ML20134H522

Premixing of Steam Explosions: PM-ALPHA Verification Studies

ML20134H522
Person / Time
Site:	05200003
Issue date:	09/30/1996
From:	CALIFORNIA, UNIV. OF, SANTA BARBARA, CA
To:
Shared Package
ML20134H482	List: ML20134H488 ML20134H501 ML20134H522 NSD-NRC-96-4880, Forwards 3 DOE-supported Repts Entitled, Study of Steam Explosions in Nuclear Sys, Premixing of Steam Explosions: PM-ALPHA Verification Studies & Propagation of Steam Explosions: Esprose.M Verification Studies for NRC Review
References
DOE-ID-10504, NUDOCS 9611140134
Download: ML20134H522 (196)

Text

.~. q DOE /ID-10504 PREMIXING OF STEAM EXPLOSIONS:

September 1996 PM-ALPHA VERIFICATION STUDIES T. G. Theofanous, W.W. Yuen, S. Angelini 4

[*

Reactor Advanced e

Severe Accident Department of Energy Program p$k**AD K 05 003 A

PDR

DOE /lD-10504 PREMIXING OF STEAM EXPLOSIONS:

PM-ALPHA VERIFICATION STUDIES T. G. Theofanous, W.W. Yuen, S. Angelini September 1996 Center for Risk Studies and Safety Departments of Chemical and Mechanical Engineering University of California, Santa Barbara Santa Barbara, CA 93106 Prepared for the U. S. Department of Energy Idaho Operations Office Under ANL Subcontract No. 23572401 l

__.. ~. _ -..

i L

t 1

ABSTRACT An overall verification approach for the PM-ALPHA code is presented and imple-mented. The approach consists of a stepwise procedum focused principally on the multi-field aspects of the premixing phenomenon. Breakup is treated empirically, but it is shown that, through reasonable choices of the breakup parameters, consistent interpretations of existing integral premixing experiments can be obtained. The present capability is deemed adequate for bounding energetics evaluations.

l t

i k

?

l l

i I

1 l

?

l l

l L

iii

TABLE OF CONTENTS ABSTRACT................................ iii ACKNOWLEDGEMENTS.........................

vii

1. INTRODUCTION 1-1

2. MULTIFIELD ASPECTS.........................

2-1 2.1 Analytical Tests 2-1 2.1.1 Single Particle Settling....................

2-1 2.1.2 Drift Flux Relations and Settling of Particle Clouds 2-4 2.2 Experimental Tests.......................

2-14 2.2.1 Single Particle Settling..................

. 2-14 2.2.2 The MAGICO Experiments

. 2-14 2.2.3 The QUEOS Experiments

. 2-14

't INTEGRAL ASPECTS 3-1 3.1 Code Comparisons.......................

3-1 3.1.1 Comparison with CHYMES 3-1 3.1.2 Comparison with PM-ALPHA-3D 3-1 3.2 Experimental Tests........................

3-2 3.2.1 The MIXA Experiments 3-2 3.2.2 The FARO Experiments..................

3-13 4 BREAKUP ASPECTS..............

4-1 5 NUMERICAL ASPECTS 5-1 5.1 Space / Time Discretization 5-1 5.2 Numerical Diffusion 5-1 6 CONCLUDING REMARKS.....

6-1 7 REFERENCES.............

7-1 APPENDIX A The PM-ALPHA Models A-1 APPENDIX B The Mixing of Particle Clouds Plunging into Water B-1 I

v

ACKNOWLEDGEMENTS i

This work was supported under the ROAAM program carried out for the US DOE's Advanced Reactor Severe Accident Program (ARSAP), under ANL subcontract No.

23572401 to UCSB. Special thanks go to Dr. L. Meyer and Drs. D. Fletcher and B. Turland for their help in clarifying aspects of the QUEOS data and MIXA experiments and data, respectively.

i i

d i

)

1 i

l vii

1 INTRODUCTION The purpose of this document is to present a verification statement supporting the use of the computer code PM-ALPHA in assessing premixing of steam explosions in reactor geometries and conditions. Our specific interest is in obtaining reasonably conservative results on explosion energetics and damage potential, so as to be of use in safety analyses, and for licensing purposes as well. The overall approach has been described previously (Theofanous et al.,1995). It involves a methodology (Theofanous,1996) and a set of codes, as illustra ted in Table 1. The codes are supported by respective verification documents, and the approach is exemplified by the first application, as also noted in Table 1. The present report will be recognized as one of this suite of documents, and it should be studied in this context, as part of a whole. Most necessary in this respect is the description oHEa modelling approach and mathematical formulation of PM-ALPHA. They constitute the first three chapters of the PJ. ' PHA code manual, and they are reproduced in Appendix A here, too,forconvenienc

. the same vein, a familiarization with "The Study" (DOE / ID-10489) is highly recommended, prior to delving into the present details.

The structural outline of our verification approach is illustrated in Figure 1. It pro-

{

vides a systematic frame for the verification task, and thus a means to conclusion in this inherently open-ended endeavor. The same figure.

ed to chapters and sections, also serves to guide the reader through the wide variety, topics in this document. As the var-ious elements in this figure ere self explanatory, we defer all explanations to the respective topic. The rationale for separating int), and our view of, Multifield and Breakup aspects,

)

and our einphasis on the former, derive from our modelling approach (see Appendix A).

The Integral aspects provide a reasonable justification that this approach is consistent with available experience. However, as precious as this integral experience may be, it is and will likely remain rather limited (both in scope and measurements), hence our emphasis on the fundamentals under the Multifield aspects, for now, and on the Breakup aspects in the immediate future.

All calculations in this report have been done with the models described in Appendix A, implemented in the original 2D version of the code named PM-ALPHA. We now have a 3D code also, using the same models, but based on a largely different numerical scheme.

Tho code, called PM-ALFHA.3D, has been verified at this point by comparison to PM-ALPH A in one problem, as discussed under " Integral" aspects, code comparisons.

1-1

l Because of the large number of figures and tables involved, the numbering is inde-4 pendent for each section and subsection. Each subsection begin ivith a new page number.

j The figures and tables follow the text, and in referring to them the section number is men-tioned only if they are from another section. Also, the equation numbers are independent in each section. The nomenclature is explained as it is used and, to the extent p.^ssible, it 4

is made consistent among sections. All references are collected at the end of the report.

d Il 3

i I

E1 I

I' 1

IIi 3

I I

l-2 I

i Table 1 Steam Explosion Energetics and Structural Damage Potential Introdtetory and Overall Approac'.i The Study-DOE /ID-10489tl>

Topical Element l Codes Documents Initial Conditions Special Purpose Models In-Vessel SE: DOE /ID-10505W" Ex-Vessel SE: DOE /ID-10506W*

Premixing PM-ALPHA Manual: DOE /ID-10502W Verification: DOE /ID-10504W THIRMAL Manual: EPRI TR-103417W Propagation ESPROSE.m Manual: DOE /ID-10501(7)

Verification: DOE /ID-10503W Structural Response ANACAP-3D/ABAQUS Manual:W Verification: ANA-89-0094(10)

Integration / Application In-Vessel SE: DOE /ID-10505t2)~

Ex-Vessel SE: DOE /ID-10506W*

(1) T.G. Theofanous, W.W. Yuen, S. Angelini and X. Chen, "The Study of Steam Explosions in Nuclear Systems," DOE /ID-10489, January 1995.

(2) "T.G. Theofanous, W.W. Yuen, J.J. Sienicki and C.C. Chu, "The probability of a reactor pressure vessel failure by steam explosions in an AP600-like design," DOE /ID-10505.

(3) *T.G. Theofanous, W.W. Yuen, J.J. Sienicki and C.C. Chu, "The probability of containment failure by steam explosions in an SBWR-like lower drywell," DOE /ID-10506.

(4) W.W. Yuen and T.G. Theofanous,"PM-ALPHA: A computer code for assessing the premixing of steam explosions," DOE /ID-10502, April 1995.

(5) T.G. Theofanous. W.W. Yuen and S. Angelini," Premixing of steam explosions: PM-ALPHA verification studies," DOE /ID-10504.

(6) THIRMAL-1 Computer code for analysis ofinteractions between a stream of molten corium and a water pool. Vol.1: Code Manual, EPRI TR-103417-VI, Project 3130-01 Final Report (December 1993). Vol. 2: User's Manual,. EPRI TR-103417-V2, Project 3130-01, Final Repon (December 1993).

(7) W.W. Yuen and T.G. Theofanous, "ESPROSE.m: A computer code to simulate the transient behavior of a steam explosion based on the microinteractions concept," DOE /ID-10501, April 1995.

(8) T.G. Theofanous, W.W. Yuen, K. Freeman and X. Chen " Escalation and propagation of steam explosions: ESPROSE.m verification studies," DOE /ID-10503.

(9) H.D. Hibbit, et al.,"ABAQUS Version 5.3," 1994.

(10) R.J. James,"ANACAP-3D-Three-dimensionalanalysisofconcretestructures: theory, user's

)

and verification manuals," ANATECH No. ANA-89-0094,1989.

(*) The SBWR was discontinued.

(") Actually issued as DOE /ID-10541 under the title: " Lower Head Integrity Under In-Vessel Steam Explosion Loads," by T.G. Theofanous, W.W. Yuen, S. Angelini, J.J. Sienicki, M.

Freeman, X. Chen, and T. Salmassi.

1-3

PM-ALPHA Verification Physics Numerics Ch.5

• Space / Time Discretization 5.1 umer cal DHfusion 5.2 Multifield Aspects Ch.2 I

I I

Analytical 2.1 Breakup Aspects Ch.4 Expen. mental 2.2

• Single Particle 2.1.1

• Drift Flux 2.1.2

• Single Particle 2.2.1

• MAGICO 2.2.2 b

• OUEOS 2.2.3

• BILLEAU Integral Aspects Ch.3 Code Comparisons 3.1 Experimental 3.2 i

Expected

• CHYMES 3.1.1

• MIXA 3.2.1

• PM-ALPHA.3D 3.1.2

• FARO 3.2.2

• ALPHA i.

Figure 1. Overview of the verification effort and guide through the Report.

M M

M M

M M

M M

M M

M M

M M

M M

M M

M

I 2

MULTIFIELD ASPECTS The purpose of this step in the verification plan is to obtain unambiguous checks on the code's capability to capture " momentum" and " heat transfer"/" phase change" inter-actions in two-phase and three-phase interpenetrating continua, under well controlled,

)

and precisely known conditions. Of particular and greater interest are the internal struc-ture of the mixing zone as compared to external (motion of outer boundary) or integral (steam flow rate) measures.

For momentum interactions in two-phase systems, we take advantage of simple ana-lytical solutions for a single particle, obtained at the infinitely dilute limit in PM-ALPHA, and of the drift flux formalism to describe slip, supported extensively by experimental data (Wallis,1969).

For more complex situa tions in three-phase systems, including phase change, we have j

to resort to experiments, and we have a whole array of such, devised specifically for this purpose. They involve particle " clouds" poured into water, and they include the original MAGICO tests and the upgraded series MAGICO-2000, designed with the help of PM-ALPHA, the more recent QUEOS tests conducted at FZK in Germany, and the BILLEAU tests currently carried out at Grenoble, France.

2.1 Analytical Tests i

2.1.1 Single Particle Settling i

A single particle falling in a quiescent infinite fluid reaches a steady value of the velocity when the gravitational force is balanced by the drag exerted by the fluid (terminal velocity). The gravitational force on a spherical particle in a fluid is given by:

1 3

F rot. = gxd (P2 - pt)g (2.1) y where d is the particle diameter, and p3 and #2 are tre fluid and particle densities re-spectively. Still for a spherical particle, the drag is given by Hanratty and Bandukwala (1957):

1 Farog = g ord p,y2 (2.2) 2 C

where Co is the drag coefficient and V is the relative velocity between the particle and the fluid. For a sphere in the Newton regime (5 x 10 < Re < 2 x 10 ), as is of interest here, 2

5 the drag coefficient is constant (Co = 0.44) and the balance between Eqs. (2.1) and (2.2) 2-1

I yields the following expression for the terminal velocity:

p2 - vi Yo = 1.74 gd (2.3)

1. 1 The PM-ALPHA runs were executed by specifying a very dilute particle volume fraction (typically 1%) in one cell just above the free water level in a large-enough com-putational grid to ensure that the condition of infinite medium was satisfied. An initial l

velocity somewhat greater than the expected terminal velocity was assigned to the parti-l, cles. (Parametric tests with lower values of the initial volume fraction and different values of the initial velocity gave identical results.) During the calculation, a representative par-ticle is traced in a Lagrangian fashion. The results are shown in Figures 1 and 2. These j

figures also contain experimental data which are discussed in Section 2.2.1.

J B

4 Il Il I'

I I

I I

I I

2-2 I

70 i

i o experiment, 2.7 mm O expenment. 6.3 mm,

• - - -

• PM-ALPHA. 2.7 mm PM ALPHA. 6.3 mm E 50 7

===== terminal, 2.7 mm -

-terminal. 6.3 mm

.8 0

o 40 7 0

6 g',~.

a c 'd '

E 0

2 30 o,

o6, o

O

'ct -

3 20-0 T

b.

O o.O O

O y

107 b

t *.,

• ^

0 0

- 0.2 0.4 0.6 0.8 1

Time [s]

Figure L Advancement of single particles in water; ZrO.

2 70 O expenment. Al,q 2.0 mm

• • ""*"''**d**

6Q

- - - -. PM-ALPHA, Al,0, 2.0 mm PM-ALPHA, steel 2.4 mm E

50

.....,,,,,in,,, 4,,q 2.o mm O

O

-termh'.al, steel 2.4 mm

.b 40 -0 o

0 5

0 E

o 2 30 7 o

Oo b

} 20 O

e

....o

. o i

10.-

N

-3,o j

'* * *. O I

,*^o 0

O

.5 1

1.5 2

Time [s]

Figure 2. Advancement of single particles in water; Af 0 and steel.

