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.

“lLE HYDROGEN DIFFUSION FLAMES BURNING TN A MARK-IIILA- U::--84-13] g

CONTAINMENT DESIGND[’:k:fl011411

AUTHORIS) J. R. Travis

SUBMITTED 10 Joint ANG/ASME Confermce on Design, Construction, andOperntion of Nuclear l’owcrP1.a”.ts, Allgust 5-8, 1984,Portland, (kegnn

l) W’l,AIMlill

~~~~h~~~ LosAlamos,NewMexico8754gLCJSAlamos Naticnal Laborator

HYDROGEN DIFFUSION FLAMES BURNING IN A MARK III CONTAINMENT DESIGN*

J. R. Travis

Theoretical ~ivision, Group T-3University of California

Los Alamos National LaboratoryLos Alamos, New Mexico 87545

ABSTRACT

For the fjrst time, a time-depende~t, fully three-dimensional analysis of

hydrogen diffusion flames combusting in nuclear reactor containment has been

performed. The analysis involves coupling an EulerIan finite-differel.ce fluid

dynamic technique with the global chemical kinetics of hydrogen combustion.

The overall induced flow patterns are shown to be very complex and greatly influ-

ence the mximl!m wet-well temperatures and pressures and wall heat fluxes.

I. INTRODUCTION

In re.sponee to the United States Nuclear Regulatory Commission, we have

analyzed diffusion flames lmrning above the pool in the wet-well of the MARK 111

containment design. In this accident sequence, a transient event from 100% power

is followed by loss of all coolant-injection capabilj.ty. The reactor vessel

remains pressurized as the coolant water in the reactor vessel begin~ to boil

away. When the core becomes uncovered and heats up, after roughly 40 minutes in-

to the accident, zirconj-Jm and steel oxidation leads to the generation of hydro-

gen which is then released through safety relief valves (SRV’S) into the suppres-

sion pool. Under certain conditions, this release of hydrogen (e.g., with an ig-

nition source) lezds to the formation of cliff gion flames above the release areas

in the ~uppression pool. These flames may persist in localized regions above the

suppreaslon pool for tens of minutes and thcrefnre could lead to cwerheating of

nearby penetrations in the dry-well or wet-well walls. It is of most interest to

calculate the temperature end pressure of the containment atmosphere in the wet-

well region and the heat flux loads on the dry-well and wet-well walls up to l(lm

above the suppression pool surface. ‘l’h”major contribution; however, of tliis

aIuIlysiH is the calculation of the overall induced flow patterns whi~i~allows

identificatiorl cf oxygen st~=ved regions and region~ where diffutiiou fLames may

lift off ,he pool surface.

A. The Mixture Equations

The mixture mass conservation equation is

Q+ v*(p;)at

=0 ,

where

4

P=IP;P ~ = macroscopic density of the individual spet:ies (H20, N2,a

a=lH2 or 02),

~= mass-average velocity vector.

The mixture momentum conservation equations are given by

a(p;)at

-..+ V“(puu) -Vp+ r)

where

P = pressure,

o = v.f.zcousstress tensor,A

P - local density relative to the average density

1:m gravitatiolltilvector, at-d

I = strut.turnl dra~~vector.

The coefficients of viscoHity, u and A, wlIiclIappear in tl}cvisct)(lsstress

tensor, c.~. ,

[T m 2,,* - /iv*: ,rr

and p is interpreted as the “eddy viscosity”, are defined by the simple algebraic

turbulence model

In this ❑odel, s is equal. to a length scale (1.50 m for these calculations) and

@ is the turbulent energy intensity (0.151~1 for these calculations),

so

p= 0.56 01:1 .

The structuriil dra~ vector Is given by

~ = CDp(Area/Volume)~l~l ,

where

structure areaArea/Voiumc = —

structure volume ‘

where

I = mixture specific internal energy

Km “eddy conductivity”,

T = mixture temperature, and

Q = e~ergy source and/or sink per unit volume and time.

The aipecific internal energy is related to the temperature by

I = ~ Xa(Io)a+ ~ X= (T (Cv)a dT ,a-l a =1 To

where Xa Ie the ❑ ass fraction, (Io)a is the Epecific incer:,~lenergy at the ref-

erence temperature, To, for specie a and the epccific heato at coneta~t volume,

(C ) , have been represented over the temperature range (200: 2500) degreesva

Kelvin by the linear approximation

(Cv)a-Aa+3aT .

