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


1. Motivation

− difficulties in the simulation of turbulent reacting flows at high Schmidt numbers



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



Kλ

ScKB λλ =

DSc ν=Bλ

Bλ

1. Motivation

− sketch of the Batchelor-scale scalar field



KB λλ =KB λλ <<

gas-phase flow liquid-phase flow1≈Sc 1>>Sc

1. Motivation

− object of investigation: coaxial jet mixer



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



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:

04.06.2010

8


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

© 2010 University of ROSTOCK | Institute of Technical Thermodynamics 8

2. Modeling

− turbulence modeling

• dynamic mixed model (Vreman) for

• dynamic mixed model extended to scalar fluxes and

04.06.2010


turbijτ

turbiJ turb

iH

adopted by a specialclipping procedurebased on the Taylor series approximation toavoid numericalinstabilities


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

04.06.2010


OHNaCLNaOHHCL 2+→+ ω

CBA →+ ω

kr

( ) BABABABABAk CCkCCCCkCkCCCRT

ETAr =+==

−= ''

0 expβ

0


2. Modeling

− experimental observations of the reaction zone



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

04.06.2010

12


=

2',min

fCr f

kkk

εω

∂∂

∂∂

+=

iiturb

turbf x

fxf

ScScννε

( )ffffCf f −=2'

kr


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

04.06.2010


mdB µλ 1≈

mdk µλ 30≈


4. Results

− axial velocity and mixture fraction

04.06.2010

14



4. Results

− velocity energy spectrum

04.06.2010

15



4. Results

− scalar energy spectrum Sc~1 vs. Sc~1000

04.06.2010

16



4. Results

− concentrations of reagents NaOH and HCL as well as NaCl

04.06.2010

17



4. Results

− competitive consecutive reaction

− reaction constants

04.06.2010

18


SRBRBA

→+

→+2

1

ω

ω

smolmk

smolmk

3

2

3

1

63.1

7300

=

=


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)

04.06.2010



Thank you for your attention!

04.06.2010


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


m. walter, n.kornev and e.hassel institute of technical...

Documents