Reynolds stress model for recirculating flows



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Texas Tech University


The progress of the Reynolds Stress Model (RSM) has been slow due to the numerical difficulty in ensuring coupling of Reynolds stresses with mean velocities and the lack of improvement in modeling. In the present study, a special interpolation technique is employed to compute the Reynolds stress gradients in a non-staggered grid arrangement to avoid any unrealistic zig-zag solution that occurs when linear interpolation is used. To improve the RSM, the dissipation rate equation is modified to give better prediction on recirculating flows.

The Navier-Stokes equations, Reynolds stress equations and dissipation rate equation are solved in this study. The governing equations are discretized using a non-staggered grid finite-volume scheme. The discretized equations are then solved by an implicit, time-marching, pressure-correction based algorithm.

Two test cases which are representative of most flows are selected to verify the present method. Both test cases only need orthogonal grid formulation, eliminating any anomaly such as numerical instability caused by a non-orthogonal grid formulation. As a first test case, the numerical predictions obtained from the present method are compared with the direct numerical simulation results for channel flow. A second test case, involving more complex physics, is selected to test both the turbulence model as well as the numerical algorithm. In the present study, the backward-facing step which exhibits an abrupt change in flow characteristics over the step expansion, is used to demonstrate the capability of the model to predict recirculating flows. The results of the present calculations including mean velocities, Reynolds stresses, dissipation rate, friction factor, pressure coefficient and reattachment length are compared with the standard k — £ model results and experimental data. The present RSM results agree with experimental data, and the recirculating bubble and reattachment length predicted by the present RSM are better than the standard k — e model predictions.



Reynolds stress -- Mathematical models, Turbulence -- Mathematical models