2 3 2-3

I 2.1.2 Drift Flux Relations and Settling of Particle Clouds Consider the one-dimensional system illustrated in Figure 1. The equilibrium condi-tion, with the particles simply suspended by the flow, can be found from 22 vi = -

(2.1) a(1 - o) where vi and (1 - o) are the liquid velocity and volume fraction in the channel, and J is 21 the drift flux. For a monodispersed system of spherical particles J is generally given by 21 b = o(1 - o)

(2.2) vx where v = 2.39 (for Re > 500,i.e., Richardson and Zaki,1954), and vm is the rise (or sink here, i.e., vx < 0) velocity of a single particle in an infinite volume of fluid. We thus obtain I

v2 = -(1 - o)t.39v (2.3) or in terms of the superficial liquid velocity, J, (equal to the liquid velocity at the inlet, i

v) o J = v = -(1 - o)2.39 i

o p

(g,4)

This can be solved for o as a

1/2.39 5

a = 1 - (--

(2.5) vn to obtain the equilibrium particle concentration for any given value of vo. The particle sink velocity, v, is given by Eq. (2.3) in Section 2.1.1.

x A large number of calculations were carried out to test whether PM-ALPHA em-bodies, through its drag laws (see Appendix A), these results. Besides reproducing the equilibrium conditions, ofinterest was determining how (and in fact whether) equilibrium l

is approached from an initially off-equilibrium state, and what is the role of inertia, not reflected in the above drift flux formulation, in these transient states.

g Approach to Equilibrium. Calculations were run with off-equilibrium initial condi-tions, as indicated in Figure 2, with 5mm glass particles (density 2.6 g/cm ) and water in a l

a 1.2 m long channel. The numerical model consisted of 40 (axial) nodes, the lower 34 occu-pied by water and particles (uniformly distributed at the specified initial concentration),

g' and the top 6 occupied by steam. All components were initially at rest, and the calculation commenced by imposing the water flow condition at the inlet. All calculations led to 2-4 I

l P

an equilibrium state, which as depicted in Figure 3 was actually quantitatively accurate.

l Figure 4 depicts typical results of the " shift" from the initial non-equilibrium condition to the final equilibrium. A further perspective of these results, in the form of the drift flux function, Eq. (2.2), is provided in Figure 5. The PM-ALPHA values for the drift flux in this figure were obtained from the computed equilibrium values of particle volume fractions and liquid velocities by b = o(1 - a)1 (2.0) i v

v x

x Further tests were carried out in the same geometry, with smaller (2 mm) and denser a

'(7.8 g/cm ) particles. These results are also shown in Figure 5, as particles type 2 and 3 respectively.

i Transient Behavior. In the glass-water system runs, equilibrium was reached typically within ~10 seconds. Typical results of the transient evolution are shown for the runs with an initial concentration of 20% and an inlet velocity of 15 cm/s by the time trajectories in Figures 6 and 7. These figures show the evolution in time of particle concentration and

- drift flux for a fixed node in the computational grid. Increasing the velocity to 35cm/s yields Figure 8. Switching from glass particles to steel (7.8g/cm ) and an inlet velocity of a

20cm/s gives the peculiar transient shown in Figure 9. When for the latter conditions the velocity is increased to 60cm/s, equilibrium is reached after the rather long transient of Figure 10.

j Sedimentation. Another set of results is shown in Figures 11 and 12, for a longer, closed column (3 m), and a highly non-uniform initial particle concentration. In these calculations, mimicking a sedimentation process, there were 100 axial nodes, the top 7 of which, again, formed a steam gap. The top 10 liquid nodes were specified to contain particles with a volume fraction of 50% and null velocity. Figure 11 shows the transient in a node initially

. loaded with particles as it is slowly, by gravity, depleted. Figure 12 shows the transient in a lower position in the grid, which sees its concentration first increase and then decrease as the particles, by gravity, flow through it. Equivalent results for heavy particles are shown in Figures 13 and 14. An interesting demonstration of dynamics due to inertia effects can be seen in Figure 15, obtained with the same conditions as Figure 13 but with the particles initially in the vapor space and a downward velocity of 1 m/s. Further down in the column these inertia effects die off, as Figure 16 shows.

2-5

- _.. ~ -

I I

constant pressure

' opening steam gap p

I

}':;g, water-particles mixture W/

I

• ',.f..

1

., !.;^,

l I'

!5!:: l if constant inflow i

Figure 1. Schematic of collective particle effects simulations.

l j

0.6 i

i i

i drift-flux model x

T 0.5 x

x PM-ALPHA innial conditons.

i N

x x

5 l

x x

x E

X D

o,4 x

x x

x x

X g

x x

4 4

x x

x x

3 0.3 x

x x

x

]

x x

X T

x x

x y

0.2 N

x x

x x

m 0.1 x

x x

x x

x x

x x

x x

j 0

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Particle Volume Fraction I'

i Figure 2. Initial Conditions in PM-ALPHA simulations.

I 2-6 II I

0.5 i

i i

i i

i i

+

+

drift-flux model s

0.4

++

T

+. PM-ALPHA g

+

b

+

E T,

0.3

+

+

• o

+

. ~5

+

0.2

+

m

+

tJ 0.1

+

t 0

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Particle Volume Fraction Figure 3. Equilibrium Conditions reached in PM-ALPHA simulations.

0.5 i

i i

s 0.4

/

5 I

- g 0.3 2

s d

0.2 n

ht f

g 0.1 E

O

~

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 i

Particle Volume Fraction f

Figure 4. Shift from initial to equilibrium conditions for representative PM-ALPHA sim-I ulations.

l.

f-2-7 I

L

Il I

0.15

....i..

i

..i-

'i i

i 4

+

+

+

+

g' O 12

+

s E,

E

/

+

Wi 5

3 0.09 m

0.06 I

.5 drift flux model O

0.03

+ PM-ALPHA, particle type 1 g

o PM-ALPHA, particle type 2 and 3 3

0 O

0.1 0.2 0.3 0.4 0.5 0.6 0.7 Particle Volume Fraction Figure 5. PM. ALPHA simulations compared to the drift flux curve.

I

0. M (

t N20-1.j20 :

0.12

((

I

.F,. A

.3 0.1 u.

e 5

-O 0.0L A

u

] 0.06 2

Eo E 0.04 a

I 0.02 0

O 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction I

Figure 6. Transient for glass beads, o = 20%, vo = 15 cm/s, for node in the upper part of the column.

I 2-8 I

... =.

4 l

0.2 N20-1.j30

',,....* *f ** *..,,\\

s 0.15

)

E 9&

=

o'C m

0.1 4

.9 l

4 E

N-5 0.05 0

O 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction Figure 7. Transient for glass beads, o = 20%, v = 15 cm/s, for node in the lower part of o

the column.

j i

0.14 N20-5.j30 0.12

[

-y 0.1 1

i A

O 0.08 m

@ 0.06 5

.@ 0.04 Q

0.02 0

O 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction i

Figure 8. Transient for glass beads, o = 20%, v0 = 35 cm/s, for node in the lower part of the column.

1 2-9

I I

02 g

i B20-20.j30 g

.3 y 0.15 a

a:

1 e

y

.?**.

3 a

l b,, ',,

1 l

m 0

0.1 d

g a

a Q

E o 0.05 l

0 E:

0 0.1 0.2 0.3 0.4 0.5 0.6 g,

Particle Volume Fraction 1

1 l

Figure 9. Transient for steel beads, a = 20%, vo = 20 cm/s, for node in the lower part of the column.

)

1 02 B20-60.j30 y 0.15 Q*

y;

,9hr

.v' e

c 7e Q

$ o1 h

o m

E E

6 0.05 0

0 0.1 02 0.3 0.4 0.5 0.6 Particle Volume Fraction I;

~

Figure 10. Transient for steel beads, o = 20%, v0 = 60 cm/s, for node in the lower part of the column.

I 2-10 I

i 0.16 i

i

,;.c--

550.jl0 0.14 b

~~g 1

g 0.12 i

c:

0.1 o

m 0 0.08 c

)\\

o

} 0.06 u

E

)

E 0.04 -/

1 i

0.02 0

0 0.1 0.2 0.3 0.4 0.5 0'

Particle Volume Fraction Figure 11. Sedimentation in PM-ALPHA simulations for glass beads, initial concentration of 50%. Node at the top of the column.

0.14 e

i S50.j30 0.12 v' f x

)

y 0.1

~

5

$ 0.08 m

.E

,j 0.06 2o

.E 0.04 O

0.02 i

0 0-0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction Figure 12. Sedimentation in PM-ALPHA simulations for glass beads, initial concentration of 50%. Node in the middle of the column.

2-11

~. _._

I I

I 0.15

, x..........

S' 0'-h'.j l'0 -

li 5

5 5l c

0.1 ec Q

0

~2 3

g 6 0.05 3

.s i

O I

I gl O

0 0.1 0.2 0.3 0.4 0.5 0.6 g

Particle Volume Fraction Figure 13. Sedimentation in PM-ALPHA simulations for steel beads, initial concentration of 50% Node at the top of the column.

I 0.14 S50-h.j30 0.12 x

E y

0.1 e

'C Q 0.08

$a

,@ 0.06 li E

u E 0.04 I'1 0.02 0

O 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction I

Figure 14. Sedimentation in PM-ALPHA simulations for steel beads, initial concentration of 50% Node in the middle of the column.

2-12 I

.i i

0.14 S50-h2.jl0

]

O.12 g

0.1

• g.4 8 g

p Q 0.08 e

8 0.06 m

5

.@ 0.04 Q

0.02 O'

o 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction Figure 15. Sedimentation in PM-ALPHA simulations for steel beads, initial concentration of 50%. Node at the top of the column. Initial particle velocity Im/s downward.

h 0.14 S50-h2.j20 0.12 xy 0.1 ccQ 0.08 m

@ 0.06

\\

's 5

E 0.04 6

0.02 0

O 0.1 0.2 0.3 0.4 0.5 0.6 Particle Volume Fraction Figure 16. Sedimentation in PM-ALPHA simulations for steel beads, initial concentration of 50%. Node in the middle of the column. Initial particle velocity Im/s downward.

2-13

I 2.2 Experimental Tests 2.2.1 Single Particle Settling The results of Section 2.1.1 were supplemented by observing the settling of single particles in the laboratory. The experimental data are shown against the predictions in g

Figures 1 and 2 of Section 2.1.1. The measured velocity of aluminum oxide particles appears to be slightly lower than predicted. This could be due to small quantities of air g

(microbubbles) trapped on the relatively rough surface of this light particle.

m 2.2.2 The MAGICO Experiments This worked spanned two experiments: the original MAGICO, and the subsequent MAGICO-2000, with temperatures up to 1500 C. The results are summarized in Appendix B. We have found a way to overcome the sticking of ZrO particles, and expect to run tests 2

l at 2000 C in the near future.

2.2.3 The QUEOS Experiments These experiments have become available recently (Meyer and Schumacher,1996; Meyer,1996); they are very similar in concept to those of MAGICO-2000, and involve sim-ilar masses of particles. The key differences are higher particle density and concentration (compacted cloud), and somewhat higher temperatures. Another major difference is that g

MAGICO characterized the internal structure of the premixture, while QUEOS provided 5

the steaming flow rates. Both experiments measured the level swell, from which average premixture void fractions can be deduced, and the outside appearance and motion of the premixing zone.

The remarkable conclusion from these tests (Meyer,1996) was that the steaming, and related water depletion in the premixture, was much less than " expected." (Presumably, in the absence of any predictions for QUEOS, this " expected" referred to the author's own inference from the MAGICO-2000 tests). On the contrary, our analyses will demonstrate that these results were perfectly reasonable and consistent with PM-ALPHA predictions.

Moreover, we will demonstrate that the experimental conditions created a highly sensitive regime, quite useful from a fundamental perspective, but not quite relevant to the reactor conditions of interest here. To our knowledge, no other analyticalinterpretations of these tests are available.

I The QUEOS experimental apparatus is illustrated in Figure 1. The particulate is transferred from the furnace region to an intermediate chamber in the pipe that connects 2-14

4 the furnace to the test vessel, and then it is released to the test vessel. These operations are carried out by fast-acting valves (sliding doors). In this manner, the particulate is released, as a " slug," from its maximum packing density of 55 to 65% for the Mo and ZrO2 spheres respectively. Some axial spreading occurs due, mainly, to the door opening time measured at ~40 ms. Thus, from an initial height of ~8 cm (for the 10 kg Mo, or 7 kg ZrO tests), the cloud extends to ~28 cm yielding an average estimated volume fraction of 2

~17% This is about one order of magnitude greater than the volume fraction employed in the MAGICO experiments. Since the total particle volumes and the lateral dimensions of the pours were about the same, this implies also about an order of magnitude shorter clouds (and higher concentrations) in QUEOS as compared to MAGICO-2000. As can be deduced by comparing the QUEOS (see below) with the MAGICO-2000 (see Appendix B) results, these differences have major implications on particulate-water contact, and associated vapor production and mixing dynamics.

Another key difference relative to MAGICO-2000 was the saturation status of the water pool. In the saturated MAGICO-2000 runs, true saturation over the whole pool depth was obtained, by boiling with immersion heaters at the pool bottom. In QUEOS, the pool was brought to a uniform temperature of 99.5 C by circulation through an external heater, aided by radiation lamps. The quoted uncertainty is i0.2 C (L. Meyer, personal communication). This means that the subcc oling varied from 0.5 0.2 C at the pool top, to 3 i 0.2 C at the pool bottom. Because of the compact cloud structure, and its rapid descent through the pool, steaming occurred as a " puff," with significant condensation effects in the latter portion of this descent, and it is recalled that in MAGICO-2000 we found measurable effects even with a subcooling of only 3 C. As a consequence, this small, but non-negligible, subcooling creates a rather sensitive regime for vapor flow rates in the experiments, particularly those at the lower end of vapor production potential such as Q10 (large particles) and Q11 (small particles, but also half the volume). We believe that it would be very useful to conduct some QUEOS tests under fully saturated conditions.

It may be worth noting also that due to the release mechanism and masses involved in QUEOS the resulting particle clouds should be expected to be highly non uniform and that the internal structure has not been determined experimentally. Fortunately, the impact of non-uniformity appears (based on PM-ALPHA sensitivity studies) to be overshadowed by the shortness of the cloud, its compact, in any case, nature, and the important deceleration and radial spreading suffered upon interaction with the water pool. In the calculation reported here, we used uniform clouds at the 17% 2% average volume fraction quoted in the report. It was obtained from cold particle pours and was found to be independent 2-15

I of material and particle size. We checked this value using cloud images from two hot runs (Q10 and Q11; see Figure 2) and the results were within the specified error bounds-for Q11, a renormalization is needed, to account for the lower mass, but the volume is essentially the same (this confirms the assertion above that the particle cloud elongation for all these pours depends mainly on the door opening time). Applying the same approach for Q17 (for which no images are available to us yet) we used a volume fraction of 17%

In this first approach to the interpretation of the QUEOS experiments, we selected a l

total of six runs, three cold and three hot ones. The cold runs were Q5, Q6, and Q8, and they were chosen to include both materials (ZrO and Mo), and all three particle sizes (4.2, g

2 5, and 10 mm). The hot runs selected from the experiment report were Q10 and Q11; they included both materials (ZrO and Mo), and two particle sizes (4.2 and 10 mm). They were 2

typical of low and intermediate steaming rates over the range of experimental conditions in the report. Additional data became available more recently (Meyer,1996), and from these we chose Q17 as the run that gave the maximum steaming among all the QUEOS experiments run so far. This test was run with 10 kg of 4.2 mm Mo spheres at 2200 K.

In the simulations of the hot runs some special considerations needed to be given to the radiant energy transport and related phase changes. These special needs are due to the combination of relatively low (compared to reactor) particle temperatures (~2000 C), and the small but non-negligible subcooling (~0.5 C at the top, increasing to ~3 C at the pool bottom). More specifically, at the dominant wavelength for 2000 C, the radiant energy absorption in water occurs within ~1 mm from the interface, and it is more appropriate for it to be treated within the interfacial boundary condition (Eq. 3.28 J

in Appendix A), rather than added in the liquid bulk (Eq. 3.11 in Appendix A) through the non-local radiation model appropriate in the 3000 C range (absorption length 3 cm).

gi For a completely saturated liquid pool this distinction is not important, since the proper 5

amount of phase change will occur irrespective of whether the energy is deposited at the interface or at the liquid bulk. On the other hand, even with a small amount of subcooling (0.5 to 3 C), a significant amount of energy can be absorbed in the bulk, prior to boiling, especially for particle clouds that are small in relation to the size of the pool, and hence the bulk radiation treatment is not appropriate if the absorption length is very small, as is the case in these experiments. Further, it should be noted that the local, interfacial, treatment is consistent with the water-rich premixtures obtained in the QUEOS experiments, and it accounts for heat transfer from the interface to the liquid bulk via convective effects.

The computational domain employed is shown in Figure 3. The QUEOS test chamber is modelled as a cylindrical volume with the same cross sectional area (80 cm in diameter).

2-16 I

We use grid sizes, A: = Ar, of 2.5 or 5 cm, and a time step of at = 5 x 10"'s in all calculations. In order to interpret the pressure transient data and the induced subcooling thereof, special consideration must be given to simulate the venting mechanism in QUEOS.

