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Register a new userElastic turbulence in two-dimensional Taylor-Couette flows
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We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model, also performed at high Weissenberg numbers with the program OpenFOAM. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law $Phi propto (mathrm{Wi} -mathrm{Wi}_c)^{gamma}$ with $mathrm{Wi}_c=10$ and $gamma = 0.45$. The power spectrum of the velocity fluctuations shows a power-law decay with a characteristic exponent, which strongly depends on the radial position. It is greater than two, which we relate to the dimension of the geometry.
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Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow and with a recent theoretical model. This suggests that, contrary to the prevailing view, turbulence in linearly stable shear flows may be generically transient.
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We create a highly controlled lab environment-accessible to both global and local monitoring-to analyse turbulent boiling flows and in particular their shear stress in a statistically stationary state. Namely, by precisely monitoring the drag of strongly turbulent Taylor-Couette flow (the flow in between two co-axially rotating cylinders, Reynolds number $textrm{Re}approx 10^6$) during its transition from non-boiling to boiling, we show that the intuitive expectation, namely that a few volume percent of vapor bubbles would correspondingly change the global drag by a few percent, is wrong. Rather, we find that for these conditions a dramatic global drag reduction of up to 45% occurs. We connect this global result to our local observations, showing that for major drag reduction the vapor bubble deformability is crucial, corresponding to Weber numbers larger than one. We compare our findings with those for turbulent flows with gas bubbles, which obey very different physics than vapor bubbles. Nonetheless, we find remarkable similarities and explain these.
Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $mathcal{O}(10^9)$ and the roughness width is varied between $0.47leq tilde{s}=s/d leq 1.23$, where $d$ is the gap width. Experimentally, we explore $text{Ta}=mathcal{O}(10^{12})$ and $0.61leq tilde s leq 3.74$. For both approaches the radius ratio is fixed at $eta=r_i/r_o = 0.716$, with $r_i$ and $r_o$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport as function of $tilde s$. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.
We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylors hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static point-like numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylors frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly non-homogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.
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