Lectures on CFD (Multiphase Flow)

Computational Fluid Dynamics: multiphase flow

By: Dr. Alam Nawaz Khan Wardag

Department of Chemical Engineering, PIEAS, Islamabad. Email: [email protected]

Office: H block

mailto:[email protected]

Layout of Lectures

• Classification by Nature of Phases

• Flow Regime Classification

• Characteristics of Classes

• Multiphase Modeling Approaches

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Lectures on Computational Fluid Dynamics: Multiphase Flow

Gas-Liquid or Liquid-Liquid Flows

• Bubbly Flow: discrete gaseous or fluid bubbles in a continuous fluid E.g. : absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbers

• Droplet Flow: discrete fluid droplets in a continuous gas –E.g. absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbers

Classification by Nature of Phases

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Multiphase Flow


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• Slug Flow: large bubbles in a continuous fluid –E.g. large bubble motion in pipes or tanks

• Stratified/Free-Surface Flow: immiscible fluids separated by a clearly-defined interface –E.g. sloshing in offshore separator devices, boiling and condensation in nuclear reactors

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• LIQUID-SOLID FLOWS

• Slurry Flow: transport of solid particles in liquids. – E.g. slurry transport, mineral processing

• Hydrotransport: Densely-distributed solid particles in a continuous

liquid – E.g. mineral processing, biomedical and physiochemical

fluid systems

• Sedimentation: Settling of solid particles in a column of liquid. – E.g. mineral processing

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• m

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• GAS-SOLID FLOWS

• Particle-laden Flow: Discrete Solid Particles in a continuous gas.

–E.g. cyclone separators, air classifiers, dust collectors,

and dust-laden environmental flows

• Pneumatic Transport: Conveying of Solid Particles by gas in Pipelines.

–e.g. transport of cement, grains, and metal powders

• Fluidized Beds: Solid Particles suspended in a upward flowing gas.

–e.g. fluidized bed reactors, circulating fluidized beds

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• GELDART CLASSIFICATION

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• DRAG FORCE

• The drag coefficient is defined as the ratio of the force on the particle and the fluid dynamic pressure caused by the fluid times the area projected by the particles

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Skin Friction Skin Friction / Form Drag Skin Friction / Form Drag Form Drag


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• m

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• THREE PHASE FLOWS

– Bubbles in a Slurry Flow

– Droplets and Particles in Gaseous flow

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Traditional Flow Regime Maps

1. Bubbly

2. Slug

3. Churn

4. Annular

The Basis is Flow Topology

jl = 1 m/s


Multiphase Flow

Classification by Flow Regimes

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Gas-Liquid Flow Regimes


Gas-Liquid Flow Regimes



Multiphase Flow


Gas Solid Flow

Regimes

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• Two Phase Flow (with phase change)

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Approaches to Multiphase Modeling

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• Euler-Lagrange Approach

• Euler-Euler Approach

– Eulerian Model

–Eulerian Granular Phase Model

–Mixture Model

–Volume Of Fluid (VOF) Model

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Multiphase Flow

DPM

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Euler-Lagrange Approach Discrete Phase Modeling


Multiphase Flow

Introduction to DPM

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• Calculation of the discrete phase trajectory using a Lagrangian formulation that includes

• discrete phase inertia

• hydrodynamic drag

• force of gravity

• both steady and unsteady flows

• Dispersion of particles due to turbulent eddies present in the continuous phase

• Heating/cooling of the discrete phase


Multiphase Flow

Introduction to DPM (contd.)

• Vaporization and boiling of liquid droplets

• Combusting particles, including volatile

evolution and char combustion to simulate

• Coal combustion

• Optional coupling of the continuous phase

flow field prediction to the discrete phase

calculations

• Droplet breakup and coalescence

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Introduction to DPM (contd.)

• Discrete phase α should be very small ( < 10%)

• Discrete Phase mass-fraction can be large

• The model is appropriate for the modeling of:

– spray dryers

– coal and liquid fuel combustion

• Inappropriate for:

– modeling of liquid-liquid mixtures

– fluidized beds

– any application where the volume fraction of the second phase is not negligible

• See Fluent user guide for coupling of DPM & other models e.g combustion, reactions etc.

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DPM Theoretical Bases

• Fluid Phase:

– Eulerian formulation as a single phase fluid with

or without turbulence.

• Dispersed Phase:

– Individual particle motion is traced through

particle equation of motion.

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• Force Balance

– Up = particle velocity

– FD = Drag Force

– Fx = Any Other force

– Both forces are as Force/particle mass (~acceleration)

Particle Equations of Motion

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• Virtual Mass Force

– Force (rate of momentum) required to accelerate

the surrounding fluid

– Significant for very small particle (dp ~ microns)

and when ρ > ρp

– Remember – boundary layer around particles are

not captured.

– Calculated as:

• Pressure gradient force:

Other Forces, Fx

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• Thermo-phoretic force

• When particle is in fluid with temperature gradient

• DT,p is the thermo-phoretic coefficient, to be provided by user

Other Forces, Fx

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• Or use the Talbot formula for Thermo-phoretic force:

Other Forces, Fx

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• Brownian Force

– For very small particles

• Saffman’s Lift force:

– This is lift force due to shear (particle in a velocity gradient region)

Other Forces, Fx

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Euler-Euler Approach

Eulerian (two-fluid) Model

Short Course on “Computational Fluid Dynamics for Industry” at Pakistan Institute of Engineering and Applied Sciences on September 9-10, 2013

• Overview

• The Eulerian multiphase model allows multiple

separate, yet interacting phases.

• The phases can be liquids, gases, or solids in nearly

any combination.

• An Eulerian treatment is used for each phase

• Any number of secondary phases can be modeled

(memory is the limit).

• For complex multiphase flows, however, you may find

that your solution is limited by convergence behavior

Eulerian Model



Multiphase Flow

• A single pressure is shared by all phases.

• Momentum and continuity equations are solved for

each phase.

• Several interphase drag coefficient functions are

available, which are appropriate for various types of

multiphase regimes. (You can also modify the

interphase drag coefficient through user-defined

functions, as described in the separate UDF Manual.)

• All of the k-e turbulence models are available, and

may apply to all phases or to the mixture

Eulerian Model contd.



Multiphase Flow

H:/Fluent 6.3/Docs/fluent6.3/help/html/udf/main_pre.htm

Conservation of Mass for Phase q • A separate mass balance equation is solved for every

phase q

• q is the volume fraction of qth phase

Conservation Equations



Multiphase Flow

Conservation of Momentum • A separate momentum balance equation is solved for

every phase q

• q is the qth stress-strain tensor

Conservation Equations



Multiphase Flow

Limitations

• Particle tracking (using the Lagrangian

dispersed phase model) interacts only with

the primary phase.

• Inviscid flow is not allowed.

• Melting and solidification are not allowed.

• Sharp Interfaces cannot be captured

Eulerian Model



Multiphase Flow

Euler- Euler Approach

Euler-Granular Phase Model

• For dense particulate flows, the DPM cannot

be used due to significant volume fraction of

solid phase

• Solid phase is modeled as a special type of

fluid using Kinetic Theory of Gases

• This Granular fluid has special correlations

for

– Granular Pressure

– Granular Viscosity

– Granular Temperature

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Multiphase Flow

EGPM

• Granular Phase modeled as Dense Gas

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Multiphase Flow

EGPM contd.

• Viscosity models for Solid phase

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Multiphase Flow

EGPM Governing Equation

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Multiphase Flow

EGPM Governing Equations Contd.

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Multiphase Flow

EGPM Governing Equations Contd.

• Various closure relations are used to model

the solid phase flow behavior

• The three most common are

– Gidaspow: good for dense fluidized bed applications.

– Syamlal: good for a wide range of applications.

– Sinclair: good for dilute and dense pneumatic transport lines and risers.

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Multiphase Flow

EGPM

• OpenFOAM simulation of granular flow

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Multiphase Flow

Algebraic Slip (Mixture) Model

• Solves one set of momentum equations for

the mass averaged velocity and tracks

volume fraction of each fluid throughout

domain.

• Assumes an empirically derived relation for

the relative velocity of the phases.

• For turbulent flows, single set of turbulence

transport equations solved.

• This approach works well for flow fields

where both phases generally flow in the

same direction.

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Multiphase Flow

ASM Governing Equations

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Multiphase Flow

ASM Governing Equations contd.

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Multiphase Flow


• Slip Velocity and Drag

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Multiphase Flow


• Limitations

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Multiphase Flow

Volume of Fluid Model

• This is an Interface Tracking Method

• Other such methods are – Level set method

– Moving front method

• Applied to immiscible fluids with clearly defined interface. – Shape of the interface is of interest.

• Typical problems: – Jet breakup.

– Motion of large bubbles in a liquid.

– Motion of liquid after a dam break.

• Steady or transient tracking of any liquid-gas interface.

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Multiphase Flow

VOF contd.

• Transient VOF simulation of Liquid Gas

interface

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Multiphase Flow

VOF Governing Equations

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Multiphase Flow

VOF Governing Equations contd.

• The Volume Fraction equation is solved to

track interface

• There are two schemes for interface

definition

– Piecewise linear scheme

– Donor-acceptor scheme

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Multiphase Flow

VOF Governing Equations contd.

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Actual Interface Piecewise Linear

Scheme

Donor-Acceptor

Scheme


Multiphase Flow

Porous Media Flow Modeling

• There are two main approaches to model

single or multiphase flow in Porous media

– Microscopic i.e. Pore scale modeling

– Macroscopic modeling

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Multiphase Flow

Pore-scale Modeling

• This requires resolving of every particle and

the interstitial spaces on mesh level

• The usual equation for transport phenomena

are solved with particles as solid boundaries

• Computationally expensive

• Find application in research and

development of better macroscopic models

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Multiphase Flow

Pore-scale Modeling

• CFD simulation of flow at Pore-scale level

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Multiphase Flow

Macroscopic modeling

• The Pore-scale modeling approach cannot be

used at an industrial scale

• Overall flow patterns are more important in

practical applications

• The porous medium is modeled as a

momentum sink in the Navier-Stokes

equation

• Two type of models exist

– Darcian model (for Stoke flow)

– Non-Darcian model (for Inertial flow)

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Multiphase Flow

Porous Flow Model Governing Equations

• Darcian law for Porous medium

– The pressure gradient due to Porous medium is

given as

– is the permeability coefficient for the porous

medium

– is the viscosity of fluid

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Multiphase Flow


• Non–Darcian (inertial) flow coefficient

• This is given as

– C2 is the inertial pressure loss coefficient

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Multiphase Flow


• The Momentum Sink term including both

Darcian and Non-Darcian terms for ith

direction is

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Multiphase Flow

• END

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Multiphase Flow

Documents

Lectures on CFD (Multiphase Flow)