overall heat transfer coefficient of water

Modèle à 2T
Pour la caractérisation thermique
d’écoulements biphasiques en
millifluidique
M. Romano, C. Hany, LoF, CNRS UMR 5258, France
C. Pradere, J. Toutain, J.C. Batsale, TREFLE, CNRS UMR 5295 , France
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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General context
Goals: Determination of kinetic and enthalpy of chemical reaction or
phase change in millifluidic droplet flow
Applications: Chemical reaction in co-flow or droplet
Laminar flow (low Reynolds number)
Mixing by species diffusion
Steady state (x = vt)
Mixing is faster
1 droplet = 1 batch microreactor
Drawback : Estimation of fields of thermophysical properties (thermal properties, flow properties,
heat sources) in fluidic chip during thermal process
→
 ∂T ( x, y , t )
∂T ( x, y , t )
∂T ( x, y , t ) 
+v
div ( λ . grad T ( x , y , t )) + φ ( x , y , t ) = ρ C p 
+u

∂
t
∂
x
∂y


Tools :
Temperature fields measurements at microscales (InfraRed camera), analytic and numerical
modelisation (quadripole, finite difference…) and inverse methods (nodal: OLS, TLS and modal: SVD approaches)
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Experimental setset-up and methods
Goals: Determination of kinetic and enthalpy of chemical reaction or
phase change in millifluidic droplet flow
Advantages of millifluidic reactor
* Small volumes of reagents (µl)
* Study of chemical reactions under flow
* Enhancement of transfer phenomena
* Operates under isoperibolic thermal conditions
(control of the temperature of the chemical reaction).
IR Thermography + Inverse Methods
* IRT technique is applied to measure the temperature profile
* Inverse method based on analytical simplified model is used
in order to obtain thermokinetics parameters such as enthalpy
Spectroscopy
* Evolution of chemical reactions can be followed, in order to
measure the experimental conversion by online analysis.
* Allows high accurate characterisations of the kinetic
parameters of chemical reactions.
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Why working in isoperibolic thermal conditions
Microfluidic chip
Millifluidic chip
IR temperature
IR temperature
The thermal transfer is easier
No diffusion outside the channel
Well known boundary condition
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Main drawback
How to estimate thermophysical parameters inside such complex system
Direct thermal modelisation
→
div ( λ . grad T ( x , y , t )) + φ ( x , y , t ) − hS (T ( x , y , t ) − T0 ) =
r

→
ρ C p  v grad T ( x , y , t ) +
∂T ( x , y , t ) 

∂t
∂t

Heavy inverse data processing
Imposed wall
temperature
Diffusion in biphasic media (water-oil) + wall
Convection between droplets and oil
Chemical reaction into the droplet
Field of velocity
PFA tubing
Simplified the thermal study
Imposed wall temperature
Oil
Droplet
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
Working in the space of the droplet
Neglect the diffusion along x direction (S/V, Bi<1)
5/18
First idea: simplified the thermal conditions
Working directly into the droplet space (Lagrangian transformation)
IR
Camera
Measured temperature
Visible
Camera
Visible mirror
Transmitting IR
Measured visible droplets
Experimental device
Estimation of the mean velocity
Evolution versus time of droplet and oil temperatures
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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First idea: simplified the thermal conditions
Working directly into the droplet space (Lagrangian transformation)
0.8
QT =10 ml/h
QT = 20 ml/h
0.7
QT = 30 ml/h
V (cm.s-1)
0.6
0.5
0.4
0.3
0.2
0.1
0
5
10
R=QH/QG
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Very good hydrodynamic stability
7/18
Second idea: Assuming the problem can be seen as a periodic established one
( , )
( )
( , )
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Third idea: Neglect the thermal diffusion between the two phases
Visible and IR images
Analytical simulation in the space of the plugs
Analytical temperature profile along z as function of time
Question: Use a thin body approximation (neglect z diffusion)
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
9/18
Thermal modelization
Used of thin body thermal model
Averaging of the temperature
Resolution in Laplace domain
 θp

