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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