TY - JOUR

T1 - Effects of polymer stresses on analogy between momentum and heat transfer in drag-reduced turbulent channel flow

AU - Kim, Kyoungyoun

AU - Sureshkumar, Radhakrishna

N1 - Funding Information:
This work was supported under the framework of international cooperation program managed by National Research Foundation of Korea (No. NRF-2014K2A1A2048497) and the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support (No. KSC-2016-C3-0008). K.K. would like to acknowledge the support for the code optimization from National Institute of Supercomputing and Networks (NISN).

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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 Prt 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 ρuθ 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 Prt near unity.

AB - 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 Prt 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 ρuθ 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 Prt near unity.

UR - http://www.scopus.com/inward/record.url?scp=85044409048&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044409048&partnerID=8YFLogxK

U2 - 10.1063/1.5018859

DO - 10.1063/1.5018859

M3 - Article

AN - SCOPUS:85044409048

VL - 30

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 3

M1 - 035106

ER -