Implementation of a Free Stream Turbulence Diffusion Model in FLUENT Code for Calculation of Heat and Momentum Transport in a Flat Plate Boundary Layer

Abstract

A model for the diffusion of turbulent kinetic energy (TKE) for high free stream turbulence (FST) boundary layers is implemented in commercially available FLUENT CFD code to predict the effects of high free stream turbulence on heat and momentum transport in a flat plate boundary layer using Launder and Spalding’s standard k-ε model. The computational results are compared with experimental data sets. When experimental and/or standard initial profiles and standard k-ε model were used for calculations of Stanton number and skin friction coefficient under high FST intensities the results were close to the experimental data (within 2%). However. TKE profiles had large deviations (within approximately 40 %) compared to the data for both moderately high FST (Tui = 6.53%) and very high FST (Tui = 25.7%) intensities. Since TKE values are used in calculations of skin friction coefficients and Stanton numbers through calculation of turbulent viscosity from k and ε, getting a correct result for these quantities from the wrong calculations of TKE seems contradictory. In an earlier study it was concluded that the TKE calculations were low compared to the data because k-ε models do not model the diffusion of high FST correctly. To correct this discrepancy, a new model for TKE diffusion was developed and used it in TEXSTAN code. The objective of the current study is to generalize this model and use it in more complicated geometries by applying to FLUENT code. Therefore at this first phase of this study, this diffusion model was implemented in the Launder and Spalding k-ε model contained in FLUENT code using User Defined Functions (UDF) by modifying the turbulent kinetic energy transport equation. The constant Cμ which exists in the turbulent viscosity equation was also modified using experimental data. This model considerably increased the TKE values for both moderately high and very high FST intensities showing that it functions as it was intended. While TKE perfectly matched with the experimental data sets (within 1–2%) for moderately high initial FST intensity, it still did not yield very good results for very high initial FST intensity. Under very high FST intensity TKE does not match data very well near the wall. The Stanton number and skin friction coefficient increased (about 30%) as expected since the new diffusion model increases TKE levels ner the wall. At this point it should be mentioned that standard k-ε model is a high Reynold number turbulence model which use wall functions near the wall. In earlier studies the new diffusion model was applied to a low Reynold number model in TEXSTAN code. In the continuing studies high Reynolds number k-ε model in FLUENT will be modified to create a low Reynolds number model via UDFs in order to get better predictions of the Stanton number and skin friction coefficients by use of damping function fμ and adjusting the value of turbulent Prandtl number. This study reports on progress in overall goal of implementing a new TKE diffusion model in FLUENT code.