The equation-of-state for the a~”erage fluid pressure P. 18 given by the

ideal gas mixture equation

where Ku is the gn~ constant for E!pccic?u. The eddy conductivity is found” by

aHtiuming the ~’randtlNumber, l-k,equal co unity, ~.e.j

tllua

/1(-c~,

P

where

c~ = ; Xa(Cp)a = ; X= R= + (Cv)a .a=l a-l

The energy source/sink term has several,contributions: (1) chemical energy

oi hydrogen combustion, C!f; (2) heat transfer to the structure, Qs; and If the

computational zone is adjacent to a containment wall there is heat transfer to

Lhe wall, ~; therefore,

Q =Qf-Q8-~ ,

where

Qf - WI= - 85% of the chemical energy per unit volume and time, Qc, pro-

duced by hydrogen combusting (the other 15% of the chemical

energy is radiated to the wet-well and dry-well walls),

QH = h~(Area/Volume)(T - Ts), and

Qw = hw(Aw/V)(T - Tw).

In the shove relations, hs is the structural heat transfer coefficient,

1000 W/m2*K for these analyses, hw is the wall heat transfer coefficient,

20 W/mz*K tor these calculations, Ts is the structure temperature, Tw ic the

wall lempernture, Aw is the wall ~urface areti,and V ia,che computational zone

volume ndjncen[ to thu W/lIl. WaJ.1Iieattransfer is cf.iculatca by

aTM “#+hwAw(T-Tw)+Qr” O

where

(/=

k

We have

= total amount of

to a particular

energy per unit time radiated from all hydrogen flames

computatimal zone wall area, knd

= wall thermal conductivity 0081 W/m~K for these calculations .

assumed a simple penetration model for calculating the wall heat flux.

Using the analytic solution for a transient thermal wave penetrating into a smni-

infinite medium, we can write

3T Tw - Tref

&- “ ‘— 9/ltpt

where Tref IS the deep wall reference temperature, and

B = thermal diffusivity, 4.9 x 10-7 m2

~ for these analyses .

B. The Scmcies Transport Equations

The dynamics of the individual species are determined by

apH20 ‘H20— + V“(PH20U)at

- v- pYV~ - ‘H + So ~2 2

ap.. P~2.<+ v0(PN2a

at- v= pyv — =0 ,

P

a% p“

--2+ v~(p,j)at

-v.pyv~ “-s}l ,P 2

.ana

aPO

J + V.(poat

i) - v- pyv

2

where the “eddy diffusivity”,

PfJ~=-

P SO* ‘

\y, is determined by setting the Schmidt Number to

unity, y = VIP, imd SH and S are determined by the chemical kinetice presented2 02

below. Summing t!lcabove species transport equations results in the mixture mass

conservation equation.

c. Chemical Kil\etics—.

We are employing global chemical kinetics in which the only reaction mod-

elled is

2H2 + 02 ~ 2H20 + Qc .

Hydrogen combustion proceeds by mans of many more elementary reaction steps and

intermediate chemical species. The chemical reaction time scale is, however,

very short compared with flui 1 dynamic motions and waningful calculations can be

accomplished using this simplified

Here, Qc is the chemical energy of

global chemical kinetics scheme.2

combustion per unit volume and time, i.e.,

+- 4.778 X 105 & ~ ~ .c

cm m .s

The reaction rate, ~, is modelled by Arrenhius kinetics as

.:

W-cf:exp(-104/T) ,

‘2 ‘2

3m

where M is the uoiecular weight and Cf = 3.3 x 105 —— Now , the sourcemole - 8 “

terms SH and S are found by02

‘H2=2%2; ,

and

S02 - Mo2~ “

III. SOLUTION PROC5DLJR.E

The abo’?eequations are written in finite-difference form for their numeri-

cal solution. The nonlinear fil?lte-diffeceuce equations are then salved itera-

tively using a point relaxation method. Since we are interested in low-speed

flows where the propagation of pressure waves need not be resolved, we are there-

fore utilizing a modified ICE1 solution technique where the species densities are

functions of the containment pressute, and nat of the local pressure. Time-tie-

pendent solutions can be obtained in one, two, and three space dfnenstons in

plane and in cylindrical geometries, and in one- and two-space dimensions in

spherical geometries. The geometric region of interest is divided into wny

finite-sized space-fixed zones called computational cells that collectively term

the computing msh. Figure 1 shows a typical computati.oral cell with the veloci-

ties centered on cell boundaries. All scalar quantities, such as I, p, ~nd pa’s,

are positioned at the cell-center designated (i,j,k). The finite-difference

equations for the quantities at time tm(n+l)bt form a system u coup’ed, nonllne-

ar algebraic equations.

