Modelling mesoscale turbulence in clustered gas–solid flows based on particle-resolved simulation data

Gas-phase turbulence in a bubbling gas–solid fluidised bed is modelled using the data from particle-resolved direct numerical simulations. The subgrid particle-induced turbulent kinetic energy (TKE) is modelled as a function of filter width, filtered solid volume fraction, particle Reynolds number and filtered gas-phase strain rate tensor. Within the volume-filtered framework, we demonstrate that the fluid Reynolds stress models originally developed for a homogeneous system remain applicable to the inhomogeneous fluidised bed, provided that the inhomogeneous drag and particle-induced TKE models are used for the dissipation rate interfacial term. An algebraic model for the anisotropy of gas-phase velocity variance is developed by simplifying the proposed Reynolds stress equation model, which incorporates the effects from both filtered slip velocity and filtered fluid strain rate. The new models are shown to agree well with the direct numerical simulation data of clustered particle settling systems, indicating good applicability of our models for various clustered particle-laden flows.