An elliptic blending Reynolds stress transport equation model for Newtonian fluids has been extended to predict polymer-induced drag reduction FENE-P fluids. The conformation tensor equation which is related to the polymer stress is adopted from the model form of Resende et al., and the models of redistribution and dissipation rate terms for the Reynolds stress transport equation are considered by the elliptic blending equation. Also, the new model terms for viscoelastic turbulent transport and viscoelastic dissipation in the Reynolds stress transport equation are introduced to consider the polymer additives effect. The prediction results are directly compared to the DNS data to assess the performance of the present model predictions.

An algebraic model for turbulent heat fluxes is proposed on the basis of the elliptic blending equation. The algebraic model satisfies the temperature-pressure gradient correlation characteristics of near-wall region and the flow center region far away from the wall. That is, the turbulent heat flux conditions for both regions are connected by the solution of the elliptic blending equation. The predictions of turbulent heat transfer in a plane channel flow have been carried out with constant wall heat flux and constant wall temperature difference boundary conditions respectively. Also, the rotating channel flow with constant wall temperature difference is considered to test the applicability of the model. The prediction results show that the distributions of the turbulent heat fluxes and mean temperature are well captured by the present algebraic heat flux model.