Modeling and simulation of

Mutiphase flows

(CFD tips)

Pouriya Niknam

Supervisor: Dr. Daniele Fiaschi

Multiphse flow introduction, definition and types

Tips on multiphase simulation

Outline

2

Definitions

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.

Multiphase flow is important in many industrial processes:Riser reactors.

Bubble column reactors.

Fluidized bed reactors.

Scrubbers, dryers, etc.

Typical objectives of a modeling analysis:Maximize the contact between the different phases, typically different chemical compounds.

Flow dynamics.

Optimization /scale up/ new geometries

Why model multiphase flow?

Flow Specificbubblydroplet

particle-ladenslug

annularstratified/free surface

rapid granular flow

Model SpecificLagrangian Dispersed Phase

Algebraic SlipEulerian

Eulerian GranularVolume of Fluid

Process SpecificSeparationFiltration

SuspensionEvaporation

Reaction

?

multiphase or multicomponent?

– Distinguish multiphase and/or multicomponent

• Liquid/Gas or Gas/Liquid

• Gas/Solid

• Liquid/Liquid

– Technically, two immiscible liquids are “multi-fluid”, but are

often referred to as a “multiphase” flow due to their similarity

in behavior

Single component Multi-component

Single phaseWater

Pure nitrogen

Air

H2O+oil emulsions

Multi-phase Steam bubble in H2OCoal particles in air

Sand particle in H2O

Phase interaction & Species interaction

Dispersed/Interfacial

• Flows are also generally categorized by distribution of the components

– “separated” or “interfacial”

• both fluids are more or less contiguous throughout the

domain

– “dispersed”

• One of the fluids is dispersed as non-contiguous

isolated regions within the other (continuous) phase.

• The former is the “dispersed” phase, while the latter

is the “carrier” phase.

• One can now describe/classify the geometry of the

dispersion:

• Size & geometry

• Volume fraction

Bubbly Pipe Flow – heat exchangers in power plants, A/C units

Gas-Liquid Flow

Aeration:-produced by wave action

- used as reactor in chemical processing

- enhanced gas-liquid mass transfer

Ship wakes – detectability

Cavitation – noise, erosion of structures

Weather – cloud formation

Biomedical – inhalant drug delivery

Liquid-Gas Flow

Gas-Liquid FlowEnergy production – liquid fuel combustion

Biomedical – inhalant drug delivery

Environmental – avalanche, pyroclastic flow, ash

plume, turbidity currents

Gas-Solid Flow

Granular Flow – collision dominated

dynamics; chemical processing

Chemical production – mixing and reaction of immiscible liquids

Liquid-Liquid

Sediment Transport – pollution, erosion of beaches,

drainage and flood control

Solid-Liquid

Settling/sedimentation, turbidity currents

Material processing – generation of particles & composite materials

Energy production – coal combustion

Solid-Gas

Aerosol formation – generation of particles & environmental safety

• One-way coupling: Sufficiently dilute such that fluid feels no effect from presence of particles. Particles move in dynamic response to fluid motion.

– Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer.

– No influence of particulate phase on the continous phase.

• Two-way coupling: Enough particles are present such that momentum exchange between dispersed and carrier phase interfaces alters dynamics of the carrier phase.

– Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer.

– Particulate phase reduces mean momentum and turbulent kinetic energy in fluid phase.

• Four-way coupling: Flow is dense enough that dispersed phase collisions are significant momentum exchange mechanism

• Includes all two-way coupling.

• Particle-particle collisions create particle pressure and viscous stresses.

Coupling between phases

Empirical correlations.

LagrangianTrack individual point particles.

Particles do not interact.

Algebraic slip modelMixture model

Dispersed phase in a continuous phase.

Solve one momentum equation for the mixture.

Neither particle-wall interaction nor particle-particle are taken into account

Two-fluids theory (multi-fluids)Eulerian-Eulerian models: two co-existing fluids

Solve as many momentum equations as there are phases.

Particle-wall interaction taken into account, particle-particle usually not.

Eulerian-granular model (EGM)Both particle-wall and particle-particle interaction are taken into account

dispersed phase model (DPM)Eulerian/Lagrangian

Solve the trajectories of individual objects and their collisions, inside a continuous phase.

