A Scale-Adaptive Variant of the Spalart-Allmaras Eddy-Viscosity Model

Abstract

A method is presented for introducing scale-adaptive capabilities into the SpalartAllmaras one-equation turbulence model that allows it to resolve large-scale turbulent flow features. Unlike detached-eddy simulation, scale-adaptive methods dynamically respond to the resolved turbulent content without an explicit dependency on the local grid size, and the compatibility of the relevant length scales makes it more resilient to modeled stress depletion. The formulation is based on existing scale-adaptive models, comparisons of the relevant length scales in boundary-layer flows, and the desire to preserve the existing steady RANS capabilities of the model when appropriate. Results are presented that demonstrate the capabilities of the scale-adaptive Spalart-Allmaras variant and are compared to results using traditional unsteady RANS and detached-eddy simulation. Nomenclatured = distance to nearest wall k = turbulent kinetic energy L = turbulent length scale LvK = von Karman length scale Re = Reynolds number Reθ = momentum-thickness Reynolds number S = strain-rate magnitude uj = Cartesian velocity component xj = Cartesian coordinate Δ = characteristic grid size ε = turbulent dissipation κ = von Karman constant μ = molecular viscosity μt = turbulent eddy viscosity ν = kinematic viscosity  = modified eddy viscosity Ω = vorticity magnitude ω = turbulent specific dissipation

Modelagem híbrida URANS-LES para escoamentos turbulentos

“…Equações estas que servirão como base para a apresentação das diferentes modelagens de fechamento aqui utilizadas. Serão discutidas as modelagens: LES, proposta por Smagorinsky (1963) e modificada por Germano et al (1991) e Lilly (1992); URANS, propostas por Spalart & Allmaras (1992) e Menter, Kuntz & Langtry (2003); bem como dos modelos híbridos, propostos por Spalart et al (1997), Menter, Kuntz & Bender (2003), Coder (2015) e Menter & Egorov (2005) (FREIRE, 2002).…”