This is achieved by placing obstacle cells with adiabatic and stationary particles at the exit as shown in Figure 3. The volume fraction of the particles in the exiting cell is adjusted te match the venting area of the experiment (92 cm ). The particle volume fraction in the 2

adjacent cells is set to be 50% of that in the exiting cell to assure a smooth variation of particle volume fraction in that region. To simulate the effect of friction loss associated with venting, the drag coefficient between steam and particles in the obstacle cells is calibrated based on the observed data on steam flow rate vs pressure. The initial particle cloud is shown schematically in Figure 3. The starting time of the calculation is taken to be the initial contact between the particle cloud and the water surface. The results of the computations are presented, in conjunction with the experimental data, in the following.

These comparisons focus on the time frame up to 0.4 s, at which time the particles hit the pool bottom, and are " captured" by the collection cells employed in the experiment.

First, we examine the flow regime development by superposing calculated volume fraction contours to the experimentally obtained images of the premixing zones. Such results for runs Q8, Q10, and Q11 are shown in Figures 4,6 and 7 respectively. [ Note: As seen for Q8 a 2.5 cm grid is sufficient to controi numerical diffusion to an adequate level. For all other runs, due to schedule limitations, we used a 5 cm grid. Results are to be confirmed by repeating all these runs with 2.5 cm grid also.] An illustration of the velocity field in Q8 is provided in Figure 5, to show the closing-in of the cavity created as the dense particle cloud plunges into cold water. The only observable deviation is, perhaps, a somewhat stronger " pinching" effect in this closing-in observed in the experiment. This may be due to somewhat stronger, than calculated, circulation induced in the surrounding liquid,

and its potential significance is to produce a somewhat more abrupt cutoff effect in steam flow (due to condensation) in experiments with marginal steaming rates (see pressure comparisons for hot runs, below). This cavity formation behavior and closing-in has been, in fact, first predicted with PM-ALPHA, and confirmed by observation in specially conducted cold runs in MAGICO-2000. Also, for the condition of the hot MAGICO-2000 runs (inlet particle volume fractions of only a few percent) such cavity formation is not predicted, nor is it observed.

More easily discernible comparisons of flow regimes can be made with respect to specific features such as front advancement using Lagrangian particles (Figure 8), and level swellusing collapsed liquid level from PM-ALPHA (Figure 9). The only significant 2-17

I!

discrepancy is observed for the hot runs Q10 and Q11. This discrepancy can be explained by the " pinching" effect noted above, and associated condensation phenomena. In partic-ular note in Figures 6 and 7 that between 0.2 and 0.3 s the steam cavity has closed (in the l'

experiment) and that this corresponds well with the termination of the rapid level rise, as seen in Figures 9d and 9e. In the calculation, on the other hand, as seen in Figures 6 and 7, the condensation and closing-off of this region is delayed, and as a consequence the level 1

continues to rise for another ~100 ms, creating the discrepancy. As noted above these runs will be repeated with 2.5 cm grid, which is expected to better resolve these interfacial phe-nomena, and hopefully better reflect this " pinching" due to rapid condensation. It should be emphasized, however, that such phenomena are exaggerated here due to the small, compact character of the particle clouds and the small subcooling (for large subcoolings the timing of this behavior is not very sensitive).

l Integral aspects of the thermalinteraction were obtained experimentally by measuring B

steam flow rates exiting the vent pipe, and pressure transients in the enclosed gas space 5

above the pool. Related comparisons with PM-ALPHA results, for the three hot runs, are presented in Figures 10,11, and 12. These figures include also the integrated volumes of steam, so as to obtain a more direct perspective on the magnitude of the interaction.

We thus determine total volumes of about 60,80, and 200 t for runs Q10, Q11, and Q17 l

respectively. We can then clearly see that Q10 and Q11 produced minimal interactions, and this also can be seen by the slight increase in pressure observed in the gas volume.

Indeed, a quantity of 60 or 80 ( is only a very small fraction of this gas space-it has a volume o'. ~200 f. The pressure comparisons should be examined in this context, and for the trailing portion of the traces the sensitivity of condensation under such conditions, as noted above, should be included in the consideration.

In Q17 the total steam production of ~200 ( is about the volume of the gas space, but here a very special (and pathological) mechanism comes into play. The mechanism g

involves the radiant heating of the free pool surface during the 0.5 s time period it takes 3

the particle cloud to traverse the gas space above the pool. Roughly estimated on the basis of the lower cross sectional area of the cloud, this radiant energy flow is 0.5 s is 1.8 x 10 J.

4 Absorbed in a 2 mm upper surface layer of water (1 mm absorption length at 2200 K) it would produce a superheating of ~6 K. Note the absence of nucleation sites, so that rapid g

flashing would occur only upon contact with the particle cloud, yielding 14 / of steam volume (at 1 bar), which is almost exactly what is missing in the PM-ALPHA prediction shown in Figure 12. Note that this " missing" volume of steam is only a small fraction of the total produced in the interaction; however,its rapid release, as envisioned by the proposed 2-18 I

f l

mechanism, would be all that is needed to explain the " extra" pressurization observed in the experiment. Similar estimates for Q10 and Q11 yield an extra steam volume of only 6 L This further enhances the already good quality of pmdiction, shown in Figures 10 and

11. We are currently working to include this mechanism in PM-ALPHA, so as to obtain more complete interpretations of the QUEOS experiments.

Finally, we consider the degree of voiding in the premixing zone. This can be done on an overall, average, basis, based on the level swell observed, and the mixing region volume, obtained from an outline of the visualimage. To more specifically address void fractions in the lower part of the zone that contains the particles, one needs to consider l

(subtract) the apparent cavity (" funnel") seen in the visual images, and this is complicated by not knowing the amount of liquid within it. Moreover, it is not possible to discern from the visual records what fraction of the total mixture volume contains particles, whem the highly depleted (in water) funnel ends, and what is the extent of the in-between, two-phase (steam-water) region. By assuming that the " funnel" did not contain any water, Meyer deduced that the water content in the particle-mixing-region was ~80% Our PM-ALPHA result for the central region of the mixture, containing the main portion of the particle cloud, is shown in Figure 13. The agreement, clearly, is not quantitative; however, it is noted that the general trend is similar in that the premixture is not highly depleted of water. Clearly, local measurements are needed to reliably assess the quantitative aspects.

Such measurements have been attempted in QUEOS, but it is clear from the discussion that the data obtained are preliminary at this time.

It is hoped that from the above the reader will deduce the highly sensitive nature of the hot QUEOS runs available at this time and will share our perspectives, expressed at the beginning of this section, that these data, while interesting from a fundamental point of view, are not quite relevant to the fitness-of-purpose needed here. It is expected that these sensitivities will be to some extent alleviated by the larger masses currently employed in QUEOS. It is also recommended that fully saturated pools be included in the test matrix (together with less pressure drop at the venting line by providing more vents), as well as subcoolings larger than merely few degrees.

[

L 2-19

I I

I 1

i Pneumatic Release Mechanism

,w w

C 1

f!' I 3 l

6mv High-Temperature Furnace (2600 K) i d

b Argon-atmosphere Steom-Flowmeter 3ys i

SLUICE

"~

Fast Acting-4

/

?

2

,= a 3mv

{(

steam-atmosphere i

. O Pyrometer a

h if u_

m L,.

I N $8 Y g

i g -

N Heated Camera i

Water -k I

om v

,,,,u,un,un I

Figure 1. Schematic of the QUEOS facility (from Meyer and Schumacher,1996).

I 4

2-20 I

4

'ih.k M-Y(Q j

, r,.m MM$kNo,emh dh,op

...:.....y. = 7i,5 ~.,

m 1

4 8

$.l.5",$T[wir@..

M J

meupv c % e m.4 d

j.

,& %Q~p%,15,..

s

.hChli!lN.pg' e:.b el~ QY%*-

l wa%ya3vbgr.r.. v;t*gt:

.wn

.w;; v, ~

ey t~

wJ g *s.,? r,!

ty

M.

n

< n w.** '9', "i, ag

$. -A #mwi c ffpfa,.eg g

m:

-~ w_-

5?Mi%7pT

@dF

'I '

y: pew

• wvA.

' n%

u &l*k;w>

.Q,hyg wye 8 1 P +" ; l m..

r D T,

w..;%,. g;h, hp_@%g.f;-, n

+s r\\

y

~

+

s umww

+r

-7~--

yt. c.

yntWcN ump _As, u

n~.-'O.

- ps,%s%- - 3

.s w

.p;r~-pm,b; e n

.~ % "i, -

6 R-d 4

-CBc.a% g,u.c+o.sg g >d s m

w a 3m W

,s n r ;; r_--

n =, r = 1:n:::m m ~ m....

mLt% m

-y, u

e L.b ' hce

..};, s.N.

f p.:,

2 -a

,,n

.;n.

.e.

w u,

'}'v

.g 1

.d'..

i. 4 s -

. /:

c

-r>

t;

. o,

• 4-y 1

1 s.

7 1.-

{

4

-., Q,.- a,-@ *. 4 l.>

?

,y.

n....

.s.,

, ]h =, n.

N g

r y,,

.....w

, x g

(, j.

_,;G(49

=

.m.

?'

. w.J

-.. r :..tc

• m.z

' *?,..!'M e..

Figure 2. Particle images for runs Q10 (top row) and Q11 (bottom row). The left and middle columns are taken with high-speed cameras from two sides 90 from each other.

The far right is taken with a video camera.

1 A

1 particle cloud Of = 0.073 v = 500 cm/s Of = 0.53

. a g

g,;.

M:::.El 4--exit boundary

50

M t:.

n

..

at 1 bar tl3 O. X. O.".O.:

0:0: ::

:0:0:-

0:O:0::

p

: ~ : : ~ :s A

E Oo 4

5 ooo f

v v

80 cm

,n wr Fig. 3. The computational domain used in the PM-ALPHA simulation of the QUEOS experiments. The porous obstacles near the exit cell are to create the proper flow restriction and exit pressure drop.

2-2L

_)

(

)

(

)

(

r --

1 r,. -,. '

7~-_

,._. y ;

)

,t

?

"1 'r h {p{

g ' '

]

.d !;

g 3

"v' c;

t i

.a N

' ii! - [i O "

Ei U

I 0.10 l

^

l

.wk.h,' iOd.. ' yd. ~, NJ ! $fh,,:!J@-m ;p 0.90 Ac 3-r.

M_ _

. _ _.-. - t.

_wN

• i -. $

$. %e ~ l? A

'~

w 9

(L i

9 v

3 9,a,s 9y. b>

g

.an.

5

,.y s f y 4;- t ;

i, r.

. n.=~ g s

m.

~

5 y y g[k Y I, JIl. 6;h Alif, 5

{

't e, O'~~~~7 V

f.

N b

A 9

g m

i l

Ars ?

l W

li e M pf l

t

{

G

[rf f

i i

i,

=w,c-i c==-

_V y

p

- Q+A.,:w.:{k." : -

?,. :

1 i

2

'1 y

a 7

0.02 3-*

t X-1.7 5

0.10 1

I i

1 i.

.)

1 4

4 i

t i

i i

l-a _

+

6+4-w t --

L-Fig. 4. Comparison of predicted against observed flow regime development in test Q8.The experimental image has been made partially transparent, by computer processing, so as to allow superposition of the computed contours. Times are 0.01s,0.09 and 0.17s after first impact of the particles on the water.The color scale for the particle volume fraction is on the left, that for the void on the right.

y-9 y-q 9-g q

p

- -,.ww m g)w g e*=gy pypppa prew/ga,.rylp gd yrg g.

,q

- s g

t

....--. v u a

t".p;db{,: f $r? i' y; gi

. _ f '

='g g g g_,

- 4 y;-(gYg g,

.s

n V

k:, > p

>9

} m'.c-y D

~

l

.b R

h J.,t s.E-g l

jf;;fa

..:c d

)

g-!t 3

9 g

g

,$ pi%

j!i/[fkif I) l

[ff]@M$f3[

I

[$M5 3

i

$y y

a c

t ut 1 > 1 -:

y i

l.- J p.

Mi 3

-r A

,.c b

il t.

Aq 9...

j

,~

$a;.h ',

h.,

l.S,,:a $yk!,,,

? h fd (hk El l

.Y L-dlll

.'w?

,.)

i ou -

k,k Np

?q]$,3 qlI4 'h hQg%d a

w 0.03 (20 Wh

&c.w) p:'n.d 0.10 pb~.

g

.~

m 3

04ni

. m 7, M 1m t%l s

D,@,Q";$ ' %w(p_y

\\, C7ch,,!'

y'in!. v. a- ) l @,?. j.ii

^

.m l-g(. _

n.4 n =n -

(l.m..y c. pJ. wt p

. -.s-qA,

)

^%

h,,P%y j9:[

~)"

-A,,o. dp /n t.

\\,+

b.ty ^ymme

.e

_ - _ _ ce*=

~

• 4 =

.w

~ ~ ~ = m s Fig. 4(continued). Times are 0.25s,0.33 and 0.41s after first impact of the partides on the water.

e i<

n

..;gg,$!p1ym"....

,..j dih

.- I t

.-;Z

.....,..,.;,l a%y n

4 iiln 5

d

. W.~.+.... '

M y d.

0b c..

s9

.wp._...

2 o e j

yq1

\\-

0. t

.hw....,. ~.f px jNf,p. !,

t 0%c 1

a

.,r6vp'/e

..... ' 1 1t n.,a.THhMg:. icv.-

3.

9 n

0i AQlM(

s1 d s

, I1!. <<

, ;,.,j.

,i 0 mi yl.

44J '.

4t*

p,[&,i4}i4>1-

, s9 s

0 oi

_ _ /. ',q._.

• t.6 ;.gpa.$

qci,

efr) r n

.(,

f an E.....,.,..:::

.i.

s ai E

y o

e pt

_;~

c

j,3.

T...* :... ~.

g.. j!

ms a

m

.,.;.m j H (I.qw<,s 7

sr

.. 3.

i

....;p j*

i~,,

Tef nd

.-. N..

.... j

. i i Pl u

yS, Q

q i

5 0

5 o

t m

5 7

5 2

s -

l 2

1 i

l et na y

tr o c

.wD...*.:.+r tmi :pJ.. j ; t. Q,,,.:...............

f

.:.',t

j.,

oc o l

s ns

,p j

Aoe 6..".M,....i;.q,,,.9. : r. y' \\.mg:.....

Pat s'.

i 7.. _

Ht m 7..

ci 4

Lr y f

7 _.... :..

7f4 A

, Mc.3_

t

-da

,i@43:s....

Mo o d

.,L di c

i

,a

?A,., g. :

3

,n l

h.- Q :m g e..,.

,, 7 n n. % d,m: g n.,... b e s

- - J PVe ir

.s v

(

y r.

-.; i_ qn:./,!.q

. d

, /,..

t s.

e ic d a x

ewu

. i

>~

.h 'L t

.m c

l ef i

.s

.,... j:ad dh d t

.,,,, j.

e

.rr,,r j N j.,,...,..

i r nu

..u

.a p o 'q i

9[d, d sl l

e e 0

0 o

el ch 5

5 i

i t 1

f t

yrf

,',,,..i.:

..},I!,'

.i :

+,,

ao t

Hnj.!

r i

cpe

'r.

