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Statistics of velocity fluctuations in a homogeneous liquid fluidized bed

Elise Alméras

Frédéric Risso

Olivier Masbernat

Rodney O. Fox

  • FR FERMAT, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France

  • Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, Toulouse, France

  • Laboratoire de Génie Chimique (LGC), CNRS-INPT-UPS, Université de Toulouse, 31400 Toulouse, France

  • Department of Chemical and Biological Engineering, Iowa State University, 618 Bissell Road, Ames, Iowa 50011-1098, USA

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Phys. Rev. Fluids 6, 034301 – Published 8 March, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.034301

Abstract

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction αp. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of αp and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of αp, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low αp. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions.

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Phys. Rev. Fluids 6, 034301– Published 8 March, 2021
  • Received 29 September 2020
  • Accepted 4 February 2021
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