Effects of polymer stresses on analogy between momentum and heat transfer in drag-reduced turbulent channel flow

The effects of polymer stresses on the analogy between momentum and heat transfer are examined by using a direct numerical simulation (DNS) of viscoelastic turbulent channel flows using a constant heat flux boundary condition. The Reynolds number based on the friction velocity and channel half height is 125, and the Prandtl number is 5. The polymer stress is modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (DR) (52%) cases are examined. The Colburn analogy is found to be inapplicable for viscoelastic turbulent flows, suggesting dissimilarity between the momentum and heat transfer at the macroscopic coefficient level. The mean temperature profile also shows behaviour different from the mean velocity profile in drag-reduced flows. In contrast to the dissimilarity in the mean profiles, the turbulent Prandtl number Pr_t predicted by the DNS is near unity. This implies that turbulent heat transfer is still analogous to turbulent momentum transfer in drag-reduced flows, as in Newtonian flow. An increase in DR is accompanied by an increase in the correlation coefficient ρ_uθ between the instantaneous fluctuations in the streamwise velocity u and temperature θ. The correlation coefficient between u′ and wall-normal velocity fluctuations v′, ρ-uv, exhibits a profile similar to that of ρ-θv in drag-reduced and Newtonian flows. Finally, the budget analysis of the transport equations of turbulent heat flux shows a strong similarity between the turbulent momentum and heat transfer, which is consistent with the predictions of Pr_t near unity.