Transition to turbulence via flame patterns in viscoelastic Taylor–Couette flow

Abstract

Transition to inertio-elastic turbulence in Taylor-Couette flow with shear-thinning and viscoelastic polymer solutions is investigated when the rotation rate of the inner cylinder is increased and the outer cylinder is fixed. In two polymer solutions of PEO with elastic number E ∈ {0.16; 0.30}, the first instability of the circular Couette flow appears as spirals propagating in opposite directions along the axis of cylinders. Just above the onset of the spirals pattern, the localized solitons of the strong radial inflow called flamelike flow appear abruptly inside waves. The abrupt apparition of the flame-like flow is the signature of the subcritical transition to turbulence. The number of the flame-like flows follows a Gaussian distribution at given Ta number. The averaged number of the flame-like flow increases as the rotation rate is increased and it saturates in the inertio-elastic turbulence. The soliton of the strong radial inflow (flame-pattern) is created when it amplitude exceeds a critical value. The distribution of the critical amplitudes of the flame patterns follows a Gaussian law at given Ta number. The transition to turbulence is described by a mathematical model based on an error function of the probability to observe a strong inflow (flame-pattern). The statistical data of the critical amplitude and the probability to observe the flame patterns are used with the mathematical model in order to determine the stability curve of the transition to turbulence. The analysis of the transition to turbulence is completed by the characterization of the spatiotemporal properties.

Vortex merging and splitting events in viscoelastic Taylor–Couette flow

“…Our simulations show that, unlike other transition scenarios to elasto-inertial turbulent states (e.g. the transition via flame patterns (Latrache & Mutabazi 2021) or the transition driven by defects Latrache et al. 2016), the transition to the VMS regime does not involve any three-dimensional instability and it is associated with instabilities of an axisymmetric vortex pattern which are induced solely by elastic effects.…”

“…The DM transition takes place at low-to-moderate values () and values quite below those at which the onset of TVF happens in the Newtonian case. The second type of transition, known as transition via flames (Latrache & Mutabazi 2021), occurs at similar but larger values (). Again, the transition is initiated from the RB pattern, which in this case undergoes an instability that results in the emergence of flame-like structures.…”

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

“…All images are space-time diagrams (with time on the x-axis and the axial distance on the y-axis) constructed from flow visualization, and represent steady-state cases for which the control parameters were constant. Illustrations were taken from [23,45,47,69,81]. (Online version in colour.…”

Diffusion and convection in nature

“…In the paper by Bingchuan Nie, Yutao Shao and Feng Xu [ 10 ], the authors explore the impact of boundary conditions when isothermal and isoflux conditions coexist in different parts of the section of a wall, with possible applications to the study of building envelopes and their thermal performance. In the paper by Noureddine Latrache and Innocent Mutabazi [ 11 ], the transition to turbulence is investigated in Taylor–Couette flow of a viscoelastic polymer solution by varying the rotation speed of the inner cylinder of the apparatus. A similar apparatus is utilised in the paper by Awasthi and Hoshoudy [ 12 ], where the impact of heat and mass transfer on instability are investigated.…”