The solution nthod starts with the explicit calculation of the chemical

kinetics yielding the source terms in the species transport equations and

b,

specific internal energy density equation. Next, the convection, viscous stress

tensor, gravity, and drag terms are evaluated in the mixture momentum equations

and an estimate of the time advanced velocities is obt&ined. The solution method

then proceeds with the iteration phase:

(1) The (P~)n+lts are found from the specied transport equations using the

latest iterates for (p)~+l-n+1

and u .

n+l(2) The global or average fluid pressure, P. is determined by integrating

the equation-of-state over the computational mesh.

(3) The equation-or-state is modified slightly to find the mixture density

using the (p&)n+lts and P~+l from steps (1) and (2)

(4) with p~+:,k [from step (3)] and the latest iterates for ~n+l the resid-)

ual, Di,j,k’

in the mixture mass equation i~ calculated. If the con--

I-4

vergence criterion is met, for example Di,j,k

<~wherec=lOx

‘;,j,k’

n+1then no adjustment i9 made to the local pressure, pi ; k, and

$-)-n+l

the velocities u~ j,k for cell (i,j,k). When the convergence criterion#

is met for all cells in the computational me~h, the iteration phase of

the cycle is complete.

(5) For any cell that the criterion is not met, tke l~cal pressure is

changed by an amount

where

aD 26t2& i,j,k =

6r2 + (ri&3)2 + 622 ‘

and Q is a constant over-relaxation f.lctorselected 1.0 ~ ~ < 2.0, and

the nmmenta are changed ckreto the new pre:sure gradient. The veloci-

ties are found by simply dividing the momenta by the updated densities.

Stepr ~!) - (5) are repeated until the convergence criterion as presented In step

(4) is J,atisfied on the entire computatiand me.h. After the iteration ph~se la

complete, the tipecificinternal energy de~sity equation Ss evaluated and the com-

putational tjue step is finished with the advancement of th~ time step.

Iv. GLOMETRY, COMPUrATIONAI, MESH, AND INITIAL AND HOUNDARY CONDITIONS

TileMARK III containment t!esign is shown s(’1’ema~icallyin rig. 2. We are

only concerned with the containment volume above the water level so we approxi-

mate the containment with the configuration presented illFig. ~),which has the

same [atmospheric contajnmcnt volume as that of Fig. 2. The outer vertical con-

tainment WU1l (wet-well WLIL1) is concrete 0.75 m (2.5 feet) thick and the inner

vertical WU1l (dry-well wall) is concrete 1.2 m ( 5 ieet) Lhich. The tlnnuliir rt’-

gion be~wcen these two walls is called the wep-vvll. Hydrogen }:lvlrgcrs or

~ources are ;Jctuully ML the bottom of tlw supple ~sioll pool Wj.tllill I IU of tllL’ ill-

ner wall. Tlw nine source~ can IW thou};;~t of iIH Ci.rallurj ~~ m (1.lilm[’tc’f”, cellLcrt’d

uzimuth~llly titlh, 411$ f3HJ 13bJ 152, lt14,2tb, 28Hj :Iml 32H de}ftee~. l~j~.4

~iV(:}l Ll]e Id(+/lof t]w sou~~e~ r(’1.ilttV(’ to t;lt! WCt-Wrl.l lllld Lilt? cont:llnmclltW.’I1lSO

The gcomi?try n~ shl~wn I,nth~,two pcr~pecttvc vicw~ of k’i~~m 5 Hld h llldl-

C;lt{!N tl)ut tril(~ tllrrl~-dlmcll} l.oll:ll.lty 0[ till’ ront:ll.llmullLa I’lw hvAlwxt~ll Hourl’(’s

firu HIIOWII NL tlw huttom MH durk rcctnllfiulurr~’~inns. ‘1’11(*rylllldrlcnl (’OMl)lll iI-

tional ush approximating this geometry IB presented in Fig. 7 which shows each

of the computing zones. A pfe shaped region of the computing merh tndlcati~g the

dimensions is presented in Fig. 8. Hydrogen enters the computing =sh at the

bottom (J-2) of specific cells in the annular ring (1=8) with a temperatur~

equalling 71*C and pressure eq~lalling 105 Pa. The initial. conditions in the con-

tainment is dry air h: 21°C and 1!35Pa. The azmuthal positions of the hydrogen

sources within the ring 1=8 are specified at K = 4, 6, 8, 13, 15, 16, 20, 22, and

24 which corresponds to computational zonericentered at 322.5, 29,2.5,262.5,

187.5, 157.5, 142.: 82.5, 52.5, and 22.5, respectively. The OMSS flow rate of

100 lb/reinis distributed eqcally among the ,~inenources.

