REYNOLDS-STRESS SIMULATIONS OF A FULLY-DEVELOPED CHANNEL FLOW USING A NEW VELOCITY/PRESSURE-GRADIENT MODEL

Novel models for the velocity/pressure-gradient correlations through the fourth order have been developed by the authors and successfully compared against Direct Numerical Simulations (DNS) in a priori testing in planar wall-bounded flows. In the current work, the models for second-order velocity/pressure-gradient correlations are tested using a posteriori simulations in a planar fullydeveloped channel flow. In this initial Reynolds stress transport (RST) model testing, the turbulent diffusion and dissipation terms are represented by their DNS profiles to isolate the effects of velocity/pressure-gradient modelling. In such a formulation, only the equations for mean velocity, shear stress, and Reynolds stress in the normal-to-the-wall direction are coupled. Simulations are also conducted with the RST equations, where all terms but those corresponding to molecular diffusion are represented by DNS data. Two solvers were used to independently confirm the computational results: a second-order accuracy numerical code for fully-developed twodimensional axisymmetric flows and the open-source OpenFOAM software. Results reveal a significant sensitivity of the RST equations to the accuracy of DNS data used to represent terms in the equations. This issue can be addressed by incorporating the DNS “balance” error as a source term in the RST equations. No balance terms are required in the coupled equations for the mean velocity and the shear stress. Successful testing of the velocity/pressure-gradient model has currently been achieved with these two equations. Coupling with the transport equations for normal Reynolds stresses is currently in a process, with an effort being directed towards overcoming a sensitivity of these equations to other factors including minor variations in velocity/pressure-gradient correlations. INTRODUCTION Recently, there has been renewed interest in using RST models for high-Reynolds-number external aerodynamics (Gerolymos et al., 2011; Cécora et al., 2012; Rodio et al., 2014). A major impetus behind this interest is the difficulty of existing oneand two-equation models to consistently predict separated flows. Among terms requiring modelling in the RST equations are velocity/pressure-gradient correlations. A traditional approach to modelling these correlations is to separate them into the pressure diffusion and the pressure/velocity-gradient (pressure-strain) correlations (Rotta, 1951). Although the approach simplifies the mathematical formulation of the problem, it introduces difficulties in the modelling of the separate terms. For example, the majority of models for the pressure-strain correlations are based on the assumption that only strictly valid in homogeneous flows (Rotta, 1951). There is also little support for the gradient diffusion model (Daly and Harlow, 1970) typically used to represent diffusion-type terms including the pressure-diffusion correlations. An integrated approach for modeling the velocity/pressure-gradient correlations through the fourthorder correlations was recently proposed in Poroseva and Murman (2014a,b). The models for these correlations were successfully verified in a priori testing using DNS data for a fully-developed planar channel flow (Jeyapaul et al., 2014) and a zero-pressure-gradient boundary layer over a flat plate (Spalart, 1988; Sillero et al., 2013). This integrated approach (theoretically) removes the need for wall damping or similar treatments to account for the behavior in the buffer and viscous layers near the wall. The goal of current work is to validate the models for the second-order velocity/pressure-gradient correlations through simulations conducted with an RST model. MODEL FORMULATION Here a brief review is provided, and the reader is referred to the original references (Poroseva and Murman, 2014a,b) for full details. A tensor-invariant model for the „slow“ part of the velocity/pressure-gradient correlations ij Π ( ) ( ) 1 s T ij ij B D Π = − (1) was obtained by analyzing tensor properties of the second term in the exact integral-differential expression (without the surface integral): June 30 July 3, 2015 Melbourne, Australia 9 P-38