01 multiphase flows- fundamental definitions

1
Multiphase Flows
https://ir.linkedin.com/in/moammad-jadidi-03ab8399
Jadidi.cfd@gmail.com
Dr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)

Presented by: Mohammad Jadidi 2
Multiphase Flows Choosing a Multiphase Model
 The first step in solving any multiphase problem
is to determine which of the regimes described
in Multiphase Flow Regimes best represents
your flow.
 As a general guide, there are some parameters
that help to identify the appropriate multiphase
model as follows:
 Particulate Loading
 Volume Fractions
 Superficial and Phase Velocities
 Response Time
 Stokes Number
 Dilute and Dense Flows
 Phase Coupling
 Other Considerations
Multiphase
Models
Euler-Lagrange
approach
DPM
Euler-Euler
Approach
Eulerian
Model
Mixture
Model
VOF
Model

Multiphase Flows Fundamental Definitions: Primary & Secondary phases
Multiphase flow is simultaneous flow of:
 Materials with different states or phases (i.e. gas, liquid or
solid).
 Materials with different chemical properties but in the
same state or phase (i.e. liquid-liquid systems such as oil
droplets in water).
The primary and secondary phases:
 One of the phases is continuous (primary) while the
other(s) (secondary) are dispersed within the continuous
phase.
 A diameter has to be assigned for each secondary phase
to calculate its interaction (drag) with the primary phase.
particle size distribution is modeled by
assigning a separate phase for each particle
diameter
NOTE: A secondary phase with a particle size
distribution is modeled by assigning a separate
phase for each particle diameter.

4Presented by: Mohammad Jadidi 4
Multiphase Flows Fundamental Definitions: Volume Fractions
 The volume fraction of the dispersed phase is
defined as:
 the volume fraction of continuous phase is:
 And by definition, the sum if the volume
fractions must be unity

Multiphase Flows Fundamental Definitions: Particulate Loading
Note: that the word “particle” is used in this discussion to refer to a particle, droplet, or bubble
The material density ratio(ϒ):
Particulate loading (β) :
material density ratio is greater than 1000 for gas-solid flows, about 1
for liquid-solid flows, and less than 0.001 for gas-liquid flows.
Particulate loading has a major impact on phase
interactions. The particulate loading is defined as
the mass density ratio of the dispersed phase (d) to
that of the carrier phase (c).

Multiphase Flows
Average distance between the individual particles of the
particulate phase can be estimated as follows. (Crowe et al
(1998))
For example, for a gas-particle flow with a
particulate loading of 1, the interparticle
space is about 8; the particle can therefore
be treated as isolated (that is, very low
particulate loading).
Fundamental Definitions: Average distance between the individual particles
𝜅 =
𝛽
𝛾
𝒅 𝒅
𝐿

Multiphase Flows Fundamental Definitions: Superficial and Phase Velocities
 The superficial velocity of each phase is the mass flow rate of that phase divided by
the pipe area A and phase density. The superficial velocity for the dispersed phase is:
 The phase velocity is the actual velocity of the phase, and it is related to the
superficial velocity by the volume fraction
In other words, superficial velocity is the velocity of the
phase if the phase occupied the whole pipe area

Multiphase Flows Fundamental Definitions: Relaxation Time or Particle Response Time
The response time of a particle or droplet is the time
required for a particle to be released from rest to
achieve 63%, (𝒆−𝟏 / 𝒆), of the free stream velocity
When does the particle follow the flow?
Typical relaxation times in process applications
𝜏 𝑝 =
𝜌 𝑑 𝑑 𝑑
2
18𝜇 𝑐

Multiphase Flows Fundamental Definitions: Stokes Number
Stokes Number (St) is a dimensionless parameter
that describes a particle’s flow in a particular
fluid. Stokes number is determined by the ratio
of the relaxation time of the particle (τp), a
characteristic dimension of the obstacle
obstructing fluid flow (LF) and the fluid’s velocity
(V F):
 If St <<1, the particle response time is much less than the
characteristic time associated with the flow field. In this case the
particles will have ample time to respond to changes in flow velocity
and, the particle and fluid velocities will be nearly equal
 If St>>1, then the particle will have essentially no time to respond to
the fluid velocity changes and the particle velocity will be little
affected by fluid velocity change
Normalized particle distribution for varying Stokes number
𝜏 𝑝 =
𝜌 𝑑 𝑑 𝑑
2
18𝜇 𝑐
𝜏 𝐹 =
𝐿 𝐹
𝑉𝐹

Multiphase Flows
Answer:
Snow particles with a low Stokes Number are
carried by the moving fluid. Rain particles
with a high Stokes Number settle onto the
windshield. If there was no resultant fluid
flow, both particles would settle.
Calculation:
 A value of 20m/s (≈ 45mph) is used as a model velocity for the
car and resultant airflow. The car is assumed to have a
characteristic dimension of D = 1 m. Air at 0 degrees Celsius has
a dynamic viscosity of 1.71 ∗ 10−5 Ns/m2.
 Stokes Number for a raindrop Sk = 584 is calculated from a
diameter of dp = 0.003m = 3mm and a density of ρ = 1000
kg/m3.
 Stokes Number Sk = 58 for snow is calculated using the same
diameter and a density of ρ = 100 kg/m3.
Question:
“Why is it that I get more snow on my windshield when my car is
stopped at a light than when it’s moving, but I get more rain on my
windshield when it’s moving than when it’s stopped?”
Fundamental Definitions: Stokes Number-Example