There ~re tremendous heat sink~ in the containment e.g., 2.2 x 136 kg sLeel

with heat trarsfer surface area equalling 2.7 x 104 m2p from which an uverage

sulfacc area per unJi volume can he found. Thn structural heat transfer and drag

formulations both use thitiaverage value to compute bent and momentum exchange,

respectively, within a computi3tionul zone.

TAt!LliT

AZMUTllAL POSITIONS OF TIIEHYDROGEN SOURCES WITliIN KING 1=8

GiIse “B” cnHIJ “c” CFI!I[! ““~’”

Azmutlltill%~itions Azmuthul Posltlonti Azmutlml Position

K

4

b

H

1‘!

1()

20

21

22

24

~rees

322.5

29:!.!)

202.’j

lJ7.’j

lf’+2.5

H2.’)

07.’)

52.’>

22.’)

11,

4

f)

H

1:!

IJ

1()

20

22

2.’)

WK.WL K D12gr(?cH— —

322.’) 22 52.5

292.’)

2t)2.’i

lHI.5

1s7.s

]1,~.’)

82.’)

S2.’)

:?2.’)

v. RESULTS

Fig. 9 diaplaya velocity vectors in an unwrapped (constant radius WS.

height) configuration. The radius is at the radial center of the hydroktin source

cells (1=8), which can be seen at the bottom of each plot by the openings. For

example, there is a double source between 135 and 165 defirees .md seven eingle

sources distributed aiong the azm~’thal tiimenuion. With nini=distributed so~lrceb.

and distributed ae they are, Fig. 9 shows the development of very strong buoyancy

driven flows in the partial hot chimney at 45 ~egreea and the full hot chimneys

at 135 and 315 degrees. A cold chimney (downflow) devel~ps at 225 degrees

completing the convective 100PB. The partial hot chimney (45 degrees) is blocked

by a concrete floor about half way to the top and is diverted toward the outer

wall and Upwi]rd around the enclosed volumes shown in this figure. The horizontal

lines designate concrete floors where no mass, momentum or energy is allowed

flux across these lines. Thus we see tilehot products of combustion bene~lth

floors at ~ay 270 degrqe~ convecting horizontally and contrthuttn}: to the fu

hot chin!neyat 315 degrees. Maxi.mum giIs temperilturc~ tiregenerally found if]

regions of nultiple sources aud benui~th concrete floors a~ rleplcted in Fig.

to

the

1

[).

imum

Summary results are presented in the next figures. Figure 19 shows the max-

and minimum wet-well temperatures and containment atmosphere pressure.

Note that the maximum temperature would alwaya be the adiabatic flame tem-

perature for the composition of gases at that particular Lime. We corroctly cal-

culate the adiabatic flame temperature; however, because of the coarseness of the

computational mesh, the temperature of any zone in which combustion is taking

place will always b lower than the actual adiabatic flame temperature. Mass

historiel ~or H20, HI, and 02 are also included. Note that at roughly 1600s,

oxygen is totally depleted in the containment. Spatial di~tributions for heat

fluxes to the inner and outer wet-well walls at 10 feet and 30 feet above the

pool surface are presented in Fig. 20 for various times (60, 150, 600, and 1800

seconds). The hydrogen apurger or source azmuthal positions are indicated on

each figure.

cations. For

the heilt flux

Maximum heat flux values correspond one far one at the sparger lo-

azrnuthal locations 142.5 and 292.5 degrees wher~ large values of

occur, wc have }:lvenbcut tlux histories titthe 1(Ifeet and 3(It(?et

VI. CONCLUSIONS

This is the most sophisticated &nalysis to this date of diffusicm flames in

reactor containment. Improvements can be made in the wall heat transfer treat-

ment, the amount of radiant heat transferred from each chemical energy source,

the turbulence model and the chemical kinetics representation; however$ the ef-

fects of these phenomena are accounted far, and the fluid dynamics of the overall

induced flow pntterns a“.erelatively insensitive to changes in these parameters.

In strictly conserving .nass,momentum, and energy throllghout the computational

mesh, these time-dependent, fully three-dimensional

sidered benchmarks analyses.

