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Fourth International Symposium on Turbulence and Shear Flow Phenomena
June, 27-29, 2005, Marriot Hotel, Williamsburg, Virginia, USA

DOI: 10.1615/TSFP4

A REYNOLDS-STRESS EXPRESSION BASED ON DNS DATA IN NON-LINEAR EDDY-VISCOSITY TURBULENCE MODEL FOR COMPLEX FLOWS

pages 537-542
DOI: 10.1615/TSFP4.900
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ABSTRAKT

A Reynolds-stress expression used in a non-linear eddy-viscosity turbulence model is developed based on the Direct Numerical Simulation (DNS) data of fully developed turbulent channel flow of Kim et al. (1987) for both Reτ = 180 and 395. The data are initially used to analyze the accuracy of various Reynolds-stress expressions used in the non-linear turbulence models in order to find the expression that gives the closest Reynolds-stress values to the DNS data. The use of the DNS data directly in the expression is to ensure that the errors in the solutions are not from the modeled transport equations of the turbulent kinetic energy and its dissipation rate. It is found that both Reynolds shear stress and normal Reynolds stresses from the Reynolds-stress expression of Craft et al. (1996) are closer to the DNS data than the other expressions for both Reynolds numbers. The present work aims to further improve the accuracy of the expression of Craft et al. in predicting the Reynolds stresses and consequently the mean velocity profiles. The main objective of the current work is to find the fµ expression based on the non-linear Reynolds-stress expression of Craft et al. that gives the closest agreement to the values of fµ extracted from the DNS data. It is found that the Reynolds-stress expression of Craft et al. with the fµ of Gibson and Dafa'Alla (1994) gives the closer agreement to the DNS data for all Reynolds stresses and mean velocity profile in the case of fully-developed turbulent channel flow. The expression is then evaluated for more complex three-dimensional flow through a straight square duct where there are secondary flows. The DNS data of Gavrilakis (1992) are used for comparison. The present expression shows the improvement in the prediction of the mean spanwise velocity profile at the position near the edge of the duct. The damping function of Gibson and Dafa'Alla is hence the more suitable damping function to be used with the non-linear Reynolds-stress expression of Craft et al.

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