Direct Numerical Simulation Of Viscoelastic Taylor-Couette Flow

Investigation on flow transition and turbulence dynamics in viscoelastic fluids presents a frontier scientific challenge in the fields of nonlinear science and complex turbulence.Such an investigation not only promotes scientific understanding of fluid mechanics,but also is of fundamental significance for engineering applications.This dissertation focuses on the viscoelastic Taylor-Couette(TC)flow,dedicating to the development of numerical methods and the exploration of polymer/flow interaction mechanisms under multiple nonlinear effects including elasticity,inertia,rotation and curvature.To this end,the following issues are addressed in this dissertation:(1)numerical methods for viscoelastic turbulence in cylindrical coordinates;(2)high-order transition route;(3)maximum drag enhancement(MDE)asymptote;(4)maximum drag reduction(MDR)asymptote.The primary results are briefly summarized as follows:1.A high-fidelity,robust and efficient finite difference algorithm for polymerinduced turbulence in cylindrical coordinates is proposed.By implementing staggered grids,the axis singularity in viscoelastic constitutive equations is effectively addressed.To attain numerical stability,the shock-capturing KurganovTadmor scheme is extended for cylindrical coordinates and its computational efficiency is optimized,facilitating large-scale numerical simulations of viscoelastic turbulence.Extensive simulations on two classic flow configurations,namely viscoelastic pipe flow and TC flow,are carried out to verify the accuracy,convergence,robustness,and broad applicability of the proposed algorithm.More importantly,this new algorithm avoids the inherent deficiencies caused by the artificial diffusion for classical algorithms,accurately captures small-scale shocklike structures in complex viscoelastic turbulence,and faithfully reproduces the experimental observations.Moreover,a spectral/finite difference hybrid method is developed,which is a simple modification of pseudo-spectral methods and also exhibits strong robustness.These studies provide new guidance and references for the development of numerical methods for viscoelastic flows in the future.2.A novel flow transition route is reported in a large-radius-ratio(η=0.912)TC flow with moderate elasticity(El=0.15).Specifically,as the driving force increases,the primary instability causes a flow transition from an azimuthal base flow to a flow composed of rotating standing wave,which in turn transitions to disordered oscillations followed by an intriguing modulated traveling wave flow pattern and eventually to elastically dominated turbulence(EDT).The modulated traveling wave is reported for the first time and is shown to be composed of a spiral mode and a rotating standing wave mode.Distinct flow regions have been identified in the EDT state,namely,an elasticity-dominated outer-wall region and an inertia-dominated inner-wall region.It is found that the intense merging and splitting events of the large-scale vortices in the outer-wall region are the main flow features of EDT.This novel turbulence state is mainly sustained by elastic forces,i.e.,the turbulent kinetic energy is mainly generated by the polymer stress fluctuations via the interaction between the large-scale vortices and the polymers in the outer-wall region.3.The existence of a polymer-induced MDE asymptote in a wide gap(η=0.5)turbulent viscoelastic TC flow is demonstrated via direct numerical simulations.Specifically,the turbulent drag is gradually enhanced as the elastic force(Wi)is increased and eventually saturates above a critical Wi.The mean velocity profile in this novel MDE state closely follows a logarithmic-like law with an identical slope(κK=2.32),which is insensitive to fluid inertia(Re).Flow structure analysis shows that the inertia-generated vortices are greatly suppressed by polymers,while the elastic/inertio-elastic Gortler vortices survive and establish an EDT-dynamics barrier against unbounded drag enhancement.This vortical dynamics perspective is corroborated by the turbulent statistics and the competition of driving forces.It is elucidated that the flow features related to the inertial vortices are suppressed,while those related to elastic/inertio-elastic G?rtler vortices are enhanced.Furthermore,it is unequivocally demonstrated that the MDE state is realized in the EDT regime much alike the MDR asymptote.This points to the fact that the asymptotic drag modification behavior is an inherent property of EDT flow state.4.By varying curvature effects,asymptotic flow states with various extents of turbulent drag modifications are achieved in viscoelastic TC flows.Of particular interest,the MDR asymptote in a curved-streamline configuration is reported for the first time.Specifically,as the elastic force is gradually increased,the extent of drag enhancement/reduction gradually increases and eventually saturates above a critical W i,realizing MDE/MDR states depending on curvature effects.Flow structure analysis reveals that these asymptotic flow states are realized in the EDT and/or elasto-inertial turbulence regimes characterized by diverse vortices structures.The changes in vortical structures induced by polymer additives account for the suppression of Reynolds stress and the generation/mixing of polymer stress.Hence,the saturation of turbulent vortices leads to "a MDR state of Reynolds stress" and "a MDE state of polymer stress".Eventually,the superposition of these two distinct asymptotic states enables the flow to achieve a wide range of drag modification in asymptotic flow states.These findings provide a novel approach to answer the long-standing question regarding the fundamental nature of MDR and stimulate future studies in searching for asymptotic states in flows that involved multiple vortex generation mechanisms.