VII. ACKNOWLEDGMENTS

It is a pleasure to express appreciat~on to T,

calculations should be con-

I). Butler, .J.K. Dukowicz,

F. H. Harlow, and P. ?. OfKourke for their ‘~elpfuldiscussic)ns throughout this

work.

VIIIO REFERENCE

10 F. H. I!tlrlowand A. A. Arnsden, “Numerical. Fluid DynLlmi,csCalvulfltlon ML’tlloclfor All. FJ.ow Speeds,” J. (k)mput. J%vs. ~, 197 (1971)0

2. ‘J’. D. Bllt.ler, L. D. Cioutman, .J.K. l)tlkowicz,and .J. ‘~.lt~lm:;!l{lw,“Multi-dlmellsiol~illNum~’rtc:ll!ii,mulatiof) of Rc{ictivt’ Flow III l,lltc’rll;~l(Jt)mh(lstloll

J’;nfli.m?s,”Prog. lln~?rflyComt)usto _.,Sci. 7 293 (1981).

v

Fig. 1.Locmtlons of velocity component6

for ● typical cell in cylindri-cal guonetry.

,

I(

I

1

[I

4 I L

1--- 1?.65m--i

DRYWELL

T

v v

Fig. 3. Schematic View of the HARK-III Gmtaimrect Design showins thegeometry used in :he Calculation. N ttmt the Containment lJol_a are ~ualare Equal in Ffgs. 2 amj 3.

184°

15

90°

0°

=--------’270°

\

FRONT VIEW

180°

~ig. ‘).Perspective Front Viw o! Containment ~howir~ ExcludedVolumes, Concrete Floors, and Locations of l{ydrogcl~Sources for Caav C.

1800

270°

90°

/–=-k

0°

Fig. f’.Perspective Back Vie# of Containment Showing ExcludedVol!Jmes, Concrete Floors and Locations of l{ydro~enSources for Case C.

180”

270°

0’

19[9 20 “

9cl”

I—-1

~j.a. “?.

Computing Mesh for Containment Geometry.

--l 2./~

TE0.u“)

I

/JIIIII

I

III

tr ‘-

Fig. 8.

Perspective View of a Pie Shaped Zone within the ComputingMesh.

‘oo-1

‘oI

. . .

,r

. . .

. .

,. ...

,., .,

,.. ,

—.

I

i

. . .

. .

.,m

. . .

---- , ,

. . .

,.. .

.,.

I

I

. 1,11

—— —

. . .

. . ,

. . .

. . . .

.

. .

,.

. .

1!

..-.

.

. .

. .

Fig. 9. Unwrapped (constant radius, 1=8 vs. axial dimension, z) Velocity Vectors

at 120s. Vmax=7.4 m/s alldWmaxm7.9 m/H

I I

‘Y

—. . — —— —.

Fig. 10. Unwrapped (constant radius, 1=8 vs. axial dimension, z) Gas

Contours dt 120s. Tmax’:1233K aTldTmin=399K

,,

.—— ——

——

I

Temperature

—— — — .— —.

-+&4KA- A&hi&A —Fig. 11. Unwrapped (constant radius, 1=8 VFi. Hxi~l dim~li~l:;n, Z) HydrO~eIl ~PnSir\~

Contours at 12Gs.

“——— 1

* A4a7&A——

Fig. 12. UnwrappedEnergy of

— — — —.— —

(constant radius, 1=8 vs. axial dimension, z) Chemical

Combustion COnLCN.IrS at 120s.

o

9PJ

‘arI

‘oI

——

—. .—— — — .— —

Fig. 13. Unwrapp(?d (C?OIIfItnnt- ru.1’luf+, T=N VH. nxlnl dlmliilr~loll,z) (lXVR\)llDensity Contour9 nt 12(W.

.

“os ‘o

-1 I I I—.

1?I

T

.

I

m

. \..- \,

/ ?

f,

.. .

.

. 9 ● #

..-

..-

. .

. .

i

.I .

——

J ~,I.m*

i

i

1

1

a

IIii,

.-jI

-1

I

-i

4

.,

——

\ ----I

d ~“ ● ,/ #’8

P1 ----

— -- —.- _ —.. . --—

“ ‘g? y B ‘o

d- ‘0I I

i

1,

—— —.

1——.

I I f

c’

\ y

\\~. , .../.l/,, = , ,;, - .

‘\ ‘ ,’1-al,\ ,’ — .“

t \ —.. ..

