Comparison of several models of the laminar/turbulent transition

J Fürst,J Příhoda,D Šimurda,P Straka,Petra Dančová,Petr Novontý

doi:10.1051/epjconf/20134501032

Abstract

The contribution deals with modelling of the laminar/turbulent transition using several transition models. Transition models of various types were tested: a) the model with the algebraic equation for the intermittency coefficient according to Straka and Pøíhoda; b) the three-equation transition model with the transport equation for the energy of non-turbulent fluctuations proposed by Walters and Cokljat; c) the γ-Reθ model with the transport equation forthe intermittency coefficient of Langtry and Menter. The transition models were compared by means of test cases covering both flat-plate boundary-layer flows with various free stream turbulence and the flow over an airfoil including the effect of foregoing wake on the transition. The agreement of numerical results with experimental data is in all cases quite satisfactory.

Highlights

The adequate modelling of the laminar/turbulent transition is very important for the correct prediction of wall-bounded flows as the transition substantially influences the skin friction and the energy losses as the heat transfer.The laminar/turbulent transition in the internal and external aerodynamics is usually modelled either by models based on the equation for the intermittency coefficient or by the three-equation model with the equation for the energy of non-turbulent fluctuations proposed by Walters and Leylek [1].The transition models with the algebraic and/or transport equation for the intermittency coefficient need empirical relations for the onset and the length of the transition region and should be modified for local variables only for the application in complex boundary conditions using unstructured grids
Transition models of various types were tested: a) the model with the algebraic equation for the intermittency coefficient according to Straka and Příhoda; b) the three-equation transition model with the transport equation for the energy of non-turbulent fluctuations proposed by Walters and Cokljat; c) the -Re model with the transport equation for the intermittency coefficient of Langtry and Menter
The transition models were compared by means of test cases covering both flat-plate boundary-layer flows with various free stream turbulence and the flow over an airfoil including the effect of foregoing wake on the transition

Summary

Introduction

The adequate modelling of the laminar/turbulent transition is very important for the correct prediction of wall-bounded flows as the transition substantially influences the skin friction and the energy losses as the heat transfer. The laminar/turbulent transition in the internal and external aerodynamics is usually modelled either by models based on the equation for the intermittency coefficient or by the three-equation model with the equation for the energy of non-turbulent fluctuations proposed by Walters and Leylek [1]. The transition models with the algebraic and/or transport equation for the intermittency coefficient need empirical relations for the onset and the length of the transition region and should be modified for local variables only for the application in complex boundary conditions using unstructured grids. The three-equation model seems to be more general as can be used without any restrictions

Mathematical model

Algebraic transition model

Results

Conclusions