Particle-wall interaction always taken into account, particle-particle usually not

Fully resolved and coupled.

Increased

com

plexity

Modeling approach

Trajectories of particles/droplets are computed in a Lagrangian frame.

Exchange (couple) heat, mass, and momentum with Eulerian frame gas phase.

Discrete phase volume fraction should preferably be less than 10%.

Mass loading can be large (+100%).

No particle-particle interaction or break up.

Turbulent dispersion modeled by:Stochastic tracking.

Particle cloud model.

Model particle separation, spray drying, liquid fuel or coal combustion, etc.

Modeling approach, DPM

User must know the characteristics of the flow.

Flow regime, e.g. bubbly flow, slug flow, annular flow, etc.

Laminar or turbulent

Dilute or dense

Secondary phase diameter for drag considerations.

Phases interaction...

Multiphase flow regimes

Available Solvers

• There are two kinds of solvers available in FLUENT – Pressure based and Density based.

• The pressure-based solvers take momentum and pressure (or pressure correction) as the primary variables.– Pressure-velocity coupling algorithms are

derived by reformatting the continuity equation

• Two algorithms are available with the pressure-based solvers:– Segregated solver – Solves for pressure

correction and momentum sequentially.

– Coupled Solver (PBCS) – Solves pressure and momentum simultaneously.

Pressure-Based

(segregated)

Density-Based

(coupled)

Solve Mass

Continuity;

Update Velocity

Solve U-Momentum

Solve V-Momentum

Solve W-Momentum

Pressure-Based

(coupled)

Solve Turbulence Equation(s)

Solve Species

Solve Energy

Solve Other Transport Equations as required

Solve Mass

& Momentum

Solve Mass,

Momentum,

Energy,

Species

Choosing a Solver

• The pressure-based solver is applicable for a wide range of flow regimes from low speed incompressible flow to high-speed compressible flow.– Requires less memory (storage).

– Allows flexibility in the solution procedure.

• The pressure-based coupled solver (PBCS) is applicable for most single phase flows, and yields superior performance to the standard pressure-based solver.– Now available for multiphase (Eulerian)

– Requires 1.5–2 times more memory than the segregated solver.

• The density-based coupled solver (DBCS) is applicable when there is a strong coupling, or interdependence, between density, energy, momentum, and/or species. – Examples: High speed compressible flow with combustion, hypersonic flows, shock

interactions.

Convergence Difficulties with multiphase• Numerical instabilities can arise with an ill-posed problem, poor-quality mesh and/or

inappropriate solver settings.

– Exhibited as increasing (diverging) or “stuck” residuals.

– Unconverged results are very misleading!

• Troubleshooting1. Ensure that the problem is well-posed.2. Compute an initial solution using a

first-order discretization scheme.3. For the pressure-based solver, decrease

underrelaxation factors for equations having convergence problems.

4. For the density-based solver, reducethe Courant number.

5. Disabling Volume fraction &phase equations6. Remesh or refine cells which have large

aspect ratio or large skewness. (Remember that you cannot improve cell skewness by using mesh adaption!)

Continuity equation convergence

trouble affects convergence of

all equations.

Modifying Under-Relaxation Factors

• Under-relaxation factor, α, is included to stabilize the iterative process for the pressure-based solver

• Use default under-relaxation factors to start a calculation.

• Decreasing under-relaxation for momentum often aids convergence.– Default settings are suitable for a

wide range of problems, you can reduce the values when necessary.

– Appropriate settings are best learned from experience!

Modifying the Courant Number• A transient term is included in the density-based solver even for

steady state problems.– The Courant number defines the

time step size.

• For density-based explicit solver:– Stability constraints impose a

maximum limit on the Courant number.• Cannot be greater than 2

(default value is 1).• Reduce the Courant number when

having difficulty converging.

• For density-based implicit solver:– The Courant number is not limited

by stability constraints.• Default value is 5.

Starting from a Previous Solution• A previously calculated solution can be

used as an initial condition when changes are made to the case setup.

– Use solution interpolation to initialize a run (especially useful for starting fine-mesh cases when coarse-mesh solutions are available).

– Once the solution is initialized, additional iterations always use the current data set as the starting point.

