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Mechanism of kinetic energy transfer in homogeneous bidisperse gas-solid flow and its implications for segregation

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Subramaniam, Shankar

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Most gas–solid flows encountered in nature and industrial applications are polydisperse, and the segregation or mixing of particle classes in polydisperse gas–solid flows is a phenomenon of great practical importance. A statistically homogeneous gas–solid flow with a bidisperse distribution (in size or density) of particles is a canonical representation of polydisperse flows. A key feature that distinguishes the bidisperse flow from its monodisperse counterpart is the exchange of momentum and kinetic energy between the particle classes due to collisions, which are important for applications outside the very dilute regime. The average exchange of linear momentum between particle classes due to collisions occurs through the particle–particle drag term. The conservation equations for average momentum corresponding to each particle class can be used to deduce the average slip velocity between the particle size and density classes, which is the signature of particle segregation. In this canonical problem, the steady value of particle mean slip velocity results from a balance between three terms, each in turn involving the body force or the mean fluid pressure gradient, the gas–particle drag, and the particle–particle drag. The particle–particle drag depends on the particle velocity fluctuations in each class [Louge, M. Y. *et al.*, “The role of particle collisions in pneumatic transport,” J. Fluid Mech. **231**, 345–359 (1991)], thereby coupling the mean and second–moment equations. For monodisperse gas-solid flows the transfer of kinetic energy from the mean to second-moment equations was explained by Subramaniam and co-workers who proposed the conservation of interphase turbulent kinetic energy transfer principle [Xu, Y. and Subramaniam, S., “Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows,” Phys. Fluids **19**(8), 085101 (2007)], and this was subsequently verified by particle–resolved direct numerical simulation [Mehrabadi, M. *et al.*, “Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas-solid flow: Fixed particle assemblies and freely evolving suspensions,” J. Fluid Mech. **770**, 210–246 (2015)]. The principle shows that the power supplied to the mean flow to maintain the mean slip velocity between solid and gas phases partitions into transfer terms that supply power to maintain fluid and particle velocity fluctuations. One question this paper seeks to answer is what the role of particle–particle drag is in this transfer process in bidisperse flows, given that the particle–particle drag does not appear in the mixture mean momentum conservation equation for the solid phase. The conservation equations for mean momentum and kinetic energy in each particle class are coupled through interphase and interclass exchange terms. This coupling between the mean momentum and kinetic energy equations due to interphase and interclass interactions is explained by extending the conservation of interphase turbulent kinetic energy transfer principle originally proposed for monodisperse gas-solid flows to bidisperse suspensions. This explains the role of particle–particle drag in the partitioning of kinetic energy in velocity fluctuations between particle classes and provides insight into segregation and mixing of particle classes in industrial devices.

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This article is published as Mehrabadi, Mohammad, and Shankar Subramaniam. "Mechanism of kinetic energy transfer in homogeneous bidisperse gas-solid flow and its implications for segregation." *Physics of Fluids* 29, no. 2 (2017): 020714. DOI: 10.1063/1.4974502. Posted with permission.