(493b) Filtered Model for Energy Transport in Gas-Solid Flows

We employ a kinetic-theory¹ based
two-fluid model to develop a filtered two-fluid model² for energy
transport in gas-solid flows. The filtering procedure gives rise to terms describing
the filtered interphase heat transfer and filtered thermal 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.³
Filtered thermal diffusion is investigated by imposing a lateral mean gradient
in the temperature of each phase. Interphase energy transport is investigated
by prescribing a heat source(sink) in the solids(gas) phase, such that the
energy content of the mixture is preserved and a local temperature difference
is established between the two phases. 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 variation of the filtered
transport coefficients with respect to filtered particle volume fraction,
and scaling with respect to filter size, is discussed.

¹ Gidaspow, D. Multiphase Flow and Fluidization;
Academic Press: San Diego, CA 1994.

²Agrawal, K., Loezos, P.N.,
Syamlal, M., Sundaresan, S. The role of meso-scale structures in rapid
gas-solid flows. J. Fluid Mech. 2001,
445, 151-185.

³ Igci, Y., Andrews, A.T. IV,
Sundaresan, S., Pannala, S., O'Brien, T. Filtered Two-Fluid Models for
Fluidized Gas-Particle Suspensions. AIChE
J. 2008, 54, 1431-1448.