Reynolds number porous medium

Here again, the usual porous medium Reynolds number is defined by Eq. (13-12) without the numerical factor (2/3) ... 

The hydraulic diameter and the superficial velocity can be introduced into the definition of the porous medium Reynolds number to give Eq. 3.19 ... 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

At high Reynolds numbers (high turbulence levels), the flow is dominated by inertial forces and wall roughness, as in pipe flow. The porous medium can be considered an extremely rough conduit, with s/d 1. Thus, the flow at a sufficiently high Reynolds number should be fully turbulent and the friction factor should be constant. This has been confirmed by observations, with the value of the constant equal to approximately 1.75 ... 

An expression that adequately represents the porous medium friction factor over all values of Reynolds number is... 

Washing. As ice moves upward through the column, it behaves as an unconsolidated porous medium and carries brine with it, held by viscous and capillary forces. The flow is entirely laminar, because the Reynolds number based on particle diameter is always less than 0.05. The brine is carried thus at the surface and in the fillets between the particles. The downward flowing wash water moves between the particles and mixes with the brine mainly by molecular diffusion. Salt will diffuse from the brine to the wash water. 

Rep Reynolds number based on particle diameter in a porous medium... 

The usage of the flow equations can be summarized as follows. For the case of a one-dimensional single fluid flow, either equation 106 or 108 can be used to predict the normalized pressure drop factor in a porous medium. The determined normalized pressure drop factor is related to the pressure drop by equation 11. For the simple case of packed spherical beads, ds and e are known a priori. The Reynolds number is evaluated using equation 93. For random packs of nonspherical particles, the particle s sphericity needs to be known. Equation 73 can be used to estimate ds. For the case of consolidated porous medium, one can estimate ds from the knowledge of the intrinsic permeability using equation 14. 

Absolute and Effective Permeability. The permeability of a porous medium is a measure of the fluid conductivity of the medium that determines the flow rate at a given pressure gradient. The permeability of a porous medium can be determined using Darcy s equation as follows. The porous medium, usually a core, is saturated under vacuum with a fluid of a known viscosity. The fluid is then injected into the core in a linear mode at a constant flow rate under isothermal flow conditions. If the porous medium is homogeneous, isotropic, the core is placed in horizontal direction, and Reynolds number of the injected fluid is less than unity, then Darcy s law can be used to determine permeability. Darcy s law is... 

Figure 20. Flow resistance vs eynolds number (Re) for a PAA copolymer of ultrahigh molecular weight (M 27 X JO ) in 0.5 M NaCl a, first run b, second run after forcing the solution through the porous medium at Re = 15 c, third run after forcing the solution through at Re = 20 d, Newtonian fluid. The onset Reynolds number where the non-Newtonian effect sets in (Reo) is indicated for curve a. (After ref. 22.)...

No analytical solution is available for the modified Brinkman momentum equation (Eq. 13), which can only be solved numerically. However, due to the low Reynolds number flow in the microcapillaries, we can safely ignore the high Reynolds number term, i.e., pF4>u / /K 0. To emphasize only the electrokinetic wall effect, we can further assume that the porosity is uniform in the porous medium, i.e., cj) = Under these... 

The relation is usually considered valid for creeping flow 4iere the Reynolds number, as defined for a porous medium, is less than one. The Reynolds number in en conduit flow is the ratio of inertial to viscous forces and is defined in terms of a characteristic length perpendicular to flow for the system. Using four times the hydraulic radius to replace the length perpendicular to flow and eorrecting the velocity with porosity yields a Reynolds number in the form ... 

The flow of resin through a fibrous reinforcement is usually considered to follow Darcy s law for flow through a porous medium. Assuming low Reynolds number flow, a Newtonian fluid, and that the impregnated section of the reinforcement is fully saturated, Darcy s law can be written... 

Hill, R.J., Koch, D.L., 2002. Moderate-Reynolds-number flow in a wall-bounded porous medium. J. Fluid Mech. 453, 315-344. 

The concept of a porous medium supposes that the grains forming the porous medium are small. This notion is only meaningful in the context of a flow inside the porous medium. Small signifies that the flow inside the porous medium is slow. The Reynolds number, calculated from the velocity of the flow inside the porous medium, the characteristic size of the pores and the kinematic viscosity of the fluid, should be sufficiently small for the flow inside the porous medium to be laminar. 

Darcy s law is vahd only for a sufficiently slow flow, which is laminar inside the porous medium. The validity criterion for Darcy s law is expressed by a Reynolds number, written using the length scale -Jk that characterizes the porous medium. The following criterionfor the validity of Darcy s law is generally agreed upon ... 

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