Comparison of low Reynolds number k-ε models in simulation of momentum and heat transport under high free stream turbulence

Calculations of the effects of high free stream turbulence (FST) on the transport of momentum and heat in a flat plate turbulent boundary layer are presented. Four well known low Reynolds number k-ε models namely Launder-Sharma, K.-Y. Chien, Lam-Bremhorst and Jones-Launder were used in order to investigate specifically their prediction capabilities under high FST conditions (initial FST intensity, Tu(i) > 5%). These models were implemented in computer code TEXSTAN, a partial differential equation solver which solves steady flow boundary layer equations. Firstly, these models were compared with empirical data and standard correlations to test how they predicted very low FST (Tu(i) = 1%) cases. Predictions of all models for skin friction and heat transfer were good (within ±5% of data and correlations) with the exception of the Lam-Bremhorst model which predicts skin friction and heat transfer within about 10% of empirical data and correlations. For turbulent kinetic energy (TKE) profiles, Jones-Launder and Launder-Sharma models had problems predicting the peak value of TKE. Subsequently, all these models were used in order to predict the effects of high FST (Tu(i) > 5%). Predictions became poorer (over-prediction up to more than 50% for skin friction and Stanton number, and under-prediction of TKE up to more than 50%) as FST increased to about 26%. The high FST data sets against which the predictions were compared had initial FST intensities of 6.53% and 25.7%. Physical reasoning as to why the aforementioned models break down with increasing FST is given.