In the present work, a multiscale modeling approach has been followed in which the entire process has been modeled for a single droplet in two dimensions. The idea is to solve the detailed model at the droplet-particle scale from first principles so that an “effective” correlation for the heat transfer with evaporation from the droplet may be used as an input in a larger “reactor-scale” model (e.g. Gupta and Subbarao, 2001, 2003; Nayak et al., 2005). Presently, two mechanisms of heat transfer are considered: convective heat transfer from the gas phase, and heat transfer to the droplet in the presence of solid catalyst particles.
For heat transfer from the gas phase, it is found that hydrodynamics of circulation inside the droplet results in minimum temperature somewhere in between the outer surface and center depending on the conductivity and circulation rate. For example, for the gas phase velocity of 6.1m/s it occurs at 0.7*R (radius) distance from the center. To account for the droplet shrinkage a quasi-steady state model is used in which heat transfer coefficients are obtained for a stepwise change in the droplet diameter. Time scales for heat up without vaporization and with vaporization are compared. Resulting Nusselt number correlations are compared with an earlier published model of heat transfer from evaporating droplets (Buchanan 1994).
For modeling the heat transfer from the solid phase to the evaporating droplet, a “level set (CFD) method” is used for solving the compressible two-phase problem. The basic advantage of level set method is in tracking the interface without involving the numerically intensive moving mesh (Osher and Sethian, 1988). A source term is included in the incompressible continuity equation, which is then coupled with the heat transport equation to model the entire vaporization process (Juric and Tryggvason, 1998). Hydrodynamics resulting from the phase change process is obtained. Heat transfer rates for the case of no vaporization and with vaporization are compared. Nusselt number correlations for heat transfer from the solid particles are reported.
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