Thermal stress & cooling of
J-Parc neutrino target
Introduction
neutrino target
requirement for target

Thermal stressCoolingheat transfer coefficientcooling testsummary

S . Ueda
JHF target monitor R&D groupIntroduction
 Beam

50[GeV] proton,0.75[MW]3×1014 [protons / spill] , 5[μsec/spill]
3.3[sec](between spills) , 8[bunch/spill] Material

graphite or C/C composite
Because of; high melting point(~3700℃)
thermal resistance Coolingwater cooling Shapecylindrical
900mm long(2λint) & 12~15mm radius

Cooling pipe
from one-sidehornbeam
Target

900mm

23

 Thermal shock resistance Possibility to cool
The effects of target radius Larger radiuspion yield decreases
 Smaller radiusz Temperature increases

1.2
1.0
0.8
0.6
0.4

radius0.2 σbeam =
2.5
0

2.5

5

7.5

10

more thermal stressz surface area decreases
difficult to cool

The optimization is needed

12.5

15

Target Size(mm)[K] More pion

Pion yield

Requirements for target

Temperature riseat center

4

Energy deposit
degreeRJ/gZ

cal. w/ MARS

[J/g]heat distribution in 1pulse (15mm radius)
r=13mm
r=15mm

20%differenceThermal stress Stress estimation
quasi-static stress(non-uniform heating)

dynamical stress(rapid heating) Material fatigue

σ zstat ≈ −2 E α T0
3 1 −ν

E α T03 (1 − ν )E α T0≈ −3 (1 − ν )σ rstat ≈ −σ φstatσ zdyn ≈ ±1E α T0
3

E :Young’s modulus
ν:Poisson ratio
α:linear expansion coeff.
T0:Temperature at center

after repeating stress(106 times),
tensile strength become 0.8 (IG-110).

5Material properties Ⅰ Temperature dependence
tensile strength[J/g]

specific heat

max temp. rise(G347)
r=13mm 234.2[K]r=15mm 200.6[K]almost the same6

Material properties Ⅱ
Young’s modulus(G347)[Gpa]

10-6[1/K]

thermal expansion coeff.(G347)

temperature dependence exists
these effects should be taken into account.

7

8

Safety factor
 Definition
safety factor = ( tensile strength / σeq )σ eq = {(σ x − σ y )2 + (σ y − σ z )2 + (σ z − σ x )2} / 2 ≤2 −νEαT03(1 −ν )

 Result (include fatigue、material properties)
σeq
Typetensile
Toyo Tanso
IG-43
Tokai Carbon G347

σeq

strength[Mpa]r=13[MPa]r=15[MPa]

37.2
31.4

8.92(3.3)
6.43(3.9)

7.48
5.55

29.8
25.1

(4.0)
(4.5)

() is safety factor

These graphite have sufficient safety factor

9Cooling Requirement
 cool down 60kJ in 3.3 sec
 keep Tsurf under 100℃
 α is a key parameter!
Q = α S(Tsurf - Twater) = α SΔＴ
Tsurf = Twater + ΔTTwater ← ΔT ← αQ: heat transfer [kW]S: surface area [m2]Tsurf : temp. at surface[K]Twater : temp. of water [K]α：heat transfer coeff.
[kW/m2/K]

Twaterα depends
cooling test
α need to be measured

waterQtargetTsurfAnalytical estimation of ΔT ΔT(t)depends on： Trise(r)・ heat transfer coeff ： α・ initial condition[K]

Temp. rise at 5μsec
Averagedin z direction

ΔＴ
α=610

11

Water temperature Twater(r)(at Z=900mm)
Tsurf = Twater + ΔT
to estimate maximum Tsurf ,max of Twater is necessarybeamQwater

Twater has max at Z=900mm

heat transfer ∝ ΔT

[℃]

Z=0mm

Z=900mm

Water temp.
α=620[l/min]

Twater takes maximum
valuetarget
at 0.8sec

beam in12

 Calculation result[℃]

α & flow rate
Tsurf ＝ΔT ＋ Twater
more water flow ratewater temp rise : smaller
acceptable α : lower
 Relation between α ＆flow ratesatisfy Tsurf <100℃
15[l/min] -> more than 6.5[kW/m2/K]
20[l/min]->more than 5.8[kW/m2/K]
Is needed

Flow rate& αallowable13

Cooling test
 Purposemeasure the heat transfer coeff.