,g!

o ed

..- i....r

.. $ng9e'- l ~.... eh u w'*.. 3:.:. vt t .t,>9 i f eog ..si,;. rp*..~@b. n 1lfgk m: h .h. t a ~. t c ~. m ..i i g.3 j;l. nmh f a l g op i t .W e i t- . E. M4i oiT .n@l+.t,4., i p' t a s s .{ a

• g/. +y<*..m t

/ t t i r r l i f a m s v e. .2{,s ur ,r l rl e ea .%mi.}o'si .l l t 3 I f t c . a ns ,-il 'i,,.:.:.: 5 i s r ,,j: ' . ll g 4. % lo . 1 0 o %c.$ sI F01 c i yf o 0 0 0 o 1 1 5 5 0

8 Ov. O o .a a. ic o. c on ..e (' ; i gp'- c. ge.. o.c v r,ih)va -Q 'C O C c e ~ ^ s,L C 4.b-u 4 o ]V g g - - - ~ ~ l) ~ { }$ 0 $h H O dH\\ @ SE ,m.bh p~'awmam y(pym Wmw w&]% Of =V _. 7 pWA.'N. 3 p k EA-m :. Tl >4QO _.a/ y3y ar m.. w. q,~ h1 , "_ #w] \\ ' V ' e - (y4 im gA' A% ..? w i oo- .~ .<y1 Ah6 :-ddid,.m} p.

f.,j U4n&p:

.a < > F{ ~

• ~c p;

1Tt \\ ,.g 6 ' r 4:Mu .M kJ&:!. cn ..g W;J,;- ~_c y m ;; sg -,,g m y + ~g ,Jit :(( .h Tl/; M.h j /g :.I Tidj h m *y k fb \\. h[i k@; i i we.r,.s N s w a ,....-ap 7?,'%O - -J wn,., o Qay -. {">& . <-/ - f;?ff'i ~ ? -5Y1;'m [W-ian.me==a}:, f. f,~g Q o, }G.ik:. j zg2o

1". If

.E. b eg t *o2 1 I W A> 1l kDA 0 >= 6 O 46b C6CO ooun cv c k,.hO

' }

M C on s Tf4MSTMIM5E94Wf42YE5th ho pg i @ ac$ e,e. m 1 ;.o e ed nm 7., [h

c. :;.~__-.- ~.,

e 4 r T* f " - - l+.. -a 5:wlll ', -%" i., s +q ,[ F: [ g fd; nC i g Q i4[If 3 7 xaci *c

s s J[

r g;+t 4 m-w w@w. and s, i, 4 v. . i e -; i+

1.

g}7

n

n. 'y %

a 4 .: n ; ' .t. =n a.9 s-.: 4 w ,,,l ; 4g, t *.C m - } j,, f ; ,. ' j f,; ,4 y

f. b

, hf'.)

1

$ ? 1.'

g m z,. n ,s%9 e n'(.I, ?.db kn eg b > a, o m.,v q .a o.E o , t 3 : ',l - ?s m ~ a p. (.p.

d..h

. ; j_,2: ---%. ! } M.. t,1 1 O t - .% M;f n.. ~ 0 ; l,#2 + '.., 1 s 1 CC 0.5 yg jJi, i;jgip st#R*M.?.ZE22LC " E d "

• a g a >o x ;

.g g o .t n oc gGcu ']' ! l. 6 j 3 8., h,g y -* , av ).;'; g; 7 D g%f e r ' _ 7l gM4 d) C C w iC.5 8 O e So o 2n

s-a e .._,.s s, .x,2. ,.a.s .._.a-2... .,,,.-=.-.m s- ~=,na-4 ..,-s_+t, aa 1 l' l-o o e n 6 o f f ~ _.._._..) q..._.--... ~ l N 3 a 4 e iM M r.,!.,. ? E 'f fYf +. w a.- *- wlllh{0hk $' g:.g=.=_ab3Eh!.k D 0hb W ~Y,

• f,

v. ~ :M:w. ;. p a z

, wv rv N j kW* x.sT:my,. - .c:gx. 3. 8 M } 9 1 .C

s..

, w ~,- ~ yy cg yNg4, c., wa ; ; ' , 7- #.3 g> i+g 5 a. vf o . f.

p.C

- ), %)% {le Qi- .l } ?i . yh l G n. +v O N l b ?Q /.w:=>=m R,:. pg&g%.l*gi g. (Vy/- g ..~ --- g A ~ pwqyp-( ms4,. d* 4 f,3j j ~ 4 a

5. - 'k g

, kfp, t / ,=a (W,.,ew. _,/ s v y;- gu % - g a.ne. - w i-Q r-e ' e/ n s w;r. < f. e I?7f I~- P [! y., +.4 79 -%kgf.id'l h e,. j$$$ ') Nm..m m met w h bin k $.. w I 'N i$ c: f 6 i 1 l .I l a. L-.. ~ w C Z 7o l

• c 4

C c \\~k m o.\\ -L~ h Tf p2l?f'QL - . t.'.m. +: M.l*W r[. [w'y u myu o

p. a

-:=... +9 .sr u .)

• \\

NkNd ~. [7Y 3 $Nbbb N} we &...r c;&wp s+k l l wm q i sp w

q...a.

v!. w:.': nM'A W. ^ e ,At y m q-1 s 6 N,,ysf.. mi, 1

4) ' y "@.4 '

l ] 49 4 4,G 'ht b )' W , MQI 9 / *tj - "

• i,. $,ek s/T "'

l i e c ' y'Q V % Q ~ - %qy3' ~.O %,? ~r-Q %, Q :.. ' ). g . %Qj. 9-- M cau yap y. ~-. C heYS' Eh'O ba YN f '

• N"*P'"I b C

l"S& . humgagsg;.i$$bW5E$m.cmidluw.. h a, d 8 O, O o 2 27

1 f N b E[bbkhi

1. ~ ~"(# '

0.09 b "f,MQ:~#""p"dVf*j"7 i sSS'%" E* p.g 0.90 "*F c w p' g% U ,e w#* lg. _. _.C~3 ... g .Nm a ~~N1... -. G:gyV '~~ cg,y& QfNNic: dh ~ fg-Q. ' 2 ~G W4

gfp,

_=c_-q ?;.,gf ~glh'd , g bi(Q i hy h ? ly i ~. s, i e wp %; Y u g[p. g cA p \\.\\ v ' j y) /g(h. dfi,\\ a ),,,7 7 si .w. \\S t

c g

.p- '- {p/ is y qo j .j; n .ne e h

f I'>

[/ j, }(.. v, h044E!. tl{ '[' m: i j s p y -..l A, S w ,,'/4 [. N \\, %:~~ W O:- .lg Q h. $ \\ f ] //jj! L ve _p ~ A N'-M__ 'k '/ / f a h s {\\\\N " ////// }d; [ / {;~ y fj \\\\ s !!! \\T \\Cd'// k,nj!; le} I. h N.\\ A /g / f_ I O C E N$$v,U +i 0.10 0.01 Mi S y g t g _u-t xuusawww.:.uarres ma:=cxs.Lacu etwn: 4 Fig. 7. Comparison of predicted against observed flow regime development in test Q11. The experimental image has been made partially transparent, by computer processing, so as to allow superposition of the computed contours. Times are 0.1s and 0.2s after first impact of the particles on the water. The color scale for the particle volume fraction is on the left, that for the void on the right.

m i O O 05 C ci O IIWon..;, : W 1: : $$Y 'L. ' d .o l N 3 I{k r I p m M(>I u w m.: e r d.v,ngs=,52W:a j \\ I z :c..._ x w s o

i / u.

pp m [m 1 =.7 ; c.u, ;MTZ*%%d g j 3 sid,,, 1-

f. g f;y

,b. . ri 4 s-.,,,,,..rN4. :i %,,,, i K. %, y i i,.} S h .b w ~%. 4W % M.,m9s@;:n s a s T ?' l h=f0LL h &..:% w;?W Nfmigh.ex$ S.Ql--l.; ?' } v 3 a i < : r. -';iJ. ,4 y m a. ' h3di I-- ~ .e r7 K ~ -, r'.j m Q f \\ E

• **7

.q g flee. g;. t .f a-i ) n.-n x /' a m m a xx*w u E N M i E $ " a,v umw m a ni un Nc,.nN ,h ME c:: 4 J. Q 4 1 O 4 th r I.) 't' I g

• C C

A7.3.M1DLMia% vgl..,- iN M 4 5 F M h' c'A T E +y 75 @

g .P W[ ; 1 0 $w. j 1-( L--

/ h - # w w.. x A A a

i Ysyrvg>mx ? w.r Q is'.j d:As," M V.:gl m %-l. i i e i u 'w P 6 , + %;., @(b GJ? .- 1 1_ i t R , '.4 i s \\N LSh%{ Ql%'fy o.. ~ /W,. I 6 E %?p-1 J' - 1 y p 6 .. s % ' :es. D Gy Ngj}- .- ? M +- ' ' j/ 4 /* .QU. ef 9^ ff /h ^. z= 5 1 & % L., u, f g;,,' 6 l',g A gy ) E I,Q } 'g\\\\ Kpf;4f,$ .l o. m NIUWWhd h d'RTA;L75L "Y.:. C, N T8I,.,/ v y b .d) a 1.. l ,. <; no ,d. t .. : ll g P O. 4 O O l 2-29

iI l I ~ 4 ec 0 n av S d . O a t A 5 n tn i eH 3 o r P f . mL 0 d ir e . eA r . p M u x s . eP a i 3 c 0 me h t dn 5 a 2 s 0 no ] i tc i d s e

2. [e rp 0m A

H iT P L 5 A-1 M 0 P ne e w ,i 1 e t 0 bno s ira 5 p 0 m m 0 o. C5 .Q ar r 8 o ef rt O un 0 0 0 0 0 0 0 ge 2 0 8 6 4 2 Fm i m 1 1 6o2oc Wi 5od gc25.O E c y*O 1 lllj!

Il 1 l1 x 4 0 d a t 6O no r i n 3 d 5 f t e m 0 e r i u r s e a p e . x 3 m .e d0 e h t d na ' 5 s i ' 2 n 0 o i t c i d ] s e r r

2. [e p

0m A H i T P LA 5 1 M 1 0 P n e e r w i 1 e t 0 b n r os ir 5 a 0 p6 mQ 0 or Cof 1 .t bn 8 e 0 m er e 0 0 0 0 L 0 0 u c 2 0 8 6 4 2 gn 1 1 ia Fv ec1cS6 E2%g E 0Q 5 c 5 p5 l'

120 r .1 ,T, ...i i. i,, r r 3 -7 experiment 08 l PM-ALPHA 100 6s. G o 80 2:o cn f3 60 9 'g ~. r3 oe 8 40 c 1 2 O 20 i i 0 '''"22

• '' m ' ' ' ' ' ' ' ' ' ' ' ' ' ' " -

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 8c. Comparison between PM-ALPHA predictions and the measured front advance-ment for Q8. i l l

1l,I4 l)I ill 4 ~ 0 da ' 0 t 1 n ' 0 o r nA 5 f t ' eH 3 d mP 0 er L ir u eA s p a xM e 3 m ' eP 0 e h t d na 5 s i 2 n 0 o i t c i d ] s er i

2. [e p

' 0m A T PH i LA 5 i 1 M 0 P ne e w 1 e t i 0 b n os ir 5 a0 r 0 p1 x 0 mQ or Cof .t dn 8e O m er e 0 0 0 0 n 0 u c 2 0 8 6 2 p gn 1 1 ia Fv E3 Eg oo @5 Eot gcs.O e c gAW ll l il 1i l 6

i 120 r ,,.7 rm experiment 011 PM-ALPHA 100 6 r U t G o 80 1: O co a> w -5 60 F 4+ 6 8 L g 40 c2 .m C 20 O t '2 '''''2- '2 ' ' ' ' ' u 2 2-0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 8e. Comparison between PM-ALPHA predictions and the measured front advance-ment for Q11. The deviation at latter times appears to be due to front shape instability as was observed also in MAGICO-2000 runs.

104 3 i 103 - 102 Ei U T \\ D 101 m a%3 100'- 99 experiment 05 PM-ALPHA 1 ^ 98 -0.1 0 0.1 0.2 0.3 0.4 Time [s] Figure 9a. Comparison between PM-ALPHA predictions and the measured level swell for Q5. (t = 0 represents the time at which the particle clouds contact with water). The ~100 ms shift may be due to experimental uncertainty, which was not specified. See also Figure 9a'.

t t d 104 ..,.1,, i. 1 r.. ,r. 11 I t 103 l ~ 102 Ei 3 Ta> y e 101 h J s-g i i 3 100 l t [ i-99 experiment 05 l PM-ALPHA f i i i i i ui_1 i i > i_1__1 iii1 98 -2" i* L_ui_. - t i _i_a _1_ i i i 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 f Time [s] I Figure 9a'. Figure 9a shifted by 100 ms. r k t l I

104 i i-iii-i i 103 E Ji 102 ~v>v 101 a$ i 100 experiment O6 PM-ALPHA 99 O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 9b. Comparison between PM-ALPHA predictions and the measured level swell for Q6. (t = 0 represents the time at which the particle clouds contact with water). The ~50 ms shift may be due to experimental uncertainty, which was not specified. See also Figure 9b'.

i 104 ,,1 1. 1,, 1, 1 r, r r b 103 i i 102 i Ei V e> y o 101 a i 5 w I .e wn3 100 99 experiment Q6 l PM-ALPHA l 98 2 ' ' ' ' ' ' '2 L_n. .l I ....I .. i. un.. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] 1 Figure 9b'. Figure 9b shifted by 50 ms. j t I

w ~ 104 1.. v. i i.. .i i.. .i r i I 103 l 6 3 102 ~5> U _a w2 101 n i 100 experiment 08 PM-ALPHA '''''''''^"I' 99 O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 9c. Comparison between PM-ALPHA predictions and the measured level swell for Q8. (t = 0 represents the time at which the particle clouds contact with water). The ~60 ms shift may be due to experimental uncertainty, which was not spHfied. See also

104 'i r- '~ r 103 ~ 4 102 ~ Ei 3 ~is 101 Y a 8

• 2a3 100 l

L 3 90 level 08 exp i level Q8 l t 98 ''''''''il>m1 '1a1' 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] l Figure 9c'. No explanation for the instrument "undershoot" (shown hem for 0 < t < 0.06 l s) to below the steady value was provided in the experimental report. It may be electrical [ pickup due to the approach of particle cloud.

c-i l 110 experiment Q10 PM-ALPHA 108 ~ I /- \\ - 106 h / N / ~ v M $ 104 / w ~ u ~ G3 / 3 102 ~ 100 A i. ,,i' ...i,,,,,,,,, 98 -0.1 o .3 0.4 0.5 Time [s] Figure 9d. Comparison between PM-ALPHA predictions and the measured level swell for Q10. (t = 0 represents the time at which the particle clouds contact with water). See text for explanation of the discrepancy.

l l l l 110 i i i i .1 experiment Q11 PM-ALPHA 108 / 106 / 85 / ~ N 104 / 4 J / i N y 3 102 I [ 100 i t 98 -0.1 0 0.1 0.2 0.3 0.4 0.5 l Time [s] i Figure 9e. Comparison between PM-ALPHA predictions and the measured level swell for Q11. (t = 0 represents the time at which the particle clouds contact with water). See text for explanation of the discrepancy. i i

l l 4 w 0 o lf m ae t 5 i ' 3 s d ' 0 e r us a e i ' 3 m 0 e h t d na 5 s 2 n T o 0 itc i d ] e s r

2. [e p

A ' 0m H i T P LA-5 1 M r 0 P n E ee tA w neH te mP ' 1 b eA 0 iL r no p-s xM ir eP a 5 p 7 0 m 0 o 0Q C. 0 a1 1 r u eo O rfu e 0 0 0 0 0 0 0 0 0 gt 0 5 0 5 0 5 0 5 ia Fr 4 3 3 2 2 1 1 [ 622 MMS 9.W62g w ll

I F t k t f 70 ,7 rn r' i ir i '7-i experiment 60 PM-ALPHA m 6 c ca 50 6 c o> 40 6 N* cs i QJ M 30 o .=2 20 l c 6 I oU 10 l 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 I Time [s] l Figum 10b. Comparison between PM-ALPHA predictions and the measured cumulative steam volume released in Q10. t i L l t M M M M M M M M M M M M M M M M M M

1Ii!l!IiiI I'11lll! )ilI< .lI{ 1 { 4 0 e r tA u neH imp sse L ' 5 r r i eA ' 3 p p-xM ' 0 de eP ru sae ' 3 m i 0 e h t dn 5 a i 2 s 0 no i tc ] i s d

2. [e e

1 r p 1 ' 0m A i T H PL 5 A 1 0 M e0 P n wQ e1 1 1 0 e r t bo 2 f i ne oc sap i 5 ra s i 0 psa 0 mg o e Ch t ci.n 7 0 0 ~ t 1 n 5 4 3 2 1 1 9 8 7 ee 0 0 0 0 0 9 9 9 ri s u n 1 1 1 1 1 0 0 0 ga i r Ft Tnd ymUg ps% c ,ll ll

} i i 500 1.. r T-T ri "T i i t 400 7s m 6 m 300 .8m M t Y 6 e g 200 6 h 100 i experiment l PM-ALPHA 2" 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] l t Figure lla. Comparison between PM-ALPHA i rdictions and the measured steam How i i rate for Q11. i

100 r i. .i....i ...i.. ,1 .i. 80 2 o 6a o 60 N. m + 2 4 (D 40 o> .g .53 6 20 3U experiment PM-ALPHA 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figum lib. Comparison between PM-ALPHA predictions and the measured cumulative steam volume released in Q11.

