Theory and simulation of dispersedphase multiphase flows

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Postgraduate Course in Multiphase Flows
Theory and simulation of dispersed-phase
multiphase flows
Organized by Center of Excellence in Multiphase
Flow Research Lappeenranta University of
Technology Lecturer Payman Jalali,
Docent Autumn 2007
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Contents

• Introduction (Industrial applications and
  theoretical study) 1 hour
• Basic properties of dispersed phase flows, size
  distribution definitions 3 hours
• Particle-fluid interaction model 3 hours
• Particle-particle interaction model 3 hours
• Continuous phase equations 3 hours
• Droplet-particle cloud equations 1 hour
• Numerical modeling
• 1. Dilute flows (Lagrangian models) 1 hour
• 2. Dilute flow (two-fluid model) 1 hour
• 3. Dense flows (Lagrangian approach) 1 hour
• 4. Dense flows (Eulerian approach) 1 hour
• Molecular Dynamics (MD) simulation techniques
• 1. Event-driven algorithms 2 hours
• 2. Soft-sphere or Discrete Element Method
  (DEM) 4 hours

Main references 1- C. Crowe, M. Sommerfeld, Y.
Tsuji. Multiphase flows with droplets and
particles. CRC Press (1998). 2- T. Pöschel, T.
Schwager. Computational Granular Dynamics.
Springer (2005).
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• Evaluation criteria
• 1- Homeworks (5 problems each for 10 points),
  totally 50 points out of 100.
• 2- Project 1, CFD simulation of dispersed
  two-phase flows, totally 25 points out of 100.
• 3- Project 2, Molecular dynamics (MD) type
  simulations of dispersed two-phase flows, totally
  25 points out of 100.
• Background
• Postgraduate-level knowledge of fluid
  mechanics, heat transfer, and dynamics.
• Familiar with the following computer packages
  FLUENT, MATLAB and a programming language such
  as C, FORTRAN.
• Other related courses
• EnJ2110100 Numerical modeling and data analysis
  methods in heat and fluid flow engineering
  Macroscale and nanoscale 10 ECTS
• EnJ 2110300 Theory and modelling of multiphase
  flows 10 ECTS

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Introduction (Industrial applications and
theoretical study)
Classification of Multiphase, multicomponent flows
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Introduction (Industrial applications and
theoretical study)
Classification of Multiphase flows
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Introduction (Industrial applications and
theoretical study)

• Industrial applications
• Spray drying The figure shows a counter-current
  flow spray dryer used in drying foods, detergents
  and pharmaceuticals.
• C. Crowe, M. Sommerfeld, Y. Tsuji. Multiphase
  flows with droplets and particles. CRC Press
  (1998).

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Introduction (Industrial applications and
theoretical study)
Industrial applications 2) Pollution control
Cyclones used for separation of solid particles
from the gas stream emitted to atmosphere for
particle diameters larger than 50
micrometer. C. Crowe, M. Sommerfeld, Y. Tsuji.
Multiphase flows with droplets and particles. CRC
Press (1998).
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Introduction (Industrial applications and
theoretical study)
Industrial applications Pollution control
Electrostatic precipitator collects small-size
particles from a solid-gas mixture using
electrostatic forces and flow turbulence. C.
Crowe, M. Sommerfeld, Y. Tsuji. Multiphase flows
with droplets and particles. CRC Press (1998).
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Introduction (Industrial applications and
theoretical study)
Industrial applications Pollution control
Venturi scrubber is a simple device to collect
solid particles on droplets introduced to the
mixture. Droplets are much larger than particles
and they can be collected easily from the flow
(containing particles) C. Crowe, M. Sommerfeld,
Y. Tsuji. Multiphase flows with droplets and
particles. CRC Press (1998).
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Introduction (Industrial applications and
theoretical study)
Industrial applications 3) Transport systems
They are divided into several different
categories. a) Pneumatic transport including
homogeneous flows, dune flow, slug flow and
packed bed. C. Crowe, M. Sommerfeld, Y. Tsuji.
Multiphase flows with droplets and particles. CRC
Press (1998).
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Introduction (Industrial applications and
theoretical study)
Industrial applications b) Slurry flows in
which large solids such as rock, coal chunks or
mad are transported by liquid. c) Fluidized
beds in which gas flow fluidizes solid particles
in the vessel.
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Introduction (Industrial applications and
theoretical study)
Industrial applications 4) Manufacturing and
material processing a) Spray forming Molten
metal is sprayed and carried by a gas and
deposited on a substrate. C. Crowe, M.
Sommerfeld, Y. Tsuji. Multiphase flows with
droplets and particles. CRC Press (1998).
Molten metal
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Introduction (Industrial applications and
theoretical study)
Industrial applications b) Plasma spray coating
Plasma carries solid particles and coats the
surface of a substrate as a result of heat
transfer from plasma to particles and melting
them. C. Crowe, M. Sommerfeld, Y. Tsuji.
Multiphase flows with droplets and particles. CRC
Press (1998).
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Introduction (Industrial applications and
theoretical study)
Industrial applications c) Abrasive water-jet
cutting By adding abrasive (hard) particles to
water and injecting it onto a metallic surface
under 60,000 psi or so with a jet velocity of
1000 m/s the metal is cut. C. Crowe, M.
Sommerfeld, Y. Tsuji. Multiphase flows with
droplets and particles. CRC Press (1998).
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Introduction (Industrial applications and
theoretical study)

• Industrial applications
• d) Synthesis of nanophase materials for grain
  sizes from 5 to 50 nanometer.
• Injection of precursors into diffusion or
  premixed flames. It results particles from 1-500
  nm.
• Thermal reactors Precursors enter the furnace in
  the form of an aerosol. Chemical reactions occur
  as the multiphase mixture passes through the
  furnace. The size control depends on the
  regulation of temperature and flow velocity.

