Theory and modeling of multiphase flows

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Theory and modeling of multiphase flows
Payman Jalali Department of Energy and
Environmental Technology Lappeenranta University
of Technology Lappeenranta, Finland Fall 2006
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Modeling of gas-solid systems
Different regimes of fluid-solid flows can exist.
-Packed bed There is no gas velocity or low
gas velocity. Solid particles contact each other
and gas flows through the pore space between
solid particles. For monosized spherical
particles, in normal pouring of them in the bed
the solid volume fraction is 0.58 to 0.60. If the
bed is shaked for some time the packing will get
more compact while its structure still remains
random. Then the packing density is around
0.64. - Minimum fluidization When the gas (or
liquid) velocity is gradually increased the
pressure drop rises too. At some gas velocity the
force due to pressure drop is balanced by the
weight of the solid in the bed. This state is
called minimum fluidization where solid particles
loose their contacts with each other. The height
of the bed is continuously increased especially
in liquid-solid mixtures.
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Modeling of gas-solid systems
-Bubbly flow In gas-solid mixtures we may see a
transition from smooth fluidization to a state
where bubbles of gas appear rising upward while
growing.
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Modeling of gas-solid systems
Ergun equation for frictional pressure drop in
packed beds
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Modeling of gas-solid systems
Minimum fluidizing velocity, umf, is obtained
from the balance of forces Drag force by upward
moving gas weight of particles
The fluidization properties of a powder in air
may be predicted by establishing in which group
it lies. The corresponding chart is called the
Geldart classification of powders (A,B,C,D) Table
1 presents a summary of the typical properties of
the different powder classes.
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Modeling of gas-solid systems
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Modeling of gas-solid systems
http//www.erpt.org/012Q/Video4.mpg
A spouted fluidized bed of rice (Group D solids)
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Modeling of gas-solid systems
http//www.erpt.org/012Q/Video5.mpg
Bubbles in a two-dimensional fluidized bed of
Group A powder. Through splitting and
coalescence, bubbles achieve a maximum stable
size, effectively independent of gas velocity or
vessel size.
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Modeling of gas-solid systems
The continual increase in size of bubbles in a
two-dimensional fluidized bed of a Group B
powder. Bubbles increase in size with distance
from the distributor and with increasing gas
velocity. Bubble size is limited only by the
vessel size.
http//www.erpt.org/012Q/Video8.mpg
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Modeling of gas-solid systems
In case of any difficulty to open the video
files, visit http//www.erpt.org/012Q/rhod-04.htm

An attempt to fluidize a Group C powder produces
channels or a discrete plug.
http//www.erpt.org/012Q/Video9.mpg
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Modeling of gas-solid systems
Multi-fluid method Transport equations governing
the conservation of mass, momentum, and
scalar variables like turbulent quantities kl and
?l for gas-liquid flows, enthalpy (hk) and
concentration of chemical species (Yj,k) are
derived for each phase k.
Conservation of mass for phase k
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Modeling of gas-solid systems
Conservation of momentum for phase k
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Modeling of gas-solid systems
Conservation of scalars for phase k
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Modeling of gas-solid systems
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Modeling of gas-solid systems
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Modeling of gas-solid systems
Particulate dynamics simulations can be also
useful to calculate particle-particle drag
forces. (See the movie in next page)
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Modeling of gas-solid systems
This is one part of the shear cell in our
simulations using hard-disk particulate dynamics
simulations in which particles experience binary
collisions. Blue particles are wall particles
shearing the packing. Shear dilation can be
clearly seen close to the walls.
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Modeling of gas-solid systems
In CFB, the concentration of solid is low due to
high gas velocity. Gas flow is turbulent. FCC
(Fluid Catalytic Cracking) is a process in which
vaporized heavy hydrocarbons crack into
lower-molecular-weight compounds in the presence
of a catalyst.
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Modeling of gas-solid systems
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Modeling of gas-solid systems
Note These equations are written in tensorial
notation form. Check out which index relates to
position and which index to the phase. Then argue
which equations are for scalars and vectors.
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Modeling of gas-solid systems
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Modeling of gas-solid systems
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Modeling of gas-solid systems
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Modeling of gas-solid systems
Axial velocity of solid phase
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Reference

• Kunii D., Levenspiel O., Fluidization
  Engineering, 2nd Ed., Butterworth-Heinemann
  (1991)
• Hjertager B.H., Basic numerical analysis of
  multiphase flows, Lecture notes, HUT, ESPOO
  (2006)
• http//www.erpt.org/012Q/rhod-04.htm