© 2011 ANSYS, Inc. June 7, 2012 1

Multiphase Modeling in Automobile Industries

Hossam Metwally

© 2011 ANSYS, Inc. June 7, 2012 2

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 3

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 4

Why Model Multiphase Flows?

Powertrain

• Piston Cooling

• Boiling in Cooling Jacket

• Cavitation in Water Pump

• Fuel Injector

• Lubrication

HVAC System

• Two-Phase Heat Exchangers

• Oil Separation

Cabin Flows

• Window Deicing

• Window Defogging

Fuel System

• Tank Filling

• Fuel Sloshing

• Fuel Vapor Emissions

Transmission System

• Clutch Performance

External Flows

• Tire Splashing / Hydroplaning

• Rain Water Management

• Windshield Wiper Performance

Manufacturing Process

• Spray Painting

• Casting

There are numerous examples of Multiphase Flow problems relevant to Automotive Industries

© 2011 ANSYS, Inc. June 7, 2012 5

• Bubbly flow: Discrete gaseous bubbles in a continuous liquid

• Droplet flow: Discrete fluid droplets in a continuous gas

• Particle-laden flow: Discrete solid particles in a continuous fluid

• Slug flow: Large bubbles in a continuous liquid

• Annular flow: Continuous liquid along walls, gas in core

• Stratified/free-surface flow: Immiscible fluids separated by a clearly-defined interface

bubbly flow droplet flow

particle-laden flow

slug flow

annular flow free-surface flow

Multiphase Flow – Definition and Regimes

• Flow of two or more immiscible fluids – Not for miscible fluids that mix at molecular level

Species transport models used miscible flows

© 2011 ANSYS, Inc. June 7, 2012 6

Separated flow

VOF

Dispersed flow

Eulerian model

Lagrangian models

Multiphase Models in ANSYS CFD

© 2011 ANSYS, Inc. June 7, 2012 7

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 8

• VOF model is used to model immiscible fluids with clearly defined interface.

– Two gases cannot be modeled since they mix at the molecular level.

– Liquid/liquid interfaces can be modeled as long as the two liquids are immiscible.

• VOF is not appropriate if interface length is small compared to a computational grid

– Accuracy of VOF decreases with interface length scale getting closer to the computational grid scale

• Typical problems:

– Liquid Sloshing

– Tank Filling

– Jet breakup

– Gear Lubrication

– Cooling of piston

– Steady or transient tracking of any liquid-gas interface

VOF Model : General Overview

© 2011 ANSYS, Inc. June 7, 2012 9

• Phases

• Arbitrary number of phases are allowed

• Any phase can be primary or secondary – not important in VOF model.

• Usual practice is to have secondary phase which has less presence in the domain

• Three ways phases may interact in VOF:

– Mass exchange

– Heterogeneous reactions

– Surface tension with optional wall adhesion effect

• VOF Scheme

• Explicit and Implicit

• Controls how phase continuity equation is solved (volume fraction through which interface is tracked)

• Implicit body force (Designed for flows with large body forces)

• Gravity acting on phases with large density difference.

• Flows with large rotational accelerations (such as centrifugal separators and/or rotating machinery).

• The force is handled in robust numerical manner.

Volume of Fluid Model Inputs

© 2011 ANSYS, Inc. June 7, 2012 10

• Explicit Scheme

– Default and used only with unsteady simulation

– Explicit scheme solves the volume fraction in sub time steps.

– Number of sub time steps is dictated by the value of the Courant number.

– The default value 0.25 is robust and should not be changed.

• Implicit Scheme

– Implicit scheme solves phase continuity equation (volume fraction) iteratively together with momentum and pressure.

– Available with both steady and unsteady simulation

Volume of Fluid Model Schemes

Advantages Disadvantages

Explicit VOF

Allows use of Geo-Reconstruct scheme (scheme which renders a sharp interface without numerical diffusion). Should be used in simulation of flows where surface tension is important because of highly accurate curvature calculation.

