Direct Numerical Simulation Of Viscoelastic Turbulent Taylor-Couette Flow

Complex fluids exist widely in nature and are continually engineered for various applications.The interaction of flexible polymers with fluid flows is one of the most challenging subjects in soft matter physics and fluid mechanics.Introducing soluble long-chain polymer additives is known to have profound effects on Newtonian Taylor-Couette.(TC)turbulence.The nonlinear viscoelastic response of polymeric fluids gives rise to a new class of instabilities and flow states that dramatically alters the turbu-lence dynamics and transition routes.We study three typical problems of turbulent viscoelastic TC flows via direct numerical simulations:1)the curvature dependence of turbulent drag enhancement(DE);2)a high-order transition route and 3)the in-ertially/elastically dominated mechanism of turbulence.The main research results are summarized as follows.For the viscoelastic turbulent TC flows of different radius ratios,we report numer-ical results that clearly elucidate the mechanism that leads to curvature dependence of DE.Change in the angular momentum transport and its inherent link to transitions in vortical flow structures have been explored to depict the influence of the curvature of the flow geometry on DE.Specifically,it has been demonstrated that a transition in vortical structures with increasing the radius ratio leads to weakening and elimination of the small-scale Gortler vortices and development and better organization(occupying the entire gap)of large-scale Taylor vortices which are also evinced by the patterns of angular momentum current.The commensurate change in DE and its underlying mechanism are examined by contributions of convective flux and polymeric stress to the angular momentum current.The finding paves the way for capturing highly local-ized elastic turbulence structures in direct numerical simulation by increasing geometry curvature in traditional turbulent curvilinear flows.Inspired by an additional finding obtained for the above study that the Newtonian turbulent Taylor vortex flow of a large radius ratio is stabilized to a flow state resem-bling the laminar-like Taylor vortex flow as a result of polymeric elasticity,we study the elasticity-induced flow transitions in TC flows of radius ratio 0.912 of polymeric solu-tions at high Reynolds number(Re=3000).Intriguingly,a high-order transition route from inertial to elasticity-dominated turbulent flow(EDT)has been discovered.This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration.The first step stabilizes the inertial turbulence(IT)to a laminar flow much alike the modulated wavy vortex flow.The second step destabilizes this laminar flow state to EDT,i.e.,a spatially smooth and temporally random flow with a-3.5 scaling law of the energy spectrum reminiscent of elastic turbulence.The flow states involved are distinctly different than those observed in the reverse transition route from IT to elasto-inertial turbulence in parallel shear flows,underscoring the im-portance of polymer-induced hoop stresses in realizing EDT.The intricate competition between inertial and elastic nonlinearities underlying this transition route is substan-tiated via the changes in total turbulent kinetic energy and elastic potential energy as well as the inertial and elastic stresses.Finally,in order to elucidate the dynamical and statistical features of small-scale Gortler vortices near the cylinder walls and their related effects in viscoelastic turbulent TC flows of a small radius ratio,we investigate the inertio-elastic turbulent TC flow(for a radius ratio of 0.5)at Re ranging from 500 to 8000,through a new numerical method developed to overcome the inherent defect of traditional spectral methods with an artificial diffusion term introduced.It is found that the turbulence dynamics can be categorized into two regimes based on Re.The first regime that takes place for low Re and the dynamics is essentially dominated by the elasticity nonlinearity.It is suggested that in elasticity-dominated turbulence,the main contribution to transport and mixing of momentum,stress and energy is coming from large-scale flow structures in the bulk region.While the second regime occurs at large Re with the dynamics mainly dominated by the inertial effect.In contrast to the elasticity-dominated regime,the transport and mixing of physical quantities in inertia-dominated turbulence are fundamentally results from the impact of small-scale flow structures in the near-wall regions.Nevertheless,the existence of small-scale elastic vortical structures identified as elastic Gortler vortices has been observed for all Re considered here and they are demonstrated to develop herringbone streaks near the inner wall but with sufficiently longer time scale than their Newtonian counterparts due to its elastic origin.Furthermore,the flow-microstructure coupling analyses elucidate that the elastic Gortler instability in the outflow regions with high polymer extension is triggered by significant hoop stresses.Detailed study on the budgets of mean streamwise enstrophy,mean kinetic energy,turbulent kinetic energy and Reynolds shear stress demonstrate that increasing fluid-inertia hinders the generation of elastic stresses,leading to a monotonic depletion of the elastic-related nonlinear effects on the dynamics and statistics.