simulations of unsteady flows. Some background information is prerequisite to a meaningful summary of the procedure. Among experts in CFD, it is well known that combination of the Reynolds-averaged Navier-Stokes (RANS) approach and eddy-viscosity turbulence models offers limited capability for simulating unsteady and complex flows. The RANS approach includes an assumption that most of the energy in a given flow is modeled through turbulence-transport equations and is resolved in a computational grid used to simulate the flow. RANS also overpredicts eddy viscosity, thereby yielding excessive damping of unsteady motion. The eddy viscosity attains an unphysically large value because of unresolved scales, and suppresses most temporal and spatial fluctuations in the resolved flow field. One approach used to overcome this deficiency is to provide a mechanism for the RANS equations to resolve motion only on the largest scales and to use a hybrid model to represent effects at smaller scales. The RANS approach involves the use of a standard two-equation turbulence model in which the effect of turbulence is summarized by a viscosity that is a function of (1) the time-averaged kinetic- energy density (k) associated with the local fluctuating (turbulent) component of flow and (2) the time-averaged rate of dissipation of the turbulent-kinetic- energy density ( ). In PANS, which was developed to overcome the grid dependency associated with other hybrid turbulence models (including that of RANS), the standard two-equation turbulence model is replaced by another two-equation model in which one solves for the previously unresolved k and , which are now allowed to vary in space and time.