Poor convergence for skewed meshes. Poor convergence if phases are compressible

Implicit VOF

Does not have Courant number limitation (can be run with large time steps or in steady state mode) Can be used with poor mesh quality and for complex flows (e.g. compressible flows)

Numerical diffusion of interface does not allow accurate prediction of interface curvature, so accurate prediction of flows where surface tension is important is not feasible

© 2011 ANSYS, Inc. June 7, 2012 11

• Zonal Discretization Option

– This option provides diffusive or sharp interface modeling in different fluid (cell)zones based on the value of zone dependent slope limiter.

Zonal Discretization

(Zone 1) (Zone 2) (Zone 3)

Slope Limiter (Beta) Scheme

Beta = 0 First Order Upwind

Beta = 1 Second order upwind

Beta = 2 Compressive

0 < Beta < 1 , 1 < Beta < 2

Blended scheme

© 2011 ANSYS, Inc. June 7, 2012 12

• Phase localized compressive scheme facilitates diffusive and sharp modeling of distinct interfaces.

• Phase based discretization is based on effective slope limiter in interfacial cells, where slope limiter is taken as interfacial property between phases.

• Could be effectively used for the cases where HRIC/Compressive schemes produce undesirable behavior.

• It is available with VOF model and Eulerian multiphase using “immiscible fluid model” option.

Phase-1 Phase-0 Phase-2

“Phase localized compressive scheme” with all slope limiters = 2, is same as “Compressive” scheme.

Phase localized Compressive Scheme

© 2011 ANSYS, Inc. June 7, 2012 13

• Variable time stepping

– Scheme for explicit VOF

– Automatically adjusts the time step based on

• Global Courant number

– Controls can be provided for

• Max and min time steps used

• Change factor for time steps

• It is useful for explicit problems as the time step determines the stability for speed of the solution

Variable Time Stepping With Explicit VOF

© 2011 ANSYS, Inc. June 7, 2012 14

Coupled VOF Solver

• Solves the momentum, pressure based continuity and volume fraction equations together.

• The full implicit coupling achieved through an implicit discretization of pressure gradient terms in the momentum equation and implicit discretization of face mass flux in continuity and volume fraction equations.

• Formulation involves the following linearization

– Linearization of phase mass flux in VOF equation

– Linearization of body force due to gravity in momentum equation

• Coupled VOF solver aims to achieve faster steady state solution compared to segregated method of solving equations.

© 2011 ANSYS, Inc. June 7, 2012 15

Examples and Validations

© 2011 ANSYS, Inc. June 7, 2012 16

• Box (20cm x 10cm x 10cm) half filled with water

• 2,000 hex cells used for both runs

• Tank has a sinusoidal motion

Traditional method

DM method

tVgx cos

tVv sin

Alternative Tank Sloshing Approach

© 2011 ANSYS, Inc. June 7, 2012 17

A rectangular tank is 20% filled with liquid

The periodic swaying of the tank is studied using FLUENT

Results are compared to experiment1 for

• General flow patterns

• Pressures recorded at three sites (shown)

1Hadzic, et al., Numerical Simulation of Sloshing, Proc. SRI-TUHH Mini Workshop on Numerical Simulation of Two-phase Flows, Ship Research Institute, Tokyo, Japan, 2001.

Tank Sloshing Validation

© 2011 ANSYS, Inc. June 7, 2012 18

Sloshing Validation

Velocity vectors colored by static pressure

Static Pressure comparison at pressure taps p1,p2,p3

Red-> Experiment Blue-> FLUENT

© 2011 ANSYS, Inc. June 7, 2012 19

Experimental result represented by the dotted line

Free surface level ( t = 0.08 s)

Plots for total pressure vs time at a point-1 (comparison with experiment)

Reference : Simulation of Fuel Sloshing- Comparative Study, Matej Vesenjek, Heiner Mullerschon, Alexander Hummel, Zoran Ren,

Sloshing Validation

© 2011 ANSYS, Inc. June 7, 2012 20

Fill required at each start cycle

Cavity is drained after each engine use

Initial fill is idle engine condition for a duration of 30 seconds

Then, full throttle acceleration ramp for an additional 30 seconds

Cavity volume = 4.4 liters

Water Jacket Filling

Original Design

Modified Design Courtesy of Volvo Penta

© 2011 ANSYS, Inc. June 7, 2012 21

Evaporative Fill

Gasoline filling case with fuel evaporation (i.e. phase change)