1 i 1.12 experiment PM-ALPHA 1.1 1.08 m i a M e, g g 1.06 / to m su 1.04 / 1.02 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 v Time [s] l Figure 11c. Comparison between PM-ALPHA predictions and the measured pressure transient in the gas space for Q11. 6

x \\ ) 1000 ,s r T 8 ment Q17 PM-ALPHA 800 ~ m ~ E m [ 600 N [ I h w_ w E 400 / g _ / .~ ./ m3v) 200 ~ 7 0 t O' 0 02 0.25 0.3 g 35 9.4 Figure 12a. Comparison between PM-ALPHA predictions and measured steam flow rates for Q17. The missing peak is due to a special mechanism as explained in the text.

I 250 i i.. i experiment 017 PM-ALPHA -m E 200 3!, o 60 o 150 h ~ N th o o $ 100 2: m s h 50 U 0 O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 12b. Comparison between PM-ALPHA predictions and measured cumulative steam volume released in Q17. W W M M M M M M M M M M M M m m m m

1.35 experiment Q17 1.3 PM-ALPHA 1.25 1 5a 1.2 7 o 1.15 7 / ~ 1.1 7 ff 1.05 F 3r....,....,....i.... 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 12c. Comparison between PM-ALPHA predictions and measured pressure tran-sient in the gas space for Q17. The missing peak is due to a special mechanism as explained in the text.

1 r 4-7 i 1 r-cO To l 5 0.8 h c ? m t j 0.6 5 rt w r LA C 13 0.4 ^ '~ c = Nuw o 0.2 particles > 3% 2 - - - - - quoted data O O 0.05 0.1 0.15 0.2 Time [s] Figure 13. The average liquid fraction as found in the simulation of Q11, averaged over the computational cells with more than 3% volume of particles. The result is compared to i a quoted value of 80% (Meyer,1996).

1 3 INTEGRAL ASPECTS 3.1 Code Comparisons 3.1.1 Comparison with CHYMES About three years ago PM-ALPHA and CHYMES were compared directly in two sequential papers in the open literature (Fletcher,1992; Theofanous and Yuen,1994-see Appendix 5 of DOE /ID-10489). The conclusion was that, once the two codes were made to address the same problem, the comparisons, even at the details of mixture zone composition, were excellent. 3.1.2 Co aparison with PM-ALPHA-3D As noted already, the PM-ALPHA-3D code was recently developed and it involves a different numerical scheme from that in PM-ALPHA. The basic solver is the same as that used in ESPROSE.m-3D, and it has been verified by comparison to ESPROSE.m, as discussed in DOE /ID-10503. Here, we present a further numerical test by comparing the 2D versus the 3D versions of the premixing code. As a test problem we chose typical MAGICO-2000 conditions (see Appendix B), with a 2% volume fraction cloud of 3 mm particles at 1500 C, and a saturated water pool in a 2D Cartesian geometry. The grid size was 3 cm (a total of 10 x 30 grids) and the time step 10-5 s. Unlike the MAGICO tests, we have a closed air gap, so that it can pressurize with time. The results obtained with the two codes are compared in Figure 1 for the pressure transients, and in Figure 2 for the detailed evolution of the mixture zones. The overall behavior is very similar, but it is noted that the condensation and associated " pinching" of the two-phase dome (see Figure 2 at 0.35 s) is slightly different. This difference also shows up in the pressure transients of Figure 1. While not pronounced, and perhaps expected given the sensitive nature of a condensation phenomenon coupled to macroscopic liquid motion. We expect this to be clearly affected by even small differences in numerical diffusion, which certainly exist due to the different numerical schemes. This difference is being investigated further. 3-1

. - ~ I. I i j k 1.3 4 PM-ALPHA-2D i 1.25 ~~#""' l C 1.2 i E / \\ / ~ j l 1.15 ' ~ ~ ~ I b' 1.1 i j 1.05 1 0 0.2 0.4 0.6 0.8 1 i Time (s) i s I Figure 1: Comparison between the PM-ALPHA-3D and PM-ALPHA-2D prediction of the 4 pressure transient. g d a .l I d I: 4 j i 3-2.

l I Void Fraction

:- 2:rs:w n ; a a 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.0i 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D i

i i I I t i i 6 I g i l t e I l 9 i I I t I t i 6 t i l 4 i t 4 time =0 sec time =0 sec Figure 2. Comparison between the PM-ALPHA-3D and the PM-ALPHA-2D prediction of the premixing behavior. 4 3-3

l Void Fraction

. : 4 m,....rn;m 0.1 0.3 0.5 0.7 0.9 Fue' Volume Fraction PM-ALPHA 2D PM-ALPHA 3D

. _......; r 7- - -'u_.-.. =.._..: r '-"'~ ~ ~i, time =0.1 see time =0.1 sec Figure 2. (continued). 3-4

i l Void Fraction ..,.no aw ::mygga 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.0k 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D 4 .1- - ~...... 9 - f)}j) 7-x (e. l}) ([ - I \\ u / \\-.. -. a i 1 time =0.2 see time =0.2 sec Figure 2. (continued). 3-5 1

Void Fraction mmsuma 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction . w. ?:n_. : - 0.01 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D 7 p ;- ,4 a-s } k } ( A)/ \\, 's / .......?

---

s time =0.3 sec time =0.3 sec Figure 2. (continued).

5-b

i 1 1 4 4 4 Void Fraction . c, eacus a,.a 0.1 0.3 0.5 0.7 0.9 .,, Fuel Volume Fraction PM-ALPHA 2D PM-ALPHA 3D i 1 i _ - U -.;_ .;.2O ~ \\ 'b I k ( __ _] l \\ i s s t. ' - - - - - ~ < time =0.4 sec time =0.4 sec d 4 Figure 2. (continued). i 4 3-7 e

e Void Fraction ..., u n,3.7. g m 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction PM-ALPHA 2D PM-ALPHA 3D l w;= = =_. -..- \\ 2: ,/ gu !, El-,I s ) \\ C~~]/ \\. \\'~ - - - - -/ ...._../ time =0.5 sec time =0.5 sec Figure 2. (continued). 3-8

Void Fraction I O.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.01 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D 7- ~ ~ ~, ~ /^ ~ \\ \\ / \\'-- '/ \\.. _ _ _ _ _ _./ time =0.6 sec time =0.6 sec Figure 2. (continued). 3-9

4 t 1 Void Fraction I .. ;. ;.::n w em,,;, wwu =u 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.05 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D i I l =' O i lu j - N f I '\\ [ '\\ \\ I \\ / \\ / \\ _ _ _ ___ j m-...-- time =0.7 sec time =0.7 sec i Figure 2. (continued). 1 3-10

1 Void Fraction .:#nen .-...s...-wm 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction j 0.01 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D l f s.;. Nc N U / ' N. ,s

s.,

's s / 't / i i i \\ l l i,,'s._._-- ._.../ i time =0.8 see time =0.8 sec Figure 2. (continued). 34(

Void Fraction 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.01 0.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D /D'\\ W... / Q m ~ / v / m/ g 8 /, x x f '\\ f i t _i \\, ) \\. /

c..

p

t.,.

- y, ,7 y~. 3 g time =0.9 sec time =0.9 sec Figure 2. (continued). 3@

l 1 i l Void Fraction ... ;,,&.g. 2..,..;,.. 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction 0.01 O.02 0.03 0.04 0.05 0.06 PM-ALPHA 2D PM-ALPHA 3D l 7 s., Na 9:= n 'd V v v b d ['y'; j \\_ 1 (, ( -g I ) t )

=======g..

=. = - =

time =1 sec time =1 sec i Figure 2. (continued). i 3-11 I

3.2 Experimental Tests In this section we consider premixing experiments with the hot material being in the molten state, and hence subject to breakup in the course of the interaction. Available integral tests of this type include the MIXA tests which were run with urania (20% Mo) at ~3600 K, and the FARO tests run with UO melts at ~3300 K. Besides the unknown, 2 variable length scales of the melt during the interaction, these tests are also interesting in requiring a non-local radiation transport formulation-the absorption lengths in water are 3 and 50 cm at 3000 and 3600 K respectively, and this is further complicated by the presence of variably voided regions (see Appendix A). 3.2.1 The MIXA experiments The MIXA experiments were run in the UK in conjunction with the CHYMES code development and validation effort (Denham et al.,1992; Fletcher and Denham,1994). They involved the pouring of kg-quantities of thermitically generated UO melts (containing 2 ~20% of Molybdenum) at 3600 K, into near-saturated water pools. The experimental apparatus is schematically illustrated in Figure 1. The " droplet former" shown in the figure consisted of a graphite grid, and was found to break up the melt stream into droplets of approximately 6 mm diameter. Besides visualimages of the interaction, pressurization and steam flow rate data (in the vent pipe) were obtained. Of the several published tests, the MIXA06 seems to have been the most completely documented. It also included the longest skirt (see Figure 1) that helped streamline the droplet flow vertically downwards. This test was, therefore, selected for simulation here using PM-ALPHA. It involved a 3 kg melt pour, and the water pool was within 1 K from saturation. The melt release time for all the tests was nominally quoted to be in the range of 1 to 1.5 s, but the 1 s value appears to be appropriate for MIXA06. The computational domain is shown in Figure 2. The square-section vessel is replaced by a circular-section vessel with the same cross sectional area. We use a grid of 4 x 30 cells, each cell being 5.25 cm by 5.25 cm in size (confirmatory calculations with a still more ) refined grid are underway) with an initial steam gap of 99.75 cm (vs the experimental value of 100 cm), a water level of 57.75 cm (vs the experimental value of 60 cm) and a melt pour diameter of 10.5 cm (vs the experimental value for the pour side of 12 cm). The melt inlet rate is set at 3 kg/s with an initial melt droplet size of 6 mm. As in QUEOS, we need to model the restriction of the vent line in the experimental facility. This is accomplished by placing cells with a specified porosity and drag coefficient to match the vent area and pressure drop characteristic in the experiment. We found the effect of the subcooling to be 3-14

-~ _ negligible. Time zero in the results shown below corresponds to the time the cloud front hit the water surface. In the simulations breakup was characterized by a S-value of 20 (see Appendix A), a breakup cutoff void fraction of 85% (for voids above this value breakup is not allowed), and a minimum particle size of 1.2 mm. Sensitivities to the latter two parameters were de- { termined by including combinations for cutoff values of 80% and 83%, and for a minimum particle sizc of 1 mm. The flow regime comparisons with the experimental data are shown in Figure 3. The -j more quantitative features of the interaction such as advancement of the melt front, and of the two-phase level swell, are shown in Figures 4 and 5 respectively. The data were i obtained from Fletcher and Denham,1994, and for the level swell it is not clear whether, if any, of the two-phase layer above the liquid wem included. Certainly the " level" should be within the liquid /two-phase layer interface and the two-phase layer / gap interface. These j lower and upper limits are represented in Figure 5 in terms of the height of the collapsed water column and of the position of the 10% liquid contour line. The delay in the initial rise of the water level for the calculation, may be attributed to a superheating mechanism similar to that discussed for the QUEOS Q17 experiment above. At first impact, nucleation ~ sites are provided to the liquid which steams vigorously. The extent of this phenomenon in MIXA has to account for the much larger penetration length of the irradiation emitted at 3600 K; this detail is under further investigation. Pressure transients, steam flow rates, and cumulative steam volumes vented are shown in Figure 6, and for variations of the breakup parameters in Figures 7,8 and 9. The sensitivity is remarkable, and provides useful perspectives on the inherent limita-1 tions of taking a predictive approach on the details of such problems. 3-15

I I I l a. Pnesure E; " don Lines / =, i ~ e Droples Fonner l / i . Bursting Disc charge conminer / de.l / i y;.,;4-- W R.l i m .i _ - iv= 'l Valve i' ."1 t: F*

• c.."7 : '"

l 5 A, j ,l Glass Face g g- & e

== /. ' [j % Skin

l l

- j a Mixing Vessel N' ll s ~ m " ' si f /; h V e m Pipe g

e j

Lg /I mi ~ 45;- .E.i/ ! con.* g Ph>wanear - - d 3 5 l r "..,'." w-. - P ',l.........! VcesTank m a \\!i $A I h p j $ 'pf. u ....L..,...... _ 2 _...........a... \\y .+. r, / a. / >p,. ................y................y............. W k M=== Tank Puupng and Henang Systern I Figure 1. Schematic of the MIXA facility (from Denham et al.,1992). I 3-16:. I

1 10.5 cm Of = 0.11H M 51 / a g M w -..ai ney .q. -7 % c.,e at 1 ber IF1r1r er. 0.sss7 wetconotens y = 00 cm/s of = 0.0515 T = 3600 K 42cm 8 0 b 5 m n 1r 1r Figure 2. The computational domain used in the MIXA06 simulations. I-3-t1 l

~ ) l i i !i i 'O l j I l j I I ljb i d' }N:2 x iA' 4 i i U . l i s..a }.__ / i i t-b i t: i + 1

I f! !

' l. l h.: L/ f I,*fh Ifj' ' = - i 4 ,\\ jr f: '/' \\ / (. t j i l l l ! N. i j 1

f.,~

'\\ ~ l \\ d w s M 0$$ b U O b/ d )(/ $dI lld L_ 'ty g gy y ygp g).qj) 'N ll i g ~ E-* f Of j i .g z l l j L_ .._..J t=0.08s t=0.18s t=0.26s t=0.38s t=0.56s Fig.3. Comparison of predicted against observed flow regime development in MIXA06 The experimental contour (black line) corresponds to the location of the lumious melt. The straight black line represents the initial water level. Void fraction (blue tones) span from 10 to 90%, in 10% intervals. Melt contours (red tones) span from 0.5 to 4.5% in 0.5% intervals.

