A Reynolds stress model of turbulence and its application to thin shear flows

Abstract

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor $\overline{u_iu_j}$ and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components. For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress $-\overline{u_1u_2}$ the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-layer flows including examples of flow remote from walls, those developing along one wall and those confined within ducts. Three of the flows are strongly asymmetric with respect to the surface of zero shear stress and here the turbulent shear stress does not vanish where the mean rate of strain goes to zero. In most cases the predicted profiles and other quantities accord with the data within the probable accuracy of the measurements.