ICANS-XI International Collaboration on Advanced Neutron Sources KEK. Tsukuba, October 22-26.1990

Preliminary Thermal and Stress Analysis of the

SINQ Window

G . Heidenreich PAUL SCHERRER INSTITUTE CH-5232 Villigen-PSI, Switzerland

ABSTRACT

Preliminary results of a finite element analysis for the SINQ proton beam window are presented. Temperatures and stresses are calculated in an axisymmetric model. As a result of these calculations, the H&cooled window (safety window) could be redesigned in such a way that plastic deformation resulting from excessive stress in some areas is avoided.

I. Introduction

A thermal and structural analysis of the proposed design for the proton-beam window for the SINQ Pb-Bi target has been performed using the commercial engineering analysis system ANSYS [l]. A full description of the window design is given elsewhere 121. In brief, the overall assembly consists of two parts (see Fig 1): an inner window cooled on one side by the flow of the target Pb-Bi and an outer safety window made from two plates with water flowing between. The interspace has a He-flow (which plays no role in the cooling) and the whole assembly is to allow passage of the proton beam from vacuum to the target whilst also supporting the Pb-Bi. The main objects of the present study are the estimation of primary operational limits and safety margins for the window. The temperatures and stresses depend upon the current density of the proton beam. In normal oper- ation, all the beam passes through the up-stream meson target (Target E) and gives a peak current density of 25pA/ cm* at the design current of 1500pA. Under certain operating conditions a part of the beam will bypass Target E and result in long-term peak current densities of up to 105pA/cm*.

In the worst case, the full beam misses Target E giving a peak current density of up to 265pA/cm*:

such an extreme fault condition is expected to be rare and to last for only a short time. In the following analysis a safety factor 1 3.5, based upon the yield strength, has been calculated for the PbBi-cooled window and for peak current densities of up to 105~A/cm*. The HzO-cooled window (safety window) can, with slight design changes, have a safety factor of 2 2. At the extreme fault condition, where a peak current density of 265pA/cm2 is expected, the stresses in the PbBi-cooled window exceed the yield strength within a radius 5 12mm and plastic deformation occurs: this is due to the high peak temperature (about 83OOC). A brief description of the model details will be given in section 2. In section 3 temperatures and stresses are calculated for a peak current density of lOEipA/cm *. In section 4 the second HzO-cooled window design changes to avoid excessive stresses are discussed. The window stresses under the ex- treme fault condition (peak current density of up to 265pA/cm*) will be discussed in section 5.

536

II. Model Details

The analysis has been performed with an axisymmetric’model: the outlines of the ikite element model, which corresponds to the proposed vfindow design, is shown in-Fig I.’ The‘materfal properties of the selected steel X 2OCrMoVl 21 ( DIN 1.4922 )-are given belowi

:

Elastic modulus 206 kN/mma

Poisson ratio : : 0.3 Thermal conductivity 0.624 ~(rnt@‘C 1 _ ” 1

‘.

1.12 lo-s/% _ (

Thermal expansion _. ,A_ :_

Yield strength vs. temperature:

20 200 .300"400 460 480 -'500 550 I-- ."C ' : -: 490 432 392 353 316 293 265 216 1 N/mm’

PbBi .’ ’

\

-He - Interspace

HZO-cooled safety window

ANSYS 4.4 UNIV VERSION all 13 fQ90 02:09:3t PREP7 C&MENTS TYPE W

Target-Tube

: ’ Flange :

\ Nose

Figure 1:. Outlines of the axisymmetric finite element model used in the present analysis.

II.1 Power Deposition .

The power density distribution is approximated by a two-component gaussian and calculated as a function of radius r with the following equation:

53i

where

IO = 1500 pA is the maximum total current,,

E, = 1.69 W//LA) mm, the energy deposition by ionisation-loss, ur = 13.4 mm, the S.D. of the fraction by-passing Target E,

Q2 = 43.6 mm, the S.D. of the ‘normal’ beam and

90 = 0.016 W/mm3.

The above equation takes account of a part-, E, of the beam bypassing Target E, which produces a smaller beam spot with a standard deviation of ~1. The uniform background contribution q,, comes from neutrons, gammas etc. backscattered from the target {3].