Liquid Phase: Gasoline (volatile liquid so it evaporates quickly)

Gas Phase: Air/Fuel Vapor Mixture

VOF model, RNG Turbulence model

Vapor emissions reduced by 2X by modifying

recirculation tube design

Modified Design Original Design Courtesy of Mark IV

© 2011 ANSYS, Inc. June 7, 2012 22

Oil Splashing

•Sliding Mesh/ Moving Deforming Mesh (MDM) is used along with VOF Model

•VOF Scheme: Implicit Compressive scheme

•Similar Examples •Gear lubrication •Cooling of piston/clutch/break

Oil Splashing in Gear Systems

oil splashing off crank shaft and oil pan walls

© 2011 ANSYS, Inc. June 7, 2012 23

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 24

Mixture Model : General Overview

• The mixture model is a simplification of the Eulerian multiphase model. • Solves one set of momentum equations for the mass averaged velocity and tracks volume fraction of each fluid throughout domain. •Derives a constitutive relation for the relative velocities based on local equilibrium over the length scales. •For turbulent flows, a single set of turbulence transport equations is solved. •For non-isothermal flows, a single energy equation is solved based on mixture properties.

Typical Applications : • Cavitation Model :

- Fuel Injector Cavitation - Cavitating Flow in a Centrifugal Pump - Cavitation in a Gerotor

• Homogeneous Boiling Model -Engine Jacket Boiling

© 2011 ANSYS, Inc. June 7, 2012 25

Mixture Model inputs :

Activate the mixture model.

Choose gas under Phase

Click on Set...

© 2011 ANSYS, Inc. June 7, 2012 26

Cavitation :

- Generation of vapor bubbles in a liquid due to a local reduction in pressure below the vapor pressure of the liquid at a given temperature

- Cavitation= nucleation which occurs for P < Pvapor

- Boiling= nucleation which occurs for T > Tsaturated

From a basic physical point of view, cavitation and boiling are similar processes.

• Cavitation can cause

• Physical damage

• Flow blockage, unwanted unsteadiness

© 2011 ANSYS, Inc. June 7, 2012 27

Fuel Injector Cavitation

Vapor Volume Fractions on the Injector Surface

Mass flow rate with cavitation = 0.01287 kg/s Mass flow rate from non-cavitating flow =0.015 kg/sec 14% of mass reduction due to cavitation

• steady-state • inlet pressure 1,710 bar • outlet pressure 0 bar • fluid - diesel fuel • vaporization pressure of 55 Pa • Schnerr-Sauer cavitation models • Realizable k-e turbulence model

© 2011 ANSYS, Inc. June 7, 2012 28

Cavitating Flow in a Centrifugal Pump

• Inlet: Flowrate of 210m3/hr • Exit: Abs pressure (600-350) kPa • Water: Vap pressure of 2620 Pa. • Schnerr-Sauer Cavitation model • Realizable k-e turbulence model • Rotational speed was 2150 rpm. • Coupled – pressure based solver

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0 1.5

Cavitation number

He

ad

ris

e c

oe

ffic

ien

t

Hofmann et al [20]CFD

© 2011 ANSYS, Inc. June 7, 2012 29

Unsteady Cavitating Flow in a Vane Pump

Vapor Volume Fraction Over Pump Surface

1. User-defined function (UDF) controlling the mesh motion.

2. Pressure inlet – 0 bar 3. Pressure outlets - gauge pressure: 120 bar 4. The segregated SIMPLEC solver was used with

PRESTO pressure scheme, 2nd-order convective schemes and 1st-order time stepping.

5. The standard k-e model with non-equilibrium wall functions

6. Schnerr-Sauer cavitation model 7. Three cases with rotational speed of 6,000, 7,000

and 8,000 rpm. 8. The Zwart-Gerber-Belamri model was only used to

run 7,000 rpm case. 9. The liquid phase was treated as compressible oil,

while the vapor phase was assumed to be constant.

