Candelier, Fabien and Mehlig, Bernhard and Magnaudet, Jacques
Time-dependent lift and drag on a rigid body in a viscous steady linear flow.
(2019)
Journal of Fluid Mechanics, 864. 554-595. ISSN 0022-1120
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(Document in English)
PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 526kB |
Official URL: https://doi.org/10.1017/jfm.2019.23
Abstract
We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.
Item Type: | Article |
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HAL Id: | hal-02052051 |
Audience (journal): | International peer-reviewed journal |
Uncontrolled Keywords: | |
Institution: | Other partners > Aix-Marseille Université - AMU (FRANCE) French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE) Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE) Other partners > Göteborgs Universitet (SWEDEN) |
Laboratory name: | |
Statistics: | download |
Deposited On: | 22 Feb 2019 10:56 |
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