Research on Predictive CO2 Models and Microchannel Definition By Yvonne Moussy, PhD

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

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

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.

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.

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 0.0005 cm (1)Thickness of remaining part of silicon chip 0.0195 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 0.00164 W/(cm˚K) 0.00168 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 0.01105 cm2K/W 0.01235 cm2K/W (2)Thermal resistance bump bonding, 𝑅 𝑡,𝑐 𝑏𝑢𝑚𝑝 " 0.067 cm2K/W Thermal resistance of silicon in chip 0.00863 cm2K/W 0.00961 cm2K/W Thermal resistance adhesive 100, 𝑅 𝑡,𝑐 100 " 1.82515 cm2K/W 1.78816 cm2K/W Thermal resistance of silicon substrate layer 0.00619 cm2K/W 0.0069 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.

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.

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.

Flow boiling facility

Microchannel No glue. Direct deposit of thermocouple. Wires from Tt 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

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

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

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

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

H depends on microchannel orientation z 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

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

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

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

Project #2: Improving CO2 Correlation Prediction Accuracy

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

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) 6 200-349 -7.8 , -3.2, 4.2, 5, 5.8 10.0-20.2 121 102 Wu J et al. (2011) Circular, horizontal Stainless steel 1.42 300-600 -40, -35, -30, -20, -10, 0 7.5-29.8 339 201 Yun et al. (2005) Rectangular microchannels, horizontal 1.14, 1.54 200-400 5 20 29 22 Yun et al. (2003) Horizontal, circular 170-320 10 10-20 70 59   Choi KI et al Smooth 1.5 3.0 -5 30-40 120 81 Oh
 et al (2011) Smooth, 4.57 600-900 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

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

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

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)

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

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

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

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

Thank you for your attention Questions