A New Low-Reynolds Number k-ε Model for Simulation of Momentum and Heat Transport Under High Free Stream Turbulence

Abstract

A modified low-Reynolds number k-ε model for predicting effects of high free stream turbulence (FST) on transport of momentum and heat in a flat plate turbulent boundary layer is presented. An additional production term incorporating the effects of FST intensity (velocity scale) was included in the TKE equation. The constant cμ in the equation for the transport coefficient μt was modified using empirical information. These modifications were applied to two well tested k-ε models (Launder-Sharma and K-Y Chien,) under high FST conditions (initial FST intensity, Tui > 5%). Models were implemented in a two-dimensional boundary layer code. The high FST 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 models became poorer (overprediction upto more than 50% for skin friction coefficient and Stanton number, and underprediction of turbulent kinetic energy (TKE) upto more than 50%) as FST increased to about 26%. In comparison, the new model developed here provided excellent results for TKE in the boundary layer when compared to the data set with Tui = 6.53%. Results for skin friction coefficient and Stanton number were also very good (within 2% of mean experimental data). For the case of data set with Tui = 25.7%, results of skin friction coefficient, Stanton number and TKE have also vastly improved, but still have scope for more improvement. The present model incorporates physics of free stream turbulence in turbulence modeling and provides a new method for simulating flows with high FST. Future work will focus on including length scale effects in the current model to obtain better predictions for the higher intensity case (Tui = 25.7%) and simulate flows typical in gas turbine engine environments.