 Howheat up the graphite with DC current ,and cool by flowing water Measurement

temperatures,water flow rate ,current

Q
α =S ( T surf − T water )α: heat transfer coeff.
Q:heat transfer
Tsurf :surface temperature
Twater :water temperature
S:surface area

[kW/m2/K]
[W]
[K]
[K]
[m2]

Setup of cooling test Current~ 1.2kA(20kW)
 Water flow
8.9 , 12[l/min] Target radius 15mm

water
thermocouples

targetDC current

Current feeds
900mm

1415Cooling test results
α increase withsurface temperature& water flow rate[kW/m2K]


6.5[kW/m2/K]
at 15[l/min]compared withthe α condition

extrapolate withtheoretical formula[℃]Comparison w/ theoretical formula Theoretical formula0 . 023 × Re 0 . 8 × Pr 0 . 4 × λα =dRe(T) :Reynolds number
Pr(T) :Prandtl number
λ(T) ：Thermal conductivity
ｄ：equivalent diameter Result
Data and calculation
seems to agree
at 20 [l/min] ,α expected to satisfies the condition !

16

17SummaryThermal stress
r=15mmcooling calc.

cooling test

IG-43
G347max stress7.48[MPa]5.55[MPa]safety factor
4.0
4.5

relations between α ＆ flow rate
r=15mm 15[l/min] ,6.5[kW/m2/K]
20[l/min] ,5.8[kW/m2/K]
possible to cool at more than 20[l/min]Schedule Next cooling test with more flow rate

We plan to test with 20 [l/min] this month

18

19

reference1
 off-axis-beam⇒high intensity
Super-K.

narrow energy band
Target Horns

Decay Pipeθreference2

20

21

reference３
stat
stat
stat
dyn
σ,
σ,σ,
σrφz
 zαE statσz =2REα statσr =1R1 −ν  R0

−rT(r)
drT(r)
∫201 −ν  R

σφstatrT (r )dr −2 ∫


rT(r)
dr

2 ∫0r
1r

Eα  1 R1 r=
 2 ∫ rT (r )dr + 2 ∫ rT (r )dr − T (r ) 1 −ν  R 0r 0σ zdyn = ± Eα{2R∫ rT (r )drR2 0}

σ eq = (σ x − σ y )2 + (σ y − σ z )2 + (σ z − σ x )2 / 2 ≤2 −νEαT03(1 −ν )

22reference４
 ΔT(r) time development
When the target surface is cooled (at r=R)with α,temperature difference between Tsurf and Twater（at r,time=τ) : ∆ T ( r , τ ) is,T0 ( r ) T ( r , 0 ) = ur + v
 ∂T
1 ∂T
∂ 2T)
= a (+2
τrr∂∂r∂ ∂T α
Tr= R= −λr∂
r= R

ただしR∞

2 ∫ T 0 ( r ) rJ 0 ( q n r ) drn =1 R2∆ T ( r ,τ ) = ∑qn RJ1(qn R) =λ:heat conductivity
a:thermal diffusivity0{J 0 ( q n R ) + J 1 ( q n R )}αRJ 0 (qn R)(n = 1,2,⋅ ⋅ ⋅)λe− q n2 a τ

J 0 (qn r )reference５

ΔT[K]

ΔT[K]

23

reference624

参考６ 熱量と中心温度から表面温度
長さ方向に熱の移動がないと仮定した場合、ターゲット内部では一様発熱。
dT
Q(r ) = −2πrcλ= πr 2 qdr

Q(r)rλ = Ae −aT
1 aqR 2Tsurf = − ln(+ e −aTcenter )a4A

λ： 熱伝導度c ： 比熱q : 単位体積当たりの発熱量
R ： 半径2526

冷却試験
 dataQ
α =S ( T surf − T water )12.2

14.94.2POWER :4.2kW~19.4kW
flow rate :8.9 ,12[l/min]each data points are averaged
19.4

15.2
12.4
4.2

27

Primary
ProtonPrimary proton
beamline line
beam

JPARC neutrino beamline

50GeV

ring

Cryogenics

Extraction point
Extraction(ข಴ߒὐ)
point

targetTargetvolumeDecay volumeDecay(፣უ㗔ၞ

130m

target station
Targetstation

Beam dump
beam dump(ࡆ࡯ࡓ࠳ࡦࡊ)280m

Proton beam kinetic energy
50GeV (40GeV@T=0)# of protons / pulse
3.3x1014
Beam power
750kW
Bunch structure
8 bunches
Bunch length (full width)
58ns
Bunch spacing
598ns
Spill width~5µs
Cycle
3.53sec

Muon monitor
muon monitor(ࡒࡘ࡯ࠝࡦࡕ࠾࠲࡯)Neardetector
Nearneutrino೨⟎ᬌ಴ེdetector

J-PARC ニュートリノ 実験

28

目的 νμ → νe νμ disappearance
 CPV in lepton sector

十分な統計が必要
J-PARC K2K
Energy (GeV)

5012(1012ppp)

330

6beam間隔(sec)

3.3

2.2

Power

750

5.2Int.

(kW)

π+μ+
νμ
decay pipeproton

ホーン

ターゲット

[Gpa]

29

Water flow 1

watertarget

900mm

30

Water flow 2
 swatertarget

900mm

31

32

 S4cm5cm
熱電対電極

電極

4.7cm
91cm