A Model for Diffusion of Turbulent Kinetic Energy for Calculation of Momentum and Heat Transfer in High FST Flows

Abstract

A modified low-Reynolds number k-ε model (named YI-diffn. model) for predicting effects of high free stream turbulence (FST) on momentum transport and heat transfer in a flat plate turbulent boundary layer is presented. An additional turbulent kinetic energy (TKE) diffusion term incorporating the effects of FST intensity (velocity scale) and length scale was included in the TKE equation. This model was developed with experience from many years of experimental and theoretical studies in the area of high FST flows. The constant cμ in the equation for the transport coefficient μt was modified using experimental data. These modifications were applied to a well-tested k-ε model (K-Y Chien called KYC in this study) under high FST conditions (initial FST intensity, Tui > 5%). Models were implemented in a 2-D boundary layer code. The high FST zero pressure gradient data sets against which the predictions (in the turbulent region) were compared had initial FST intensities of 6.53% and 25.7%. In a previous paper, it was shown that predictions of the original k-ε models became poorer (over prediction up to more than 50% for skin friction coefficient and Stanton number, and under prediction of TKE up to more than 50%) as FST increased to about 26%. In comparison, the new model developed here provided excellent results (within ±3% of experimental data) for skin friction coefficient and Stanton number for both the data sets. TKE results were excellent for Tui = 6.53%, but have scope for improvement in the case of Tui = 25.7%. The present model incorporates physics of transport of free stream turbulence in turbulence modeling and provides a new method for simulating flows with high FST. Future work will focus upon improving the model further and applying it to practical applications like flow over gas turbine blades.