Partially Lagging One-Equation Turbulence Model

Abstract

A partially lagging one-equation eddy viscosity model, based on the transformation of the turbulence closure through Bradshaw et al. (“Calculation of Boundary Layer Development Using the Turbulent Energy Equation,” Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593–616), is proposed. The model attempts to account for the turbulence history effects by spatially lagging the destruction/diffusion terms. The amount of relaxation is based on the von Kármán length scale. The present model does not assume equal diffusion coefficients of the and equations; therefore, third-order velocity gradients emerge. The performance of the present model is assessed against the Spalart–Allmaras model (“A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 1992-0439, 1992) and the one-equation model proposed by Menter (“Eddy Viscosity Transport Equations and Their Relation to the Model,” Journal of Fluids Engineering, Vol. 119, 1997, pp. 876–884), which is based on Bradshaw et al. (“Calculation of Boundary Layer Development Using the Turbulent Energy Equation,” Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593–616), and the assumption of equal diffusion coefficients. The behavior of the one-equation transformed model without the presence of third-order velocity gradients is also examined. The proposed model is validated through a comparison to a wide class of internal and external turbulent flows.