cfd modelling of turbulent mass transfer in a mixing channel

CFD Modelling of Turbulent Mass Transfer

in a Mixing Channel

Lene K. Hjertager Osenbroch, Bjørn H. Hjertager and Tron SolbergAalborg University Esbjerg

Esbjerg, DenmarkHomepage: hugin.aue.auc.dk

Prepared forComputational Fluid Dynamics in Chemical Reaction Engineering IV

June 19-24, 2005, Il Ciocco Hotel and Conference CenterBarga, Italy

Overview

Objectives Flow Configuration PIV/PLIF Experiment Governing Equations Turbulence and Micromixing Models Numerical Results Conclusions

Objectives

Objectives of current project

PIV/PLIF measurements of mass transfer and chemical reactions in turbulent liquid flows

– pure mixing/mass transfer– acid-base chemical reaction (Poster presentation)

CFD modelling of mass transfer and chemical reactions (Poster presentation) in turbulent liquid flows

Flow Configuration

Confined wake flowChannel dimensions

Mixing channel– Length 640 mm– Cross-section 60 mm x 60 mm

Feed channel– Length 330– Cross-section 20 mm x 60 mm

Flow conditionsFluid : Water

Feed channel A : VA,b/ VB,b= 1, 0.5 , 0.25

Feed channel B : ReB = ρ VB,b Dh,B/µ = 5100

x, Uy,V

D=60 mm

VA,bCA,b

VB,bCB,b

d=20 mm

640 mm

330 mm

PIV/PLIF System

y/d=19.59

y/d=22.94

VB,bCB,b

VA,bCA,b

D=60 mm

d=20 mm

y/d=5.94

y/d= -0.41

y/d=2.94y/d=2.59

Position 3

Position 2

Position 1

Nd:YAG LaserPLIF camera

PIV camera

570 nm filter

532 nm filter

Mirror

Mirror

Rhodamine 6G +5µm polyamid particles

xz

y

PIV/PLIF Measurements (1)

20 mm

C = 1

C = 0

y

x

Instantanous velocity and concentration

PIV/PLIF Measurements (2)

Pure mixing experimentConcentration of species A

– High concentration (C=1) red– Low concentration (C=0)

blue

Instantaneous images at three different heights

Note heterogeneous structures

Averages produced using 200 images

C = 1

C = 0

C = 1

C = 0

C = 1

C = 0

0.25:11:1 0.5:1

PIV/PLIF Measurements (3)Mean concentrations

1:1 0.25:10.5:1

PIV/PLIF Measurements (4)RMS concentrations

1:1 0.25:10.5:1

Conservation Equations

Mass

Momentum

Mixture fraction

0=∂∂

j

j

xU

( ) ; Tj

j j j T

Ux x x Sc Scφ φ

φ

µφ µρ φ⎛ ⎞∂ ∂ ∂

= Γ Γ = +⎜ ⎟⎜ ⎟∂ ∂ ∂⎝ ⎠

( ) 2; ( )3

ij jij i ij T ij

j j j j i

UUpU U kx x x x x

τρ τ µ µ δ ρ

⎡ ⎤∂ ∂∂∂ ∂= − + = + ⋅ + − ⋅⎢ ⎥

∂ ∂ ∂ ∂ ∂⎢ ⎥⎣ ⎦

,A b

CCφ =

Turbulence and mixingmodels

Turbulence Models

Standard k-ε modelRNG k-ε modelChen-Kim k-ε model

Micromixing model

Multi-peak presumed PDF model (Fox 1998)

Multi-Peak PDF Model (1)Presumed PDF

Transport equation for probability pn

Transport equation for probability-weighted concentration sn

Conservation relations

( ) ( )( )1

; , ( , ) ,pN

n nn

f x t p x t x tφ ψ δ ψ φ=

= −∑

( ) ( ) ( )pGxp

xpU

xp

t nj

nT

jnj

jn +⎟

⎟⎠

⎞⎜⎜⎝

⎛

∂∂

Γ∂∂

=∂∂

+∂∂ ρρ

( ) ( ) ( )spMxs

xsU

xs

t nj

nT

jnj

jn ,+⎟

⎟⎠

⎞⎜⎜⎝

⎛

∂∂

Γ∂∂

=∂∂

+∂∂ ρρ

1 1 11; 0; 0

p p pN N N

n n nn n n

p G M= = =

= = =∑ ∑ ∑

Multi-Peak PDF Model (2)

Local concentration in environment/peak n

Mean concentration

Variance of concentration fluctuations

nn

n

sp

φ =

1 1

p pN N

n n nn n

p sφ φ= =

= =∑ ∑

22 2

1

pN

n nn

pφ φ φ=

′ = −∑

Multi-Peak PDF Model (3)Five environement/peak micromixing model

Typical modelling of Gn and Mn for environment/peak 3

Probability fluxes

Rate of micromixing

Inlet stream 1: Inlet stream 2:

1 2 3 4 5

1

1

11p

φ ==

5

5

01p

φ ==

2 1φ < 31 0φ> > 4 0φ >

3 2 4 3 3 2 2 4 4 3 32 ; 2G r r r M r r rφ φ φ= + − = + −

nn pr γ=

1 1; ; 1.0mm

k CC φφ

γ ττ ε

= = =

Mean Axial Velocity (V)

1:1 0.5:1 0.25:1

Mean Transverse Velocity (U)

1:1 0.5:1 0.25:1

Turbulence Velocities

1:1 0.5:1 0.25:1

Mean ConcentrationTurbulence models; 1:1 case

Turbulent Schmidt number; 1:1 case

Mean Concentration

0.5:1 0.25:11:1

Concentration Fluctuations

1:1 0.5:1 0.25:1

Five-peak presumed PDF model 1:1Probability

Density Functions

Five-peak presumed PDF model 0.5:1Probability

Density Functions

Probability Density

Functions

Five-peak presumed PDF model 0.25:1

Overall mixing characteristics

Coefficient of variation => Measure of macromixing

Decay function => Measure of micromixing

( )2

1

A

N 1CoVC

N

i Ai

C C

A area=

−

−= −

∑

A

Arms

Cc

d =

Coefficient of variation (CoV)and decay function (d)

1:1 0.5:1 0.25:1

Concluding remarks (1)

The different k-ε turbulence models do not manage to capture the correct recovery from wake to channel flow, especially for the 1:1 case

The defects in the flow modelling also transfers to the mixing predictions

A reduction of the turbulent Schmidt number (0.15 for 1:1 case and 0.5-0.7 for the other) is needed to achieve good predictions of both mean and rms concentrations

The five-peak presumed PDF model predicts the streamwise decay of micromixing reasonably correct

Concluding remarks (2)

The concentration PDF’s are reasonably predicted by the five-peak presumed PDF model

The overall mixing characteristics (CoV and decay function) are reasonably predicted

A LES turbulence model is probably required to improve the flow modeling

Solution of the multi-peak PDF method should use thedirect quadratic method of moment (DQMOM) technique