II.2 Heat Transfer on the PbBi-cooled Window

The heat transfer coefficients for the PbBi-cooled surface were derived from a thermal-hydraulic culation [4] and are given in tabular form as a function of radius.

cal-

rh4 ..:o 1 2 3 4 5 7.5 > 10 ’

h(mW/tim2/OC);: 0 4.7 6.7 7.5 8.0 8.4 9.1 9.3 :

A constant bulk temperature (Z’pbBi .s 226°C) for the PbBi in the region of the window has been assumed.

II.3 Heat Transfer on the H&?-cooled Window

The film heat transfer coefficient on the HsC-cooled surfaces are derived from a modified Dittus- Boeiter equation [5] which takes’into.account the thermal entrance length of the heated region. For subcooled boiling, the Shah-correlation [6) has been used. Two regimes of subcooled boiling are defined: the low subcooling regime where the following equation holds:-

* = \E,

and the high subcooling regime

s=*,+*

‘3 is defined as:

“=x?x

and g,, is the value of 9 at zero subcooling and given by:

\E 0 = 230B0°*’ Bo 2 0.3 lo? *

9 o = 1 + 46B0°.’ Bo 5 0.3 lo-*

538

The transition point between the two regimes has been calculated by the Saha-Zuber correlation [7]:

When Pe < 70000

2

(AT,&+ = o.oo22qdk/A,l

when Pe ~-70000

.

(AL& = .

154.&/(Pe~p) .,

The cooling of the safety window can be supplied either by the main coohng circuit-for the target

@-bulk = 128OC) or by a separate circtit (Tbu(k = 4OOC). The predicted heat transfer coefficients, for both bulk temperatures and for different fiuid velocities and pressures, are tabulated below. A thermal entrance length of Xl = 3cm has been used to calculate the film heat transfer coefficient: the value of Xl corresponds approximately to the full-width half-maximum of thebeam~bypassing Target E. A constant bulk temperature is assumed in the flow direction. The critical heat flux has been estimated from the empirical formula given by SMirshak [8]:

_ ‘_ .

qchf = 151(1+ O.l197v)(l+ O.O0914AhT,&

5 5 AT,d(,C) 5 75 1.5 5 v(m/sec) 5 14 *

.

+ 0.186p) (W/cm2)

1.7 5 p(h) 5 6.2

. ;

Heat transfer for the H20-cooled window (dl = 277~71)

case %tdk Tazt ~~20 Vfluid Xl 4 Q&f

“C “C bar m/set cm W/cm2joC W/cm2 a) 40 180 10 2 3 1.4 1220

.’ b) i ,, i ,I c- ,, j. 4 i )S i 2.6 1450 c) t 11 ,,, ‘n t ._ S.-t ,> 3.7 ” 1690

I 4 128 ” ” 2 ‘, .2.0 796 e) ” ” ” 4 3.5 940 f) ” ,’ I’ 6.. ’ 4.8 1100 i r I 40 160 6.2 2 ”

h) ” ” ” 4 ”

1.4 840 2~6 1000

s I

i) I,.” t ” ” t 6 ‘I?‘[ 3.7 -I 1170

j j

I I t

128 ” ’ 2 ” 2.0 520 h) ” ” ” 4 ” 315 620 1) ” ” .“.. 6.. ” .4.8.. ~?20.

.!

The wall temperatures T,,, for the two windows as a function of the heat flux q are shown in Figs 2 & 3. As can be seen in these figures, case b) or c) should be chosen to avoid. subcooled boiling at a current density of 105pA/cm2: this corresponds to a.he+t &IX of 355W/cm2 for the 2mm thick window. In the stress analysis, only case b) has been used to calculate the temperature distribution within the H’zO-cooled window.

Figure 2: Wall temperature T,,,(“C) vs heat flux q(W/cn*): T&,,& = 40”C,p~20 = lObar

Figure 3: Wall temperature T,(“C) vs heat flux q(W/cm*): Tb& = l28”C,p~20 = lObar

540

III. Thermal and Stress Analysis for a Peak Current Density of 105p&?z2

In the following analysis it is assumed, that 33% of the beam bypasses Target E and gives a peak current density of ltE~A/cmr.

