Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow

Abstract

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