1. Research on Predictive CO2 Models and Microchannel DefinitionBy
Yvonne Moussy, PhD

2. Outline: Projects at CERN
A predictive model of CO2 evaporative cooling in microchannels
Non-correlation model
2. Improving Correlation Prediction Accuracy
Peer-review journal paper submission - in next few days
3. A precise microchannel definition and experimental verification

3. Project #1 A predictive model of
CO2 evaporative cooling in microchannels
The method avoids the use of correlations as much as possible.

4. Using thermal circuit concepts. Conservative case.
Flowing CO2
Temp = -40˚C
Chip 2 W/cm2
Sensor
Adhesive 100
Silicon substrate
Solder
-37.5˚C
-33.67˚C
-33.82˚C
-33.64˚C
-33.8˚C
-37.48˚C
Temp = -20˚C
-18.34˚C
-14.58˚C
-14.74˚C
-14.55˚C
-14.72˚C
-18.32˚C
Figure 1. Using conservative estimated value for h. Temperature profile across the sensor/chip assembly.
Using thermal circuit concepts. Conservative case.

5. Need local 2-phase flow heat transfer coefficient, h
conservative estimate was assumed for h
h varies with length along microchannel
h is a proportionality constant, h=q/(Tw-Tf), [W/(m^2C)]
One goal of this paper is to determine the local heat transfer coefficient.

6. Thermal Conductivities Convective heat transfer coefficient
T=-40˚C
T= -20˚C
Thicknesses
(1)Thickness of sensor, Lsensor
0.02 cm
(2)Thickness of bump, 63/37 SnPb
0.002 cm
(3)Thickness of heat generating part of chip cm
(1)Thickness of remaining part of silicon chip cm
(4)Thickness of adhesive 100
0.003 cm
(1)Thickness of silicon substrate, Lsilicon
0.014 cm
Thermal Conductivities
(5)Conductivity of sensor, Ksensor
1.81 W/(cm˚K)
1.62 W/(cm˚K)
(2)Conductivity of 63/37 SnPb
0.509 W/(cm˚K)
(4)Conductivity of adhesive 100
W/(cm˚K)
W/(cm˚K)
(6)Conductivity of silicon, Ksilicon
2.26 W/(cm˚K)
2.03 W/(cm˚K)
Convective heat transfer coefficient
(7)Convection heat transfer coefficient, hco2
0.8 W/(cm2K)
1.2 W/(cm2K)
Thermal resistances
Thermal resistance of sensor
cm2K/W
cm2K/W
(2)Thermal resistance bump bonding, 𝑅 𝑡,𝑐 𝑏𝑢𝑚𝑝 "
0.067 cm2K/W
Thermal resistance of silicon in chip
cm2K/W
cm2K/W
Thermal resistance adhesive 100, 𝑅 𝑡,𝑐 100 "
cm2K/W
cm2K/W
Thermal resistance of silicon substrate layer
cm2K/W
cm2K/W
Thermal resistance of convection
1.25 cm2K/W
0.83 cm2K/W
Table 1. Values used in the temperature calculations of the sensor/chip assembly. These are the most conservative cases.

7. End user products
z (streamwise length)
Temperature ˚C
Sensor temperature
Figure 3: Immediate plot of sensor temperature with micro-channel distance can be determined, if the local two-phase heat transfer coefficient, h, along the micro-channel is known. Real time results are not necessary as all results combinations can be tabulated and immediately recalled for any combination of input values , as discussed later.

8. Method Determine h analytically with experimental inputs
Rationale: the two-phase heat transfer coefficient for CO2 in a micro-channel of this geometry and thermofluid conditions does not exist.

9. Flow boiling facility

10. Microchannel No glue. Direct deposit of thermocouple. Wires fromTt
glue
No glue. Direct deposit of thermocouple.
Second wafer with small groove
for the thermocouple is
glued to the first wafer.
Wires from
thermocouple
q”eff=const Tt
Tw,b Ht Hb
q”eff=const
Wires from
thermocouple

11. Microchannel What is important in the microchannel design
Thermocouples between the silicon wafer
Thermocouple temperature will help us determine Twall

12. Theory 𝑇 𝑤,𝑏 = 𝑇 𝑡 − 𝑞 𝑒𝑓𝑓 " 𝐻 𝑡 𝑘 𝑠
𝑇 𝑤,𝑏 = 𝑇 𝑡 − 𝑞 𝑒𝑓𝑓 " 𝐻 𝑡 𝑘 𝑠
𝑞 𝑒𝑓𝑓 " 𝑊 𝑐ℎ + 𝑊 𝑤 =ℎ( 𝑇 𝑤,𝑏 − 𝑇 𝑓 )( 𝑊 𝑐ℎ + 2𝜂𝐻 𝑐ℎ )
𝜂= tanh (𝑚 𝐻 𝑐ℎ ) 𝑚 𝐻 𝑐ℎ and 𝑚= 2ℎ 𝑘 𝑠 𝑊 𝑤
𝑥 𝑒,𝑛+1 = 𝑥 𝑒,𝑛 + 𝑞 𝑒𝑓𝑓 " ( 𝑊 𝑐ℎ + 𝑊 𝑤 )Δ𝑧 𝑚 ℎ 𝑓𝑔
Tf = Tsat
Tsat is determined from the local Psat