III.1 Temperatures and Heat Flow

The above load and boundary conditions have been used to calculate the temperature distribution within the structure. Pigs 4 & 5 show the surface temperature of the IIZO-cooled safety window and the PbBi-cooled window respectively as a function of distance along the surface to the center. The calculated heat flow from the structure to the fluids inside (r 5 80mm) and outside the beam region (r 18Omm) are as follows:

Heat flow to IjIzO :

l’L Window element (r s 80mm) 5840 W 2” Window element (p < 80mm) 5560 W Both Window elements (80 (: r < 90mm) 3310 W

Heat flow to PbBi:

Window element (r 5 80mk) 6720 W Window element (80 <, r 5 90mm) 1530 w

Target-Tube 191 W/cm :

360

320

280

210

200

160

12Q

so

kD

3 I DIST 0 1 ‘20 1

I 40 1 ‘60 1 ‘a0 I ‘too

10 30 50 70 90

._ . . . . . .

ANSYS 4.4 MIV YENSiON Jul. 30 1990 18: 16:47 POST1 DSYS-i6

zz: PATH PLOT NODl-1301 NODZ-1360 JEUP

POST1 DSYS-16 STEP=1 : lCER=i PATH PLOT NOD+1701 NOD211760 TEW

Figure 4: Temperature distribution (“C) of the HsO-cooled window plotted as a function of the dis- tance (mm) to its center.

I

475

450

425

400

375

350

325

300

275

2%

225 0 16 52 48 64 80

8 24 40 56 72

ANUS 4.4 UNIV i’ERSlON JUL 15 1990 24:0?: 12 POST1 DSYS-Il. STEP-1 ’

I TER-1 PATH PLOT NODl-1 NOD2-51 rEta=

POSTl~ . . DSYs=12 STEP= 1 lTER=l PATH PLOT NOD 11506 NoD2=55 1 TEMP

zv -1 DfSf=O.6666 XF 4.5. YF 10.5 ZF 10.5

Figure 5: Temperature distribution (“C) of the Pb~Bi-cooled window plotted as a function of the distance (mm) to its center.

III.2 Stresses :

A linear structural analysis based upon the calculated temperature distribution has been performed for the following static pressures:

PH20 = 10 bar

PHe = O&lo bar

PPbBi = 5 bar

In the Figs 6 & 7, the calculated component stresses S, for the two windows are plotted as a function of the distance along the surface to their centers. Here, S, represents the in-plane component stress in the radial direction. As can be seen in the figures, the main contribution comes from bending stress induced by the thermal’load. Prom the calculated stress distribution the von Mises stress has been used to evaluate a safety factor, based upon the temperature dependent yield strength. The stress maxima and corresponding safety factors are summarized below for the different load cases:

542

Von Mises Stress (N/mm2) and safety factor () -(ppbBi.= Zbar, pH20 = lObar)

Load i thermal R’ko I yes ye= case pae(ber) 0 0 10

l*:lY O-cooled z r < 50mm - 150 (3) - 50 (3) - .- window Ir>50mmI( - j If

2”dH90-coolkd I r < 50mm II 40 I 4?1(1

I -‘---- v&ldow

I. window

n 1 \ 81) ‘432 (.88) r > 50mm 11 145 1 360 (1.3) 340 (1.4)

00 100 I, , (3.5) (3.5) r > 50mm fl 100 ‘1 P90 (2.0) 170 (2.5)

I PhBi-cooled I r < 50mm II 40 I U

The safety factor in the center part of the PbBi-cooled window reaches a value > 3.5, while the second HzO-cooled window sbows.a safety factor < 1 at its center, where plastic deformation may occur.

I

SY 500

400

ml

206

100

I

-100

-290.

-300

-400

-500 0 20 40

‘i.0 60 60 100

10 30 70 90

‘. ._

Figure 6: Component stressesS,(N/ mni2) plotted along the surface of the 2”dX20-cooled window as a function of the ‘distance [ham) to its center (phi = Obbir). :.

ANSYS 4.4 UNIV VERSION JUL I7 1990 18:06; 19 POST 1 OSYS-lb STEP-1 ITER-1 ?ATH PLGT HODl-!301 N002-1366 sr.- __, CSYS= 16

POST 1 DSYS- : 6 STEP=1 t TER-1 PATH PLOi NODl-1701 N002=1766’ SY CSYS-16 *

zv ‘I, otsl=o.6666 Xf 4.5 YF 4.5 . Zf =0.5

543

1

SY 125 ,

100

35

50

/ -? .<’

\ ‘.