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Introduction (Industrial applications and
theoretical study)
Energy conversion and propulsion a)
Pulverized-coal-fired furnaces Radiation makes
volatile gases get out of coal particles. Then
they burn and coal particles burn later slowly.
Efficient mixing of volatiles and gas for
efficient combustion is a challenging issue.
Coal particle-air mixture
C. Crowe, M. Sommerfeld, Y. Tsuji. Multiphase
flows with droplets and particles. CRC Press
(1998).
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Introduction (Industrial applications and
theoretical study)
Energy conversion and propulsion b) Solid
propellant rocket fuel Aluminum powder is used
as the fuel of the rocket. Aluminum burns and
small alumina droplets (1 micron) produced.
Presence of particles lowers specific impulse of
the rocket.
C. Crowe, M. Sommerfeld, Y. Tsuji. Multiphase
flows with droplets and particles. CRC Press
(1998).
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Introduction (Industrial applications and
theoretical study)
Energy conversion and propulsion c) Fire
suppression and control.
C. Crowe, M. Sommerfeld, Y. Tsuji. Multiphase
flows with droplets and particles. CRC Press
(1998).
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Basic properties of dispersed phase flows

• Definitions
• Dispersed phase flows include two phases 1)
  phase 1 is the continuous background phase, 2)
  phase 2 is constituted of materially not
  connected regions, namely droplets or particles.
• Density This is referred as material density
  too,

To have a stationary average, we need to have
about 104 molecules. For a gas, it is
which corresponds to a cube with a10-7 m. If the
system dimension Lgtgta then ?V is a point.
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Basic properties of dispersed phase flows
- Number density
- Volume fraction For the dispersed phase,
For the continuous phase (void fraction),
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Basic properties of dispersed phase flows

• Bulk density It can be also called apparent
  density,
• m is the mass of one particle (if uniform)

mixture density
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Basic properties of dispersed phase flows

• Mass concentration The ratio of dispersed phase
  mass to the continuous phase mass,

• Loading The ratio of dispersed phase mass flux
  to the continuous phase mass flux,

u, v are velocities of the continuous and
dispersed phases, respectively.
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Basic properties of dispersed phase flows

• Spacing of particles or droplet A key question
  arises whether the system is continuum or not?

• Question 1 What is the closest packing
  corresponding to this arrangement?
• Question 2 Example the closest packings of
  monosized circles (2D) or spheres (3D) and derive
  the spacing relation to the volume fraction for
  2D and 3D cases.

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Basic properties of dispersed phase flows
If L/D gtgt1 then the dispersed phase elements can
be treated as isolated. Some manipulation of
different variables result
So individual particles or droplets could be
treated as isolated (no influence of the
neighboring elements on the drag or heat transfer
rate) in most gas-solid and gas-droplet flows.
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Basic properties of dispersed phase flows
Example The size of limiting volume, ?V0, to
form a stationary average can be calculated for
Np particles
If L/D10 D100?m
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Basic properties of dispersed phase flows

• Response times
• The time that a particle or droplet responds to
  changes in flow velocity or temperature.
• It is used as a characterization parameter.
• Momentum response time
• From the equation of motion for a particle in a
  gas, we have,

v particle velocity u gas velocity The
Reynolds number for dispersed phase is
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Basic properties of dispersed phase flows
(1),(2) ?
? ?c gas viscosity (continuum phase)
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Basic properties of dispersed phase flows
Now, we can show what is the physical meaning of
?V. If we put t ?V
?V is the time required for a particle released
from rest to achieve 63 of the free stream
velocity.
2) Thermal response time Similar to the
equation for momentum, we write the thermal
balance equation for one particle (Q why?)
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Basic properties of dispersed phase flows
?T is the time required for a particle to achieve
63 of a step change in the temperature of the
carrier phase.
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Basic properties of dispersed phase flows
For gas PrO(1) For liquid PrO(100)
Stokes number It is the ratio of a response time
to a characteristic time of the system. For
particle velocity, we can define
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Basic properties of dispersed phase flows
The carrier phase acceleration is
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Basic properties of dispersed phase flows
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Basic properties of dispersed phase flows
Exercise Estimate the collision time in a group
of particles with uniform diameter D through
which one particle is traveling with a relative
velocity vr with respect to other particles.
Within a time interval ?t the particle will
intercept all the particles in the tube with
radius 2D and the length vr.?t.
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Basic properties of dispersed phase flows
In the tube, the number of particles can be
calculated as
Collision frequency is estimated as
Note that vr is an average relative velocity, but
not an instantaneous velocity.
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Basic properties of dispersed phase flows
We can write
For dilute flow
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Basic properties of dispersed phase flows
vr could be related to the fluctuation (?) of
the particle motion due to turbulence of the
carrier fluid.