On the similarity of variable viscosity flows

Abstract : Turbulent mixing is ubiquitous in both nature and industrial applications. Most of them concern different fluids, therefore with variable physical properties (density and/or viscosity). The focus here is on variable viscosity flows and mixing, involving density-matched fluids. The issue is whether or not these flows may be self-similar, or self-preserving. The importance of this question stands on the predictability of these flows; self-similar dynamical systems are easier tractable from an analytical viewpoint. More specifically, self-similar analysis is applied to the scale-by-scale energy transport equations, which represent the transport of energy at each scale and each point of the flow. Scale-by-scale energy budget equations are developed for inhomogeneous and anisotropic flows, in which the viscosity varies as a result of heterogeneous mixture or temperature variations. Additional terms are highlighted, accounting for the viscosity gradients, or fluctuations. These terms are present at both small and large scales, thus rectifying the common belief that viscosity is a small-scale quantity. Scale-by-scale energy budget equations are then adapted for the particular case of a round jet evolving in a more viscous host fluid. It is further shown that the condition of self-preservation is not necessarily satisfied in variable-viscosity jets. Indeed, the jet momentum conservation, as well as the constancy of the Reynolds number in the central region of the jet, cannot be satisfied simultaneously. This points to the necessity of considering less stringent conditions (with respect to classical, single-fluid jets) when analytically tackling these flows and reinforces the idea that viscosity variations must be accounted for when modelling these flows.
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Submitted on : Thursday, October 5, 2017 - 3:36:55 PM
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L. Voivenel, L. Danaila, E. Varea, B. Renou, M. Cazalens. On the similarity of variable viscosity flows. Physica Scripta, IOP Publishing, 2016, 91 (8), pp.084007. 〈10.1088/0031-8949/91/8/084007〉. 〈hal-01611245〉



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