Effect of rheological properties on drag reduction in turbulent boundary layer flow

Abstract

Direct numerical simulation of a zero-pressure gradient drag-reducing turbulent boundary layer of viscoelastic fluids was systematically performed at the momentum-thickness Reynolds number Reθ0=500 and Weissenberg number We=25 using constitutive equation models such as the Oldroyd-B, the finitely extensible nonlinear elastic Peterlin model at the maximum chain extensibility parameters L2=100, 1000, and 10 000, and the Giesekus model at the mobility factors α=0.01, 0.001, and 0.0001, where the ratios of solvent viscosity to zero shear rate solution viscosity, β, were 0.9, 0.99, and 0.999. For the case that the elongational viscosity for the steady elongational flow was identical, the streamwise variation in the drag reduction (DR) was thoroughly investigated, and then the effects of rheological properties such as the elongational and shear viscosities and the first and the second normal stress differences on DR were clarified. It is found that the streamwise profile of DR shifts downstream with the decrease in the first normal stress difference. The shear-thinning property and the first normal stress difference slightly affect the maximum DR, while the decrease in the magnitude of the second normal stress difference results in the decrease in the maximum DR.