Self-sustaining cycle of purely elastic turbulence

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

“…Specifically, the first three-dimensional DNS of purely ET in TC flow of dilute polymer solutions has been realized via two different transition routes: (i) a novel flow transition pathway from EDT to solitary vortex (or diwhirls) and eventually to ET as Re is progressively decreased over seven orders of magnitude, i.e. from 1000 to 0.0001 at a constant Wi=30 [25], and (ii) from a laminar base state to a diwhirls dominated flow state and finally to ET with increasing Wi from 0 to 120 at very small Re=0.01 [26]. As depicted in figure 2 a , ET is dominated by highly stretch flow-oriented structures (Q<0).…”

“…As depicted in figure 2 a , ET is dominated by highly stretch flow-oriented structures (Q<0). Specifically, as depicted in figure 3 e – g , the dominant spatio-temporal flow feature in the purely ET regime is that of unsteady diwhirls near the outer wall and axially and azimuthally travelling elastic waves in the inner wall region, respectively (see the space–time plots in references [25,26]). Moreover, the azimuthal elastic wave speed is shown to be nearly 50 times faster than the axial elastic waves, and the speed scales as Wi0.71 [26], which is consistent with recent results obtained by experiments in viscoelastic channel flow with obstacles [72].…”

“…Specifically, as depicted in figure 3 e – g , the dominant spatio-temporal flow feature in the purely ET regime is that of unsteady diwhirls near the outer wall and axially and azimuthally travelling elastic waves in the inner wall region, respectively (see the space–time plots in references [25,26]). Moreover, the azimuthal elastic wave speed is shown to be nearly 50 times faster than the axial elastic waves, and the speed scales as Wi0.71 [26], which is consistent with recent results obtained by experiments in viscoelastic channel flow with obstacles [72]. In addition, in the ET flow state, both temporal and spatial spectra display a steep power law decay in the frequency and wavenumber domain, especially at the inner half gap where the flow exhibits significant turbulent characteristics (figure 4).…”

“…In this inertialess turbulent flow state, turbulence is generated solely due to the highly nonlinear coupling of flow and microstructure evolution at very small Re ≪1 and at sufficiently large Wi≫1 [19–21]. A hall mark flow structure of ET is a highly asymmetric radial velocity distribution induced by the large-scale coherent structure dubbed ‘diwhirls’ that results in a strong extensional inflow and commensurate significant polymer stretch, which is now understood to be a key ingredient of the self-sustaining cycle of ET [20,21,25,26]. The two-dimensional numerical simulations of ET in TC flow with the Oldroyd-B constitute model performed by Buel et al.…”

“…However, the two-dimensional simulations cannot capture the axial dynamics of diwhirls, leaving the underlying turbulent dynamics associated with this important and unique flow structure in the ET flow regime far from understood. The first three-dimensional DNS of ET has just been performed by Liu, Khomami and co-workers with a finitely extensible nonlinear elastic-Peterlin (FENE-P) constitute model [25,26]. Specifically, it is demonstrated that by increasing El at vanishing Re, the incipient purely elastic instability gradually leads to a chaotic flow composed of unsteady diwhirls that originate in the outer wall region and almost span the entire gap, in addition to axially and azimuthally travelling elastic wave flow patterns that populate the inner wall region and extend to half of the gap width.…”