10. Drop in volumetric efficiency!! 11. Unbalanced transient force on pump!!

© 2011 ANSYS, Inc. June 7, 2012 30

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 31

Eulerian Model Applicability

• Eulerian Model applicability

• Flow regime

• Bubbly flow, droplet flow, slurry flow, fluidized bed, particle-laden flow

• Volume loading

• Dilute to dense

• Particulate loading

• Low to high

• Application examples

• Flows with high particulate loading

• Slurry flows

• Sedimentation

• Fluidized beds

• Risers

• Packed bed reactor components

© 2011 ANSYS, Inc. June 7, 2012 32

Dispersed Phase Diameter

• Particle diameter is used in interaction drag force calculations

• There are three ways to calculate dispersed phase diameter

– Constant – if you know the representative size of the dispersed phase describing your size distribution

– User-defined – if you know some correlation for your particle size as function of local flow parameters (velocity, temperature, pressure)

– Using IAC or the Population Balance Model (Sauter mean diameter)

© 2011 ANSYS, Inc. June 7, 2012 33

Heat Transfer in Eulerian Model

211212 TThQ

22

21112

Nu6d

hp

3/1prim

2/1 PrRe6.00.2Nu pp

• The Gunn correlation is frequently used for Eulerian multiphase simulations involving a granular phase.

• The Ranz-Marshall correlation is frequently used for Eulerian multiphase simulations not involving a granular phase.

© 2011 ANSYS, Inc. June 7, 2012 34

Mass Transfer in Eulerian Model

• Mass transfer defined through phase interaction panel

• Mass transfer models available with mixture and Eulerian models

– Cavitation

– Boiling

– Evaporation-condensation model

– User defined mass transfer

– Mass transfer due to heterogeneous reactions

– Nucleation and growth in population balance models

© 2011 ANSYS, Inc. June 7, 2012 35

Three boiling model options are available: • RPI Boiling Model

– Applicable to subcooled nucleate boiling • Non-equilibrium Boiling

– Extension of RPI to take care of saturated boiling • Critical Heat Flux

– Extension of RPI to take care of boiling crisis

Bubble diameter: • Algebraic formulations and UDF options

Interfacial transfer models include: • A range of sub-models for drag and lift, and

turbulent dispersion • Liquid-vapor interface heat and mass transfer

models

Contours of vapor volume fraction in a nuclear fuel assembly

Boiling Models

© 2011 ANSYS, Inc. June 7, 2012 36

• Coupled DPM and the Eulerian Multiphase Model

– Track particle in Lagrangian framework, calculate

cell volume fraction and use it in Eulerian

momentum equation of primary phase

– Momentum coupling through drag force

• Particle-Particle interaction options:

- Kinetic theory

- Discrete Element Method (DEM) : Soft-sphere collision model

• Typical applications

– Cyclone separator

– Fluidized bed

– Riser

Dense Discrete Phase Model (DDPM)

© 2011 ANSYS, Inc. June 7, 2012 37

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 38

DMP Model : Overview

ICE

Boiler

Cyclones

Spray Nozzle

Scrubber

Courtesy of Lurgi

• Many engineering flows involve interaction between a gas phase and lightly loaded particles/droplets, such as:

– Cyclone separators

– Pulverized coal/oil fired boilers

– Internal combustion engines

– Spray dryers, etc.

• This interaction is computed by the Discrete Phase Model (DPM) in ANSYS CFD

© 2011 ANSYS, Inc. June 7, 2012 39

DPM in ANSYS CFD

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

– Exchange energy, mass, and momentum with Eulerian gas or liquid phase

• Discrete phase volume fraction < 10%

– Mass loading can be large

– No particle-particle interaction

• Turbulent dispersion modeled by

– Stochastic tracking

– Particle cloud model

• Ideally suited for situations where particles enter and leave computational domain

• Particle types:

– Inert particle heating and cooling – Droplet evaporation/boiling – Devolatilization – Char combustion