Multiphase Flows Fundamental Definitions: Dilute and Dense Flows
 A dilute flow, is one in which the particle motion is controlled by
the fluid forces (drag and lift)
 A dense flow, on the other hand, is one in which the particle
motion is controlled by collisions
 In collision-dominated flow the collisions between the
particles control the features of the flow, such as in a
fluidized bed
 In a contact dominated flow, the particle motion is
controlled by continuous contact such as in a shear
granular flow
There is a further classification of dense flows: collision-and
contact-dominated.
Dense
flows
Collision-
dominated
flow
Contact
dominated
flow

Multiphase Flows
 One-way-coupled : the fluid carrier
influences the particles via drag and
turbulence, but the particles have no
influence on the fluid carrier
Fundamental Definitions: Phase Coupling
Schematic diagram of coupling
 Two-way-coupled: the fluid carrier
influences the particulate phase via drag
and turbulence, but the particles in turn
influence the carrier fluid via reduction in
mean momentum and turbulence
 Four-way- couple : there is two-way
coupling plus particle pressure and
viscous stresses due to particles

Multiphase Flows
Dispersed two-phase flow as a function of the particle volume
fraction and inter-particle spacing
Fundamental Definitions: Phase Coupling
NOTE: Four-way coupling effects become
important when particle volume fraction
exceeds 𝟏𝟎-3

Multiphase Flows Fundamental Definitions: Weber number
Weber number describes the ratio between deforming inertial forces and stabilizing cohesive forces for liquids
flowing through a fluid medium. For example, the Weber number characterizes the atomizing quality of a spray
and the resulting droplet size.
 When a liquid flows through a second fluid phase
(gas or liquid), then the aerodynamic force
FA causes the drops to deform and ultimately
disperse.
 The cohesion force FK associated with the surface
tension or interfacial tension ,σ, opposes the
increase in surface area which is caused by the
deformation. The drop is therefore held together by
the surface or interfacial tension.
If the deforming force increases due to a
higher speed or longer process length, the
drops of a spray disperse more easily and
drops of oil in an aqueous environment are
split apart more easily. A high surface or
interfacial tension counteracts this process.

Multiphase Flows Fundamental Definitions: Weber number
If the deforming force increases due to
a higher speed or longer process
length, the drops of a spray disperse
more easily and drops of oil in an
aqueous environment are split apart
more easily. A high surface or interfacial
tension counteracts this process.
VIDEO: Weber number

Choosing a Multiphase Model
Multiphase Flows

Multiphase Flows Choosing a Multiphase Model
Multiphase Models
Euler-Lagrange
approach
DPM
Euler-Euler Approach
Eulerian
Model
Mixture Model VOF Model
There are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the
Euler-Euler approach

Multiphase Flows
 The VOF model is a surface-tracking technique
applied to a fixed Eulerian mesh.
 It is designed for two or more immiscible fluids
where the position of the interface between the
fluids is of interest.
 In the VOF model, a single set of momentum
equations is shared by the fluids, and the volume
fraction of each of the fluids in each computational
cell is tracked throughout the domain.
Choosing a Multiphase Model-Euler-Euler approach-Volume of Fluid (VOF)
The VOF models require a proper mesh
and numerical advection scheme to
approximate the transport of the scalar
function in an accurate manner avoiding
numerical diffusion
Hydrodynamics and Wave Impact Analysis

Multiphase Flows Choosing a Multiphase Model-Euler-Euler approach-Volume of Fluid (VOF)
Applications of the VOF model include:
 Stratified flows
 Free-surface flows
 Filling
 Sloshing
 Motion of large bubbles in a liquid,
 Motion of liquid after a dam break,
 Prediction of jet breakup (surface tension)
 Steady or transient tracking of any liquid-gas
interface.
Sloshing

Multiphase Flows Choosing a Multiphase Model-Euler-Euler approach-The Mixture Model
The mixture model solves for the mixture
momentum equation and prescribes relative
velocities to describe the dispersed phases.
Applications of the mixture model include:
 particle-laden flows with low loading
 bubbly flows
 sedimentation
 and cyclone separators
NOTE: The mixture model can also be used without
relative velocities for the dispersed phases to model
homogeneous multiphase flow.

