The main objective of the present investigation is to obtain numerical predictions for two-dimensional, confined, low-Mach number recirculating flows involving heat transfer. Attention is focused mainly on the flow downstream of a sudden expansion in a pipe. Such flows are characterized by levels of heat transfer in the neighborhood of the reattachment point several times higher than that for fully developed flows at the same Reynolds number.

A system of modeled transport equations for the Reynolds stresses u_iu_j and the energy dissipation rate e is proposed. This model is based upon the one point turbulence closure introduced by Launder, Reece & Rodi (1975) and Hanjalic & Launder (1976). Special attention is paid to the modeling of the pressure-strain correlation and the dissipation terms near solid walls. Several coefficients are reevaluated. The generation term of the e equation is revised. The model is tested first in isothermal flows. Transport equations for u_iu_j, ε and the mean momentum are solved numerically up to the walls using a finite-difference procedure. Predictions obtained with the proposed model are in good agreement with available measurements in recirculating and non-recirculating flows. The influence of the choice of the discretization scheme on the predictions is discussed.

Heat transfer phenomena are predicted using an algebraic stress model for the scalar fluxes u_ic to close the mean temperature equation. Constant properties are assumed and a single time scale is used in the model. Predictions for the Nusselt number in recirculating and non-recirculating pipe flows are in good agreement with experimental data.