Continuum Simulations of Multiphase Heat and Mass Transfer in Wet Granular Mixtures Modeled As Separated Phases

Heat and mass transfer considerations in multiphase flows such as wet granular mixtures, where solid, liquid, and gas co-exist, are important in many industrial processes such as pharmaceuticals manufacturing and petrochemicals processing. They are also paramount in key industrial processes involving solvent removal by thermal drying of powders and wet granules. Continuum simulations involve solving the averaged equations for conservation of mass, momentum, and energy by treating the granular medium as a continuum. The interphase exchange terms are equal but of opposite signs in the phases, and accurate solutions of the coupled set of equations require solving them in terms of transformed variables that span a subspace of reduced dimension. This is because the singular value decomposition of the matrix corresponding to the coupled set of equations shows it is singular. In this study, we propose a novel iterative solution procedure to solve the coupled heat diffusion equation in three phases if one or more singular values of the matrix are zero. Singular value decomposition is used to solve the matrix in a reduced subspace by eliminating the zero singular values, and the corresponding columns of the left and right singular vectors. Continuum multiphase simulations of heat transfer between solid, liquid, and gas phases, and mass transfer between the liquid and gas phases in a stationary granular bed, are performed using the proposed iterative procedure. Further realities of particle drying due to solvent boiling and wet bulb evaporation mechanisms are incorporated into the coupled heat and mass transfer Computational Fluid Dynamics (CFD) simulation to obtain realistic results. The numerical results obtained using the multiphase continuum simulations are verified using a previously developed analytical model for heat transfer in a cylinder filled with stationary wet granular material, to establish accuracy.