Continuous phase flow field calculation

Particle trajectory calculation

Update continuous phase

source terms

© 2011 ANSYS, Inc. June 7, 2012 40

Discrete Phase Model (DPM) Setup

© 2011 ANSYS, Inc. June 7, 2012 41

• Breakup modeling is the key to spray and atomization simulations

• Available Break-up Models in ANSYS FLUENT

– Taylor Analogy Breakup (TAB)

• Suitable for low-speed jet (We < 100)

– Kelvin-Helmholtz Breakup model (Wave)

• Suitable for high-speed jet (We > 100)

– Kelvin-Helmholtz / Rayleigh-Taylor Breakup model (KH-RT)

• Suitable for breakup of high-speed jet

– Stochastic Secondary Droplet (SSD)

• Random size of child particle

Modeling Breakup

© 2011 ANSYS, Inc. June 7, 2012 42

Spray calibration for Non-evaporating sprays

Spray Penetration Length

Finer Mesh show mesh independent results

Mesh Dependence Study SSD Model Time-step dependence Study SSD Model

Kumzerova, E. and Esch, T., “Extension and Validation of the CAB Droplet Breakup Model to a Wide Weber Number Range”, Proc. of the 22nd Europ. Conf. on Liquid Atomization and Spray Systems, Paper ILASS08-A132, Como Lake, 2008.

© 2011 ANSYS, Inc. June 7, 2012 43

• Objective

• Modeling oil separation in a PCV oil separator

• Modeling wall film drainage & strip-off at sharp edges

• Mesh:

• Element type = Polyhedra

• Cell count = ~118K

• Models:

• Oil mist particles modeled using DPM model as inert particles

• Wall film modeled using New Eulerian Wall Film (EWF) model

Oil Separation Modeling using EWF Model

Gas flow = 5.6 kg/hr Oil flow = 36 kg/hr

Pressure outlet = 0 Pa

Gas flow = 5.6 kg/hr Oil flow = 36 kg/hr

© 2011 ANSYS, Inc. June 7, 2012 44

Results (Wall Film Development and Drainage)

Film thickness of up to 1 mm was found in this case

© 2011 ANSYS, Inc. June 7, 2012 45

Results (Particle Strip-off)

© 2011 ANSYS, Inc. June 7, 2012 46

Eulerian Wall Film Model

• Solves for film mass, momentum, heat transfer

• Particle/Phase collection, film formation, transportation, Splashing ,Separation, Stripping.

• Eulerian wall film can be coupled with Eulerian-Lagrangian(DPM) and Eulerian-Eulerian multiphase frame work.

Assumption: • EWF model assumes that film always flows parallel to the surface so normal component of film velocity is zero. • The film is assumed to have:

A parabolic velocity profile & A bilinear temperature profile

across its depth.

Limitations: • Available only with 3D solver • Compatible with stationary walls only • Not compatible with MRF zone & Periodic BC’s • Heat Transfer Modeling compatible only with DPM coupling of EWFM

© 2011 ANSYS, Inc. June 7, 2012 47

Current Status

Physics Cab be Modeled using EWF model?

Liquid Droplet Collection

Film Running on the Surface (Shear, Gravity & Viscous Forces)

Particle Splashing X (will be available in Future releases)

Particle Stripping

Particle Separation

Film Heat Transfer with gas and wall with DPM X With Eulerian

(will be available in Future releases)

Viscous & Kinetic Heating

Evaporation & Condensation X (will be available in Future releases)

Melting & Solidification Possible through UDF

Sublimation Possible through UDF

Collection Efficiency Calculation 14.0 (with a small UDF)

© 2011 ANSYS, Inc. June 7, 2012 48

Erosion Modeling Example

• Challenges ► Equipment erosion from higher

flow rates and increased solids concentrations

► Substantial economical maintenance and shut down costs

► Quite common in many aspects of oil and gas processing

• ANSYS CFD Solutions – CFD modeling can predict erosion rates for field

conditions over the lifetime of the equipment – Optimization of production, operation,

inspection and maintenance. – Maximum erosion in complex flows and

geometries can be predicted to within a factor of 2-3 Courtesy of Total—Process and Refining Division

