The calculation of fully developed turbulent flows using a new mixing length model

In the prediction of turbulent flow and heat transfer, it is important to be able to quantify accurately the contribution of turbulence to the transport processes, particularly near the boundary of the flow. The damping influence of the boundary on the turbulence (as is, for example, reflected in van Driest's modification to the classical mixing length model of Prandtl) is well known, but as yet it is not completely catered for by existing models for the whole range of geometry. In this paper, a new mixing length model is described. By harmonically oscillating the whole of the duct boundary in the flow direction, (following the earlier idea of Stokes), the local damping in the duct cross section is determined. The local damping factor is then used with Buleev's mixing length expression to determine the turbulent diffusivity. The new model, with its wider application, is then used in the conservation equations to predict fully developed velocity distribution in a square duct.