13. Theory Δ 𝑃 𝑡𝑝 =Δ 𝑃 𝑡𝑝,𝐴 +Δ 𝑃 𝑡𝑝,𝐺 +Δ 𝑃 𝑡𝑝,𝐹
= 0 𝐿 𝑡𝑝 − 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐴 − 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐺 − 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐴 𝑑𝑧 (1)
− 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐴 = 𝐺 2 𝑣 𝑓𝑔 𝑑 𝑥 𝑒 𝑑𝑧
− 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐺 = 𝑔𝑠𝑖𝑛𝜃 𝑣 𝑓 + 𝑥 𝑒 𝑣 𝑓𝑔
− 𝑑𝑃 𝑑𝑧 𝑡𝑝,𝐹 = 2 𝐷 ℎ 𝑓 𝑡𝑝 𝐺 2 𝑣 𝑓 1+ 𝑥 𝑒 𝑣 𝑓𝑔 𝑣 𝑓

14. This method avoids the use of correlations (as much as possible).
For correlations, 30% accuracy is considered good.

15. H depends on microchannel orientationz h
vertical upflow
horizontal
vertical downflow
At low mass velocities, there were differences in the htp vs z.
However, at higher mass velocities the htp vs z values were nearly identical.
There exists a minimum mass velocity independent of orientation

16. End User Product: Combinations of Pin, M. Tabulate results
End User Product: Combinations of Pin, M. Tabulate results. Real-time not needed.
x (streamwise length)
Temperature ˚C
Sensor temperature

17. However, optimal operation may not mean safe operation.
can also find the minimum temperature gradient along the sensor from all of our Tsensor versus z plots
However, optimal operation may not mean safe operation.
Pin
Mass flow rate
unsafe

18. Status Design for microchannel done Need to fabricate microchannel
Measure the thermocouple temperature
Matlab program has been written
1 peer-reviewed journal paper expected

19. Project #2: Improving CO2 Correlation Prediction Accuracy

20. Rationale
9 CO2-specific correlations from different research groups
Problems
Which correlation is best???
30% is considered good

21. Consolidated Database
Author(s)
Channel geometry
Channel material
Dh (mm)
G (kg/m2s)
Saturation Temp (°C)
Heat flux (kW/m2)
Total data
Pre-dryout data
Mastrullo et al.
Smooth, horizontal, circular
Stainless steel (type304) 6
-7.8 , -3.2, 4.2, 5, 5.8
121
102
Wu J et al. (2011)
Circular, horizontal
Stainless steel
1.42
-40, -35,
-30, -20,
-10, 0
339
201
Yun et al. (2005)
Rectangular microchannels, horizontal
1.14,
1.54 5 20 29 22
Yun et al. (2003)
Horizontal, circular 10
10-20 70 59
Choi KI
et al
Smooth
1.5
3.0 -5
30-40
120 81
Oh

et al (2011)
Smooth,
4.57
5, 10,
15, 20
10-40
101 54
Pamitran et al. (2011)
1.5, 3.0
1, 2, 10
20-30
156
117
Consolidated Database

25. Status Submission in next few days Focus of this paper
With Zhan Zhang, Paolo Petagna
Focus of this paper
CO2 flow boiling in microchannels
more journal papers expected
Dry out conditions, other refrigerants
Number of papers=Number of refrigerants + dry out

26. What is the size of a microchannel?
Project #3: A precise microchannel definition and experimental verification
What is the size of a microchannel?

27. No universally accepted definition (For Now)
Many authors admittedly select an arbitrary diameter of < 3 mm (Thome, 2005; Cheng, 2008a; Mastrullo, 2010)
Other authors have defined a slightly smaller diameter of 1 mm-2 mm (Zhao, 2000)
or < 1 mm (Petagna, 2014)

28. Rationale
The purpose is to define a critical dimension for a microchannel
According to theory…

29. It’s all relative
microchannel size is relative to bubble size

30. Status Solution of implicit equations (current)
Prof Emeritus A. David Snider (mathematician)
Experimental visualisation (future)
Desiree Hellenschmidt
If our theory is proven experimentally, then numerous papers are possible (not just CO2) for a variety of refrigerants.
Number of papers = Number of refrigerants

31. Previous Research low Re, high Re Exact solution to
Navier-Stokes equation

32. Thank you for your attention Questions