1. E. Da Riva1 ITS Upgrade - Air cooling Layers Geometry Change!

2. E. Da Riva2 ITS Upgrade - Air cooling

3. E. Da Riva3 ITS Upgrade - Air cooling OLD GEOMETRY

4. E. Da Riva4 ITS Upgrade - Air cooling 1.Uniform detector temperature -> (T air-OUT – T air-IN ) high enough m air 2.T sensor ~25°C->high enough h and/or low enough T air Problem specification Air velocity should be low in order to avoid mechanical stress on the staves (vibrations, etc …) Diameter [m] Stave length [m] Area [m2] Heat Flux Q [W cm-2] Beam pipe0.040 0.30.5 Sensor layer 10.0440.2200.03091152 Sensor layer 20.0940.2700.080239399 Sensor layer 30.1800.3650.2066191032 TOTAL Q [W]9501583

5. E. Da Riva5 ITS Upgrade - Air cooling Assuming the whole cross-section between beam pipe (D = 40 mm) and 3 rd sensor layer (D = 180 mm) is available for the air flow and perfect air mixing is achieved: (T air-OUT – T air-IN ) air velocity > ~ 10 m s -1 ( ~0.3 kg/s) Constraint 1: inlet/outlet air temperature difference

6. E. Da Riva6 ITS Upgrade - Air cooling Constraint 2: sensor T / heat transfer coefficient Q/(A sensors /2) = 0.3~0.5 W cm -2 [we assume that the stave is cooled at both sides] T sensor = 25°C A. T air-IN = 7 °C (dew point) ->T sensor - T air = 18 K B. T air-IN = -15 °C->T sensor - T air = 40 K C. T air-IN = - 45 °C->T sensor - T air = 70 K 0.3 W cm -2 0.5 W cm -2 Required heat transfer coefficient [W m -2 K -1 ] T sensor - T air = 18 K83139 T sensor - T air = 40 K3863 T sensor - T air = 70 K2136 WARNING: the heat transfer coefficient h could be not uniform over the sensors surface and the variation of local T sensor will be proportional to (T sensor - T air ) -> with a very low air inlet temperature and heat transfer coefficient it is more difficult to achieve a uniform (and stable) sensor temperature.

7. E. Da Riva7 ITS Upgrade - Air cooling Constraint 2: estimation of heat transfer coefficient Method A: flow between 2 concentric cylinders Each layer of sensors is treated as leak-tight for the air flow. The heat transfer coefficient at the surface of the 3 resulting volumes (enclosed between concentric cylinders) is computed by means of the Gnielinski correlation. With the real geometry the heat transfer coefficient is expected to be higher (air flow between staves, more turbulent flow due to the geometry).

8. E. Da Riva8 ITS Upgrade - Air cooling NEW GEOMETRY

9. E. Da Riva9 ITS Upgrade - Air cooling Radius [mm] Diame ter [m] Stave Length [m] Surface [m 2 ] Detector Heat Flux [W cm -2 ] 0.10.20.30.40.5 Heat Flow Rate [W] Beam Pipe19.8 0.0396 Cylinder0220.0440.2240.031316293124155 Cylinder1280.0560.2420.0434385128170213 Cylinder2360.0720.2680.06161121182242303 Total Heat Flow Rate [W] 134268402537671 Diameter [m] Stave length [m] Area [m2] Heat Flux Q [W cm-2] Beam pipe0.040 0.30.5 Sensor layer 10.0440.2200.03091152 Sensor layer 20.0940.2700.080239399 Sensor layer 30.1800.3650.2066191032 TOTAL Q [W]9501583 OLD GEOMETRY NEW GEOMETRY

10. E. Da Riva10 ITS Upgrade - Air cooling OLD GEOMETRY NEW GEOMETRY

11. E. Da Riva11 ITS Upgrade - Air cooling SUMMARY LAYER1/LAYER2 q 0.3 W cm^- 2 Δ T in/out 5 K fluidairheliumR116 (C2F6) R218 (C3F8) perfluorobutane (C4F10)R134acarbon dioxide velocity [m/s]22.932.16.34.53.47.718.0 Re1904034193447337021364483654028639 HTC [W m-^-2 K^-1]1041418885888792 Δp [Pa]1707555372759146 0.5 ρ v2322881208260132305 Speed of sound [m/s]33799113511398157262 Mach0.070.030.050.040.030.050.07 ALTERNATIVE FLUIDS

12. E. Da Riva12 ITS Upgrade - Air cooling AIRHELIUM density1.231[kg m-3] viscosity1.78E-05[Pa s] thermal cond.0.025[W m-1 K-1] Prandtl0.722[-] cpcp 1006[J kg-1 K-1] speed sound337[m s-1] density0.170[kg m-3] viscosity1.92E-05[Pa s] thermal cond.0.150[W m-1 K-1] Prandtl0.664[-] cpcp 5193[J kg-1 K-1] speed sound991[m s-1]

13. E. Da Riva13 ITS Upgrade - Air cooling C4F10 density10.586[kg m-3] viscosity1.17E-05[Pa s] thermal cond.0.012[W m-1 K-1] Prandtl0.753[-] cpcp 796[J kg-1 K-1] speed sound98[m s-1]

14. E. Da Riva14 ITS Upgrade - Air cooling Different refrigerant temperatures at the two sides The temperature of the stave is an average between the 2 temperatures We could get rid of the refrigerant in/out temp. rise constraint Promising CFD sim are going on …