Maximum drag reduction state of viscoelastic turbulent channel flow: marginal inertial turbulence or elasto-inertial turbulence

Abstract

The essence of the maximum drag reduction (MDR) state of viscoelastic drag-reducing turbulence (DRT) is still under debate, which mainly holds two different types of views: the marginal state of inertial turbulence (IT) and elasto-inertial turbulence (EIT). To further promote its understanding, this paper conducts a large number of direct numerical simulations of DRT at a modest Reynolds number Re with $Re = 6000$ for the FENE-P model that covers a wide range of flow states and focuses on the problem of how nonlinear extension affects the nature of MDR by varying the maximum extension length $L$ of polymers. It demonstrates that the essence of the MDR state can be both IT and EIT, where $L$ is somehow an important parameter in determining the dominant dynamics. Moreover, there exists a critical $L_c$ under which the minimum flow drag can be achieved in the MDR state even exceeding the suggested MDR limit. Systematic analyses on the statistical properties, energy spectrum, characteristic structures and underly dynamics show that the dominant dynamics of the MDR state gradually shift from IT-related to EIT-related dynamics with an increase of $L$ . The above effects can be explained by the effective elasticity introduced by different $L$ at a fixed Weissenberg number (Wi) as well as the excitation of pure EIT. It indicates that larger $L$ introduces more effective elasticity and is favourable to EIT excitation. Therefore, we argue that the MDR state is still dominated by IT-related dynamics for the case of small $L$ , but replaced by EIT-related dynamics at high $L$ . The obtained results can harmonize the seemingly controversial viewpoints on the dominant dynamics of the MDR state and also provide some ideas for breaking through the MDR limit, such as searching for a polymer solution with a proper molecular length and concentration.

Numerical study on the mechanism of drag modulation by dispersed drops in two-phase Taylor–Couette turbulence

“…To further study the influence of the dispersed phase on the turbulence fluctuations, we show the Favre normal stresses (figure 3d-f ), which are generally investigated by the root mean square (r.m.s.) velocity fluctuations in the constant density flow system (Zhu et al 2016;Wang et al 2023b). For the two-phase flow with ξ ρ = 1 and ξ μ = 1, the normal stress modulation is not very significant and the profiles of the normal stresses almost coincide with those for the single-phase case.…”

“…the r.m.s. streamwise velocity fluctuations decrease near the wall but increase away from the wall (Min et al 2003;Wang et al 2023b). The normal stress ρu z u z A,t shows a stronger reduction, indicating that the Taylor vortex has been significantly weakened as indicated by the averaged radial-axial velocity vectors in figure 1.…”

“…2016; Wang et al. 2023 b ). For the two-phase flow with and , the normal stress modulation is not very significant and the profiles of the normal stresses almost coincide with those for the single-phase case.…”

“…2003; Wang et al. 2023 b ). The normal stress shows a stronger reduction, indicating that the Taylor vortex has been significantly weakened as indicated by the averaged radial–axial velocity vectors in figure 1.…”