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Communication Dans Un Congrès Année : 2020

Settling behaviour of particles in Rayleigh-Benard convection

Résumé

<p>Our numerical study evaluates the settling rate of solid particles, suspended in a highly&#160;<br>vigorous, finite Prandtl number convection of a bottom heated fluid. We explore a broad&#160;<br>range of model parameters, covering particle types appearing in various natural systems,&#160;<br>and focus in particular on crystals nucleating during the cooling of a magma ocean. The&#160;<br>motion of inertial particles within thermal convection is non-trivial, and under idealized&#160;<br>conditions of spherical shaped particles with small Reynolds number it follows the&#160;<br>Maxey-Riley equation (Maxey and Riley, 1983). Two scaling laws exist for the settling&#160;<br>velocities in such system: for particles with small but finite response time, the Stokes'&#160;<br>law is typically applied. For particles with a vanishing response time, a theoretical model&#160;<br>was developed by Martin and Nokes (1989), who also validated their prediction with analogue&#160;<br>experiments.&#160;</p><p>We develop a new theoretical model for the settling velocities. Our approach describes&#160;<br>sedimentation of particles as a random process with two key constituents: i) transport&#160;<br>from convection cells into slow regions of the flow, and ii) the probability of escaping&#160;<br>slow regions if a particle enters them. By quantifying the rates of these two processes,&#160;<br>we derive a new equation that bridges the gap between the above mentioned scaling laws.&#160;<br>Moreover, we identify four distinct regimes of settling behaviour and analyze the lateral&#160;<br>distribution of positions where particles reach the bottom boundary. Finally, we apply our&#160;<br>results to the freezing of a magma ocean, making inferences about its equilibrium vs&#160;<br>fractional crystallization. The numerical experiments are performed in 2D cartesian geometry&#160;<br>using the freely available code CH4 (Calzavarini, 2019).</p><p>References:<br>Maxey, M. R. and Riley, J. J.(1983): Equation of motion for a small rigid sphere in a nonuniform flow.&#160;<br>Physics of Fluids, 26(4), 883-889.</p><p>Martin, D and Nokes, R (1989): A fluid-dynamic study of crystal settling in convecting magmas.&#160;<br>Journal of Petrology, 30(6), 1471-1500.</p><p>Calzavarini, E (2019): Eulerian&#8211;Lagrangian fluid dynamics platform: The ch4-project. Software Impacts, 1, 100002.</p>
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Dates et versions

hal-04401722 , version 1 (17-01-2024)

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Vojtech Patocka, Enrico Calzavarini, Nicola Tosi. Settling behaviour of particles in Rayleigh-Benard convection. vEGU General Assembly 2020, May 2020, Vienna, Austria. ⟨10.5194/egusphere-egu2020-5908⟩. ⟨hal-04401722⟩

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