The evolution of the coherent structures in a two-dimensional time-developing mixing layer of the FENE-P fluids is examined numerically. By the means of an appropriate filtering for the polymer stress, some characteri...The evolution of the coherent structures in a two-dimensional time-developing mixing layer of the FENE-P fluids is examined numerically. By the means of an appropriate filtering for the polymer stress, some characteristics of the coherent structures at high b were obtained, which Azaiez and Homsy did not address. The results indicate that adding polymer to the Newtonian fluids will cause stronger vorticity diffusion, accompanied with weaker fundamental and subharmonical perturbations and slower rotational motion of neighbouring vortices during pairing. This effect decreases with the Weissenberg number, but increases with b. In addition, the time when the consecutive rollers are completely coalesced into one delays in the viscoelastic mixing layer compared with the Newtonian one of the same total viscosity.展开更多
We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with nonin...We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains.展开更多
The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.
Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE...Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE） chains and FENE chain cluster. The coiled stretched transition of FENE chains was examined and the change in configuration of FENE chains was presented. The average velocity profile of the fully developed channel flow with 64 FENE chains was given and fitted well with the power-law curve. The change of chain cluster configuration was also simulated. These simulations show that DLM/FD method is capable of simulating the motion of not only FENE chain, but also FENE chain cluster.展开更多
Deterministic simulation approach was applied to simulating viscoelastic complex flows,in which,the SIMPLE algorithm based on collocated grid was used to solve the conservation equations on the macroscopic level and t...Deterministic simulation approach was applied to simulating viscoelastic complex flows,in which,the SIMPLE algorithm based on collocated grid was used to solve the conservation equations on the macroscopic level and the spectral method was used to solve the Fokker-Planck equation on the mesoscopic level.Here,the transient 4∶1 planar contraction flow for dilute polymer solution was computed by using the coupled technique and the calculated polymeric stress distributions at steady state were identical with the results of continuum approach as well as the corresponding references.Therefore,the presented results indicated that the SIMPLE algorithm based on collocated grid coupled with the spectral method can be used to simulate viscoelastic complex flows effectively.Moreover,the influence of Deborah number and viscosity ratio on polymeric stress was also investigated.展开更多
文摘The evolution of the coherent structures in a two-dimensional time-developing mixing layer of the FENE-P fluids is examined numerically. By the means of an appropriate filtering for the polymer stress, some characteristics of the coherent structures at high b were obtained, which Azaiez and Homsy did not address. The results indicate that adding polymer to the Newtonian fluids will cause stronger vorticity diffusion, accompanied with weaker fundamental and subharmonical perturbations and slower rotational motion of neighbouring vortices during pairing. This effect decreases with the Weissenberg number, but increases with b. In addition, the time when the consecutive rollers are completely coalesced into one delays in the viscoelastic mixing layer compared with the Newtonian one of the same total viscosity.
基金NSF Grant DMS-0201443NSF of China under Grants 10525101 and 10421101+1 种基金973 Projectthe Innovation Grant from Chinese Academy of Sciences
文摘We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains.
文摘The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b > 2.
文摘Distributed Lagrange Multiplier/Fictitious Domain （DLM/FD） method was employed to simulate the channel flow with polymer suspension. The polymer molecules were modeled as Finitely Extensible Nonlinear Elastic （FENE） chains and FENE chain cluster. The coiled stretched transition of FENE chains was examined and the change in configuration of FENE chains was presented. The average velocity profile of the fully developed channel flow with 64 FENE chains was given and fitted well with the power-law curve. The change of chain cluster configuration was also simulated. These simulations show that DLM/FD method is capable of simulating the motion of not only FENE chain, but also FENE chain cluster.
基金Project(IFP-A-2022-2-5-24) supported by Ministry of Education and University of Hafr Al Batin, Saudi ArabiaProject supported by University of Campania “Luigi Vanvitelli”, ItalyProject supported by COMSATS University Islamabad, Pakistan。
文摘Deterministic simulation approach was applied to simulating viscoelastic complex flows,in which,the SIMPLE algorithm based on collocated grid was used to solve the conservation equations on the macroscopic level and the spectral method was used to solve the Fokker-Planck equation on the mesoscopic level.Here,the transient 4∶1 planar contraction flow for dilute polymer solution was computed by using the coupled technique and the calculated polymeric stress distributions at steady state were identical with the results of continuum approach as well as the corresponding references.Therefore,the presented results indicated that the SIMPLE algorithm based on collocated grid coupled with the spectral method can be used to simulate viscoelastic complex flows effectively.Moreover,the influence of Deborah number and viscosity ratio on polymeric stress was also investigated.
