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
