numerical simulation of gas-liquid-reactors with bubbly
TRANSCRIPT
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 3
BackgroundPhenomenology of Multiphase-Flows – Process Technology
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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]
CFD in Chemical Reaction Engineering V – June 15-20, 2008 4
MotivationPhenomenology of Multiphase-Flows – Bubble Column Reactors
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
&GV
[Fan, 1990], [Mudde, 2003]
CFD in Chemical Reaction Engineering V – June 15-20, 2008 5
MotivationPhenomenology of Multiphase-Flows – Bubble Column Reactors
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
[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
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
- 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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 7
entity tracking models (EL)
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 8
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 9
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
Problem StatementHybrid Approach
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 10
- 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
Problem StatementHybrid Approach
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
CFD in Chemical Reaction Engineering V – June 15-20, 2008 11
- continuity equation
- momentum equation
- topological equation (continuity)
- mixture density & mixture viscosity
- phase fraction equation (continuity)
- momentum equation
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 12
- 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
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
Governing Equation Coupling of the VOF method and the TFM – interface compression
CFD in Chemical Reaction Engineering V – June 15-20, 2008 13
• 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
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 14
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 15
Numerical Results
• Prototype Examples – HIRES-TFM
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 16
Numerical Results
• Prototype Examples – HIRES-TFM
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
CFD in Chemical Reaction Engineering V – June 15-20, 2008 17
Numerical Results
• Prototype Examples – HIRES-TFM
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 18
Outlook
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • 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
CFD in Chemical Reaction Engineering V – June 15-20, 2008 19
Outlook
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
• Future Challenges – HIRES-TFM
spray spray formationformation & & jetsjets phase inversionphase inversion
CFD in Chemical Reaction Engineering V – June 15-20, 2008 20
Thanks for your attention…
Background & Motivation • Problem Statement • Governing Equations • Numerical Results • Outlook
• 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]