Direct Numerical Simulation Of Superhydrophobic/viscoelastic Taylor-Couette Flow

Direct numerical simulation has been performed on Taylor-Couette(TC)turbulence over superhydrophobic surfaces(SHS)and transition of viscoelastic TC flow.The main results and conclusions are briefly given as follows:(1)In the study on TC turbulence over superhydrophobic surfaces(SHS).We show the effect of SHS on turbulent statistic of TC turbulence and display the feature and mechanism of SHS drag reduction(DR).The hypothesis of the modified Prandtl-von Kamran-type skin-friction law for SHS TC turbulence has been verified,and the predicted torque scaling and the modified skin-friction law is in good agreement with our DNS results.Also,the dimensionless effective slip length scaling b+?Re1/2 has been reproduced numerically.The extent of DR in SHS increases progressively with Re and reaches 7.3%at Re = 50000.The DR in SHS Taylor-Couette turbulence derives from flow changes as follows:(i)In the outside of viscous sublayer,the suppression of streamwise vortices leads to the suppression of generating Reynolds stress,which is the major factor in this region.(ii)In the viscous sublayer,the slip effect of SHS weaken the average shear effect of SHS Taylor-Couette turbulence,which is the dominant mechanism in this region.The suppression of streamwise vortices and the slip effect of SHS enhance with Re,which can be regraded as a mechanism of continuous increase DR with Re.(2)Direct numerical simulation has been performed on transition of viscoelastic(TC)flow.Specifically,the transition of viscoelastic TC flow is examined by varying parameters in the following three ways:1)increasing the inertia while keeping the elasticity unchanged;2)keeping the elasticity number(a ratio of inertia to elasticity)unchanged while increasing the inertia;3)keeping the inertia unchanged while increasing the elasticity.The present calculations succeed in reproducing various typical flow states,including rotating standing waves(RSW),axisymmetric oscillatory strip(OS),non-axisymmetric OS and a flow state in form of traveling-wave.Moreover,a new flow state consisting of intermittent solitary wave has been found,which is characterized by solitary coherent structure appearing periodically and intermittently in time and localized axially with intense inflow/outflow spot.On the other hand,three transition pathways which have the same departure and destination in parameter space are examined.Based on comparing the final states of the three pathways,existence of multiple flow states has been confirmed in viscoelastic TC flows.