Repicturing viscoelastic drag-reducing turbulence by introducing dynamics of elasto-inertial turbulence

Abstract

Recently, the nature of viscoelastic drag-reducing turbulence (DRT), especially the maximum drag reduction (MDR) state, has become a focus of controversy. It has long been regarded as polymer-modulated inertial turbulence (IT), but is challenged by the newly proposed concept of elasto-inertial turbulence (EIT). This study is to repicture DRT in parallel plane channels by introducing dynamics of EIT through statistical, structural and budget analysis for a series of flow regimes from the onset of drag reduction to EIT. Some underlying mechanistic links between DRT and EIT are revealed. Energy conversion between velocity fluctuations and polymers as well as pressure redistribution effects are of particular concern, based on which a new energy self-sustaining process (SSP) of DRT is repictured. The numerical results indicate that at low Reynolds number ( $Re$ ), weak IT flow is replaced by a laminar regime before the barrier of EIT dynamics is established with the increase of elasticity, whereas, at moderate $Re$ , EIT-related SSP can get involved and survive from being relaminarized. This further explains the reason why relaminarization phenomenon is observed for low $Re$ while the flow directly enters MDR and EIT at moderate $Re$ . Moreover, with the proposed energy picture, the newly discovered phenomenon that streamwise velocity fluctuations lag behind those in the wall-normal direction can be well explained. The repictured SSP certainly justifies the conjecture that IT nature is gradually replaced by that of EIT in DRT with the increase of elasticity.

Viscoelasticity-Induced Instability in Plane Couette Flow at Very Low Reynolds Number

“…This numerical procedure has been fully established for the Newtonian turbulent channel flow by Abe et al [36]. As for the constitutive equations with the Giesekus model, a flux limiter of the MINMOD scheme is adopted to approximate the spatial derivatives in the advective terms; thus, an artificial diffusive term is not included, as first introduced by Yu and Kawaguchi [37] and commonly used even in recent works [38][39][40][41]. The periodic boundary conditions are applied in x and z: u(L x , y, z) = u(0, y, z) and u(x, y, L z ) = u(x, y, 0).…”

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

“…The above two viewpoints give completely different explanations for the MDR phenomenon, and both of them seem reasonable since the hibernation state and EIT regime all can provide a barrier to prevent laminarization for DRT. In addition, recent studies (Zhu & Xi 2021;Zhang et al 2022) found that the dynamics continue to develop with an increase of Wi even if the flow enters the MDR state. Considering that the MDR limit can be exceeded at low Re (Choueiri et al 2018;Pereira et al 2019), it is very necessary to reexamine the universality of the MDR phenomenon -the same MDR limit for different polymer solution properties.…”

“…Through decomposing pressure fluctuations into rapid, slow and polymer parts, Terrapon, Dubief & Soria (2015) confirmed that those small-scale spanwise vortex structures associated with sheets are driven by polymers directly. Recently, we focused on the anisotropy in EIT and pictured the self-sustaining energy process (see Zhang et al 2022). It was found that sheet-like structures in the streamwise direction are caused by the interaction between polymers and turbulent fluctuations, and work done by elastic stress provides energy for their maintenance.…”

“…The pioneering experiments and numerical simulations by Samanta et al (2013) and Dubief et al (2013) found that when the flow enters the MDR state with an increase of Wi, DRT flows show similar flow characteristics as observed in EIT -trains of spanwise vortices accompanied by sheets of polymer extension. Recently we found that the DRT flows of Oldroyd-B fluid show the characteristics of centre-mode-dominated structures in EIT -quasi-arrow-like extension structures through direct numerical simulation (DNS) at high Wi (see Zhang et al 2021aZhang et al ,b, 2022. By adjusting the concentration of the polymer solution in pipe flow experiments at low Re, Choueiri et al (2018) found that IT-related dynamics could be eliminated and the flow turns to be a laminar regime breaking through the MDR limit with an increase of polymer concentration.…”

“…Based on this, we re-pictured DRT and constructed a self-sustaining cycle for DRT where dynamics of IT and EIT coexist in the flow. It turned out that IT-related dynamics almost disappear at the MDR state (Zhang et al 2022).…”