Consideration of Baffle cooling scheme T. Sekiguchi KEK, IPNS

Introduction This document describes general considerations about cooling schemes. Baffle = Collimator for 1st Horn A graphite cylinder: fin = 32mm and fout = 400mm length = 1.7m Heat load: 4.2 kJ/pulse (1.2 kW) due to beam halo and ~1kW from back-scattered pions. g ~2kW heat load is expected. g Cooling is required. For calculations, it is assumed that the heat generation is concentrated at the inner surface. 400mm 32mm 1700mm

Consideration of cooling scheme Cooled by Helium or water? Water cooling Helium cooling More efficient cooling g High heat transfer coefficient Reduce radioactive waste water Radioactive waste water Open circuit is not preferable Temperature rise is very high with low Helium flow rate Merits Demerits

Option #1 (He cooling) Helium flow 10mmf pipe Heat load concentrates on inner part of Baffle g Cooling inner surface is efficient. Helium is transferred to inner cavity with 10mmf pipe. Open circuit Hand calculation is performed. Helium initial temperature = 25 ºC Very high temperature gas blows toward the beam window and the target! g Closed circuit is preferable. He mass flow rate (g/s) 1 2 10 THe@exit (ºC) 410 218 64 Reynolds number 560 1400 9240 Heat transfer coefficient (W/m2/K) 37.9 30.1 142.5 DT between He and surface (ºC) 309 389 82.2 Tmax at graphite (ºC) 719 607 146

Option #2 (He cooling) Closed circuit. He in He out Option #2 (He cooling) Closed circuit. Helium flow is divided into 6 paths. 6 holes at fhole=200mm f Not optimized. 2kW heat flow into 6 holes. g heat flow for each hole = 333W. Helium temperature rise is reduced since only 600W heat is cooled. Calculation with realistic model is needed. 10mmf 200mm (Total) He mass flow rate (g/s) 1 2 10 THe@exit (ºC) 410 218 64 Reynolds number 590 1500 9650 Heat transfer coefficient (W/m2/K) 121.2 96.4 485.9 DT between He and surface (ºC) 51.5 64.7 12.8 Tmax at graphite (ºC) 466 286 80

Option #3 (Water cooling) Water flow Option #3 (Water cooling) Cooling outer surface. 10 pipes attached on outer surface f Not optimized 2kW heat flow into 10 pipes. g Heat flow for each pipe = 200W Heat transfer coeff. is ~ 950W/m2/K with even 1l/min water flow. Calculations with realistic model is needed. To reduce the amount of radioactive waste water, the number of pipes and the pipe diameter should be reduced. 10mmf SUS pipe Water flow rate (l/min) 1 2 10 Twater@exit (ºC) 27.9 26.4 25.3 Reynolds number 2490 4970 24900 Heat transfer coefficient (W/m2/K) 950 2250 10300 DT between water and surface (ºC) 7.9 3.3 0.7 Tmax at graphite (ºC) 40.0 33.9 30.2

Summary Helium and water cooling are considered. Calculations with some heat flow assumptions are performed. In the case of He cooling, closed circuit is preferable since high temperature gas blows the beam window. We need FEM calculations with helium or water flows and expected thermal load distribution. Cooling scheme should be optimized in the cases of the options #2 and #3.

Supplements

Table #1 for calculation Helium properties under 0.1MPa condition. Temp (K) Density (kg/m3) Specific heat (kJ/kg/K) Viscosity coeff. (mPa∙s) Heat conductivity (mW/m/K) Prandtlnumber 100 0.487 5.195 9.77 72.0 0.705 200 0.244 5.193 15.35 115.0 0.693 300 0.163 19.93 152.7 0.678 400 0.122 24.29 188.2 0.670 500 0.098 28.36 221.2 0.666 600 0.081 32.21 252.3 0.663 700 0.070 35.89 278.0 0.67 800 0.061 39.43 304.0 1000 0.049 46.16 354.0 0.68

Table #2 for calculation Properties of water. Temp (K) Density (kg/m3) Specific heat (kJ/kg/K) Viscosty coeff. (mPa·s) Heat conductivity (mW/m/K) Prandtl number 273 999.8 4.217 1791.4 561.9 13.44 280 999.9 4.199 1435.4 576.0 10.46 290 998.9 4.184 1085.3 594.3 7.641 300 996.6 4.179 854.4 610.4 5.850 310 993.4 693.7 624.5 4.642 320 989.4 4.180 577.2 636.9 3.788 330 984.8 489.9 647.6 3.165 340 979.4 4.188 422.5 656.8 2.694 350 973.6 4.194 369.4 664.6 2.331

Simple simulations by ANSYS Rotational symmetry model of the option #2. Helium flow ~1g/s (0.167g/s per hole), temperature = 410 ºC Heat conductivity around 400 ºC ~80 W/m/K (const.) adiabatic Heat flow at inner surface ~2kW Heat transfer coeff. ~ 121W/m2/K Temperature @inner surface ~440 ºC Hole diameter =10mm

Simple simulations by ANSYS Rotational symmetry model of the option #2. Helium flow ~1g/s (0.167g/s per hole), temperature = 410 ºC Heat conductivity around 400 ºC ~80 W/m/K (const.) Natural convection ~10W/m2/K Heat flow at inner surface ~2kW Atmospheric temp. ~60 ºC Heat transfer coeff. ~ 121W/m2/K Temperature @inner surface ~360 ºC Hole diameter =10mm

Simple simulations by ANSYS Rotational symmetry model of the option #3. Water flow ~1l/min (16.7g/s), temperature = 27.9 ºC Heat conductivity around 30 ºC ~116 W/m/K (const.) adiabatic Heat flow at inner surface ~2kW Water pipe d=10mm Heat transfer coeff. ~ 2490 W/m2/K Temperature @ inner surface ~33.7 ºC

Simple simulations by ANSYS Rotational symmetry model of the option #3. Water flow ~1l/min (16.7g/s), temperature = 27.9 ºC Atmospheric temp ~60 ºC Heat conductivity around 30 ºC ~116 W/m/K (const.) Natural convection ~10W/m2/K Heat flow at inner surface ~2kW Water pipe d=10mm Heat transfer coeff. ~ 2490 W/m2/K Temperature @ inner surface ~34.2 ºC