Particle trajectories colored by velocity and associated erosion area for two chokes

WC Steel

WC Steel

10 %

100 %

Area of high erosion

Courtesy of DNV

© 2011 ANSYS, Inc. June 7, 2012 49

Selective Catalytic Reduction (SCR) Modeling :

Diffusion controlled

Convection / Diffusion controlled

Display by particle diameter

New multi-component evaporation Law

o Diffusion controlled

o Convection/Diffusion controlled

DPM Enhancements

o Post processing

• Particle by size

• Filter particles /streams

o Stability

• Node based averaging

© 2011 ANSYS, Inc. June 7, 2012 50

Rain Water Management

Expt

Fluent

• DPM Particle Tracking

© 2011 ANSYS, Inc. June 7, 2012 51

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 52

Deicing

• Flow and Conjugate Heat Transfer solution, using Solidification / Melting model • Fluid Zones

Passenger compartment Control panel domain Ice layer

• Solid Zone Glass windows

• Ice initially covers entire outside surface of windshield • Detailed example was presented in [1]

Courtesy Visteon Automotive Systems - Germany

© 2011 ANSYS, Inc. June 7, 2012 53

Courtesy Skoda Auto

Deicing Validation Results

© 2011 ANSYS, Inc. June 7, 2012 54

Improve Deicing Analysis

Combine Solidification / Melting with Multiphase (VOF) model

• Water dripping down the windshield under gravity

– Expand domain to include air layer on top of the ice

– Mesh requirements to capture and track free surface of melted water

• Transient solution for Flow, Turbulence, Temperature, Liquid Fraction is required

– CPU intensive

© 2011 ANSYS, Inc. June 7, 2012 55

-Introduction

-Volume of Fluid (VOF)

-Mixture Model

-Eularian Model

-DPM

-Melting and Solidification

-Single phase, multi-species

-Summary and Conclusion

Agenda

© 2011 ANSYS, Inc. June 7, 2012 56

Defogging

To remove the moisture or fog from Windshield / Windows.

Evaporation and Condensation of water from Windshield and Windows

Approach: • Species transport for dry air and water vapor

• Flow inside the cabin may be steady state

• Energy equation

• Turbulence models

• Transient solution for temperature, species concentration, and fog layer thickness

• Mass transfer rate is evaluated as a function of local vapor concentration, temperature, and partial pressure

© 2011 ANSYS, Inc. June 7, 2012 57

Defogging

Cabin Defogging Model

Initial Fog Layer = 10 μm 20 seconds of simulation

Contours of water film thickness

Courtesy Mindware Engineering

© 2011 ANSYS, Inc. June 7, 2012 58

-Several ANSYS CFD multiphase capabilities were discussed

- Sloshing, filling, lubrication (VOF)

- Cavitation (mixture model)

- Boiling (Eularian)

- Spray, drying, Eularian wall film, erosion (DPM)

- Solidification/melting

- ….

Summary

© 2011 ANSYS, Inc. June 7, 2012 59

Appendix

© 2011 ANSYS, Inc. June 7, 2012 60

Engineering operations often involve “non-spontaneous” processes

• Mixing -- Keep a mixture of components that separate naturally, mixed. Desire to improve contact between the phases to improve and enhance interfacial transfer processes

• Separation -- Need to separate components that are difficult to separate, such as fine dust from flue gases

Flow dynamics crucial to the efficiency of these processes

Non-linear effect of parameters and geometry on processes

Challenges Involving Multiphase Flows

© 2011 ANSYS, Inc. June 7, 2012 61

Eulerian vs Lagrangian Tracking

Multiphase flow

Dispersed flow

Yes

No

Eulerian tracking

Eulerian tracking

Eulerian, Mixture

VOF, Immiscible fluid model

Lagrangian tracking

DPM, DDPM

© 2011 ANSYS, Inc. June 7, 2012 62

Separated or Dispersed ?