/ \ i ‘\ ! ‘\.

I .‘. ‘.

,.SY He - side

/I

25

0

-25

-50

-75

-too

-125

I ‘L I Y ‘.. +/ \ /

,7 _-J;, . ‘\

,/’ \ Y.‘_ /’ \.

\ s’( PbBi - side

DIST 0‘ 16 22 48 64 60

6 24 40 56 72

ANSYS 4.4

UNIV VERSION JUL 17 1990 ?4:01:25 POST1 OSYS- 11 STEP-S I TER-t

PATH PLOT NODl-1 NOD2-5 ! SY CSYS= 11

zv =I DIST=O.6666 XF PO.5 w -0.5 ZF -0.5

POST 1 OSYS= 12 STEP=3 lTER=l

PATH PLOT NOD 11506 NOO2=55 1 SY CSYs=lZ

i&T::.6666 XF 10.5 w 10.5 ZF =o.s

Figure 7: Component stresses S,(N/mm2) plotted along the surface of function of the distance (mm) its center (pa= = Obar).

the PbBi-cooled window as a

IV. Redesign of the second HZO-cooled Window

From the present studies the essential influence of the temperature’drop at the window center as well as at the flange to the stress level can be seen. Therefore, the following steps have been taken:

l The thickness of the window has been decreased from 2 to lmm at its center and increased from 2 to 4mm at its edge. This is done by changing the radius of the spherical surface of the He-side from the original 154mm to 141.7mm.

l The nose of the support ‘flange has been removed.

A thermal and stress analysis has been performed for this new geometry. The von Mises peak stress in the window now occurs at the edge and is 264N/mm2; at the center, the stress is reduced from

471N/mn2 (with the original design) to 220N/mm 2. The corresponding safety factors, based upon the temperature dependent yield strength, are > 2 throughout ,the window. The component stresses S, plotted along the window surfaces are shown in.Fig g and may be compared with those for the original design in Fig 6.

i

544

.

1

sy 500

400 1 .’ . 500

200 I UA I 52v -:side

Hz.0 - side

100

3

-100

-200

-300 He - side,

-400 -

-500

0 l-r,0 1 I 40 I ‘a0 I ‘80 1

OIST

‘100 10 JO 50 70 SO

.

ANSYS 4.4 UNIV VERSION JuL 13 1990 02:45:44 POST t OSYS-22 STEb1 .tfER-1 - PATH PLGT NODl-1301 NOD2- t568

EYS=22

tv =t DlSl=O.6666 XF -0.5 YF =o.s ZF 10.5

POST 1 DSYS=l6 STEP=1 1 TER=l PATH PLOT NOD1=1701 NOD211766 SY CSYS-16

ES~Z.6666 XF -0.5 YF -0.5 ZF .-O.s.

Figure 8: Component stre.sses SY(N/mn2) plotted along the surface of the redesigned 2”dH&cooled window as a function of the (mm) to its center (pi= = Ob&). .

V. Thermal and Stress Analysis for a Peak Currerit Density

of 265/~A/cm~ *

In the following simulation, the extreme fault condition is assumed, where the full. beam bypasses Target E (E = 100%). The same boundary conditions have been used as in the previous calculations.

.

V.l Temperatures

In Fig 9, the temperature response of the PbBi-cooled window at its center has been plotted as func- tion of time. At t = 0 the beam has been changed from normal operation (a peak current density of 25j.~A/cm~) to 265jiA J cm2. The steady-state temperature distribution for each window is shown in the Figs 10 & 12. The surface temperature of the HrO-cooled window exceeds the saturation temperature of the liquid within a radius r 5 12 mm for the first and r <, 7 mm for the second window and the high subcooling regime starts. The heat flux from the fist window reaches a value of w 900 W/cm2 but is less than the predicted critical heat flux.

