Assessments ofk-kLTurbulence Model Based on Menter’s Modification to Rotta’s Two-Equation Model

Khaled S Abdol-Hamid

doi:10.1155/2015/987682

Abstract

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter’s modification to Rotta’s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale and kinetic energy. Rotta’s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes to simulate unsteady flows. The model is implemented in the CFD solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and large eddy simulation data. The results from this formulation are as good or better than the well-known shear stress turbulence model and much better thank-εresults. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Highlights

While two-equation models have been used routinely to simulate turbulence flows for the last 50 years, they are based on a kinetic energy equation and either dissipation or timescale equation to evaluate length scale
The most important difference is that the formulation leads to a natural inclusion of higher-order velocity derivatives into the source terms of the scale equation
The main objective of this paper is to find a better turbulence model with a more reliable second equation

Summary

Introduction

While two-equation models have been used routinely to simulate turbulence flows for the last 50 years, they are based on a kinetic energy equation and either dissipation or timescale equation to evaluate length scale. These two scales are obtained from the solution of two presumably independent transport equations, like the k-ε or k-ω model or any other formulations that use a k equation. The mechanism of the second equation for determining a turbulent length scale is not fully understood, and a number of formulations use a special boundary condition for simulating wall boundary conditions. The exact transport equation for k can be modeled with a few relatively straightforward assumptions

Objectives

Results

Conclusion