A Numerical Study of Thermal Dispersion in Porous Media

Thermal dispersion in convective flow in porous media has been numerically investigated using a two-dimensional periodic model of porous structure. A macroscopically uniform flow is assumed to pass through a collection of square rods placed regularly in an infinite space, where a macroscopically linear temperature gradient is imposed perpendicularly to the flow direction. Due to the periodicity of the model, only one structural unit is taken for a calculation domain to resolve an entire domain of porous medium. Continuity, Navier-Stokes and energy equations are solved numerically to describe the microscopic velocity and temperature fields at a pore scale. The numerical results thus obtained are integrated over a unit structure to evaluate the thermal dispersion and the molecular diffusion due to tortuosity. The resulting correlation for a high-Peclet-number range agrees well with available experimental data.

[1]  John F. Brady,et al.  Dispersion in fixed beds , 1985, Journal of Fluid Mechanics.

[2]  Adrian Bejan,et al.  Forced convection in banks of inclined cylinders at low Reynolds numbers , 1994 .

[3]  J. J. Fried,et al.  Dispersion in Porous Media , 1971 .

[4]  A. Nakayama,et al.  Numerical Modelling of Heat and Fluid Flow in a Porous Medium , 1994 .

[5]  R. Aris.  On the dispersion of a solute in a fluid flowing through a tube , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  S. Whitaker,et al.  One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems , 1993 .

[7]  D. Kunii,et al.  Studies on effective thermal conductivities in packed beds , 1957 .

[8]  R. E. Larson,et al.  A periodic grain consolidation model of porous media , 1989 .

[9]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[10]  Akira Nakayama,et al.  PC-aided numerical heat transfer and convective flow , 1995 .

[11]  Stephen Whitaker,et al.  Dispersion in pulsed systems—I: Heterogenous reaction and reversible adsorption in capillary tubes , 1983 .

[12]  D. A. Edwards,et al.  Dispersion of inert solutes in spatially periodic, two-dimensional model porous media , 1991 .

[13]  Ruben G. Carbonell,et al.  Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution , 1985 .

[14]  P. Cheng,et al.  Heat Transfer in Geothermal Systems , 1979 .

[15]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[16]  O. Coulaud,et al.  Numerical modelling of nonlinear effects in laminar flow through a porous medium , 1988, Journal of Fluid Mechanics.

[17]  Stephen Whitaker,et al.  Dispersion in pulsed systems—III: Comparison between theory and experiments for packed beds , 1983 .

[18]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[19]  John F. Brady,et al.  The effect of order on dispersion in porous media , 1989, Journal of Fluid Mechanics.