Longitudinal heat dispersion in porous beds with real-gas flow

Abstract

The forced convective flow of a slightly superheated vapor through a packed bed is analyzed numerically for low-to-moderate pressure range by implementing real-gas and ideal-gas models. The porous bed was taken to be composed of uniformly sized, randomly packed spherical particles. The flow of the gas through the packed bed was limited to the range of applicability of the Ergun-Forchheimer relation. The significance of longitudinal thermal dispersion was examined by alternately implementing and omitting this aspect which was incorporated in the effective thermal conductivity of the vapor phase. The use of a real-gas model at elevated pressures was found to be an important aspect for accurate results. The longitudinal thermal dispersion effects were found to have minor significance at high Reynolds numbers. The use of separate energy equations for the solid and vapor phases was observed to be justified by the studies performed. Nomenclature asr = specific surface area of the bed particles, m2/m3 cp = specific heat at constant pressure, J/kg-K dp = particle diameter, m F = geometric factor defined in Eq. (8) hsr = fluid-to-particle heat transfer coefficient, W/m2-K K = permeability, m2 k = thermal conductivity, W/m-K L = length of the packed bed, m P = pressure, N/m2 Pr = Prandtl number, jjicp/k R = gas constant for Refrigerant-11, J/kg-K Rep = particle Reynolds number, updp/im T = temperature, K t = time, s u = velocity component in x direction, m/s Z = compressibility factor e = porosity IJL = absolute viscosity, kg/m-s p = density, kg/m3 { ) = local volume average of a quantity Subscripts