Numerical Simulation of Gas-Liquid-Reactors with Bubbly

Numerical Simulation of Gas-Liquid-Reactors with Bubbly Flows

using a Hybrid Multiphase-CFD Approach

Hybrid Interface Resolving Two-Fluid Model (HIRES-TFM)by Coupling of the Volume-of-Fluid (VOF) method

and the Two-Fluid model (TFM)

using .

Dipl.-Ing. Holger MarschallChair of Chemical Engineering

Technische Universität München

TFMTFM

VOFVOF

CFD in Chemical Reaction Engineering V – June 15-20, 2008 2

Outline

Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook

• background & motivation

• problem statement§ state-of-the-art (VOF & TFM)§ hybrid approach (HIRES-TFM)

• governing equations§ basic equation (VOF & TFM)§ basic idea & switch criterion (HIRES-TFM)

• numerical results§ prototype examples (HIRES-TFM)

• outlook


BackgroundPhenomenology of Multiphase-Flows – Process Technology


spray

droplet flow

churn flow

stratified flow

dense bubbly flow

dilute bubblyflow

smoke flow

dust flow

dilute particle flow

dense particle flow

granular flow

fluidized bed

sedimentation

fixed bed

solid fixed

solid in motion

gas/liquid flow

gas/solid flow

liquid/solidflow

porous medium

liquid solid

gas

solid fixedsolid in motion

[Laurien, 2004]


MotivationPhenomenology of Multiphase-Flows – Bubble Column Reactors


&GV

[Fan, 1990], [Mudde, 2003]


MotivationPhenomenology of Multiphase-Flows – Bubble Column Reactors


[Fan, 1990], [Mudde, 2003]

§ fluid dynamics of two-phase flow systems in process apparatus and chemical reactors with transient flow structures

§ fluid dynamics, reaction andmass transfer at gas-liquidinterfaces of two-phase flow systems with spatial and/ortemporal scales over more than 6 orders of magnitude

CFD in Chemical Reaction Engineering V – June 15-20, 2008 6[Deckwer, 1985], [Fan, 1990]

reactor inletmodelling, empiricism

reactor interiorflow structure n reactor performance

requirements§ Higher Accuracy, Cutback of Conservatisms & Uncertainties§ Portability to New Geometries and Range of Parameters§ Enhanced Scale-Up Options

Problem Statement State-of-the-Art – Current Frontiers


- porous plates, perforated plates, single orifice nozzles

- multiple orifice nozzles, perforated rings,spider-type spargers

vortex shedding

g/l interfacewake interfaceparticle flow

slurry-concentration

highlow


entity tracking models (EL)


DegreeDegree of Detail &of Detail &Computational CostsComputational Costs

Modelling EffortModelling Effort &&ComplexityComplexity

Problem StatementState-of-the-Art – Hierarchy of Numerical Methods

macroscopic & mesoscopic level

interface resolving methods (EE)

field averaging models (EE)

[Paschedag, 2007]

Lattice Boltzmann

Monte Carlo

microscopic level



Problem StatementHybrid Approach

⇒ HIRES-TFM = Hybrid Interface-Resolving Two-Fluid Model• interface resolving algorithm VOF for free surface flow regions

as long as local computational grid density allows interface capturing • extended two-fluid model TFM for dispersed flow regions

where dimensions of fluid parts are comparable to or smaller than grid spacing

[Tomiyama, 1998]

à challenge• Multiscale CMFD• Large-scale CMFD

à conceptual approach• adaptive:

as coarse as possible &as detailed as required




à challenge• Multiscale CMFD• Large-scale CMFD

à conceptual approach• adaptive:

as coarse as possible &as detailed as required TFM ITFM I

TFM IITFM II

VOFVOF

TFMTFM

VOFVOF

⇒ HIRES-TFM = Hybrid Interface-Resolving Two-Fluid Model• interface resolving algorithm VOF for free surface flow regions

as long as local computational grid density allows interface capturing • extended two-fluid model TFM for dispersed flow regions

where dimensions of fluid parts are comparable to or smaller than grid spacing


- interfacial friction

- interfacial tension

- turbulence

- mass transfer

- economic resolution of interfacial structures and dynamics: local adaptivemesh refinement (AMR)

- interfacial forces• drag force• non-drag forces

(lift force, turbulent drag force)

- polydispersity• (class method)• (method of moments)• (Monte-Carlo method)• interfacial area conc.