1 lliill 1illiI l 7 t ~~- 0 n A e tn m eH e mP nc L ieA v r a 6 i pM 0 a d xeP tn o r f e h 5 t f 0 o no i ta lu m 4 0 s i ] d s [ na e t m ne i

3. T m

0 r i e px e nee w 2 0 e t b n os ira p 1 0 mo C 4 m u 4 ~- - ~ ~~ ~ O g iF 0 0 0 0 0 0 0 0 7 6 5 4 3 2 1 -b EO2b o 6OM 8c3m Td lll1

80 1,mrr r' 7-7 rrrm-i ," ~~ /- 75 3 / / Ei I 3 70 g Y 3 / u 3 65 ca 7 3 60 ' experiment - - - PM-ALPHA - 10% liquid contour PM-ALPHA - collapsed l 55 u ' i 1 - 't 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Time [s] Figure 5. Comparison between experiment and simulation of the water level swell. It is not clear whether, if any, of the two-phase layer above the liquid are included in the experimental data. See text for discussion.

p y 13 1.26 d 12 E 1 16 11 1 06 - PEALPKt i 1 0 05 1 1.6 2 Time 1:1 1000 _ 600 g r p' s i j l ~ 800 \\, a 1 400 I \\ 200 ~ - PM-ALPHA

• =

i a 0 0 06 16 2 1400 -expenment .- 1200 _ pgatpga N,,000 I600 j --j 000 ij 400 t U 200 0 i i 0 06 1 16 2 Timeis! Figure 6. Pressure, flow rate and steam volume in the simulation of MIXA06, base case: void fraction limit for breakup 85%, minimum particle size = 1.2 mm. The experimental flow rate (and steam volume data) have uncertainty in the time base (persor.al commu-nication, Turland 1996). Also, according to the same reference, the flow rates beyond 1 s (dotted line) are not reliable (potential entrained water interference with inotruments. 34( j l

I' 14 i i 1.36 13 T 126 1 e t 12 1 15 11 ~

_ _.. ~-

PE ALPHA 0 06 1 16 2 Time [s] E 1NO i 1000 7 \\ \\ 800 t b E 800 g I \\ E 400 \\ t 2 A E N 200 -emertment i __,.ur. 0 i 0 06 1 16 2 l Tmie ls) 1600 i i i i 1400 PSALPHA y-1200 t j1000 1 E 300 A P 600 li ~s 400 b l 200 l 0 0 05 1 15 2 Tune [s] 5 Figure 7. Variation of the base case, with void fraction limit of 85% and minimum particle size 1 mm. r 3 22. I

'a q3 PdALPI4 in 12 E 116 11 1 06 1 0 06 15 2 Time ls) 1000 "o i 2.~ i 4 5 7 "o \\ a s $du s s e g 5 200 s

• " * * * " =.

- PS ALP >tA 0 i 0 OS 1 15 2 Tune ls] J"" PSALPHA 4_ l ion ? E! '...-1 =0 i !v 0 n 0 06 1 1.5 2 Time is} Figure 8. Variation of the base case, with void fraction limit of 83% and minimum particle size 1 mm. 3-2.5

I lIl 1.35 j3 PM-ALPHA Il experunant i { 1 25 \\ 1.2 3 ) k 1.15 I 1.1 1 05 i i i 3 0 06 1 16 2 Time [s] I d 1MO -expentnant g -PM ALPHA MO l ~ k I

• g

\\ ' 600 \\' ~ h y t' s 400 ~ E g I 200 \\ ~ j ll 0 O 06 1 15 2 Turne (sl i 1400 i i expenment 4 ~ 1200 PM-ALPHA 4 7iMO 5 i j .00 e e g 600 p ~ t 3 400 200 l O. is 2 3 Tirne 1 1 I Figure 9. Variation of the base case, with void fraction limit of 80% and minimum particle size 1 mm. I 3-M I

I [ 3.2.2. The FARO Experiments In the FARO experiment prototypic corium melts in quantities of over 100 kg are released into near-saturated water pools at high ambient pressure (~ 50 bars). A schematic of the experimental facility is shown in Figure 1 (Magallon and Leva,1996). The interaction vessel is closed and the principal data obtained are the pressure transient in it, the level swell, water and steam temperatures, and the resulting debris collected at the bottom of the vessel at the end of the experiment. Two FARO tests (L-06 and L-08) were conducted with relatively small quantities of melt (20 kg) and a shallow pool (about I m deep). The PM-ALPHA's interpretation of one of these experiments (L-06) has been presented elsewhere (Angelini et al.,1994). L-08 is a similar test. In one of two large scale tests (L-11), the melt contained zirconium and its exothermic reaction with wa ter vapor was identified as an important mechanism affecting the pressurization (Magallon and Hohmann,1995, NURETH 7). Since the current version of PM-ALPHA does not have a chemical reaction model, the interpretation of L-11 is out of the scope of this report. The present effort is thus focused on the other large scale test L-14. Since L-14 has a larger mass discharge rate compared to L-06 (125 kg/s vs 64 kg/s) and a shorter free fall distance (1.08 m vs 1.66 m), the breakup of the melt and the radia-tive heating of steam prior to the melt reaching the water surface are not expected to be important, as they were in L-06. This is confirmed by the relatively small pressurization [ for the time (0 < t < 0.3 s) prior to the melt reaching the water pool surface. The geometry of the computational domain used in the simulation is shown in Figure 2 and the gas space is taken to include all volumes available to it in the experiment. Note that by incorporating this volume the free space above the inlet nozzle is distorted and, therefore, level swells beyond ~2 s may be distorted too. The melt release position relative to the water level is represented by modelling an inlet from an interior obstacle Calculations are carried out with a grid size of Ar = 5 cm, A: = 10 cm (confirmatory calculations with still more refined grid are underway) and a time step of at = 1 x 10-4

s. The selected time step has been verified to be sufficient for numerical convergence.

An initial melt length scale of 4 cm (the nozzle diameter is 10 cm, but the steam re-duced to ~5 cm during fall through the vapor space) is specified at the melt inlet, and it is subjected to breakup using a #-value of 50. Breakup is discontinued by a cutoff void fraction of 85%, a fuel solid fraction of more than 90%, or a minimum particle diameter 3-25 l

of 1 mm. A Weber number criterion was less limiting and did not play a role in the i computation. The principal results and comparisons with the data are summarized in Figures 3,4 and 5. We note that there is a significant interaction with a net pressurization of over 25 bars, and a pressurization rate of up to 25 bar/s. The level swell is over 1 meter, at which point it has reached the top of the gas space above the nozzle in the FARO vessel. The steam temperatures are shown in Figure 6. Note that the computation indicates significant superheating, while the thermocouple found at the same location measures near-saturation values. This is a consequence of the presence of liquid (see void frac-tion trace in the figure) which can maintain the thermocouple tip wet, and hence near-saturation, irrespective of the surrounding steam temperature in the experiment. Also,it is worth noting that the steam energy difference between corresponding to the temperature difference shown is only 10%. Other interesting results that indicate the self-limiting character of the interaction are shown in Figures 7 and 8. In Figure 7, we see that the induced subcooling, due to g pressurization, reaches ~ 30 K; while in Figure 8, we see that significant quantities of melt i solidified already about the time that the pressurization turns over in the 1 to 1.5 s time frame. The details of the computed interaction can be understood with the help of Figures 9 to 12. Specifically in Figure 9 we find the evolution of melt and steam distributions, in Figure 10, the melt temperatures, in Figure 11, the melt length scales, and in Figure 12, a sample of radiation absorption rate by the liquid coolant throughout the vessel. This latter figure exemplifies the extent of non-local radiation transport and the effect of voided regions on it. ll I I: 3-26 I

FARO furnace l Lower electrode [ Release tube closing disc (W) L '7 detectors T Release tube p (5 = So ns, h = 2.5 m) c* nirror system drive "~ l M I M Y l sideocam Depnssurtzer

• :^

.rotection valve sol s V.420,- i o Pressure equaltsatten (Ar) - a( 'i Main isolation valve 502 for melt release - - o-r (8 =120 mm) steam venting -- p Flap for 08"' [ pressure equaltsation / l ouring quenching l .telease vessel 1 3645 (volume up to 502 = 0.056 m ) (for150kg) i ( l ik gig Instrumentation ring 3085 f Hinged-flao for melt release l [ (5 m. = 100 mm) l TEllMOS vessel (f,,, = 800 mm) 2000 M (5,,, = 710 mm) I I ?! y Heating sections l l Water Elevation (mm) \\.00 (p = 660 an) I

• 0 Debris catcher k!

I k Bottom plate -240 9 ffffffffj2-(thickness = 40 mm) -390 k Figure 1: Schematic of the FARO test facility (from Magallon and Leva,1996). 3-27

...._..... -.. -.= ~.__. -. I 01m ml im. "I l' k ~ i 1 ~ l l l 2.4 m 4 l' 1 f Fuel Inlet / J L t l, water Level 1.0 m s i g i f 1 aaaaaa; h EiNKEE ret rxt ?XtTXt ?Xt Xt T rmeist rmtit.t rAtN;I EIT Et 20m rxt~xt ENE rxtat L?22Xe rxe1-;t rxtitt. rme1-;t tetitt V r,=0.35 m ,m I Figure 2: Geometry of the computational domain used in the PM-ALPHA E simulation of FARO L-14. 3 5 28

k l [ ( ( 3 _ - -.DAun4l '~~- f 2 / gi 1.5 j s'. /' 1 / / f 0.5 f / 0 O 0.5 1 1.5 2 2.5 3 TIME (sec.) [ { Figure 3: Comparison of the calculated pressure history with experimental data. ( [ { >m

I, a l! l l 3 2.5 - --.Nu.mrl ,'\\ 1 2 ~ r I s l = I \\ \\/g\\ -g 1.5 1 / d i k / (\\ 0.5 -0.5 i

)

.,O i 0.5 1 1.5 2 2.5 3 Time (sec.) i i I Figure 4: Comparison of the calculated pressurization rate with j experimental data. g I i I I I 340

[ [ f- [ 3500 l .......m o.ed PM-ALPHA 509 v aru. ALPHA 3000 - l."" 7 :7' "dP"~^ * * ,,,,,-~~ Q \\- ,-p sh~ , ~' ( [ 2500 y ,...,. s # " "" ~ n sn C f "f 2000