Sprays

Bubble

© 2011 ANSYS, Inc. June 7, 2012 63

Tank Filling

© 2011 ANSYS, Inc. June 7, 2012 64

Mixture Model Inputs :

Define…Phases…Interaction

© 2011 ANSYS, Inc. June 7, 2012 65

Cavitation in a Gerotor

• Hex mesh in the gerotor core

• Moving Deforming Mesh

– UDF for Gerotor Motion

• Schnerr-Sauer Cavitation Model

• ∆t = 2 deg.

• Simulation performed for 2 full rotations

© 2011 ANSYS, Inc. June 7, 2012 66

• Horizontal Nucleate boiling with 1 bar, 2 bar and 3 bar operating pressure pressure

• Material : 50% Aqueous Ethylene Glycol

• Properties are taken from NIST Fluid properties database

• Inlet velocity : 0.25 m/s

• Heated wall temperature is varied

Horizontal Boiling Validation Case

Reference : Bo, T. , ‘CFD Homogeneous Mixing Flow Modeling to Simulate Subcooled Nucleate Boiling Flow’, SAE TECHNICAL PAPER SERIES, 2004.

Wal

l He

at F

lux

(KW

/m2

)

Heated wall Temperature (C)

© 2011 ANSYS, Inc. June 7, 2012 67

•Heat Transfer augmentation at the wall:

-Total heat flux through a heated wall comprises of two componenets:

q = qsingle phase + qnucleate boiling

-The nucleate boiling component is modeled by Rohsenow correlation:

•Mass Transfer :

- Phase change is captured by inbuilt Evaporation-Condensation model

Homogeneous Boiling Model (HBM):

© 2011 ANSYS, Inc. June 7, 2012 68

• Used to model particles (or bubbles/droplets) in a continuous phase.

• Allows for mixing and separation of phases

– Solves momentum, enthalpy and continuity equations for each phase and tracks volume fractions

• Uses a single pressure field for all phases

– The interaction between the mean flow of both phases is modeled via interaction terms

• Drag, virtual mass, lift and other forces

• Can model heterogeneous chemical reactions using either built-in models or user-defined functions

• Can model turbulence equations for each phase

Eulerian Model – Overview

© 2011 ANSYS, Inc. June 7, 2012 69

Interphase Forces: Drag

• Drag is caused by relative motion between phases and is the most important interfacial force

– Correction is a function

of the Reynolds number

for the dispersed phase:

12

12112

fK

scale time Stokes18 1

221

12

d

)C(24

Re orrectionCd

,0)(1

n

ikiik uuK

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

4.00E-01

0 0.005 0.01 0.015 0.02

universal, paraffin oil

/3

2 gdC b

d

Viscous

)Re15.01(Re24 687.0dC

Oblate spheroid

38

dC

Spherical cap

Bubble diameter, m

Rise velo

city, m/sec 1

2121Re

vvdp

diameter phase Dispersed

© 2011 ANSYS, Inc. June 7, 2012 70

• Caused by relative acceleration between phases

• Significant only when mesh size is less than length scale of acceleration

• This situation is very rare – one example might be a gas injector in liquid at distances very close to the injector, but in reality we rarely need to resolve such scales when using the Eulerian model

• Helps in convergence and provides physical secondary phase velocities

22

211

112vm12,vm uu

uuu

uF

ttC

Interphase Forces : Virtual Mass Force

© 2011 ANSYS, Inc. June 7, 2012 71

• Caused by the shearing effect of the fluid on particles

• Lift forces are more significant for larger particles

– Not appropriate for very small particles.

• Lift force usually insignificant compared to drag force except when there is a large velocity gradient near the wall in continuous phase

11212L12,L uuuF C

Interphase Forces : Lift force

© 2011 ANSYS, Inc. June 7, 2012 72

• Reactions occurring between phases can be modeled

− Options for specifying which phase temperature will be used for calculating reaction parameters

• Inbuilt inputs for specifying

– Stoichiometric coefficients

– Arrhenius rate parameters

• Option of user defined reaction rates

Heterogeneous Reactions

© 2011 ANSYS, Inc. June 7, 2012 73

Coupling Between Phases

• One-way coupling vs. two-way coupling

• In combustion systems, typically two-way coupling of discrete and continuous phases • Fluid phase influences particulate phase via drag, heat transfer and

turbulence transfer

• Particulate phase influences fluid phase via source terms for mass, momentum, and energy equations

• Examples include:

• Inert particle heating and cooling

• Droplet evaporation/boiling

• Devolatilization

• Char combustion

© 2011 ANSYS, Inc. June 7, 2012 74

• Reitz and Bracco have outlined the existence of a length of intact liquid near the injection nozzle.

