Calculation of Convective Heat Transfer in Recirculating Turbulent Flow Using Various Near-Wall Turbulence Models

The turbulent flow about a two-dimensional blunt rectangular section is used as a test case to examine the performance of seven near-wall turbulence models. The first two models are one-equation low Reynolds number (Re) models requiring a fine grid near-wall treatment. The other near-wall turbulence models considered are based on wall functions that bridge with a single cell the thermally important near-wall region. Standard wall functions based on the local equilibrium assumption, wall functions using a two- and three-layer approach to evaluate local variations of turbulence quantities in the k equation, and extension of the two- and three-layer treatments to the ∊ equation are considered. The numerical predictions are obtained using a variant of the k-∊ model incorporating a curvature correction. The governing equations are discretized using a finite-volume formulation employing the bounded-skew hybrid differencing scheme. The solutions are obtained using a two-pass procedure, devised to allow for the correct use of the wall functions. Computations are performed for Re in the range 20,000-75,000. The various near-watt models are assessed by comparing resulting Nusselt number distributions and selected fluid dynamic results with available experimental data. A three-layer model of the wall region, applied to the k and ∊ equations, gives good agreement with the data; the standard wall Junction treatment is not satisfactory at all for this flow.