Page 222 - Fluid mechanics, heat transfer, and mass transfer

200 TWO-PHASE FLOW SYSTEMS

➢ Fibers and filtration media. ðvolume of the particleÞ
D p ¼
➢ Membranes. ðsurface area of the particleÞ
➢ Sintered metals.
¼ 6ð1 «Þ=F S S; ð7:6Þ
➢ Petroleum reservoirs.
where S is particle surface area per unit bed volume,
➢ Geological formations.
F S is the sphericity, and « is the void fraction of the
➢ Aquifers.
bed ¼ ratio of the void volume to the total volume
➢ Solid combustible materials such as coal, biomass,
of the bed. r and m are fluid density and viscosity,
and so on.
respectively.
➢ Mineral wool and urethane foam insulation Other equations are as follows:
materials.
➢ Regenerators used for heat recovery in furnaces. f p ¼ð150=N Rep Þ; N Rep 1ðKozeny--Karman equationÞ:
& Important parameters: ð7:7Þ
➢ D P for flow of incompressible and compressible
This equation is used for flow of very viscous fluids.
fluids through porous media: direct effect on
energy consumption. f p ¼ 1:75; N Rep 10; 000ðBurke--Plummer equationÞ:
➢ Diffusion through pores: in drying, catalyst beds,
ð7:8Þ
and adsorbents.
➢ Diffusion through membranes. . How is DP influenced by N Re in a packed bed?
Note: Applications involving packed beds are & At low Reynolds numbers, DP is dominated by
discussed under mass transfer and other relevant viscous forces and is proportional to fluid viscosity
topics. and superficial velocity.
. Explain what is meant by wall effect in a packed bed.
& At high Reynolds numbers, DP is proportional to
& Particles will not pack as closely in the region near fluid density and square of superficial velocity.
the wall as in the center of the bed. . What are coating flows?
& Therefore, flow resistance in small diameter beds is & In coating flows, liquid films are entrained on moving
less than it would be in an infinite container for the solid surfaces.
same flow rate per unit area of bed cross section. & In dip coating flows, or free withdrawal coating, a
& This is called the wall effect. solid surface is withdrawn from a liquid pool.
. Give equations for friction factor, f p , for flow through a . Give typical examples of porosities.
packed bed. & Table 7.1 gives typical porosities for different
materials.
f p ¼ð150=N Rep Þþ 1:75 ðErgun equationÞ: ð7:2Þ

& Here, the Reynolds number N Rep and the friction 7.1.2.2 Fluidization
factor f p for the packed bed are defined as follows:
. What is fluidization?
N Rep ¼ D p V s r=ð1 «Þm; ð7:3Þ & Fluidization involves fluid–solid systems in which
solid particles are suspended in a fluid, maybe liquid
3
2
f p ¼ðDP=LÞðD p =rV Þ½« =ð1 «ÞŠ; ð7:4Þ
s or gas/vapor, the system as a whole behaving as if it is
a fluid taking the shape of the container.
where DP/L is the pressure drop per unit bed height
and V s is the superficial velocity, defined as Q/A, & The upward velocity of the fluid balances the grav-
where Q is the volumetric flow rate of the fluid and itational pull exerted by the particles, keeping the
A is the cross-sectional area of the bed. Actual particles in suspension without allowing them to
velocities vary inside the bed. Sometimes the
concept of interstitial velocity, V i ,whichis the TABLE 7.1 Examples of Porosities of Different Materials
velocity that prevails in the pores of the bed, is used
Loose sand beds 35–50%
where
Salt 45–55%
V i ¼ V s =«: ð7:5Þ Brick 12–35%
Fiber glass 88–93%
D p is the equivalent spherical diameter of the particle
Limestone 4–19%
defined as