545

960

72D

620

560

480

400

320

240 0 1 1 1 2 1 3 1 4 1 5

0.5 1.5

t (2;

3.5 4.5

TIME

&NSYS 4.4

UNIV VERSION WC 13 1990 21:01:02 POST26

zv -1

0151-0.6666 XF -0.5 YF -0.5 ZF -0.5

Figure 9: Temperature response (“C) of the PbBi-cooled window at its center plo.tted as a functiop of time t (xc). At t = 0 the beam size has been changed from a normal operation at a peak current density of 25pA/cm2 to a peak density of 265pA/cm2.

1

900

720

et0

560

480

400

320

240

160

00

0

Vacuum -side

TEYP .

! 1

0 I ‘10 1 I

DIST

20 I JO I 40 1 ‘50 5 15 2s 35 45

.

ANSYS 4.4 UNIV VERSION AlC 10 1990 21:06:37 POST t DSYS-16 STEP-1 ITER-1 ?AW PLCT NOOl-2301 NOD2-2353 TEMP

iV =I DlST=0.6666 Xf =0.5 YF IO.5 :f -0.5

POST 1 DSYS= 16 STEP=1 I TER=l

PATH PLOT NODl=l901 NOD2=1933 TEMP

zv =l

~:sT=0*4666 =o.s IF =o.s :F 10.5

Figure 10: Temperature distribution (“C) of the first Hz&cooled window plotted as a function of the distance (mm) to its center (265pA/cm2).

546

I

$00

360

280

240

2w

160

120

30

10

a I 0 1 ‘10 1 $0 1 b 1

f DIST

ra I 0 5 I 15 25 33 45

kNSVS 4.4 lR4lV VERSION AW 10 1990 21:14:58 POST 1 ,DSYS-(6 ” SlEP- 1 I TER-1 PAW PLGT NOD+1701. :, NOD291733 TEW -

YF. -0.5 2F -0.5 ‘.

POST 1 OSYs=22 STEP=1 ITER-I PATH PLOT NODl=l3Dl NOD2= 1333 TEMP

E6~Z.6666 XF =D.5 YF -0.5 IF -0.5

2. Ii20 sool.?d window

Figure 11: Temperature distribution (“C) of the second HzO-cooled window plotted as .a function of the distance (mm) to its center (265/.~A/cn’).

1

1100

1000

400

600

700

6OD

500

4w

SW

200

loo

/ 1 H’& -. side

/

\

/

PbBi - side

TEUP 1

1

DIST

0 1 ‘16 I 32 ‘48 1 ‘64 1 b0 6 24 40 56 72

ANSYS 4.4. UNIV VERSION Aw; 10 1990 20:36:55 POST 1 DSYS-12 STEP-1 ITER-1 PATH PLOT NODI-5Q6 NOD?-55 1 TEMP

ix -1 DISf=0.6666 XF -0.5 YF =0.5 tF 10.5 ,

POST 1 DSYS=ll STEP-1 lTER=l PATH PLG? NODl=l NOD2151 TEMP

IV =l DIST10.6666

z -0.5 -0.5

2F -0.5

Figure 12: Temperature distribution (“C) of the PbBi-cooled window plotted as a function of the distance (mm) to its center (26!&A/cm”).

547

f

V.2 Stresses

In Fig 13, the von Mises stress has been plotted along the surfaces of the first HsO-cooled window as function of the distance to its center. The stress level is less than the allowable yield strength at the .

corresponding temperature and at any position of the window. In Fig 14, the component stresses S, are plotted along the surfaces of the second HzO-cooled window. At the center, the von Mises stress exceeds slightly the yield strength within a local region. The component stresses S, along the surfaces of the PbBi-cooled window are shown in Fig 15. Within a path length 5 20 mm, corresponding to a radius 5 12 mm, plastic deformation occurs and stress relaxation is expected, due to the drop of the yield strength at the high peak temperatures of up to 830°C. The elastic limit is reached at - 550°C which is about 0.5sec after the current-density increase (see Fig 9).

