M. Walter, N.Kornev and E.Hassel Institute of Technical...
Transcript of M. Walter, N.Kornev and E.Hassel Institute of Technical...
Investigation of turbulent reactingmixing processes at high Schmidt numbers
04.06.2010 © 2010 University of ROSTOCK | Institute of Technical Thermodynamics
M. Walter, N.Kornev and E.HasselInstitute of Technical ThermodynamicsUniversity of RostockGermany
5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Outline
1. Motivation2. Modeling3. Implementation and numerical setup4. Results5. Future work
04.06.2010 2© 2010 University of ROSTOCK | Institute of Technical Thermodynamics
5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
1. Motivation
− difficulties in the simulation of turbulent reacting flows at high Schmidt numbers
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5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
10010-12
chemistry time scale
mixing time scale
time (seconds)
mesh macro-mixing
subgrid
micro-mixing model
residence time
Sc = 1Sc > 1Sc < 1
spectral regimes of scalar field
ln (E)
1. Motivation
− mixing in (chemically reacting) turbulent flows is determined by the transport ofthe medium caused by vortices (macro-mixing) and the molecular mixing(micro-mixing)
− the molecular mixing is strongly influenced by the dissipation scale of the scalarfield (Batchelor scale )
− in flows with high Schmidt numbers ( ), the Batchelor scale is muchsmaller than dissipation scale of the velocity field (Kolmogorov scale )
− high Schmidt numbers are typical for liquids (pure water ~ 1000)− the correlation of both scales is determined from
Problem: is extremely small in turbulent liquid reacting flows , however all interactions on this scale have to be captured for a correct predictionof the mixing and the reaction rates
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5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Kλ
ScKB λλ =
DSc ν=Bλ
Bλ
1. Motivation
− sketch of the Batchelor-scale scalar field
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5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
KB λλ =KB λλ <<
gas-phase flow liquid-phase flow1≈Sc 1>>Sc
1. Motivation
− object of investigation: coaxial jet mixer
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r (recirculation)-mode j (jet)-mode
D− diameter pipe,d− diameter nozzle,V̇ D− flow rate pipe,V̇ d− flow ratenozzle
1 D
d
V DdV
+ <
1 D
d
V DdV
+ >
mLmDmd
4.005.001.0
===
1. Motivation
− experimental observations of the passive mixing
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macro-mixing in the jet mixerspatial resolution 0.3mm,
repetition rate 10 Hz
micro-mixing in the jet mixerspatial resolution 0.03mm,
repetition rate 10 Hz
2. Modeling
− governing equations for LES:
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1i j j turbi iij
j i j j i
u u uu upt x x x x x
ν τρ
∂ ∂∂ ∂∂ ∂+ = − + + − ∂ ∂ ∂ ∂ ∂ ∂
turbk i k ki k
i i i
C u C CD H
t x x xω
∂ ∂ ∂∂+ = − + ∂ ∂ ∂ ∂
turbii
i i i
u ff fD Jt x x x
∂∂ ∂ ∂+ = − ∂ ∂ ∂ ∂
continuity
momentum
speciesconcentration
turbulenttransport
0i
i
ux∂
=∂
passive scalar(mixture fraction)
turbulencechemistry interaction
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2. Modeling
− turbulence modeling
• dynamic mixed model (Vreman) for
• dynamic mixed model extended to scalar fluxes and
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turbijτ
turbiJ turb
iH
adopted by a specialclipping procedurebased on the Taylor series approximation toavoid numericalinstabilities
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2. Modeling
− considered chemical reaction is a fast irreversible neutralization reaction ofhydrochlorid acid and sodium chloride
− modeled as simple one step reaction
− calculation of the mean kinetic reaction rate
assumptions: infinitely fast reaction, isothermal, initial concentrations diluted
− validated by experiments using LDA and PLIF
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OHNaCLNaOHHCL 2+→+ ω
CBA →+ ω
kr
( ) BABABABABAk CCkCCCCkCkCCCRT
ETAr =+==
−= ''
0 expβ
0
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2. Modeling
− experimental observations of the reaction zone
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15 mm 55 mm
reactionzone
3. Implementation and numerical setup
− finite rate Eddy Dissipation Model for chemistry-turbulence interactionimplemented:
• in principle detailed reaction kinetics for is possible• for gaseous reactions (Sc ~ 1) the mixing rate is proportional to the dissipation of turbulent
kinetic energy modifications necessary to take better high Schmidt numbers into account• for liquid reactions (Sc >> 1) the mixing rate must be related to the dissipation of the scalar
• reaction rate
• scalar dissipation rate (Girimaji)
• scalar variance by a scale similarity model (Cook and Riley)
• finite rate EDM implemented using mixture fraction and reaction progress variables to simplifythe reaction kinetics, algebraic expressions for calculation of concentrations
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=
2',min
fCr f
kkk
εω
∂∂
∂∂
+=
iiturb
turbf x
fxf
ScScννε
( )ffffCf f −=2'
kr
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3. Implementation and numerical setup
− inlet boundary conditions• u: directMapped, inflowGenerator,
builtin turbulence generator• p: zeroGradient• f: fixedValue (coflow = zero, nozzle = one)• concentrations: fixedValue
NaOH = 50 mol/m3 (coflow)HCL = 5,5 mol/m3 (nozzle)
− Re ~ 12000, Sc ~ 1000− some comments on OpenFOAM
• chemistry-turbulence models in OpenFOAM require modifications to take high Schmidt numbers into account
• liquid-liquid reactions have still not properly considered in OpenFOAM• sophisticated models like FDF/transported PDF or ILDM/REDIM with presumed PDF are still
not available in OpenFOAM
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mdB µλ 1≈
mdk µλ 30≈
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4. Results
− axial velocity and mixture fraction
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4. Results
− velocity energy spectrum
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4. Results
− scalar energy spectrum Sc~1 vs. Sc~1000
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4. Results
− concentrations of reagents NaOH and HCL as well as NaCl
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4. Results
− competitive consecutive reaction
− reaction constants
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SRBRBA
→+
→+2
1
ω
ω
smolmk
smolmk
3
2
3
1
63.1
7300
=
=
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5. Future work
1. implementation of a new SGS model for LES based on multifractaltheory that accounts for high Schmidt number effects at high Reynolds numbers and moderate mesh resolutions
2. coupling of multifractal model and reaction kinetics with a chemistry-turbulence interaction model
3. implementation and testing of more sophisticated chemistry-turbulenceinteraction models for liquid-liquid reactions (like presumedPDF withILDM, FDF)
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Thank you for your attention!
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5th OpenFOAM Workshop, Chalmers, Gothenburg, Sweden, June 21-24, 2010
Matthias WalterUniversity of Rostock
Faculty of Mechanical Engineering and Naval Architecture
Institue of Technical Thermodynamics
Albert Einstein Str. 2
18059 Rostock
Germany
Email: [email protected]
Acknowledgement
• HRLN Supercomputing Center• Mr. J.Turnow
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