– This liquid region is approximated by packed 'blobs' with initial diameter equal to the size of the effective nozzle diameter.

• Primary and secondary droplet breakup is predicted with the KH wave instability model (Wave model ) within this liquid core.

• Beyond the liquid core, breakup is predicted with both the KH and RT models, whichever causes droplets to breakup first.

• The region where the liquid core (and therefore the KH model) dominates is described by a breakup length Lb from the injection nozzle.

• The KH-RT model depends on some adjustable parameters that may vary from case to case.

Theory : KH-RT Model

B0

Controls the size of child droplets in the KH model. Influences the rate of change of the parent droplet's

radius in the KH model. Increasing it increases the overall droplet size.

B1

Controls the rate of breakup in the KH model. Decreasing it accelerates the KH droplet breakup. Strongly influences the momentum exchange between

dispersed and gas phases in the near nozzle region. Strongly affects spray penetration in low Weber

number cases.

CL

Correlated with B1. Can be calculated with different approaches in high

Weber number regimes.

C

Controls the rate of breakup in the RT model, beyond the breakup length.

Decreasing it accelerates the RT droplet breakup.

CRT

Controls the size of child droplets in the RT model, beyond the breakup length.

Controls which droplets will breakup. Increasing it increases the diameter of the droplets allowed to breakup in the RT model.

Strongly affects spray penetration in low Weber number cases.

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• Drops larger than a critical radius are subject to breakup, Critical radius is given by

• Drops with a radius larger than the critical radius have the breakup time incremented. When the breakup time on the parcel is larger than the critical breakup time (locally calculated from conditions in the cell and on the parcel) breakup can occur

• When breakup occurs parcels are created with a target number in parcel (NP) set by the user and samples are taken from the diameter distribution at that target NP until the mass of the parent parcel is used up. The average NP for that event then is scaled to conserve mass.

Theory: SSD Model

This methodology results in improved statistics and gives the user control over error during a simulation. A smaller NP will mean more parcels but lower statistical error.

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DPM Setup

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EWF setup

Turning ON EWF on the desired walls

EWF model input parameters

In this case DPM tracked in unsteady state with unsteady flow. This is however not required as EWF model is inherently transient and can be run with steady flow and steady DPM

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• Time-step size = 0.05 s

• Iterations per time-step size = 30

• DPM iteration per flow iteration = 1

• DPM time-step size = 0.05 s

• ~4 hours of clock time to run 10s of flow

• Machine specification:

– 8 CPUs of a 24 CPU 48 GB RAM machine with 2.8 GHz clock-speed

Results (Run time)

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Spray Dryer Example

• Goal: Characterize the effect of liquid feed location

and/or angle on particle trajectories to reduce the potential of fouling

► Various combinations tested • Vane angle • Spray nozzle locations • Nozzle angle settings

10 m/s injection 2.5 m/s injection

Particle tracks colored by particle mass

Moisture contours for 2.5 m/s injection

Temperature contours Moisture

content Air flow patterns

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Evaporating sprays : KH-RT Model

Data Extraction from Simulations •For evaluating the spray penetration, 90% spray mass was used

*H. Koss, D. Bruuggemann, A. Wiartalla, H. Backer, and A. Breuer, Results from Fuel/Air Ratio Measurements in an N-Heptane Injection Spray, IDEA periodic report, RWTH Aachen, 1992.

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• Total simulated time 20 minutes

• Time step 2.5 seconds

• Compare well with test data, up to ~15 minutes

Courtesy Visteon Automotive Systems - Germany

Deicing Validation Results

Water is dripping down the windshield under gravity as time passes.