1. Coolant Performance (re thermal tests) Graham Beck WP4 25 Sept 2014 1 2010 R.Bennett: Water + 40% Glycol at -20C, 1 litre/min, 1/8” pipe: htc = 658 W/m 2 K. -Clearly not useful for QA since an order of magnitude smaller than CO 2 (8000 W/m 2 K, which already contributes 25-30% of module T rise). 2013 For tests that are meaningful at +20C, what is htc of (pure) water? Fluid dynamics equations (from Georg) – but a “typo” in my spreadsheet grossly underestimated htc. Have I now got this right?? (really needs expert corroboration) Comparing with R.Bennett value for flow rate ~ 1 litre/minute: htc [W/m 2 K] water, +20C 25,000 (turbulent) 40% glycol, -20C 658 (laminar) (red point) (factor x38)

2. Fomulae used for heat transfer coefficient (transitional flow) Graham Beck WP4 25 Sept 20142 htc = k. Nu D /D H (D H = tube diameter)

3. This (hopefully correct) estimate for htc resolves some mysteries … - 2013 LBL (Sergio) reasonably low temperatures for water-cooled ABC250 stavelet. - 2014 (Freiburg and ITk weeks): LBL water-cooled pixel stavelet temperatures not high (Gerhart Brandt) – once foam-pipe glue layer doubled up. (A separate, but important issue!!)... and raises hopes/expectations for measuring Resistance of foam-pipe glue joint in UK pixel test structure and proposed strip test structure (if can bang heads together). Graham Beck WP4 25 Sept 2014 3 At room temperature and ~1litre/minute the fluid (water) film resistance should be only a small fraction (~ 7%) of the total thermal resistance between sensors and fluid. (It will be slightly higher for the bare core). Sensitivity to core Thermal Resistance should improve in proportion to flow rate. => Water cooled measurements of structures at room temperature should be effective as a means of checking the thermal performance (at RT) of the cooling structure. Comment re module electrical tests: the cooling pipe temperature is given by the fluid temperature + fluid resistance × module power. Optimal solutions may differ between ABC250 and AB130 stavelets.

4. Potential Solution for Stave Core QA Graham Beck WP4 25 Sept 20144 From above have learned that: At low (operating) T, Water/Glycol is no good for QA: fluid resistance dominates. At room temperature and achievable flow rates, water cooling should be useful => even lower resistance than eventual, evaporative CO 2, so good sensitivity to faults. But not a test for faults that appear at lowT => Should test at low T, with evap.CO2. ! Operation of a CO 2 rig requires care & effort. At around -32C, stave core tests at BNL have been made with monophase coolant (3M Novec HFE-7100). Numbers from D.Lynn suggest that this would also be adequate in terms of htc (am investigating). This would not avoid the condensation problem (need an N2 atmosphere + IR window) but would involve only a chiller (with a decent pump) and would be a lot easier to run than a CO 2 system.

5. BACKUP Graham Beck WP4 25 Sept 20145 * 1/(25.10 -3 W/mm2K *  *2mm*98mm) = 0.065C/W. cf CO2 resistance = 1/(8.10 -3 W/mm2K *  *2mm*98mm) = 0.2C/W; Total (FEA) Sensor to Fluid =1.0C/W. => rest of structure 0.8C/W)

6. Graham Beck WP4 25 Sept 20146 Guesstimate for Pixel test structure. (Analytic - PIXRING.xlsx(Analytic - PIXRING.xlsx) 0.3 l/min, 15C, ignoring glycol => htc ≈6000 W/m 2 K.  Ts from Lump Resistor model, for 1W/quadrant: Pipe T(Buried) – T(Exposed): 1.55° (P-P’) Glue (100mm Hysol/BN):0.76° (R g ) Expected P-P’ for water at 20C, htc = 25000: 1 l/min ≈0.4° 2 l/min ≈ 0.2° (a 25% correction to glue calculation)

7. Attempt to Measure a Simple Test Structure: WP2 25 March 20147 Pipe half-embedded in foam => visible with IR camera. Aim to (somehow!) measure T discontinuity across the joint for a known thermal flux. Eventually: attached Kapton heaters to back surface + Coolant through pipe (similar configuration to the module). During assembly to chiller pipes, I broke one side of the foam – repaired with Hysol/35%BN. (ps: With the spare glue mix I made a foam block – foam block joint for the TIMTower). (pps: I have only a couple of teaspoonsful of BN left)

8. WP2 25 March 20148 Photos (after repair): + black plastic tape (~ 94% emissivity).

9. WP2 25 March 2014 Thermograms and Temperature Profiles Heaters: 2W total. Chiller T varied => ambient effects small (as expected from BoE) ×2 Lens, 16cm wd. (~ 0.2mm/pixel. Pipe dia ~ 11.4 pixels) Macro Lens, 15mm wd.(~ 50  m / pixel) Repair ≡ 237  m glue 57 pixels Same  T: useful later! 9

