I nverse problems in a microchannel The correlation metho d Tutorial - - PowerPoint PPT Presentation
I nverse problems in a microchannel The correlation metho d Tutorial 6 - C hristophe Ravey , C.Pradere I2M Departement TREFLE, CNRS UB1 Esplanade des Arts et Mtiers 33405 Talence Cedex, France Research Areas: - Fluids and Flows - Transfers
Tutorial 6 - Christophe Ravey , C.Pradere
1 I2M Departement TREFLE, CNRS UB1 Esplanade des Arts et Métiers 33405 Talence Cedex, France Research Areas:
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Acid/base droplets reaction, film 600 fps Microfluidics chip 500 µm 500 µm
Thermodynamics and kintetics data Reactor design
Scale (≈ 25 µm) Quantitative measurements (≈ µW, mK, ms) Difficulties : Instrumentations, inverse methods
Field of application: chemical reaction (Rhodia)
Chemical, pharmaceutical, medical industries…
Challenge
Controlling the reaction Data acquisition Safety
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Size reduction Fast acquisition
Electronics (µchip), MEMS, Chemistry (µreactors), Inverse methods Thermal properties Energy control
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Instrumentation for measurement
Multiscale µm-cm
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PDMS resin Glass slide µchannel
Generator
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I J K
k=n k=n+1 k=n+Nt
IR temperature fields
Push Syringe
1D thermal gradient Distorted by microflow
Flowrate Q = 500 to 1500 µL/h
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Glass 170 µm λ = 1 W.m-1.K-1
FLOW
x y z O PDMS 1 cm λ = 0.1 W.m-1.K-1 Microchannel 200 µm λ = 0.6 W.m-1.K-1
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Thin layer Highly conductive Thick layer Insulator
Tf Tg
eg ef l1 l2
x y z O
L l
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Tf Tg
eg ef l1 l2
x y z O
L l
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Finite differences
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velocity Thermal diffusivity Source term
Estimation of Pe and Ф
Estimation of Pe, Fo and Ф
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Calibration of Pe
Calibration of Fo
Calibration of Fo and Pe
time velocity v Fo* Fo*+ Pe* Pe* temperature
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X A Y ⋅ =
Y X
² ) ( )² ( ) ).( (
,
X X Y Y X X Y Y S
X Y
− Σ − − Σ − − Σ =
+1 +0.8 +0.4
=> Look for values of +1, meaning the model is valid
time velocity v Fo* Fo*+ Pe* Pe* temperature
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Nx
Spatial correlation between ∆T and Tx
Nx
if Sxi,j =1
I J K
k=n k=n+1 k=n+Nt
time velocity v Fo* Fo*+ Pe* Pe* temperature
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Temporal correlation between ∆T and Tt
I J K
k=n k=n+1 k=n+Nt
k
I J K
k=n k=n+1 k=n+Nt
k
I J K
k=n k=n+1 k=n+Nt
k
Nt Nt
k
if Sti,j =1
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time velocity v Fo* Fo*+ Pe* Pe* temperature
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T Q = 500 µL/h T0 Q = 0 µL/h (T-T0)
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time velocity v Fo* Fo*+ Pe* Pe* temperature
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time T°C Nucleation Temperature TN Freezing Temperature TF Solid Temperature TS Liquid Temperature TL
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microchannel.
walls
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Pixel in x direction (-) Pixel in y direction (-) 10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 35 40 45
0.2 0.4 0.6 0.8 Distance (cm) Distance (cm) 0.5 1 1.5 2 2.5 3 3.5 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 6700 6800 6900 7000 7100 7200 7300 7400 7500 7600 7700 Distance (cm) Distance (cm) 0.5 1 1.5 2 2.5 3 3.5 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 6600 6700 6800 6900 7000 7100 7200 7300 7400 7500 Pixel in x direction (-) Pixel in y direction (-) 10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 35 40 45 2 4 6 8 10 12 14
Initial frame Final frame Instant correlation coefficient Averaged estimated Fo mapping
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500 1000 1500 2000 2500 3000 1 2 3 4 5 6 7 8 9 10 Flow rate (µl/h) Averaged apparent Fourier number (-) Inside the channel fitted data
fitted data
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time T°C Nucleation Temperature TN Freezing Temperature TF Solid Temperature TS Liquid Temperature TL
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4cm Question: How can we localize the heat source ? High frequency recordings : 484 Hz
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Advantages : Simple and fast processing No calibration of temperature is needed (temperature variations) IR Thermography => mapping of estimated parameters Large field of applications (chemistry, crystallization, blood flows…) Drawbacks: Qualitative method (for the moment) Perspectives: Reduction of noise and filtering of signal (spatial and temporal)
SVD + convolution and/or lowpass
Quantitave estimations Improvement of derivations
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I2M Departement TREFLE, CNRS UB1 Esplanade des Arts et Métiers 33405 Talence Cedex, France
Research Areas: