The lagRST Model: a Turbulence Model for Non-Equilibrium Flows

Abstract

This study presents a new class of turbulence model designed for wall bounded, high Reynolds number flows with separation. The model addresses deficiencies seen in the modeling of nonequilibrium turbulent flows. These flows generally have variable adverse pressure gradients which cause the turbulent quantities to react at a finite rate to changes in the mean flow quantities. This "lag" in the response of the turbulent quantities can't be modeled by most standard turbulence models, which are designed to model equilibrium turbulent boundary layers. The model presented uses a standard 2-equation model as the baseline for turbulent equilibrium calculations, but adds transport equations to account directly for non-equilibrium effects in the Reynolds Stress Tensor (RST) that are seen in large pressure gradients involving shock waves and separation. Comparisons are made to several standard turbulence modeling validation cases, including an incompressible boundary layer (both neutral and adverse pressure gradients), an incompressible mixing layer and a transonic bump flow. In addition, a hypersonic Shock Wave Turbulent Boundary Layer Interaction with separation is assessed along with a transonic capsule flow. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWTBLI flows assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced. Greek Symbols

DPW-5 Analysis of the CRM in a Wing-Body Configuration Using Structured and Unstructured Meshes

“…21 These models provide the same sort of features which were explicitly built into SST (such as the variable c µ to enforce realizibilty, and a free-stream ω insensitivity) as a consequence of the history mechanism they mimic. More details are available in the original paper, 19 but one significant feature of this model is that it is so numerically stable it can be run at the same CFL as standard eddy viscosity models.…”

“…19 Matrix dissipation with a second-order central spatial convection operator, with second-order (central) diffusion operators is used for the spatial discretization. 20 Dual time integration is used for time-accurate integration, utilizing an ADI scheme with a constant CFL number for both the steady state relaxation scheme as well as for the inner iterations of the dual time method.…”

Near-Body Grid Adaption for Overset Grids

“…The use of grid adaption allows more confidence that the computed solution obtained is not affected by poor grid resolution. A coarser version of the grid used by Lillard et al 17 is used here as the original near-body grid. (Again, no off-body grids are used.)…”

Analysis of the Common Research Model Using Structured and Unstructured Meshes

“…The NASA Ames Research Center author analyzed the CRM wing-body configuration using OVERFLOW v2.2e modified to implement the lag Reynolds-stress-transport (RST) model [19]. Matrix dissipation with a second-order central spatial convection operator, with second-order (central) diffusion operators, is used for the spatial discretization [20].…”