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Register a new userA turbulent model of torque in von Karman swirling flow
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Authors
Nicolas Leprovost
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A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.
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We experimentally characterize the fluctuations of the non-homogeneous non-isotropic turbulence in an axisymmetric von Karman flow. We show that these fluctuations satisfy relations analogous to classical Fluctuation-Dissipation Relations (FDRs) in statistical mechanics. We use these relations to measure statistical temperatures of turbulence. The values of these temperatures are found to be dependent on the considered observable as already evidenced in other far from equilibrium systems.
We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank-Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Karman flow experiments in (F. Ravelet, A. Chiffaudel, and F. Daviaud, JFM 601, 339 (2008)) on a Cartesian grid. In these DNS, the flow is driven by two-counter rotating impellers fitted with curved inertial stirrers. We analyze the transition from laminar to turbulent flow by increasing the rotation rate of the counter-rotating impellers to attain the four Reynolds numbers 90, 360, 2000, and 4000. In the laminar regime at Reynolds number 90 and 360, we observe flow features similar to those reported in the experiments and in particular, the appearance of a symmetry-breaking instability at Reynolds number 360. We observe transitional turbulence at Reynolds number 2000. Fully developed turbulence is achieved at Reynolds number 4000. Non-dimensional torque computed from simulations matches correlations from experimental data. The low Reynolds number symmetries, lost with increasing Reynolds number, are recovered in the mean flow in the fully developed turbulent regime, where we observe two tori symmetrical about the mid-height plane. We note that turbulent fluctuations in the central region of the device remain anisotropic even at the highest Reynolds number 4000, suggesting that isotropization requires significantly higher Reynolds numbers.
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasi-stationary states.
We study magnetohydrodynamics in a von Karman flow driven by the rotation of impellers made of material with varying electrical conductivity and magnetic permeability. Gallium is the working fluid and magnetic Reynolds numbers of order unity are achieved. We find that specific induction effects arise when the impellers electric and magnetic characteristics differ from that of the fluid. Implications in regards to the VKS dynamo are discussed.
We study the melting dynamics of large ice balls in a turbulent von Karman flow at very high Reynolds number. Using an optical shadowgraphy setup, we record the time evolution of particle sizes. We study the heat transfer as a function of the particle scale Reynolds number for three cases: fixed ice balls melting in a region of strong turbulence with zero mean flow, fixed ice balls melting under the action of a strong mean flow with lower fluctuations, and ice balls freely advected in the whole flow. For the fixed particles cases, heat transfer is observed to be much stronger than in laminar flows, the Nusselt number behaving as a power law of the Reynolds number of exponent 0.8. For freely advected ice balls, the turbulent transfer is further enhanced and the Nusselt number is proportional to the Reynolds number. The surface heat flux is then independent of the particles size, leading to an ultimate regime of heat transfer reached when the thermal boundary layer is fully turbulent.
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