10. WP2 25 March 201410 FEA reproduces the T profile well enough. Why is the pipe so cold ? (nearly 4C below the foam: hopefully not due to the glue joint). FEA to understand what’s going on: IR FEA (Different colour palettes!) assumed: 100  m glue around the pipe fluid htc 700 W/mK

11. WP2 25 March 201411 FEA: Cut through the middle. Temperature bands: 0.5C. Thermal Flux Density vectors - look sensible. T varies slowly along the foam. Simulated  T across the glue joint ≈ 0.5C BUT:  T around the pipe circumference ≈ 4C: The thermal resistance around the circumference of the pipe (thin wall, low K) is large and comparable to the fluid film resistance. => The bare pipe T lies roughly mid-way between the embedded pipe and coolant temperatures. 0.5C bands In principle could find a correction in terms of the fluid htc and Ti conductivity. Sensitivity to glue thickness of order 100  m would already require rather precise values for these.

12. Model Estimate of the Ligament Effect Would expect some thermal penalty at the joint due to the foam being full of holes! Conduction within the foam bulk is essentially along the thin ligaments: at the glue joint there must be some  T due to the heat spreading out laterally (within the glue or the metal) in addition to the 1-d effect of the glue thickness. Isaac’s TIMTower measurements suggest that this effect is small: but there is no error bar on that measurement and it refers to a joint with a semi-infinite copper block: we are interested in a 125  m pipe wall, with K(Ti) ≈ 16 cf K(Cu) ≈ 400W/mK. Decided to build a simple FEA model of the joint, to get a feel / establish some limits. First, look at some Allcomp calculations => ligament dimensions & conductivity WP2 25 March 201412

13. WP2 25 March 201413 See Bill Miller’s slides, LBL 2011. RVC precursor (Solid K<1W/mK) CVD carbon. Post annealing > 1500 W/mK ALLCOMP use known solid densities and a simple cubic foam approximation (several refs in the literature)  Diameter and effective K of ligaments  Volume Fraction of solid material  Effective foam K (empirical fit). For Isaac’s sample (0.225 g/cc)I get: Pore dia (pitch, inc.ligament): 195  m Ligament: dia. = 37  m, K = 1000 W/mK Foam K: 41 W/mK.

14. WP2 25 March 201414 Using rounded versions of the above (Pore Pitch = 200  m, Ligament diameter = 40  m): Run FEA for a (half) cell of the cubic structure. NOTE: I’ve assumed (so far) that the cell is filled entirely with glue. Ligaments (V,H) Glue BLT (adjustable) Copper BC: T=0 In-pore Glue Q Look at extreme cases: “Pessimistic” Full length vertical ligaments (as on right) “Optimistic” Horizontal ligaments at bottom (see below) Heat sink variants: Copper (as TIMTower), base at 0C. 125  m Titanium + 8000W/m 2 K to 0C (as shown below, for zero BLT) Run for different BLT: plot the Temperature discontinuity at the joint vs. BLT.

15. WP2 25 March 201415 AN EXAMPLE: TIMTower (Copper bottom!) Vertical Ligament (pessimistic case) 10  m BLT ! Have suppressed Large Thermal Flux vectors (originating in ligament) for clarity. Note that 75% of the flux spreads sideways into the glue. i.e. in this case (since the ligament X-section is very small) it helps to have glue in the pores!! There is still some lateral spreading in the Copper, but 1-d flux is established within a short depth….

16. WP2 25 March 201416 RESULTS: Pessimistic i.e. Vertical Ligament Optimistic (H ligaments near joint) TIMTower: Titanium/CO2 “Titanium, Pessimistic” NOT run yet. In principle should also repeat all with glue excluded from pores. The intercepts here ≡ ~10  m of glueThe intercept here ≡ ~52  m of glue

17. WP2 25 March 201417 Conclusions from this simple mode (so far): - Assuming that glue fills the surface pores, the glue joint thermal resistance is given by R = R BLT + R int for BLT > 20um - where R BLT is the resistance expected from the glue Bond Line Thickness (~ BLT/K Glue ) and R int is an offset due to the foam structure, equivalent to: - 52um of glue if the foam surface consists entirely of full-length ligaments normal to the surface - 10um of glue if the foam surface consists of a square mesh of ligaments aligned with the surface. A less ordered structure (ligaments at various angles and positions) should lie somewhere in between. As the gap between the foam and metal surfaces is reduced below about 20um (in either case), the resistance falls to a negligible (but non-zero) value given by the spreading resistance within the metal structure. The joint between the foam and a 125um Titanium wall (cooled by evaporative CO2) appears very similar to the TIMTower case (at least for the “optimistic” ligament arrangement). Suggestion: Add 30  m to the glue physical thickness to allow for the spreading resistance?