Sensitizing Second-Moment Closure Model to Turbulent Flow Unsteadiness

Abstract

Different scale-supplying equations formulated in the term-by-term manner at the Second-Moment Closure modeling level were a priori tested (the velocity and Reynolds stress data were taken from the available DNS database) in the flow in a plane channel in the Reynolds number range between \(Re_\tau=395\) and 2003 (DNS from Moser et al. (Phys. Fluids 11: 943–945, 1999) and Hoyas and Jimenez (Phys. Fluids 18: 011702, 2006)), the flow over a backward facing step (DNS: Le and Moin (J. Fluid Mech. 330: 349–374, 1997)) and the periodic flow over a 2-D hill utilizing the results of the highly resolved LES by Breuer (New Reference Data for the Hill Flow Test Case, http://www.hy.bv.tum.de/DFG-CNRS/, 2005). The starting basis of this activity are the model equations governing the total viscous dissipation rate e and its homogeneous part \(\varepsilon_h=\varepsilon-0.5 \nu \partial^2 k/(\partial x_j \partial x_j)\) proposed by Jakirlic and Hanjalic (J. Fluid Mech. 439: 139–166, 2003). The third equation governing the specific viscous dissipation rate \(\omega=\varepsilon/k\), i.e. \(\omega_h=\varepsilon_h/k\) has been directly derived from the corresponding e h -equation. Afterwards, the transport equation of the inverse turbulent time scale ω h is extended in line with the \(k-\omega\) SST-SAS (Scale-Adaptive Simulation) model of Menter and Egorov (Notes on Numerical Fluid Mechanics, 2009) and applied to the afore-mentioned flow configurations in conjunction with the Jakirlic and Hanjalic Reynolds stress model equation (J. Fluid Mech. 439: 139–166, 2003).