Simple CFD Estimate of End Flange Tuner Finger Cooling
Estimated Dimensions
2cm
1cm
1cm3cm
5cm
6mm
4cm
5cm
Estimated Heat Load
FETS RFQ: 62 Wcm-2 at vane cut-back
Assume less than half this on fingers? So 25 Wcm-2 is reasonable.
IPHI RFQ end flange: 26 Wcm-2 on fingers
(CW RFQ, though, so ours will have much less than this in reality, but 25 Wcm-2 will allow large safety margin)
15°C Water in at 1 ms-1 flow rate
Water out with temperature raised and at 0 Bar relative pressure
25 Wcm-2 heat flux load on finger
High mesh density in region between finger and pipe
Copper starting temperature = 22°C
Flow Estimates
pcm
PT
2504.1
7513.1
1419.5H
av
D
vLp
H
u
D
kNHTC
Total power, P, to be removed from each finger ≈ 160 W
Water mass flow rate, , per pipe = 0.028 kgs-1 (assuming flow speed = 1 ms-1 = 1.7 l min-1)
Estimated temperature rise, ΔT, of cooling water = 1.35 °C
Pipe length, L, within copper = 10 cmAverage water flow rate vav = 1 ms-1
Pipe diameter, DH = 6 mmEstimated pressure drop, Δp = 0.003 Bar
m
Nusselt number, Nu, of water flow = 55.03Thermal conductivity of water, k = 0.6 Wm-1K-1
Estimated heat transfer coefficient = 5500 Wm-2K-1
Intersection of drilled pipes slightly disrupts smooth flow
Faster, disrupted flow round corner increases local HTC
Average HTC ~ 6000 Wm-2K-1 which agrees with estimate
Temperature rise of water ~ 2 °C which agrees with estimate
Pressure drop is slightly higher than estimate because the pipe doesn’t have a smooth bend at corner, but it’s still nice and low
Bulk copper in end flange is ~ 40 °C
Finger gets pretty warm (100 °C) but that shouldn’t matter at all
Summary
• Majority of heat removed ok• Indirect cooling means finger gets hot• …but not enough to worry about• Assumes 25 Wcm-2 heat load
(OVERESTIMATE!)• Will proceed with RF simulation to get better
estimate of heat load on fingers• Overall, this cooling strategy should be fine