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