1. ~

~~~ O 1500 1000 O 0.5 1 1.5 2 time f f_ Figure 5: Comparison of the calculated water level swell with t experimental data. b L ( p 3-31 L r

I I L 1 i I 1 500 E' i i i i i ..~.- , j.... o uxuo. PM.AumA l 3 450 ~.g / 0.8 ..'Q.. l-t 400 fy' 3 .g/ 0.6 t .I J h

• ',I 350 Data

/v g .T, PM-AUHA 0.4 = "/ T, PM-AUHA / 300 / - - - -.,P 250 0 0l5 1l5 2.5 3 0 1 Time (sec.) Figure 6: Comparison of calculated water temperature (TI), steam temperature (Tg) and data at thermocouple located at r = 20 cm, z = 300 cm and q = 1800. The calculated void fraction at the location is also shown in l the same figure. I I 3-32 i i I

( [ ( 0 i 5 l C 10 = 15 1E 20 7 25 0 0 0.5 1 1.5 2 2.5 3 Time (see) Figure 7: Water subcooling in the vessel predicted by PM-ALPHA. [ [ [ { { sss s

140 120 ...... Q ,, ~.. _,,, ~,. _.n, .une 100 -g i / ~ ,f ' g 80 j ~ 2 / 60 ,/ ~ / 1 40 /. 20 J' { l 0 2.'5 0 0.5 1 1.5 2 3 i time Figure 8: Melt freezing profiles predicted by PM-ALPHA. Each line represents melt with liquid fraction below the specified value. I I I I 3-34 I

[ Void Fraction ( .rwe...:.:w.cet u;;gg ,a 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction ( ep+. :.... t 0.02 0.05 0.1 0.2 0.3 0.4 0.5 ( I ( ) l [ __ _.z_ [ [ { ( time =0 see time =0.25 sec Figure 9: Fuel volume fraction and void fraction distributions in FARO-L14 ( predicted by PM-ALPHA { [ 3-35

[ [ Void Fraction .. s:ww ,,.-: mur. 8 m 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction { l !i l i "i i ,; 11 I [ j -4: c f ,e y s; r j[ l q i l ! I'l I r L =L: i i n n \\ ,l' ( 1/ i \\i a 4 i [ !_ k i w I h 1 time =0.5 see time =0.75 sec [ { Figure 9. (continued). f 3-37

Void Fraction 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction W w y. v : ;. : 0.02 0.05 0.1 0.2 0.3 0.4 0.5 I l: _._m ,n. - o 7 j t L I I \\ [ \\' \\ i l l l l l \\ \\ r

\\

v 1 t r ll' ll ~ \\ s\\ ^ \\ /l; ( I L i time =1 sec time =1.25 sec Figure 9. (continued). 3-39 l

Void Fraction ...,;nca xm,aa,,;. ..: n 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction w ;m-0.02 0.05 0.1 0.2 0.3 0.4 0.5 ^ ^l rw\\W 7 P l 3 L' ( m (l \\ l. t l i\\ u \\ I l- \\ '/\\- /h \\ i li \\ If \\l ) i l 1 = l!f' \\ \\ I lh' \\ I{h f N {' \\ l hy }t y yn{in n} al lf d [ time =1.5 sec time =1.75 sec 4 4 i Figure 9. (continued). 3-4 \\

Void Fraction 0.1 0.3 0.5 0.7 0.9 d"*I Volume rraction 0.02 0.05 0.1 0.2 0.3 0.4 0.5 \\l fs / ifx p 0 < - ^) D / I \\... N 1 F p n f{ r dy;\\ 3 /{ q r I e\\\\ n l. fg' %ullh ~ ,/ \\ \\ i (,r fN )!k time =2 sec time =2.25 sec Figure 9. (continued). ( 3-4b

Void Fraction ..,....:. ; y v.,,,.; ,g g, 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction mu awt.se 0.02 0.05 0.1 0.2 0.3 0.4 0.5 l li, f l l j \\ \\ jl l

l/?")\\

f} \\- Ik \\ f L \\ l \\ 0 \\ Y[1,!l u i l M V J 1 t f/+ f'd,' Y \\ f .J time =2.5 see time =2.75 sec i Figure 9. (continued). 3-46'

Void Fraction .o. uw -. : v. zu..g,ns.,, 3 0.1 0.3 0.5 0.7 0.9 Fuel Volume Fraction ' gg... / 'p, '. <a 6 3 _. 0.02 0.05 0.1 0.2 0.3 0.4 0.5 g i \\ h ~ f \\ t a _l l time =3 sec Figure 9. (continued). M1

1 Fuel Temoerature (K) 1000 2900 3000 3020 3040 3060 3080 l i I I l l l l l i i i I l se,> i time =0 sec time =0.25 sec Figure 10: Fuel temperature distributions in FARO-L14 predicted by PM-ALPIIA. 3-49

f Fuel Temoerature (K) ' ~ 1000 2900 3000 3020 3040 3060 3080 i i i l l t l t 4 t i 1 4 i i I l 1 i l l l i i ,i i i I l i i + t i l I i l I I I e v i i i i t 1 i 6 i i I 6 t i ' I i i i i I i l i i t 4 i i i [ l b ! l l i i -) f I l l !,j fi, M Y ) I s time =0.5 see time =0.75 sec Figure 10. (continued). 3-5 \\

b ...Eue!. Temperature (K) 1000 2900 3000 3020 3040 3060 3080 l i i i i / w. l i l 1 s i i t u i i I I i i i i i l 6 I l t t i i t s i i ) i. l (s u'i i i i i 1 i 4 l 1 i i i i i 6 i i i i i t i i i i l l 'sp g > i i i i i 4 i 4 1, j 3 J i i 1 l 1 i i L l l l i i l k i i i i i ,a _. s ) i i I I l t ( i i i i I -}

q-

...a

1. h ri h time =1 sec time =1.25 sec Figure 10. (continued).

3-53

l Fuel Temoerature (K) t l ,h S, I I t t I l l 1 i i s I i c.. j

• /.,

s I \\,s l l \\, ,// i ( ( l I e s, t t i / 1 \\ / -} \\. j' , ~ \\. y h I time =1.5 sec time =1.75 sec Figure 10. (continued). l l 3 '95

Fuel Temperature (K) 1000 2900 3000 3020 3040 3060 3080 o-s / l I I i i I ( ) 1 ( O

'^ 1

! i ( j (!,i T ts / 6 l ll 's O/ ! i f ! i. l 1 jll !,I '/ 4 s / 3 i [f '[i' fS JY ')'t. -N time =2 sec time =2.25 sec Figure 10. (continued). 3-51

Fuel Temperature (K) 1000 2900 3000 3020 3040 3060 3080 I I t.:i i c; l' ll ll

l 6 i l-i i t

i f' \\ I i r' i i i .i (.) ) 4 I i ll l i ^( ', ,r-s (' ~, ' s, , f( '_i /)s (.'. l i time =2.5 sec time =2.75 sec Figure 10. (continued). 3 59

1 i i l embY 1000 2900 3000 3020 3040 3060 3080 i i li ,i iI !i ' I i i l i ' i t) 1 ,L. i _'S..l.. )\\., / i i 4 time =3 sec Figure 10. (continued). 3-4i

Particle _ Diameter (cm) I I i i l ~ l \\ -q p. t time =0 see time =0.25 sec Figure 11: Fuel particle diameter distributions in FARO-L14 predicted by PM-ALPHA. I 3 63

f Particle Diameter (cm) _I_ li' l \\ l f I i l i d i I L l I I f: 4.) I o + 4 l 1 i ( t ?y ,f. k i gb w i I: y ).; A k, i time =0.5 see time =0.75 sec Figure 11. (continued). g.sc

Particle Diameter (cm) a, l i il p' g i ,, - a i i Ii i j f - ( i g ll \\ \\ L h g J l 4 l lI W i i ....Jl\\h\\ - l time =1 see time =1.25 sec ( Figure 11. (conitnued). 3-VI / __y

Particle Diameter (cm) 0.1 0.5 1 2 3 4 (es 1 il I, f \\- time =1.5 sec time =1.75 sec ( ( Figure 11. (continued). 3-U1 W

Particle Diameter (cm) 0.1 0.5 1 2 3 4 f { { { 7,, { f ~;., i { k ) i 3 g..., 1 i I \\ \\ l ) Ii I P ( l 1 $1 - - 0. time =2 see time =2.25 sec { ( Figure 11. (continued). 3-7 l ?

ium f Particle Diameter (cm) 0.1 0.5 1 2 3 4 I i_/ ij s r ', 'l l t } li l l i ' s , i i f! ) 's l l i i il i i i i i \\/ g l i l i i i i i I%, ) f \\ /( 's (-n f "01 I;, [i l time =2.5 sec time =2.75 sec Figure 11. (continued). ( MS i

.. Particle Diameter (cm) 0.1 0.5 1 2 3 4 ( ) l l,ii l i i!.i l: o i \\l. ,J 0 time =3 sec Figure 11. (continued). ( 3-1I i

o o >d4 Coo ,= G U

• P e m

a % o 8sc v> c hce u c o oc E N E827 i, =E_R s 8 5.e 88 888 o a.c e.- gepa- \\ \\\\ o c e

I

_.~t 2 e o.2 1 [. ' e-- --c =e a _ = =_.== : ; 'oa n.o e v u a e Y l, I = _ =_ _ ___ ~~- _, o agc o *.eo,o c ce -w ~~ - - q .,g = 'c i Eo !I g & s o.o> w o. v m w m I.27 - .t gtac e c" ., e 2 2,.,, c o oo .s '5 's,a eO y ^ *,Q @ T-Y h b is i [5 ia f i. 3

g g

lIS.sl$_l!_ l ,14 a,.io d_aff kG5_.*ad_uedlai&F,le_rs223Lh g > '3 o 1 v v "O w e o a.c > ummmmmmmusura g - y . _. - oa 55

e.2.C9o

~. e ~ o b0%c h h$rihkeh' : s 0 .[IL .X _.h - M _' & G Z J2.Ws! _.:T.T h % _E L & "3 tis *A2 h i.g o m.g .g c o a f tA A D 'o-n.E o e.o n oc y.- EaE=9 a .e.o E ' c -n 4m o I 3-77

I M Ti 98 8 998! M8 g_..- /_, / O e ; t-_3_4 ; p. 2.o e ~~ mg. =,a_ gg g BC 't3 A . e *... a - ca 4 & a a 4 4 o 4 6 C y O c Kp* m a d :f m g .. n^ - - ..smym:~w -e-yn y}e f g 3., 1 11 a gghog g Nf;f;'f-j -A .;g _Q.o p ...=.y: %:z g 5 Q .c M U] k i!!!1 s s a O _pg.-p mm m,~,,---- g *g s. .o. ._7-

• "W?

q. y yjyshlcky:6+:m

.O k -: a, hO -

• g,,. u us.,

,ey a +n a, sucpi r E s 3-11

4 BREAKUP ASPECTS Consideration of breakup directly in a verification effort is hampered by the lack of experimental data on the dynamics of the process. In single jet experiments one can approximately determine the position of complete disintegration, but no information is available for the breakup processes above, or the extent of further breakup below this point. The closer the melt approaches the molten corium conditions, the more intense is the interaction, and even less information of breakup dynamics becomes possible. Of course, one has the end state, by means of the solidified debris (although some ambiguities even here are possible by merging of semisolidified particles) and this may be used as one anchor, which together with measured interactions parameters, such as steaming rates, pressurization, and level swell, can be used to back out the dynamics of breakup (as we have done for the MIXA and FARO tests). Clearly, however, this is susceptible to the code's performance in the multifield aspects (hence our attention to them) and, moreover, it is open to question whether the same model of breakup can capture the behavior from one test to another, and eventually in reactor conditions. The size and melt masses of FARO are helpful in accepting an empirical approach based on it, and the planned lower pressure tests will be of further help. Meanwhile, we can use the MIXA tests which indicate that lower pressures promote breakup (higher steam velocities snowballing in combination with breakup). Thus, in combination, the two tests and their above interpretations with PM-ALPHA, provide reasonable choices of parameters to bound the breakup behavior for reactor calculations. Another avenue, complementary to the above, would involve deep investigations (both experimental and theoretical) on the fundamentals along the lines currently pursued by detailed jet and drop breakup models (Kondo et al.,1993, Burger et al.,1995 and Chu et al.,1996). 4-1 ( l

r 5 NUMERICAL ASPECTS 5.1 Space / Time Discretization With available computing power, and the usual limited lateral dimensions of melt I pours, we can go down to cm-scale nodes, even for 3D representation. Thus, for pre-mixing, we see no representation (accuracy) issues due to discretization. With respect to time discretization, we have found the proper domains to obtain robust and accurate computations, and this has not been a problem. 5.2 Numerical Diffusion Numerical diffusion is always present, but we have found that in premixing calcula-4 tions it can be effectively controlled by the use of an adequately fine computational grid. 6 Nevertheless, in the name of impmving efficiency, we plan an upgrade of the numerical scheme in PM-ALPHA along the lines suggested by the recent investigation of Fletcher (1996). 1 4 i ^1 4 1 4 i 4 5-1

6 CONCLUDING REMARKS We have tried in this verification effort to provide an in-depth testing of the multifield aspects of the PM-ALPHA code. On the numerical side we see no major outstanding issues, except perhaps for improving the control of numerical diffusion. For the time be-ing, the use of fine enough discretization and of Lagrangian particles provide sufficient control and perspectives on the issue, respectively. On the physical side, further atten-tion is needed on constitutive laws for breakup. However, the results presented here indicate that actual behavior can be represented quite well with reasonable choices of the breakup parameter #, and cutoffs due to high void, solidification, and Weber number criteria. Moreover, this experience provides useful guides for bounding the behavior, as it is our approach for reactor calculations. As discussed in Appendix A of this report, and as demonstrated by the first integral application (DOE /ID-10541), this bounding task is of reasonable proportions mainly because of the compensating effects between voiding, particle size, and solidification, on energetics. 6-1

7 REFERENCES

1. Angelini, S., W.W. Yuen and T.G. Theofanous, " Premixing Related Behavior of Steam Explosions," Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8, 1993, NUREG/CP-0127, March 1994, 99-133.

. [See also Nuclear Engineering & Design 155 (1995) 115-157.]

2. Burger, M., E.v. Berg, M. Buck, U. Fichter and A. Schatz, " Fragmentation and Film Boiling as Fundamentals in Premixing, US-Japan Joint Seminar: A Multidisciplinary International Seminar on Intence Multiphase Interactions, Santa Barbara, CA, June 9-13,1995,29-55.

3. Chu, C.C., J.J. Sienicki and B.W. Spencer, " Validation of the THIRMAL-1 Melt-Water Interaction Code," Proceedings,7th International Meeting of Nuclea r Reactor Thermal-Hydraulics (NURETH-7), Saratoga Springs, NY, September 10-15,1995, Vol. 3,2359-2384.

4. Denham, M.K., A.R Tyler and D.E Fletcher, " Experiments on the Mixing of Molten Uranium Dioxide with Water and Initial Comparisons with CHYMES Code Calcu-lations," Proc. Fifth International Topical Meeting On Reactor Thermal Hydraulics (NURETH-S), Salt Lake City, UT, September 21-24,1992,1667-1675.

5. Fletcher, D.E,'"A Comparison of Coarse Mixing Predictions Obtained from the CHYMES and PM-ALPHA Models," Nuclear Engineering and Design 135 (1992) 419-425.

6. Fletcher, D.E and M.K. Denham, " Validation of the CHYMES Mixing Model," Pro-ceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994,89-98.

t

7. Fletcher, D.E, " Multiphase Mixing: Some Modelling Questions," International Sym-posium on Two-Phase Flow Modelling and Experimentation, Rome, Italy, October 1995.

8. Fletcher, DT, Personal Communication,1996.

9. Hanratty, T.J. and A. Bandukwala, "Fluidization and Sedimentation of Spherical Par-j ticles," AIChE J., Vol. 3,1957,293-296.

10. Kondo, Sa., K. Konishi, K. Morita, N. Shitakawa and A. Furutani, " Fuel-Coolant Interactions Studies at PNC Relevant to Fast Reactor Safety," International Seminar 7-1

I on Physics of Vapor Explosion, Toraakomai, Hokkaido, Japan, October 25-29,1993, 96-109.

11. Magallon, D. and H. Hohmann, " Experimental Investigation of 150-kg-Scale Corium Melt Jet Quenching in Water," Proc. 7th International Meeting on Nuclear Reac-g tor Thermal-Hydraulics (NURETH-7), Saratoga Springs, NY, September 10-15,1995, E

1688-1711.

12. Meyer, L., "The Interaction of a Falling Mass of Hot Spheres with Water," ANS Pro-ceeding of the 1996 National Heat Transfer Conference, Houston, Texas, August 1996, 105-114.

13. Meyer, L. and G. Schumacher, "QUEOS, a Simulation-Experiment of the Premix-ing Phase of a Steam Explosion with Hot Spheres in Water," FZKA Report 5612, gl E

Forschungszentrum Karlsruhe, April 1996.

14. Magallon, D. and G. Leva, " FARO LWR Programme-Test L-14 Report, Technical Note No. I.96.25, Joint Research Centre, ISPRA, January,1996.

15. Richardson, J.F. and W.N. Zaki, " Sedimentation and Fluidization: Part I," Trans.

Instn. Chem. Engrs, Vol. 32,1954,35-53.

16. Theofanous, T.G. and W.W. Yuen,"The Probability of Alpha-Mode Containment Fail-ure Updated," Proceedings CSNI Specialists Meeting on Fuel-Coolant h/aractions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, 331-342.

17. Theofanous, T.G., W.W. Yuen, S. Angelini and X. Chen, "The Study of Steam Explo-sions in Nuclear Systems," DOE /ID-10489, January 1995.

18. Theofanous, T.G., "On the Proper Formulation of Safety Goals and Assessment of Safety Margins for Rare and High-Consequence Hazards," Reliability Engineering &

Systems Safety,1996 (in press).

19. Wallis, G.B., One-dimensional Two-Phase Flow, McGraw-Hill, New York,1969.

20. Yuen, W.W. and T.G. Theofanous, "PM-ALPHA: A Computer Code for Addressing the Premixing of Steam Evplosions," DOE /ID-10502, May 1995.

I I I 7-2 I

-. -..~..~_.- APPENDIX A EXERPT FROM PM-ALPHA: A COMPUTER CODE FOR ADDRESSING THE PREMIXING OF STEAM EXPLOSIONS DOE /ID-10502, May 1995 by W.W. Yuen and T.G. Theofanous ) i i A-1

2 i EXERPT FROM PM-ALPHA: A COMPUTER CODE FOR ADDRESSING THE PREMIXING OF STEAM EXPLOSIONS i 1 INTRODUCTION a This report presents the first formal documentation of the computer code PM-ALPHA, and is to serve also as a user's manual for it. The code is intended to simulate the pre-mixing of steam explosions; that is, the thermohydraulic transient associated with the pouring of a high temperature melt into a pool of coolant (water, in the current version of the code). The result of main interest is mixing zone compositions and associated length scales. These compositions are expressed'as volume fraction distribution maps, evolving in time. The resultant distributions can be used, with an appropriate trigger, in an esca- ~ lation/ propagation code, to compute a steam explosion. One such code is ESPROSE.m, documented in a companion report (DOE /ID 10501). In addition to the melt and coolant distribution, premixture constituents include coolant vapor and solidified melt particles produced as a result of the melt-coolant interaction. The vapor (void) introduces com-pressibility, which can affect both triggerability and propagation, while the quantity of solidified melt is important in that it cannot participate in the explosion. PM-ALPHA is based on a multifield Eulerian treatment. There are three continu-ous fields (melt, coolant, and vapor-we call them fuel, liquid, and gas or fuel, water, and steam respectively). The mathematical formulation is given in Chapter 3, and the physical model from which it is derived is described in Chapter 2. The numerical model i is rendered in two space dimensions with axial or planar symmetry-cylindrical (r,z) or ~ Cartesian (x,z) geometries respectively-and is based on a specialimplementation of the well known ICE (Implicit, Continuous, Eulerian) method. This method is used to couple i semi-implicitly the liquid and gas fields, while the fuel field is incorporated explicitly. The computational approach and detailed numerical formulation are provided in Chap-ter 4, while an overview of the computer program implementation (structure and control) is given in Chapter 5. The analysis of a sample problem with the code is presented in Chapter 6. Inputs and outputs for this sample nm can be found in Appendices D and E respectively. Let us conclude this introduction by putting PM-ALPHA in the integral steam explosion assessment context. The overall approach, with PM-ALPHA as one of the key elements, to assessing steam explosions in severe reactor accidents has bee, summarized by Theofanous et 1 A-3

I al. (1995). It involves a methodology, as outlined in Appendix A of Theofanous et al. (1994), and a set of codes, as illustrated in Table 1.1. With the exception of THIRMAL and ANACAPA/ABAQUS, the documents in this table should be studied in conjunction with each other. The following orientation-related remarks are offered.

1. The lead document (DOE /ID-10489) serves as an introduction to the problem and the analytical approach. Accordingly, it provides a discussion of the key physics, including previous literature and terminology, as well as sample results from PM-ALPHA and ESPROSE.m.