- coalescence and breakup

- turbulence incl. BIT

- mass transfer

TFM

bubbleFoamExt

VOF

interFoamExt

TFM ITFM I

TFM IITFM II

VOFVOF

HIRES-TFM




- continuity equation

- momentum equation

- topological equation (continuity)

- mixture density & mixture viscosity

- phase fraction equation (continuity)

- momentum equation


Governing Equation Coupling of the VOF method and the TFM – basic equations

( )

( ) σ

ρρ

µ ρ

∂+ =

∂ − ∇ + ∇

∇ ⋅

∇ + ∇ ⋅ + +Ttp

U UU

U U g F

µ αµ α µρ α ρ α ρ

= + −= + −

(1 )(1 )

a b

a b

( )ϕϕ ϕ

αα

∂+ =

∂∇ ⋅ 0

tU

( ) ( )ϕ ϕϕ ϕ ϕ ϕ ϕ

α αϕ ϕϕ ϕρ ρϕ ϕ

αα α

α

∂+ + =

∂− ∇ + +

∇ ⋅ ∇ ⋅t

p

effUU U R

g M

( )αα

∂+ =

∂∇ ⋅ 0

tU

=∇ ⋅ 0U

+ constitutive equationsinterfacial momentum transfer

+ model equationinterfacial tension

VOF TFM


- scalar flux second-moment closure in complex combustion models forturbulent flames

• relative velocity betweenburnt and unburnt gases

• progress variable

rU

%c

( )∇ ⋅ −% % (1 )r c cU

• problem of VOF methods: accuracy and reliability of the numerical approach to ensure the interface remains sharp

• basic idea for a sharp interface: convective transport term, counter gradient (against num. diffusion), conservative & bounded


Governing Equation Coupling of the VOF method and the TFM – interface compression


• problem of VOF methods: accuracy and reliability of the numerical approach to ensure the interface remains sharp

• basic idea for a sharp interface: convective transport term, counter gradient (against num. diffusion), conservative & bounded


Governing Equation Coupling of the VOF method and the TFM – interface compression

- convection-based sharpening algorithm in the phase fraction equation for interface capturing

• artificial compression term acting normal to the interface

• volume fraction of phase a

cU

αa

( )∇ ⋅ −% % (1 )r c cU

( ) ( )( )αα α α

∂+ + − =

∂∇ ⋅ ∇ ⋅ 1 0a

a a c a atU U

( )

α

α

α

αα

αα

∇=

∇

∇ = ∇

≤ ≤

min ,max

1 4

ac

a

ac

a

c

c

c

U U

U U U

where



Governing Equation Coupling of the VOF method and the TFM – switch criterion

( ) ( )( )αα α α

∂+ + −Γ =

∂∇ ⋅ ∇ ⋅ 1 0 d

aa a c a at

U U

( )α αΓ = ∇ ∆, , , ,...,d a a if a V We

ΓΓ =

∑

∑

d inb

d

inb

A

A

switch factor, that

- … carries the information about the interface shape

- …quantifies the local dispersion of the two-phase flow structure

- …estimates the interface reconstruction correctness of the VOF method

dΓ


Numerical Results

• Prototype Examples – HIRES-TFM


Interaction among a 5 mm bubble and many small bubbles of 0.25 mm in diameter in a 2D air-water system [Tomiyama, 2003]

5 mm

20 mm

45 mm

50 mm

small bubble regiond = 0.3 mm3% gas fraction

sb

large bubble regiond = 5.0 mm100% gas fraction

lb


Numerical Results




Numerical Results



t=0s t=0.1s t=0.2s30 mm

100 mm

small bubblesd = 0.3 mm5% gas fraction

sb

large bubblesd = 6-10 mm100% gas fraction

lb


Outlook


• Plans – HIRES-TFM

200 mm

200 mm

BOD

Y

H D dh

= 2000 mm= 200 mm= 10 mm

vs. experimental validation

simulation simulation of of a laba lab--scale scale bubble column bubble column with spargerwith sparger


Outlook


• Future Challenges – HIRES-TFM

spray spray formationformation & & jetsjets phase inversionphase inversion


Thanks for your attention…


• Acknowledgements

– Prof. Dr.-Ing. Olaf Hinrichsen & Prof. Wolfgang Polifke (TU München)– Dr. Henry G. Weller (OpenCFD Ltd.)– Prof. Dr. Hrvoje Jasak (FSB Zagreb, Wikki Ltd.)

• Contact

Dipl.-Ing. Holger MarschallLehrstuhl I für Technische ChemieTechnische Universität MünchenLichtenbergstr. 4D-85747 Garching

Tel.: +49 89 289-13512Email: [email protected]

mailto:[email protected]

Documents

Numerical Simulation of Gas-Liquid-Reactors with Bubbly