Multiphase Flows Choosing a Multiphase Model-Euler-Euler approach-The Eulerian Model
The Eulerian model is the most complex of the multiphase
models in ANSYS Fluent. It solves a set of n momentum
and continuity equations for each phase. In the Eulerian
approach both the dispersed particle phase and
continuous fluid phase are solved using the NS equations.
Coupling is achieved through the pressure and interphase
exchange coefficients.
Applications of the Eulerian multiphase model include:
 bubble columns
 Risers
 particle suspension
 fluidized beds
NOTE: It can be used to compute any multiphase flow regime, provided
that an adequate closure relation for the interfacial coupling terms are
provided

Multiphase Flows
 The Lagrangian Discrete Phase Model (DPM) in
ANSYS Fluent follows the Euler-Lagrange approach.
 The fluid phase is treated as a continuum by solving
the Navier-Stokes equations
 The dispersed phase is solved(Using: the Newton’s
second law) by tracking a large number of particles,
bubbles, or droplets through the calculated flow field.
 In DPM individual particles are treated as rigid
spheres (i.e., neglecting particle deformation and
internal flows)
 The dispersed phase can exchange momentum, mass,
and energy with the fluid phase.
Choosing a Multiphase Model-Euler-Lagrange Approach-The DPM Model
 spray dryers
 coal and liquid fuel combustion
 some particle-laden flows
Applications of the DPM model include:

Multiphase Flows
The discrete phase formulation
used by ANSYS Fluent contains
the assumption that the second
phase is sufficiently dilute that
particle-particle interactions and
the effects of the particle volume
fraction on the gas phase are
negligible. In practice, these
issues imply that the discrete
phase must be present at a fairly
low volume fraction, usually less
than 10–12%. Note that the mass
loading of the discrete phase may
greatly exceed 10–12%: you may
solve problems in which the mass
flow of the discrete phase equals
or exceeds that of the continuous
phase.
Choosing a Multiphase Model-Euler-Lagrange Approach-The DPM Model
Representation of the particle streams at the end of the injection (t=0.11 s), image shows the particles
coloured by its velocity magnitude. The particle streams are draw as spheres with proportional size
scaled 50 times more than the real diameter

Multiphase Flows
 For bubbly, droplet, and particle-laden flows in which the phases mix
and/or dispersed-phase volume fractions exceed 10%  mixture or
the Eulerian model
 For slug flows & stratified/free-surface flows  VOF model
 For pneumatic transport  the mixture model for homogeneous
flow or the Eulerian model for granular flow
 For fluidized beds  Eulerian model for granular flow
 For slurry flows and Hydrotransport  the mixture or Eulerian
 For sedimentation  the Eulerian model
Choosing a Multiphase Model based on the flow regime
The use of the DPM is limited to low volume fractions (less than or equal to 10% ),
unless you are using the dense discrete phase model (DDPM) formulation. In
addition, for the discrete phase model simulation, you can choose many more
advanced combustion models compared to the Eulerian models.

Multiphase Flows Choosing a Multiphase Model - Mixture Or Eulerian model?
 If accuracy is more important than computational effort, the Eulerian model is a
better choice. However, the complexity of the Eulerian model can make it less
computationally stable than the mixture model.
 If there is a wide distribution of the dispersed phases (that is, if the particles vary in
size and the largest particles do not separate from the primary flow field), the
mixture model may be preferable (that is, less computationally expensive).
 If the dispersed phases are
concentrated just in portions of
the domain, you should use the
Eulerian model instead.
 If interphase drag laws that are applicable
to your system are available the Eulerian
model can usually provide more accurate
results than the mixture model.
 if the interphase drag laws are
unknown or their applicability to
your system is questionable, the
mixture model may be a better
choice.
 If you want to solve a simpler problem,
which requires less computational effort,
the mixture model may be a better
option, since it solves a smaller number of
equations than the Eulerian model.

Multiphase Flows
For very low loading, the coupling between the phases
is one-way. The DPM , mixture, and Eulerian models can
all handle this type of problem correctly. Since the Eulerian
model is the most expensive, the discrete phase or
mixture model is recommended.
Choosing a Multiphase Model based on Loading and St.
For high loading, there is two-way coupling plus particle
pressure and viscous stresses due to particles (four-way
coupling). Only the Eulerian model will handle this type of
problem correctly

Multiphase Flows
For intermediate loading, the
coupling is two-way. The DPM,
mixture, and Eulerian models
are all applicable in this case
Which one is better?
Example: For a coal classifier with a characteristic length of 1 m and a
characteristic velocity of 10 m/s, the Stokes number is 0.04 for particles with a
diameter of 30 microns, but 4.0 for particles with a diameter of 300 microns.
Clearly the mixture model will not be applicable to the latter case.
Choosing a Multiphase Model based on Loading and St

28
Multiphase Flows
Thanks
https://ir.linkedin.com/in/moammad-jadidi-03ab8399
Jadidi.cfd@gmail.com
Dr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)
End of part #2 Next part:

01 multiphase flows- fundamental definitions

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (9)

Similar to 01 multiphase flows- fundamental definitions

Similar to 01 multiphase flows- fundamental definitions (20)

More from Mohammad Jadidi

More from Mohammad Jadidi (20)

Recently uploaded

Recently uploaded (20)

01 multiphase flows- fundamental definitions