Self-consistent direct numerical simulations of turbulent channel flows of dilute polymer solutions exhibiting friction drag reduction (DR) show that an effective Deborah number defined as the ratio of polymer relaxation time to the time scale of fluctuations in the vorticity in the mean flow direction remains O(1) from the onset of DR to the maximum drag reduction (MDR) asymptote. However, the ratio of the convective time scale associated with streamwise vorticity fluctuations to the vortex rotation time decreases with increasing DR, and the maximum drag reduction asymptote is achieved when these two time scales become nearly equal. Based on these observations, a simple framework is proposed that adequately describes the influence of polymer additives on the extent of DR from the onset of DR to MDR as well as the universality of the MDR in wall-bounded turbulent flows with polymer additives.
In this study, the Reynolds-Averaged-Navier-Stokes (RANS) model combined with the Cross Viscosity Equation is used, applied to the soft turbulence regime (Ra =5×105~4×107) and hard turbulence regime (Ra>4×107) of Rayleigh-Bénard convection (RBC). The relation curves between heat transport (Nusselt number) and other parameters, as well as flow pattern changes of RBC are obtained for the cases with different Rayleigh number and concentration of the polymer additive. The simulations show that the presence of polymer additive can lead to an enhancement of the heat transfer with larger effect in the hard turbulence regime than those in the soft turbulence regime. It is also shown that in the soft turbulence regime the reversal cycles are shorter than in hard turbulence regime. The symmetric vortices in the diagonal corner of enclosed space shrink and the velocities of large-scale circulation (LSC) increase accordingly.
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