I

360 4

280

200

160

120

60

40

0 I DIST

0 1 I 10 1

I 20 co 1

I 40 ‘SO

5 15 25 35 45

I. HPO-cooled window

ANSYS 4 .J UNIV VERSION AVG IS 1990 17:49: 1s POST 1 DSYS- 16 STEP- 1 I TER- 1 PATH PLOT NOOl-1901 N002-1957 SICE

zv =I OlST=O.6666 Xf -0.5 Yf ro.5 2f -0.5

POST1 OSYS516 STEP=1 lTER=l PATH PLOT NO0 la230 1 NODI-2333 SIGE

E~~Z.6666 Xf IO.5 IF LO.5 ZF =O.S

Figure 13: Von Mises stress (N/rrzm2) plotted along the surfaces of the the first H&cooled window as a function of the distance (mm) to its center (265+4/cna).

1

300

400

300

200

100

D

-100

-200

-300

-400

-SO0

SY

He - side

f

/ 0 I ‘20 1 50 1 ‘60 I ‘so 1

DIST

‘100 10 30 !m 70 90

WSYS 4.4 UNIV VERslOd Au0 10 3990 22: 14:oo

POSTI DSYS-22 STEP-1 I TER- 1 ?ATH PLOT NOD+.1301 NDD2-1360

EXS-22

POST 1 DSYS- 16 STEP-l ltER=l PATH PLOT NODl=l701 NOD2=1760 SY CSYS- 16

&T&65 KC -0.5 17 10.5 2f =D.s

Figure 14: Component stresses SU(N/mm2~plotted along the surfaces dow as a function of the distance (mm) to its center (265~A/cm2).

of the second H&cooled win-

.

400

320

240

160

60

0

-80

-160

SY

-240

-320

He - side

PbBi - side

.

-400 1 DIST

0 1 ‘16 1 132 I I 46 1 ‘a4 I b0

8 24 40 56 72

ANSYS 4.4 UNIV VERSlON AiJD 10 1990 g;;g:51

OSYS- 11 STEP-1 I TER-1 PATY PLOT NODI-t NOD29Sl

ZYS-11

&T&666 Kf 10.5 YF -0,s .I Zf -0.3

POST 1 DSYS-I2 STEP=1 lTER=l PATi PLOT HOD I-506 NOD2=SS 1 -51 csYS=12

~:Sf:.6666 Xf =O.s Yf -0.s 2f ro.5

Figure 15: Calculated component stresses (S,,(N/ ~FZTTZ’) plotted along the surfaces of the PbBi-cooled window as a function of the distance (mm) to its center (265pA/cm2). Note: in this case, the tem- perature is higher then 55OOC and outside the range of yield-strength data.

549

VI. Conclusions

The present study predicts adequate safety margins for peak current densities of up to 105~A/cm2 and hence, safe long-term operation may be expected for both windows. For higher current densities, up to 265pA/cm2, the stresses stay well within the elastic range of the selected steel throughout the H20-cooled window. However, the present linear analysis shows that the stresses in the PbBi-cooled window exceed the elastic limit. Further investigations are required to allow prediction of the lifetime and failure mode of this window: these need to include non-linear analysis and load cycling as well as the change of the material properties due to irradiation effects.

VII. Nomenclature

AT,, = AT,,, =

Tmit

~bulr

TtU

9

Q&f h Bo Pe

Xl dl dh

Xfl

T rot - Tbulk subcooling

Tw - Tat saturation temperature of fluid bulk temperature of fluid wall temperature heat flux, power density critical heat flux single phase heat transfer coefficient boiling number Peclet number thermal entrance length channel width of fluid hydraulic diameter thermal conductivity of fluid

References

111

PI

PI

PI

I51

PI

PI

(81

ANSYS, Swanson Analysis Systems Inc.,Houston, PA 15342 USA

M. Dubs and J. Ulrich, Design considerations of the target window, ICANS-XI, Japan 1990

F. Atchison, SINQ-project internal report SINQ/816/AF38-002, 1990

B.Sigg et al.,Thermal-hydraulics Investigation for the Liquid Lead-Bismuth Target of the SINQ Spallation Source,ICANS-XI,. Japan 1990

VDI-Wsmeatlas 1984, p. Gb3,Gd4

M. Shah, Generalized Prediction of Heat Transfer during Subcooled Boiling in Annuli,Heat Trans- fer Eng. vol.4 no.1, 1983

P. Saha and N. Zuber, Proc. of the 5th Int. Heat Transfer conf., vol IV, 1974, p. 175

S. Mirshak et al., HeatFlux at Burn-out, du Pont de Namours, Savannah River, DP-355, 1959