Filtered models for scalar transport in gas–particle flows

• We develop filtered models for scalar transport in gas–particle flows.
• Model for intraphase scalar transport similar to Smagorinsky model in turbulence.
• We calculate filtered Prandtl/Schmidt numbers for each phase.
• Model for interphase scalar transport is similar to that for interphase drag.
• Orders of magnitude reduction in filtered interphase scalar transport coefficient.

We employ a kinetic-theory based two-fluid model to develop a filtered two-fluid model for scalar transport in gas–particle flows. The filtering procedure gives rise to terms describing the filtered interphase heat/mass transfer and filtered scalar diffusion, which need to be constituted in order to close the filtered transport equations. In this work, the closure for these terms is accomplished by performing fine-grid simulations of the two-fluid model in a two-dimensional periodic domain. Filtered scalar diffusion is investigated by imposing a lateral mean gradient in the scalar for each phase. Interphase energy/mass transport is investigated by prescribing a heat/species source (sink) in the solids (gas) phase, such that the energy/species content of the mixture is preserved. The variation of the filtered transport coefficients with respect to filtered particle volume fraction, and scaling with respect to filter size, filtered scalar shear rate, and filtered slip velocity is discussed. We find the filtered interphase heat transfer coefficient to be as much as two orders of magnitude smaller than the microscopic interphase heat transfer coefficient. The model for filtered scalar diffusion is found to have a form very similar to that calculated for single phase turbulent flows. We also calculate the filtered Prandtl number for each phase.