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 S . Ueda heat transfer coefficient cooling test JHF target monitor R&D group summary

2 Introduction � Beam 50 [GeV] proton, 0.75 [MW] 3 × 10 14 [protons / spill] , 5 [ μ sec/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(2 λ int) & 12~15mm radius Cooling pipe from one-side horn beam Target 900mm

3 Requirements for target � More pion Pion yield 1.2 1.0 � Thermal shock resistance 0.8 � Possibility to cool 0.6 The effects of target radius 0.4 radius σ beam = � Larger radius 0.2 2 . 5 pion yield decreases 0 2.5 5 7.5 10 12.5 15 Target Size(mm) � Smaller radius [K] � Temperature increases more thermal stress � surface area decreases difficult to cool The optimization is needed Temperature rise at center

4 Energy deposit J/g degree R cal. w/ MARS Z heat distribution in 1pulse (15mm radius) [J/g] 20%difference r=13mm r=15mm

5 Thermal stress � Stress estimation � Stress estimation α 2 E T σ ≈ − stat 0 z − ν 3 1 α E T quasi-static stress σ ≈ − stat 0 r − ν 3 ( 1 ) (non-uniform heating) α E T σ φ ≈ − stat 0 − ν 3 ( 1 ) dynamical stress 1 σ ≈ ± α dyn E T 0 z 3 (rapid heating) E: Y o u n g ’ s m o d u l u s ν: P o i s s o n r a t i o α: l i n e a r e x p a n s i o n c o e f f . � Material fatigue Material fatigue � T : T e m p e r a t u r e a t c e n t e r 0 after repeating stress(10 6 times), tensile strength become 0.8 (IG-110).

Material properties Ⅰ 6 � Temperature dependence Temperature dependence � specific heat tensile strength [J/g] � max temp. rise(G347) r=13mm 234.2[K] almost the same r=15mm 200.6[K]

Material properties Ⅱ 7 thermal expansion coeff.(G347) Young’s modulus(G347) ] a p ] G K [ / 1 [ 6 - 0 1 temperature dependence exists these effects should be taken into account.

8 Safety factor � Definition Definition � safety factor = ( tensile strength / σ eq ) − ν 2 σ = σ − σ + σ − σ + σ − σ ≤ α 2 2 2 {( ) ( ) ( ) } / 2 E T eq x y y z z x 0 − ν 3 ( 1 ) � Result � Result (include fatigue 、 material properties) σ eq σ eq Type tensile 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

9 Cooling � Requirement � Requirement � cool down 60kJ in 3.3 sec � keep T surf under 100 ℃ Q : heat transfer [kW] � α is a key parameter! is a key parameter! S : surface area [m 2 ] Q = α S(T surf - T water ) = α S ΔＴ Tsurf : temp. at surface[K] Twater : temp. of water [K] T surf = T water + Δ T α ： heat transfer coeff. T water ← Δ T ← α [kW/m 2 /K] T water α depends water cooling test Q target α need to be measured T surf

Analytical estimation of Δ T 10 � Δ Δ T(t) T(t) � depends on ・ initial condition ： T rise (r) ・ heat transfer coeff ： α ΔＴ Temp. rise at 5 μ sec α = 6 ] K [ Averaged in z direction

11 Water temperature � T T water (r) (at Z=900mm) � water (r) T surf = T water + Δ T to estimate maximum T surf , max of T water is necessary water Q beam T water has max at Z=900mm Z=0mm Z=900mm ] Water temp. ℃ heat transfer ∝ Δ T [ α = 6 T water takes maximum value 20[l/min] target at 0.8sec beam in

α 12 & flow rate ] � Calculation result ℃ [ T surf ＝Δ T ＋ T water more water flow rate water temp rise : smaller acceptable α : lower � Relation between α ＆ flow rate Flow rate& α satisfy T surf <100 ℃ allowable 15 [l/min] -> more than 6.5 [kW/m 2 /K] 20 [l/min]->more than 5.8 [kW/m 2 /K] Is needed

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 Q α = − S ( T T ) surf water α : heat transfer coeff. [kW/m 2 /K] Q :heat transfer [W] T surf :surface temperature [K] T water :water temperature [K] S :surface area [m 2 ]

14 Setup of cooling test � Current ~ 1.2kA(20kW) � Water flow 8.9 , 12[l/min] � Target radius 15mm water thermocouples target DC current Current feeds 900mm

15 Cooling test results � � α increase with 6.5[kW/m 2 /K] surface temperature ] at 15[l/min] K & water flow rate 2 m / W k [ compared with the α condition extrapolate with theoretical formula [ ℃ ]

16 Comparison w/ theoretical formula � Theoretical formula × × × λ 0 . 8 0 . 4 0 . 023 Re Pr α = d 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 !

