Vortex merging and splitting events in viscoelastic Taylor–Couette flow

Abstract

Recent experiments have reported a novel transition to elasto-inertial turbulence in the Taylor–Couette flow of a dilute polymer solution. Unlike previously reported transitions, this newly discovered scenario, dubbed vortex merging and splitting (VMS) transition, occurs in the centrifugally unstable regime and the mechanisms underlying it are two-dimensional: the flow becomes chaotic due to the proliferation of events where axisymmetric vortex pairs may be either created (vortex splitting) or annihilated (vortex merging). In this paper, we present direct numerical simulations, using the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive equation to model the polymer dynamics, which reproduce the experimental observations with great accuracy and elucidate the reasons for the onset of this surprising dynamics. Starting from the Newtonian limit and increasing progressively the fluid's elasticity, we demonstrate that the VMS dynamics is not associated with the well-known Taylor vortices, but with a steady pattern of elastically induced axisymmetric vortex pairs known as diwhirls. The amount of angular momentum carried by these elastic vortices becomes increasingly small as the fluid's elasticity increases and it eventually reaches a marginal level. When this occurs, the diwhirls become dynamically disconnected from the rest of the system and move independently from each other in the axial direction. It is shown that vortex merging and splitting events, along with local transient chaotic dynamics, result from the interactions among diwhirls, and that this complex spatio-temporal dynamics persists even at elasticity levels twice as large as those investigated experimentally.

Experimental insights into elasto-inertial transitions in Taylor–Couette flows

“…This leads to a transition sequence EITfalse→FPfalse→DWfalse→CF. Recent DNS simulation by [41], however, indicated that the deceleration of the inner cylinder is not a necessary condition to achieve DW, and they can also appear for increasing elasticity at a fixed normalRe. As their name implies, each DW comprises two concentrated vortices with a narrow but strong inflow boundary between them.…”

“…In-plane flow visualization by [50–52] allowed for an early qualitative experimental description of what were later described (numerically) as near-wall Görtler vortices [39,130], albeit for a different normalRe range. This highlights the need for more thorough experimental PIV-based investigations to complement recent DNS simulations [39–41,92,152] on the role of elasticity and its interaction with inertia-driven effects. A significant part of the effect of non-negligible inertia on the nature of ET is the modification of the TDR regime through measurements of friction and torque characteristics, expanding the work of [48] on non-colloidal particle suspensions.…”

“…Each vortex pair is independent to other solitons, separated from each other by regions of purely laminar Couette flow. This asymmetry between inflow and outflow regions is characteristic of the DW instability [ 41 , 67 , 92 ]. At the centre of the inflows, the fluid initially accelerates near the outer cylinder, reaches a maximum velocity at the mid-gap, and then decelerates.…”

“…Several researchers have examined the turbulent decay exponent, , in EIT in channel and TC flow. In the channel flow, the estimates for include or [ 37 ], [ 38 ], and in TC, values of [ 39 ], [ 40 ] and [ 41 ] have been reported. The estimates of found in various studies are quite scattered but fall in the range to for both systems.…”

Turbulent Taylor–Couette flow of dilute polymeric solutions: a 10-year retrospective

“…A comprehensive experimental study of transition pathways to EDT in TC flow (or labelled as EIT) over a broad range El∼10−1−102, has been undertaken by Balabani and co-workers [59,60,75]. Specifically, they have shown a new merge-split transition to EDT via superposition of the base TV merging and splitting events on a rotating standing waves flow state [76]. Recently, a reverse transition to EDT flow was also reported in viscoelastic spanwise-rotating plane Couette flow (RPCF), which is the curvature free limit of TC flow [58].…”