1. Temperature distribution in the target
Projet Euronu, Horn
Temperature distribution in the target
Benjamin Lepers
IPHC, Strasbourg

2. Outline
1) cylinder with a uniform heat source with convection
2) model: temperature distribution in the target cylinder
3) h convection correlation
4) Impinging jets

3. Surface temperature with uniform heat source and convection
Cylinder in cross flow

4. Model Axi symmetric, cylinder of 1.5 cm radius and 78 cm in length
Material: aluminium and Carbon
Heat conduction equation solved in steady state regime.
Internal heat source coming from the proton beam (4MW, 1MW).
Distribution of the heat source q(r,z) is obtained with Fluka
Boundary conditions: thermal insulation on the wall, z = 0, 0.078
Heat convection on the cylinder surface, r = 0.015m
Coefficient of convection 5000, 50000W/(m K)

5. Convection for a cylinder in cross flow
Churchill and Berstein, J:Heat transfer, 99, 900, 1977
For u=1, 10m/s fluid velocity (for a area of 5cm*78cm, flow rate would be 39l/s, 390l/s, reynolds number are: 1.57E5, 1.57E6
Thermal properties of water are evaluated at the film temperature, Tf = (300+20)/2=160°C.
h= 8000, 50000W/(m^2K) for u=1, 10 m/s.
For the simulation, we choose h=5000 and h=50000

6. Maximum temperature located in r = 0, z = 5 cm
For a 1MW beam power, the maximal temperature for aluminium
And carbon target are: 520°C and 377°C with h=5000W/(mK)
Heat source q [W/m^3], carbon target
Q_max=3.6E9W/m^3
Temperature, carbon; max 1450°C (4MW, h=5000 W/(m^2K)
Heat source q [W/m^3], Aluminium target
Q_max=5.3E9W/m^3
Temperature, aluminum;max 2021°C(4MW, h=5000 W/(m^2K)

7. Power distribution in aluminium target, r = 0, 0.5, 1, 1.5cm
Power, distribution in aluminium, z = 0.5, 10, 30, 60 cm.
Power distribution in carbon target, r = 0, 0.5, 1, 1.5cm
Power, distribution in carbon, z = 0.5, 10, 30, 60 cm.

8. Temperature in the r direction for z = 0
Temperature in the r direction for z = 0.5, 10, 30, 60 cm, aluminium (blue, green, red, light blue)
Temperature in the z direction for r =0, 0.5, 1, 1.5 cm, aluminium
Temperature in the z direction, r=0.5, 1, 1.5cm.
Carbon target
Temperature in radial direction; z=0.5, 10, 30, 60 cm, carbon target(blue, green, red, light blue)

9. Lower temperature in carbon material Cooling feasibility h=?
Max temp °C
h[W(m^2 K)]
4MW,h=5000
4MW,h=50000
1MW,h=5000
1MW,h=50000
Aluminium
2021
805
520
216
Carbon
1450
656
377
179
Table 1: Temperature in Aluminium and carbon target, for 4MW , 1MW and h=5000, 50000W(m2K)
Lower temperature in carbon material
Cooling feasibility h=?

10. Impinging jets water jets to cool the target
Target cooling with round nozzle

11. Convection coefficient versus flow rate for a round nozzle

12. Next steps More reseach on h coefficient
Transient thermal analysis, (pulse=4E-6s, periode=20ms), temperature jump around 40°C
Include resistive losses; (joule effect)
Cooling system, pressure; flow rate.