17 Summary � Thermal stress max stress safety factor IG-43 7.48[MPa] 4.0 r =15mm G347 5.55[MPa] 4.5 relations between α ＆ flow rate � cooling calc. r=15mm 15[l/min] ,6.5[kW/m 2 /K] 20[l/min] ,5.8[kW/m 2 /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 � off-axis-beam ⇒ high intensity Super-K. narrow energy band Decay Pipe θ Target Horns

20 reference2

reference ３ 21 σ σ σ σ stat stat stat dyn � � , , , φ z r z α   E 2 R ∫ σ = − stat   ( ) ( ) rT r dr T r z − ν  2  0 1 R α   E 1 1 R r ∫ ∫ σ = − stat   rT ( r ) dr rT ( r ) dr r 1 ν −  2 2  0 0 R r α   E 1 1 R r ∫ ∫ σ φ = + − stat   rT ( r ) dr rT ( r ) dr T ( r ) − ν   2 2 0 0 1 R r 2 R ∫ σ = ± α dyn ( ) E rT r dr z 2 0 R { } − ν 2 σ = σ − σ + σ − σ + σ − σ ≤ α 2 2 2 ( ) ( ) ( ) / 2 E T eq x y y z z x 0 − ν 3 ( 1 )

reference ４ 22 Δ T(r) time development � Δ T(r) time development � When the target surface is cooled (at r=R)with α , temperature difference between Tsurf and Twater ∆ ( τ （ at r,time= τ ) : is, T r , ) T 0 r ( )   = + T ( r , 0 ) ur v   λ :heat conductivity ∂ ∂ 2 ∂ T T 1 T = +  a ( ) ∂ τ ∂ a:thermal diffusivity ∂ 2  r r r  ∂ α   T = −    T = ∂ λ r R    r = r R R ∫ ∞ 2 T ( r ) rJ ( q r ) dr ∑ 0 0 n − n τ 2 ∆ τ = q a 0 T ( r , ) e J ( q r ) { } 0 n + 2 R J ( q R ) J ( q R ) = n 1 0 n 1 n α R = = ⋅ ⋅ ⋅ q RJ ( q R ) J ( q R )( n 1 , 2 , ) ただし 1 0 n n λ n

reference ５ 23 � Δ T[K] Δ T[K]

24 reference6

参考６ 25 � 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 = − π λ = π 2 Q ( r ) 2 rc r q Q(r) dr − λ = aT Ae r 2 1 aqR − = − + aT T ln( e center ) surf 4 a A λ： 熱伝導度 c ： 比熱 q : 単位体積当たり の発熱量 R ： 半径

冷却試験 26 � data � data 14.9 Q α = 12.2 − S ( T T ) 4.2 surf water POWER :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 Proton JPARC neutrino beamline Primary proton beam line beam line Extraction Proton beam kinetic energy Extraction point ( ���� ) point 50GeV ring 50GeV Cryogenics Cryogenics (40GeV@T=0) # of protons / pulse 3.3x10 14 Beam power Target target Target station target station 750kW Decay volume 130m Decay volume Bunch structure 8 bunches ( ����� Bunch length (full width) Beam dump beam dump 58ns ( ������ ) Bunch spacing Muon monitor muon monitor 280m ( ��������� ) 598ns Spill width ~5 µ s Near neutrino Near detector detector Cycle 3.53sec

J-PARC ニュ ート リ ノ実験 28 目的 目的 � ν μ → ν e � ν μ disappearance � CPV in lepton sector 十分な統計が必要 J-PARC K2K Energy (GeV) 50 12 Int. (10 12 ppp) 330 6 beam 間隔 (sec) 3.3 2.2 Power (kW) 750 5.2 π + μ + proton ν μ ホーン タ ーゲッ ト decay pipe

[ G p a ] 29

30 Water flow 1 water target 900mm

31 Water flow 2 � s water target 900mm