Nonlinear convective transport in packed beds
The modeling of heat- and mass-transport processes through fluid-saturated disordered packed beds is undertaken with emphasis on the effect of their random microstructure. Considering the interstitial transport as a stochastic process, a phenomenological model is discovered for the drag which correctly matches the Reynolds-number dependence of the pressure drop versus flow-rate law. The quadratic (Forchheimer) inertial extension of the drag is attributed to Reynolds-Stress-like terms. Given the statistics of the interstitial velocity field, the average (effective) equations governing the transport of a conservative scalar (e.g. heat or concentration) through a randomly packed bed is derived. The effective transport coefficient can be approximated by the sum of a stagnant and a (hydrodynamic) dispersive component, the latter depending linearly on the magnitude of the local filtration velocity. Both the inertial and the dispersive effect are taken into consideration in the numerical study of the porous Bernard problem. In addition to the Prandtl number of the porous medium, the ratio of bead diameter to layer thickness is proven to be a significant additional parameter of the problem that can explain the divergence of the correlations of Nusselt as a function of a Rayleigh number.
- Research Organization:
- California Univ., Los Angeles (USA)
- OSTI ID:
- 6976797
- Country of Publication:
- United States
- Language:
- English
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