Thermal stress & cooling of J-Parc neutrino target

　 S . UedaJHF target monitor R&D group

Introduction　　 neutrino target　　 requirement for target

Thermal stressCooling　　 heat transfer coefficient　　 cooling test

summary 　

2Introduction

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

Cooling water cooling Shape 　 　 　 　 　　　　　 cylindrical 900mm long(2λint) & 12~15mm radius 　

　　　　　　　 beam

　　　　　　　　　　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　 900mm

Cooling pipe from one-side horn

Target

3Requirements for target

More pion Thermal shock resistance Possibility to coolThe effects of target radius

Larger radius

pion yield decreases Smaller radius

Temperature increases

more thermal stress surface area decreases

difficult to cool

The optimization is needed

Pio

n y

ield

5.2

radiusbeam

1.2

1.0

0.8

0.6

0.4

0.2

02.5 　 5 7.5 　 10 12.5 15 Target Size(mm)

[K]

Temperature rise at center

4Energy deposit

　 　 　 　 　 　 　 heat distribution in 1pulse (15mm radius)

　　　　 　 　 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

20%difference 　　　　　　　　　　　　　　　　　　　　　 　

J/g 　degree

Z

R

cal. w/ MARS

[J

/g]

r=13mm

r=15mm

5Thermal stress

Stress estimationStress estimation

　　　　 quasi-static stress

(non-uniform heating)　

　　　　 dynamical stress 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　

　　　 (rapid heating) 　 　 　 　 　　　 　 　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

Material fatigueMaterial fatigue

　　　 after repeating stress(106 times),

tensile strength become 0.8 (IG-110). 　

13

2 0TEstatz

)1(30

TEstat

r

)1(30

TEstat

E :Young’s modulusν:Poisson ratioα:linear expansion coeff.T0:Temperature at center

03

1TEdyn

z

6Material properties Ⅰ

Temperature dependenceTemperature dependence specific heat tensile strength

max temp. rise(G347)

r=13mm 234.2[K] almost the same

r=15mm 200.6[K]

[J/g

]

7Material properties Ⅱ

thermal expansion coeff.(G347) Young’s modulus(G347)

　 temperature dependence exists

these effects should be taken into account.

10-6

[1/K

]

[Gp

a]

8Safety factor

Definition Definition

safety factor = ( tensile strength / σeq )

ResultResult (include fatigue 、 material properties)

Type tensile σeq σeq

strength[Mpa] r=13[MPa] r=15[MPa] Toyo Tanso 　 　 　 IG-43 37.2 29.8 8.92(3.3) 7.48 (4.0)Tokai Carbon G347 31.4 25.1 6.43(3.9) 5.55 (4.5)

　　 () is safety factor

　　　　　　　 These graphite have sufficient safety factor 　

0222

)1(3

22/})()(){( TExzzyyxeq

9Cooling

Requirement Requirement cool down 60kJ in 3.3 sec keep Tsurf under 100℃

α is a key parameter! is a key parameter!

Q = α S(Tsurf - Twater) = α SΔ Ｔ 　 Tsurf = Twater + ΔT

　　　　 　 　 　 　 Twater ← 　 ΔT ← 　 α 　

α depends

cooling test

α 　 need to be measured

Q 　 　 　　　　　 : heat transfer 　[kW]S 　 　 　　　　　　 : surface area [m2]Tsurf : temp. at surface[K]Twater : temp. of water [K]

α ： heat transfer coeff. [kW/m2/K]

target

water

Twater

Tsurf

Q

10Analytical estimation of ΔT

ΔT(t)ΔT(t)

depends on 　　・ initial condition 　： Trise(r)

　　　　　　　　　　　　　　　　　　　　　　　 　・ heat transfer coeff 　： α 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　

　　　　 　α=6

Temp. rise at 5μsec

[K]

Averaged in z direction

Δ Ｔ

11Water temperature

TTwaterwater(r)(r)(at Z=900mm)

Tsurf = Twater + ΔT

to estimate maximum Tsurf ,

max of Twater is necessary

Twater has max at Z=900mm

　　　 heat transfer 　 ∝　 ΔT

　　　 Twater takes maximum value

at 0.8sec

Water temp.α=6

20[l/min]

beam in

[℃]

target

water

Z=0mm Z=900mm

beamQ

12α 　 & flow rate

Calculation result

　　　 Tsurf ＝ ΔT 　 　＋ 　Twater

more water flow rate

　　　　　 　 water temp rise : smaller

　 　 acceptable α : lower

Relation between α ＆ flow rate

satisfy Tsurf <100℃

Flow rate& α

15[l/min] -> more than 　6.5[kW/m2/K]

20[l/min]->more than 　 5.8[kW/m2/K]

Is needed

[℃]

allowable

13Cooling test

Purpose measure the heat transfer coeff.