—. ——

—. 1

. ..4

Fig. 15. Unwrapped (constant radius, 1=8 vs. axial dimension, z) Gas TemperatureContours at 1410s. T~ax=732K and Tmin=346K

I

1~-_—..—-

1 I

--——— .-1

~,.. ,

,,,,. ,

p+:; -:,”,- i’:,,:,‘ j.,s,, d’

— —. — -—— ._. —_____ 1

U14, 1-H VH. nxli Il (llnl{~llHlOli.7,) llydr(\Rt~ii D(IIIHI!V

1 r!

b;r i1

i;

~2

—— — — —— —

Fig. 17. Unwrapped (constant radius, 1=8 vs. axial dimension, z) ChemicalEnergy of Combustion Contours at 1410s.

=“r)

9

0.- .— — - -.—. — ———.— -—— — ----- -.

‘–- –1

.——..

L

I

h i--- ,.

..” ‘.

-\

-. ‘!II

—— — —

I..–;’.—..__

[

———-—.-1 ---

[ .—..- .

.-.

...--

l-i,—

D--

T =-—-

,._-:

-.. /

I

I

1:.—— i . .

—- --- --, I

MAX ANO HIN TEMPERATURE IN WET WELL

Iwr 1

.

\

~~O 200 400 600 800 10001200 1400 16G0 1800:000

T1r4E {s)

OZ(0), HZOt V) ANC) HZ(H) IN CONTAINMENT

1000

a

/

1 Irt [

O 700 400 bOO 800 1000 IZCO 1400 1600 18002000

TIME (S)

A

WIQw

wx

2(,=,I&luL

.

PRESSURE lN THE WET WELL

“r——————————1

f141 ● . * 4

0 200 400 600 SOOIGGO 1ZGG14GOI6W1OWZW

TIP4E (S)

MASS HZ IN CONTAINMENT

200

1s0.

160 -

I 40 -

120 -

100 -

80 -

60 -

40 .

20 .

0 * ,0 ZOO 400 60G 800 10001200 14GG16GO180020~

TIME (S)

=--- IG------ . . s“cn5ary Pes.ults: ~=xi~~ amd ~~mi~ Atmospheric Wet-Well Temperatures

(-~cper left?, %xim Containment Pressure (upper right), 92, H20, and H2

!%ss <r! Containment (lower left), and H2 Mass in Containment (lower right)

1800

1200 i

o so lw 150 zoo 2s0 300 3s0 400AZ IWTH4L AM&E (OEOREES)

CASE C ?Ix = 60 I SEcws

I = 10 FEET 3 = 30 FEET s = SPARGER U3CATI13US

%EAi FLUX TO TX lWER VALL

01 ?% -)&. L Jo so 100 150 200 250 300 3s0 400

140

120

100

90

60

40

20 ~o 50 100 150 200 2s0 300 3s0 400

AZ IKJTHAL ANGLE (DEGREES)

CASE C TIK = 60 I SECOM)S

1= 10 FEET 3 : 30 FEET ● = SPARCER LOCATIONS

=AT FLUX TO TK OUTER WALL

1301 1

Zo J L. Jo 50 100 150 200 250 300 3s0 400

AZ IMJTI-W- AWil-E (OEGREES)

CASE C TIW = 156 1 SECHS

l= IO FEET 3= 30 FEET Q = SPAROER WATIOWS

Fig. 2T. Rest Flux to the ~et-wel~ “Jails as a function of Azimuthal position ai~e]e~~~~ Times (60s top and 150s bottom).

WAT FLUX TO 1- I=R WALL

7G4 ? 10

?d8

AZ? HJTHAL ANGLE (OEGREES)

CASE C TI* = 600 I SECCIN3S

I = 10 FEET 3 = 30 FEET ● = SPA-R LOCATl~S

KAT FLUX 70 1- I-R Uti

70 ,~10

\1%●●

x3

ii

Qi J

0 50 1OG 15C zoo 250 30Q 350

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60

40

20 .~~~) 50 I 00 1so 200 250 300 3 0

AZ IWTHAL A-E (OEGREES)

CASE C TIHE = 600 1 SEC(MK

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HEAT FLIJX TO l= OUTER WALL

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0 50 100 I 50 zoo 250 300 350

AZ IHUTHAL ANGLE (OECREES)

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Position at Selected Times (600s top and 1800s bottom).

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