Thermal stress & cooling of J-Parc neutrino target Introduction - - PowerPoint PPT Presentation

Thermal stress & cooling of J-Parc neutrino target

Introduction

neutrino target requirement for target

Thermal stress Cooling

heat transfer coefficient cooling test

summary

S . Ueda

JHF target monitor R&D group

2

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

Introduction

3

Requirements for target

More pion Thermal shock resistance Possibility to cool The 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

Pion yield

5 . 2 radius

beam=

σ

1.2 1.0 0.8 0.6 0.4 0.2 0 2.5 5 7.5 10 12.5 15

Target Size(mm)

[K]

Temperature rise at center

4

Energy deposit

heat distribution in 1pulse (15mm radius)

20%difference

J/g degree

Z R

• cal. w/ MARS

[J/g]

r=13mm r=15mm

5

Thermal stress

• Stress estimation

Stress estimation

quasi-static stress (non-uniform heating) dynamical stress (rapid heating)

• Material fatigue

Material fatigue

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

ν α σ − − ≈ 1 3 2 T E

stat z

) 1 ( 3 ν α σ − − ≈ T E

stat r

) 1 ( 3 ν α σ φ − − ≈ T E

stat

E: Y

• u

n g ’s m

• d

u l u s ν: P

• i

s s

• n

r a t i

• α:

l i n e a r e x p a n s i

• n

c

• e

f f . T : T e m p e r a t u r e a t c e n t e r

3 1 T E

dyn z

α σ ± ≈

6

Material properties Ⅰ

• Temperature dependence

Temperature dependence

specific heat tensile strength

• max temp. rise(G347)

r=13mm 234.2[K] almost the same r=15mm 200.6[K] [J/g]

7

Material properties Ⅱ

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

temperature dependence exists these effects should be taken into account.

1

• 6

[ 1 / K ] [ G p a ]

8

Safety factor

• Definition

Definition

safety factor = ( tensile strength / σeq )

• Result

Result (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

2 2 2

) 1 ( 3 2 2 / } ) ( ) ( ) {( T E

x z z y y x eq

α ν ν σ σ σ σ σ σ σ − − ≤ − + − + − =

9

Cooling

• 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 SΔＴ 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

10

Analytical estimation of ΔT

• Δ

ΔT(t) T(t)

depends on ・initial condition ：

Trise(r)

・ heat transfer coeff ： α

α=6

• Temp. rise at 5μsec

[ K ] Averaged in z direction

ΔＴ

11

Water temperature

• T

Twater

water(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

beam Q

12

α & 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

13

Cooling 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]

) (

water surf

T T S Q − = α

14

Setup 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

15

Cooling test results

• α increase with

surface temperature & water flow rate compared with the α condition extrapolate with theoretical formula

[ k W / m

2

K ]

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

[℃]

16

Comparison 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 λ α × × × =

4 . 8 .

Pr Re 023 .

17

Summary

• 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]

18

Schedule

Next cooling test with more flow rate

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

19

reference1

• ff-axis-beam

⇒high intensity

narrow energy band

Super-K.

Decay Pipe

θ

Target Horns

20

reference2

21

reference３

• 

     − − =

∫

) ( ) ( 2 1

2

r T dr r rT R E

R stat z

ν α σ       − − =

∫ ∫

r R stat r

dr r rT r dr r rT R E

2 2

) ( 1 ) ( 1 1 ν α σ

      − + − =

∫ ∫

) ( ) ( 1 ) ( 1 1

2 2

r T dr r rT r dr r rT R E

r R stat

ν α σφ

∫

± =

R dyn z

dr r rT R E

2

) ( 2 α σ

dyn z stat stat r stat z

σ σ σ σ

φ

, , ,

{ }

2 2 2

) 1 ( 3 2 2 / ) ( ) ( ) ( T E

x z z y y x eq

α ν ν σ σ σ σ σ σ σ − − ≤ − + − + − =

22

reference４

• Δ

ΔT(r) time development T(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

{ }

∑ ∫

∞ = −

+ = ∆

1 1 2

) ( ) ( ) ( ) ( ) ( 2 ) , (

2

n n a q n n R n

r q J e R q J R q J R dr r q rJ r T r T

n τ

τ ) , 2 , 1 )( ( ) (

1

⋅ ⋅ ⋅ = = n R q J R R q RJ q

n n n

λ α

λ:heat conductivity a:thermal diffusivity

) , ( τ r T ∆

) (

0 r

T

         − =       ∂ ∂ ∂ ∂ + ∂ ∂ = ∂ ∂ + =

= = R r R r

T r T r T r r T a T v ur r T λ α τ ) 1 ( ) , (

2 2

23

reference５

• ΔT[K]

ΔT[K]

24

reference6

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

center

aT surf aT

e A aqR a T Ae q r dr dT rc r Q

− −

+ − = = = − = λ π λ π

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

• data

data

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

) (

water surf

T T S Q − = α

19.4 14.9 12.2

27

50GeV ring target station Decay volume ( Beam dump () Near detector

• Muon monitor

() Primary proton beam line target

Cryogenics Cryogenics Extraction point ()

130m 280m

JPARC neutrino beamline

Proton 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 ~5µs 3.53sec

Primary Proton beam line

Extraction point Target Target station muon monitor beam dump Near neutrino detector Decay volume

28

J-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

12 50 Energy (GeV) 5.2 750 Power (kW) 2.2 3.3 beam間隔(sec) 6 330

• Int. (1012ppp)

K2K J-PARC

タ ーゲッ ト

π+

μ+ νμ

ホーン decay pipe proton

29

a ] [ G p

30

Water flow 1

900mm

target water

31

Water flow 2

s

900mm

target water

32

S

電極 電極 熱電対 91cm 4cm 5cm 4.7cm