How heat up the graphite with DC current ,

and cool by flowing water Measurement temperatures,water flow rate ,current

α : heat transfer coeff. [kW/m2/K]

Q :heat transfer [W]

Tsurf :surface temperature [K]

Twater :water temperature [K]

S :surface area [m2]

)( watersurf TTS

Q

14Setup of cooling test

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

Current feeds

DC current

thermocouples

900mm

target

water

15Cooling test results

　 α increase with

surface temperature

& water flow rate

compared with

the α condition

extrapolate with

theoretical formula [ ]℃

[kW

/m2K

]

6.5[kW/m2/K]at 15[l/min]

16Comparison w/ theoretical formula

Theoretical formula

　　　　　 Re(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 !

d

4.08.0 PrRe023.0

17Summary

Thermal stress max stress safety factor

r=15mm IG-43 7.48[MPa] 4.0

G347 5.55[MPa] 4.5

cooling calc. relations between α 　＆ flow rate

r=15mm 15[l/min] ,6.5[kW/m2/K]

20[l/min] ,5.8[kW/m2/K]

cooling test possible to cool at more than 20[l/min]

18Schedule

Next cooling test with more flow rate

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

19reference1

off-axis-beam ⇒ high intensity

narrow energy band

Horns

Super-K.

Target Decay Pipe

20reference2

21reference ３

)()(

2

1 02rTdrrrT

R

E Rstatz

rRstatr drrrT

rdrrrT

R

E0202

)(1

)(1

1

)()(

1)(

1

1 0202rTdrrrT

rdrrrT

R

E rRstat

Rdyn

z drrrTR

E02

)(2

dynz

statstatr

statz ,,,

0222

)1(3

22/)()()( TExzzyyxeq

22reference ４

ΔT(r) time developmentΔT(r) time development　　　　 When the target surface is cooled (at r=R)with α,

　　　　　　 temperature difference between Tsurf and Twater

　 　 　 　 　 　 （ at 　 r,time=τ) : is,

　　　　　　　　　　　　　　　　

　 　 　 　 　 　 　

　　　　

　ただし

10

102

0 00)(

)()(

)()(2),(

2

nn

aq

nn

Rn

rqJeRqJRqJR

drrqrJrTrT n

),2,1)(()( 01 nRqJR

RqRJq nnn

λ:heat conductivitya:thermal diffusivity

),( rT )(0 rT

RrRr

Tr

T

r

T

rr

Ta

T

vurrT

)

1(

)0,(

2

2

23reference ５

　Δ

T[K

]Δ

T[K

]

24reference6

　

25参考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。

r

Q(r)

)4

ln(1

2)(

2

2

centeraTsurf

aT

eA

aqR

aT

Ae

qrdr

dTrcrQ

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

26冷却試験 datadata

POWER :4.2kW~19.4kW

flow rate :8.9 ,12[l/min]

　 　　　　 each data points are averaged

4.2

4.2

12.4

15.2

)( watersurf TTS

Q

19.4

14.912.2

27JPARC neutrino beamlineProton beam kinetic energy

# of protons / pulse

Beam power

Bunch structure

Bunch length (full width)

Bunch spacing

Spill width

Cycle

50GeV 　 (40GeV@T=0)

3.3x1014

750kW

8 bunches

58ns

598ns

~5s

3.53sec

Primary Proton beam line

Extraction point

TargetTarget station

muon monitor

beam dump

Near neutrino detector

Dec

ay

volu

me

　　

28J-PARC ニュートリノ 実験

　目的目的 νμ → νe 　

νμ 　 disappearance

CPV in lepton sector

　　　　　　　　　　　十分な統計が必要J-PARC K2K

Energy (GeV) 50 12

Int. (1012ppp) 330 6

beam 間隔(sec)

3.3 2.2

Power (kW) 750 5.2

ターゲット

π+μ+

νμ

ホーンdecay pipe

proton

29　[G

pa]

30Water flow 1

900mm

target

water

31Water flow 2

s

900mm

target

water

32

S

電極電極

熱電対

91cm

4cm 5cm

4.7cm