Third EUROnu Annual Meeting, RAL 2011

A.WRÓBLEWSKI & B.SZYBIŃSKI

Cracow University of Technology

Assessment of the cooling options for a Superbeam horn

Boundary conditions

How to determine the film coefficient h?

1.Engineering tables2.Simplified relations3.General convection theory (rather complicated approach)

In all above given cases two possibilities considered

1.Natural convection (slow velocity of cooling medium)

2.Forced convection

Engineering tables

Cooling medium Natural convection Forced convection

Gas 5-30 30-500

in Km

W

deg2

Simplified relations (J.P. Holman, Heat transfer)

Horizontal cylinders; convection to air

Laminar104 < Gr · Pr < 109

TurbulentGr · Pr > 109

2/1

27.0

dT

h 2/118.0 Th

degFfthrBtu

In 2

degKmW

674466.55/90.09290304

2928104.0degFfthr

Btu22

degKmW

0.9]m[160.1

degKmW

5.39]m[060.0

deg40

2

2

hd

hd

KT

o

i

Volume [m^3] Energy curr. [W] Energy part. [W]

Front face 0.417046401E-02 1400 757

Inner cond. cylinder 0.396308981E-03 6540 density by Christoph

Inner cond. conic1 0.124743689E-02 2500 1756

Inner cond. cylinder2 0.244735258E-02 1000 1117

Inner cond. conic2 0.126037287E-02 2600 584

Inner cond. cylinder3 0.120818048E-04 density like inn. conductor

357

Exit face 0.384374028E-02 4000 480

Outer cond 0.227386003E-01 1300 3344

ho=1000, he=500, hr=100 , hc=100, hi=10To=293, Te=293 , Tr=293 , Tc=293, Ti=310

ho=1000, he=500, hr=100 , hc=100, hi=10000To=293, Te=293 , Tr=293 , Tc=293, Ti=310

ho=1000, he=500, hr=100 , hc=100, hi=10000To=293, Te=293 , Tr=293 , Tc=293, Ti=310

ho=1000, he=500, hr=100 , hc=1000, hi=10000To=293, Te=293 , Tr=293 , Tc=293, Ti=310

hc: 1001000

ho=1000, he=500, hr=50 , hc=1000, hi=10000To=293, Te=293 , Tr=293 , Tc=293, Ti=310

hr: 10050

ho / To hi / Ti he / Te hr / Tr hc / Tc Current Particle Max. T300 / 350 kA

1 1000293

10310

500293

100293

100293

Yes No 21972879

2 1000293

10000310

500293

100293

100293

Yes No 336350

3 1000293

10000310

500293

100293

100293

Yes Yes 403417

4 1000293

10000310

500293

100293

1000293

Yes Yes 365377

5 1000293

10000310

500293

50293

1000293

Yes Yes 428450

Horn shell with double skin (only in inner part of cylinder )

Horn shell with double skin (only in inner part of cylinder )

Horn shell with double skin (only in inner part of cylinder )

FEM modelling in ANSYS with fatigue calculations

Fatigue analysis – VHCF S-N CurveFatigue analysis – VHCF S-N Curve

841.k

88120

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