Extension of Omega and Omega-Liutex methods to the identification of vortex structures in viscoelastic turbulent flow

Vortex structure plays a significant role in the investigation of turbulent drag reduction effect of viscoelastic turbulent flow. This paper attempts to find out an optimal vortex identification method for viscoelastic turbulent flows, and then to explore the turbulent drag reduction mechanism by analyzing the characteristics of the extracted vortex structures in the turbulent flows of viscoelastic fluids. Q, λ2, Liutex, Ω (Omega) and ΩR (Omega-Liutex) methods are adopted for the identification of vortex structures in forced homogeneous isotropic turbulence (FHIT) with/without polymer additive, respectively. The comparison among these five methods shows that the threshold values for Q, λ2 and Liutex methods should be artificially adjusted so as to suitably describe the strong and weak vortex structures in FHIT of both the Newtonian and viscoelastic fluids, while a fixed threshold value of 0.52 for Ω and ΩR methods is effective for both the Newtonian and viscoelastic fluids. The comparison between the identified vortex structures in FHIT with and without polymer additive indicates that Ω and ΩR methods are more appropriate for the vortex identification because their dimensionless values ranged from 0 to 1 can avoid the effect of the different ranges of Q, λ2 and ∣R∣ (for Liutex method) for the Newtonian and viscoelastic fluids. This also illustrates that the feasibility of Ω and ΩR methods is extended to the identification of the vortex structures in the turbulent flow of viscoelastic fluid. Finally, the characteristics of vortex structures in FHIT of viscoelastic fluid are analyzed by utilizing Ω and ΩR methods. The results show that both the strong and weak vortex structures are inhibited by increasing the concentration of polymer solution and by decreasing the Weissenberg number, especially for the weak vortex structures.