– Some suggestions on how to provide initial conditions for some actual problems:

Actual Problem Initial Condition

Heat Transfer Isothermal

Natural convection Low Rayleigh number

Turbulence Inviscid (Euler) solution

Steady or Unsteady

• Nearly all flows in nature are transient!– Steady-state assumption is possible if we:

• Ignore unsteady fluctuations• Employ ensemble/time-averaging to remove unsteadiness (this is

what is done in modeling turbulence)

• In CFD, steady-state methods are preferred– Lower computational cost– Easier to postprocess and analyze

• Many applications require resolution of transient flow:– Aerodynamics (aircraft, land vehicles,etc.) – vortex shedding– Rotating Machinery – rotor/stator interaction, stall, surge– Multiphase Flows – free surfaces, bubble dynamics– Deforming Domains – in-cylinder combustion, store separation– Unsteady Heat Transfer – transient heating and cooling– Many more

• Typically, compressible analyses are executed in a transient or pseudo-transient fashion since the problem is no longer elliptic: downstream boundary conditions cannot be felt upstream in a supersonic analysis.

– Pseudo Transient: Use of Inertial Relaxation.

Pseudo Transient

improve multiphase convergency

• Symmetry Plane?• Symmetric geometry does not necessarily mean symmetric flow

– Example: The coanda effect. A jet entering at the center of a symmetrical duct will tend to flow along one side above a certain Reynolds number

Specifying Well Posed Boundary Conditions

No Symmetry Plane Symmetry Plane

Coanda effect

not allowed

And this is so common in multiphase flow cases...

Ex. 2: Preference= 100,000 Pa

• Domain Creation – Reference PressureGeneral Options panel: Domain Models

– Reference Pressure

• Represents the absolute pressure datum from which all relative pressures are measured

Pabs = Preference + Prelative

• Pressures specified at boundary and initial conditions are relative to the Reference Pressure

• Used to avoid problems with round-off errors which occur when the local pressure differences in a fluid are small compared to the absolute pressure level

PressurePressure

Ex. 1: Preference= 0 Pa

Pref

Prel,max=100,001 Pa

Prel,min=99,999 Pa

Prel,max=1 Pa

Prel,min=-1 Pa

Pref

Reference Values

PROBLEMS WITH THE CFD METHODS

• Numerical errors

– Dissipation causes a gradual decrease in the

amplitude of an changes and boundaries or the

magnitude of changes as it propagates away

from the source of change.

– Dispersion causes waves of different

wavelengths originating to incorrectly propagate.

Sample Problem

1-D Transport Equation:

0

x

Fc

t

F

01

1

11

x

FFc

t

FF n

i

n

i

n

i

n

i

Propagation Direction

i -1 i

Let’s revisit 1-D Vorticity Transport Equation:

0

x

Fc

t

F

Symmetric Part Numerical Viscosity

• If we replace these low order schemes with high order counter parts, results dramatically improve.

2

1 2

22 x

FFFx

x

FF

x

FF

x

iiiiiii

x

F

x

FF 2/1i2/1i

2/1iF Symmetric Part + Numerical viscosity

Second order

Fourth order

Sixth order

Eighth order

First order

Third order(MUSCL)

Fifth order (WENO)

(Base Scheme) (Filter)

• Symmetric Schemes have no built-in numerical viscosity. • Needed to be added explicitly.

2/1iF Symmetric Part

i1i FF2

1

1ii1i2i FF7F7F12

1

2i1ii1i2i3i FF8F37F37F8F30

1

LR qqA2

1

2nd order:

4th order:

6th order:

This part is used tocontrol dissipation errors

This part is used to control

dispersion and truncation errors

MUSCL

2/1iF Symmetric Part LR qqA2

1

3rd order MUSCL:

LEFT STENCIL

RIGHT STENCIL

RqLq

i-1i

i+1/2

i+1 i+2

Cell Face

1st order MUSCL:

iiiiiR

iiiiiL

qqqqqq

qqqqqq

1121

11

3

1

6

1

6

1

3

1

iiiiiR

iiiiiL

qqqqqq

qqqqqq

1121

11

3

1

6

1

6

1

3

1

iiiiiR

iiiiiL

qqqqqq

qqqqqq

1121

11

3

1

6

1

6

1

3

1

MUSCL

33

Question?