Heat transfer enhancement in a ribbed channel: Development of turbulence closures

The ability to accurately predict turbulent heat transfer in massively separated flows is of immense practical importance especially in the field of heat transfer enhancement in compact heat exchangers. This paper describes new developments in the modeling of the flow and the turbulent heat fluxes in a representative benchmark flow namely that in a heated channel with periodic surface ribs. This flow, which is well-documented by experiments, poses severe challenges to conventional closures due to the significant non-equilibrium effects that are present. Several closure strategies were therefore considered ranging from the eddy-viscosity closures that are routinely used in practice, to the more sophisticated full differential transport closures that can better capture rapidly-evolving flow and thermal fields. As the heat transfer rates are largely determined by the flow conditions in the near-wall region, low Reynolds number versions of these closures were also considered. As for the turbulent heat fluxes, two alternative models were considered: the conventional Fourier's law, and a more complete, algebraic model which is explicit in these fluxes and which correctly allows for their dependence on the turbulent stresses and on the gradients of mean velocity. The models were implemented in the open source software OpenFOAM and the computations were performed with cyclic boundary conditions that are appropriate for this periodic flow. Details of models implementation are reported. Comparisons with experimental measurement indicate significant improvements over existing approaches.