A Thermal Law of the Wall for Separating and Recirculating Flows

Abstract

The characteristics of the turbulent boundary layer near a separation point are studied here. The emphasis is on providing analytical expressions for the velocity and temperature near wall solutions which are also valid in the region of reverse flow. These expressions can then be used as boundary conditions in numerical schemes that use two-equation differential models. The paper proposes a new expression for the description of the near wall characteristic length which is shown to hold also in the reverse flow region. The specified velocity profiles are based on a previous formulation of the problem by Cruz and Silva Freire (IJHMT, 41, 2097 2111, 1998) but, as written here, they are presented for the first time. The temperature profiles near the wall are also described by a newly proposed expression that reduces to the logarithmic profile in the attached region, and assumes a minus half power law profile at the separation point. In the separated region, the logarithmic profile is recovered. All results are validated through the data of Vogel and Eaton (Trans. ASME JHT, 107, 922 929, 1985).