Comparison of turbulent drag reduction mechanisms of viscoelastic fluids based on the Fukagata-Iwamoto-Kasagi identity and the Renard-Deck identity

Abstract

The friction coefficient decomposition was investigated in viscoelastic incompressible fluid turbulent channel flows based on two methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14(11), L73–L76 (2002)] and the Renard-Deck (RD) identity [N. Renard and S. Deck, “A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer,” J. Fluid Mech. 790, 339–367 (2016)]. Direct numerical simulations of viscoelastic fluid turbulent and Newtonian fluid turbulent channel flows were carried out to provide a database for comparative investigations. By comparing the friction coefficient decomposition results based on the two identities, different understandings about the turbulent drag reduction (TDR) mechanism were comparatively analyzed. It was found that the reduction of the viscous contribution to the friction coefficient is also an important cause for TDR under the RD identity, and that the TDR effect in the near-wall region is more intense than that under the FIK identity. In addition, if the weight coefficient for the shear-stress contribution to the friction coefficient in the FIK identity is interpreted as the laminar shear strain rate, the TDR mechanisms obtained by the two identities can be unified; the difference in the understandings can be attributed to the difference in base flow selected to determine the weight coefficient.