 θ

 H1 + Tp ( p + H 3 + H 2 p ) +  H 3 p + Tp  H 2
p
p



θG = 
( p + H1 + H 2 )( p + H 3 + H 2 p ) − H 2 H 2 p
 θp

 θ

 H 3
+ Tp ( p + H1 + H 2 ) +  H1 p + Tp  H 2 p
p
p



θH = 
( p + H1 + H 2 )( p + H 3 + H 2 p ) − H 2 H 2 p
Drawback: Estimation of the heat exchange coefficients
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Sensitivity study
Sβ =
∂T 1
×
∂β β
Fluids at T0=30°C and plate at Tp=25°C
Calculated temperatures
Sensitivity
Normalized Sensitivity
High sensitivity to heat
exchange between fluid and
plate
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Sensitivity study
Sβ =
∂T 1
×
∂β β
Water at T0=50°C, oil and plate at Tp=25°C
Calculated temperatures
Sensitivity
Normalized Sensitivity
Good sensitivity to heat
exchange between oil and
water
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Validation of the inverse method on noisy analytical solution
processing
Water at T0,Inverse
oil and
plate atmethod
Tp
Inverse problem formulation
t
Gauss Markov inversion
t
X H = ∫ TH dt ; X G = ∫ TG dt
[
0
TG = [1 X G X H t ] TG 0
0
(H 1 + H 2 )
-H 2 -H 1Tp
Temperature profiles TGo= 50°C THo= 25°C Tp= 25 °C noise=1
(
)
-1
P = T [X][X] ⋅ T [X]Y
]
T
4
50
Residues droplet
Residues oil
3
Droplet noisy analytical case
Oil noisy analytical case
Droplet analytical estimation
Oil analytical estimation
2
relative error (%)
45
T (°C)
40
35
1
0
-1
-2
30
-3
25
0
20
40
60
80
100
t (s)
120
140
160
180
200
-4
0
20
40
60
80
100
time (s)
120
140
160
180
200
Error lower than 1% on all the parameters
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Application of the method on experimental measurements
Fluids at the same temperature different from the plate
Profil along the channel at ti
Measured temperature
Estimated temperature and residu
4
1.25
x 10
0.5
0.4
1.2
0.3
0.2
1.1
relative error (%)
temperature DL
Good
estimation of
the parameters
Exp droplet
Exp oil
thin body model droplet
thin body model oil
1.15
Residues droplet
Residues oil
1.05
1
0.1
0
-0.1
0.95
-0.2
0.9
0.85
0
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
-0.3
10
20
30
time(s)
40
50
60
-0.4
0
10
20
30
time(s)
40
50
60
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Thermal modelization
1Dt homogenised thermal model
Averaging of the 2Temperature models
H=
40
dT
= −H(Tz − Tp )
dz
h p πdL T
ρC p
∗
∗
;
ρC
V ∗= ρG CpG VG + ρH CpH VH ; ! = " ⁄#
p
VU
Resolution in Laplace domain
35
Relative temperature (°C)
30
Complete model drop Eq. 12
Complete model oil Eq. 14
25
Two limits (oil and water)
2T, two kind of heat exchange
(wall + interface)
1DT, Mixing law
Fit complete model drop Eq. 12
by simplified model drop Eq. 18
20
Fit complete model oil Eq. 14
by simplified model oil Eq. 19
Average complete model Eq. 20
15
Fit averaged complete model Eq.20
by the simplified one Eq. 23
Oil alone in coflow Eq.23
10
Droplet (water) alone in coflow Eq.23
5
0
0
10
20
30
40
50
60
70
80
90
100
Time (s)
Very simple method for: Estimation of the heat exchange
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Experimental validation
Influence of the flow rate ratio on heat exchange
Various total flow rate for one oil and water ratio
Same total flow rate with several ratio between oil and water
The mean velocity varies linearly with the total flow rate
This velocity is independent of the oil and water flow rate ratio
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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Experimental validation
Behavior law for the H coefficients
Estimated H as function of ratio and fluids
Relationship
Overall heat transfer coefficient silicone oil 200 cSt and water drops
2.5
* 10 ml/h
1/H (m)
2
20 ml/h
30ml/
1.5
1
0.5
0
Thermal properties estimation
0
0.2
0.4
0.6
0.8
1
Overall heat transfer coefficient fluor Oil 32 cSt and water drops
2.5
Data from supplier
Estimation
Absolute
Oil
K
Oil ρCp
K
Oil ρCp
error
(J.m-3.K-1)
1/H (m)
2
(J.m-3.K-1)
1.5
1
0.5
0
Silicone oil
3.31
1.2628 x106
3.20
1.3062 x106
3%
200 cSt
0
0.2
0.4
0.6
0.8
1
Overall heat transfer coefficient fluor Oil 700 cSt and water drops
2.5
Fluorinated
1.8744 x10
2.14
6
1.9533 x10
4%
oil 32 cSt
Fluorinated
2.11
1.9810 x106
2.13
oil 700 cSt
1.9624 x106
1%
2
1/H (m)
2.23
6
1.5
1
0.5
0
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
0
0.2
0.4
0.6
0.8
1
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Conclusions and perspectives
First results show that a simplified 2T thin body model is a good
representation of droplets thermal behaviour in millifluidic reactor.
Nevertheless in isoperibolic conditions, a 1Dt homogenized model is enough
Advantages
A simple calibration of the fluid heat transfer is necessary for the study of chemical reaction
Correlation could be obtained versus flow rate ratio
Improvements
Make the calibration with different inlet temperature for oil and water (see sensitivity study)
Develop heterodyne technique to enhance the measurement
Validate the obtained heat exchange coefficient versus classical correlations
Performed slow kinetic chemical reaction
C. Pradere et al.: Journée SFT, Paris, Juin 2013.
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