Several modifications are introduced to the Elliptic Blending Differential Flux Model proposed by Shin et al. (2008) to account for the influence of wall blockage on the turbulent heat flux. These modifications are introduced in order to reproduce, in association with the most recent version of the EB-RSM, the full range of regimes, from forced to natural convection, without any case-specific modification. The interest of the new model is demonstrated using analytical arguments, a priori tests and computations in channel flows in the different convection regimes, as well as in a differentially heated cavity. (C) 2016 Elsevier Inc. All rights reserved.

The present paper focuses on the application of the elliptic blending approach to the modeling of turbulent heat fluxes, in order to account for the influence of solid boundaries. The analytical justification of the extension to the temperature–pressure gradient correlation term of this approach, originally applied to the velocity–pressure gradient, is given. The assumption of weak equilibrium enables the derivation of two new algebraic flux models valid down to the wall. It is shown, with both a priori tests and computations in forced and mixed convection regimes, that the predictions of the streamwise heat-flux and the temperature variance are significantly improved by the use of elliptic blending. A particular attention is devoted to the issue of the modeling of the correlation length scale involved in the elliptic blending for the heat fluxes, which is shown to have a significant influence on the predictions.

Four calculations, two using LES with respectively 18 and 76 million computational cells and two utilizing a URANS approach on a 2 million mesh with sophisticated first and second moment closure approaches; the phi-model and the EB-RSM combined to the EB-GGDH, have carried out for the flow through a wall bounded pin matrix in a staggered arrangement with a heated bottom wall at a Reynolds number based on the gap velocity and the diameter of the pins equal to 10, 000. Comparisons of the pressure drop, the pressure coefficient distribution, the mean and rms values of the steam-wise velocity component and the Nusselt number distribution along the bottom wall showed clearly that using a first moment closure is not adequate for the present case. Although the wall-resolved LES with 76 million cells shows a superior behavior, the second moment closure exhibits very interesting results.