2. The type of analysis needed to assess melt pour conditions, the methodological frame-work employed in the utilization of these results, and the tie-in to the premixing cal-culations can be found in the two actual applications carried out so far, as listed under

" initial conditions" in Table 1.1. 'I

3. The manuals are restricted to documenting the codes and describing the mechanics g'

of running them. The verification reports contain comparisons with analytical and 3 experimental results that test key features of both the mathematical formulation and i the numerical implementation. In addition to perspectives on strengths and limita-tions of the simulations, these specirl applications provide guidance (to the potential user) on how the codes are to be applied to various situations.

4. A full demonstration of the assessment methodology, including use of the simulation tools, is given in the two documents listed under " integration / application" in Table 1.1. Moreover, a first ad hoc demonstration of cavity (concrete) structural response under ESPROSE.m loads can be found in Rashid et al. (1995).

Consideration of the above-listed material in its totality is crucial in appreciating the nature of the uncertainties involved, both in specifying initial conditions and g in deploying the codes, as well as in gaining some perspectives on how one can 3 compensate for these uncertainties. However, this material may not provide adequate guidance for other, new, applications; thus extreme cau tion needs to be exercised while l broadening this experience base. It should be noted that all these codes could be coupled into one computational package and, in fact, PM-ALPHA and ESPROSE.m could be condensed into one code. We have intentionally refrained from doing that. Besides better transparency and convenience in describing these tools independently, this is consistent with the ROAAM approach (Theofanous et al.,1995) in isolating the key physics and decomposing the problem in g terms of these physics using a probabilistic framework. 5 A-4 l I l l

Table 1.1 Steam Explosion Energetics and Structural Damage Potential Introductory and Overall Approach The Study-DOEilD-10489W Topical Element Codes Documents ) Initial Conditions Special Purpose Models In-Vessel SE: DOE /ID-10505(2).. Ex-Vessel SE: DOE /ID-10506(3)* Premixing PM-ALPHA Manual: DOE /ID-10502W I Verificationi DOE /ID-10504W i THIRMAL Manual: EPRI TR-103417W Propagation ESPROSE.m Manual: DOE /ID-10501(7) Verification: DOE /ID-10503W Structural Response ANACAP-3D/ABAQUS Manual:M l Verification: ANA-89-0094(10) Integration / Application in-Vessel SE: DOE /ID-10505(2)*

• Ex-Vessel SE: DOE /ID-10506W*

(1) T.G. Theofanous, W.W. Yuen, S. Angelini and X. Chen, "The Study of Steam Explosions in Nuclear Systems," DOE /ID-1(M89 January 1995. (2) T.G. Theofanous, W.W. Yuen, J.J. Sienicki and C.C. Chu,"The probability of a reactor pressure vessel failure by steam explosions in an AP600-like design," DOE /ID-10505. (3) T.G. Theofanous, W.W. Yuen, J.J. Sienicki and C.C. Chu, "7he probability of containment failure by steam explosions in an SBWR-like lower drywell," DOE /ID-10506 (4) W.W. Yuen and T.G. Theofanous "PM-ALPHA: A computer code for assessing the premixing of steam explo-sions." DOE /ID-10502, April 1995. 1 (5) T.G. Theofanous and W.W. Yuen," Premixing of steam explosions: PM-ALPHA verification studies," DOE /ID-105(M. (6) THIRMAL-l Computer code for analysis of interactions between a stream of molten corium and a water pool. l Vol. I: Code Manual, EPRI TR-103417-VI. Project 3130-01, Final Report (December 1993). Vol. 2: User's Manual. EPRI TR-103417-V2, Project 3130-01, Final Report (December 1993). (7) W.W. Yuen and T.G. Theofanous, "ESPROSE.m: A computer code to simulate the transient behavior of a steam explosion based on the microinteractions concept," DOE /ID-10$01, April 1995. 1 (8) T.G. Theofanous and W.W, Yuen," Escalation and propagation of steam explosions: ESPROSE.m verification studies," DOE /ID-10503. (9) H.D. Hibbit, et al.,"ABAQUS Version 5.3," 1994. (10) R.J. James, "ANACAP-3D -Three-dimensional analysis of concrete structures: theory, user's and verification manuals," ANATECH No. ANA-89-0094,1989. i (*) The SBWR was discontinued. (**) Actually issued as DOE /ID-10541 under the title: " Lower Head Integnty Under In-Vessel Steam Explosion Loads," by T.G. Theofanous, W.W. Yuen, S. Angelini, J.J. Sienicki, M. Freeman, X. Chen, and T. Salmassi. A-5 l

iI; 2 MODELLING APPROACH The basic features of a premixing situation can be discussed with the help of Figure g 2.1. Beginning with problem definition, it involves the pool-and-melt-pour geometry 5 (including vent paths to the atmosphere, if any) and the thermodynamic states of the coolant and melt (including its material composition). A characterization of the melt stream must also be given. This requires velocity, mass pour rate, and characteristic length scale (s) at the inlet. These inlet conditions, in combination with the area specified for melt inlet (as part of the geometry) yield the melt inlet volume fraction. All of these j will be referred to collectively as " initial conditions," and they must be supplied at the outset. j l Upon entering the flow field, the melt stream, under the influence of gravity, accel-j erates downward, subject to flow resistances due to its interaction with the liquid pool and, to a much lesser extent, with the vapors in the space above it. In the liquid pool, gi the fuel-coolant momentum exchange sets the liquid in motion. The fuel / coolant energy 5! exchange leads to the generation of a third fluid, vapor, by boiling. All processes of mass, momentum and energy transfer are coupled through the pressure field and must also obey the coolant equation of state. The insert in Figure 2.1 is an attempt to illustrate all j these interactions and associated transfer mechanisms. The intimate coupling depicted is a strong function of the characteristic length scales of the premixture constituents. These length scales characterize the magnitude of the interfacial areas and hence the extent of interfacial interactions, while at the same time these interactions govern the interfacial l instabilities that lead to breakup and fragmentation (for definitions, see below), and hence E to the enhancement in interfacial areas. Our modelling approach intends to capture the a basic features of this highly complex and coupled behavior. The task is approached in two qualitatively different steps. The first step is to address the multifield aspects of the behavior, the main challenge being to describe the interfield interactions given the characteristic length scales. The second step is to address the evo-lution of the length scales within various, specified, multifield environments. The extent to which this second step can be completed is inherently limited by the very nature of the l process (superposition of multiple non-linearalities) and by the difficulties in observing l the dynamics of the process under relevant experimental conditions. So far, PM-ALPHA l has emphasized the first step. However, it includes the basic framework for the second step as well, so as to allow at least parametric studies along this degree of freedom. This framework will be ready to accommodate new, more definitive formulations as future progress allows. Each step is taken up in turn below. I A-6 I

-~ Fuel / steam momentum .@7 / and energy transfer V Fuel / water momentum and energy transfer ~ Water / steam momentum transfer and phase change >L Local Variables Steam, water and melt volume fractions EsMssil Water

• Interfacial areas per

^^ ^^ unit volume of nuxture (Area concentration) Figure 2.1. Schematic representation of a premixture, indicating key parameters of interest. The mixture is characterized locally by the volume fraction of the three phases, and the interfacial area concentration which depends on the local length scales.

I! l The multifield treatment is comprised of the field (conservation) equations in a 2D l formulation, and the constitutive laws that describe interfacial transfers. The fields are superposed in a locally homogeneous manner, but the constitutive laws allow for inhomo-l geneities, as distinguished by applicable flow regimes. Two dimensionality is recognized as an outstanding feature of premixing, leading to qualitatively different behavior from g' a " forced" one-dimensional treatment. The latter is unrealistic in yielding much stronger contact, as the only way for coolant to escape is through the counterflowing melt particle cloud. Three-dimensionality, on the other hand, can have only a limited, by compari-son, quantitative effect, as most of the flow-deflecting aspects of the behavior are already captured in two dimensions, and certainly in axisymmetric geometries. The basic intent of the flow regimes consideration is to capture certain essential transi-tions in the behavior, as dictated primarily by which of the fields constitutes the continuous phase. In particular, we must distinguish between a highly dispersed, vapor-continuous coolant, obtained at high enough void fractions, from all other liquid-continuous (bub-bly) or semi-continuous (churn-turbulent) regimes. The former flow regime allows vapor l; superheating and significant transparency to thermal radiation emitted from the melt. In the latter two flow regimes, essentially all emitted radiation is absorbed locally and the liquid-vapor mixture cannot deviate much from local thermodynamic equilibrium. Simi-larly, distinctions must be made relative to the liquid / vapor phase momentum coupling, which significantly diminishes from bubbly to churn turbulent, with a further more drastic reduction at the dispersed, vapor-continuous transition. The other key condition is ob-tained if the melt volume fraction becomes high enough for the process to resemble coolant g, flow through a " packed bed." This arises if solidified melt particles begin to accumulate E' at the bottom of the flow region. The evolution of melt length scales must account for breakup and fragmentation which arise as a result of interfacial instabilities, as noted above. These instabilities are due to body forces and differential flow velocities with the surrounding two-phase coolant. A variety of different mechanisms is possible, as is a range of length scales for the dis-turbances that grow and detach. In a first approximation we recognize two scales: one f fine enough to yield fragments that can be " captured" by the liquid field, and one large enough to continue with the fuel field. The two processes will be called " fragmentation" g and " breakup" respectively. The effect of fragmentation is to provide an additional heat transfer mechanism to the coolant beyond radiation and film boiling. This process yields a corresponding quenching, and a gradual reduction in both the length scale and the vol-ume fraction of the fuel phase. Breakup, on the other hand,is a " macroscopic" process in A-8 l

i ~ l i which fuel particles are broken up into particles with " smaller" (but of the same order of magnitude) length scale. The "new" particles are still considered as a part of the fuel phase and the reduction in length scale leads to enhancement in both the interfacial heat and momentum transfer. An interplay between the two mechanisms is possible as breakup can set up, or promote, the more intense conditions required for fragmentation. i In relation to other premixing codes, PM-ALPHA and CHYMES (Fletcher and Tha-garaja,1991), developed independently but under very similar modelling philosophies, have led the way in the 2D multifield treatment of premixing. An excellent comparison i between the two has been presented (Theofanous and Yuen,1994) with coolant kept at saturation, as required by CHYMES. With the addition of subcooling, currently imple-mented in CHYMES, the two codes should be rather equivalent, while both share a very cautious approach to treating interfacial area evolution. More recently, the codes EVA, TRIO-MC, and IFCI are also being developed to simulate the premixing phenomenon, 2 but it is too early to discuss comparisons with them. At the other extreme, we have the codes THIRMAL and FRECON. They place emphasis on the detailed description of melt jet breakup. We believe these two approaches are complementary to our 2D multifield I treatment. The breakup / fragmentation framework provided in PM-ALPHA, as described above, has been designed to take advantage of results generated by these codes. More-over, as indicated in Table 1.1, the ThiRMAL code has been included in the assessment of premixing in conjunction with PM-ALPHA. i 4 i A-9 i 4

i 3 MATHEMATICAL FORMULATION 3.1 Conservation Equations I, There are four phases allowed in the PM-ALPHA formulation: namely, water (liquid), steam (gas), fuel drops (fuel), and fragmented fuel (debris). The debris is assumed to be fully entrained by the liquid and the liquid / debris mixture is in thermal and hyd rodynamic equilibrium. There are thus four continuity equations, three momentum equations, and three energy equations. In addition, there is a transport equation of fuel length scale to simulate the effect of fuel fragmentation and breakup. In the usual manner, the fields are llI allowed to exchange energy, momentum and mass with each other. With the definition of the macroscopic density p', of phase i, i p' = 6,pg for i = g, f, f, and db, (3.1) and the compatibility condition, 6+8+8+846 = 1, (3.2) g 9 t 1 these equations can be written rather directly (Ishii,1975). Continuity Equations. Gas: Dp' + v - (p' "g) = J (3.3) gf s Liquid: Op + v - (p,' ut) = -J (3.4) Ot Fuel: Sp'I + v - (p' uf) = -Fr (3.5) g, f Debris: + 7. (p' 3u ) = Fr (3.0) g r Momentum Equations. Gas: (p' u ) + v - (p' u u ) = -8 VP - F (u - uf) - F (u - uf) (3.7) y g y s g gt y yf y + J(H[J]u + H[-J]u ) + p' g r y l A-10 I

1 f Liquid and debris: 6 g((p' + p'a6)ur) + y. ((p' + p' 6)urur) = -(Br + Bas)vp + F r(u - u )- (3.8) l s f d g g r l - Fif(ur - uf) - J(H[J]u + H[-J]u ) + Fruf + (p' + p' 3)g e g f g Fuel: B g(p' uf) + v. (p' uf uf) = -6 vp + F (u - uf) l f f f yf g l + Frf(u - uf) - Fruf + p}g (3.9) r Energy Equations. Gas: i l 0 ra y(p',I ) + v - (p' u,I ) = - P j(6 ) + V. (6,u ) (3.10) g s 9 g + Jh - R,(T - T,) + 4fg + fr,g g g g Liquid and debris: { 6 5(p'I + p'aslas(Te)) + v [(p}I + p'siss(Te))ut] = l tt t a l 'a .g(6 + Bas) + y - ((64 + Og3)u ) - Jhr (3.11) j -P t r + FrIy - Re,(T - T,) + ffi + fr,e t Fuel: a y(p' I ) + v - (p)I uf) = -FrI - ffy - iff - dr,f (3.12) ff f f l Interfacial Area Transport Equation. e l SStqD ) + v \\Dj \\ = sf + s l u o (3.13) f j l In the continuity equations we can identify the source / sink terms for phase change, J (positive for evaporation), and for fragmentation, Fr. The phase change leads to cor-responding source / sink terms in the momentum equations, Jur or Jug (depending on the direction of phase change between the liquid and gas), and in the energy equations, Jh and Jh (where h, - he corresponds to the latent heat for phase change). H[J) is the g t j A-Il

I Heaviside step function that becomes unity for positive values of the argument and zero otherwise. The fragmentation, on the other hand, leads to the source / sink term Fruf l'l for the momentum equations and Frl for the energy equations. The terms involving the f Fy's in the r.h.s. of the momentum equations represent the pair-wise momentum coupling (drag) between the three fields. The term dr,f, in the fuel energy equation, represents the radiant energy loss (from the fuel field), and the ify, if, are the interfield convective heat transfers. These last two terms appear in the gas and liquid energy equations, respectively, g while the dr,9 and dr,, represent the apportionment of the radiant energy loss from the fuel 5 (the dr,f erm). While all the above terms involve interfield transfers (or couplings) the t R terms in the liquid and gas energy equations represent bulk-to-the-interface transfers of energy, the interface being kept at saturation (T,). The difference between these terms [Rr,(T,-Tr) and R,(T -T,)] provides the latent heat necessary for phase change. Finally, y g in the interfacial area transport equation, the S and So terms represent the sources / sinks i f of interfacial area due to the processes of fragmentation and breakup, respectively. More details on the physical meaning of these " source" and " interfacial coupling terms" in j and between the three fields, and their explicit formulations-generically referred to as constitutive laws-are provided in the next section. l 3.2 Constitutive Laws The purpose of the constitutive laws is to define the interactions between the three fields, so that their motions, macroscopic densities (or concentrations), and thermody-namic states can be calculated by means of the conservation equations given in the pre-vious section. These interactions include drag, heat transfer, and mass transfer either by l phase change (gas - liquid) or by fragmentation (fuel-liquid / debris). In addition, we need to describe the length scales of the three phases. For the liquid and gas we assume that their adjustment to local conditions (relative velocities) is instantaneous, so they can be obtained from Weber number stability criteria. For the fuel the time constant for length E scale adjustment is much longer, and we wish to accommodate multiple length scales-as E a minimum a macroscopic scale that is subjected to breakup, and a microscopic scale (the debris) as the product of fragmentation. Thus our approach to length scale changes is l based on an interfacial area transport equation and constitutive laws for the " sink" terms in it, that are intended to describe these processes. Drag, heat transfer / phase change, and fragmentation / breakup are described in the following three subsections respectively. I A-12 I

l 3.2.1 Interfacial Drag As can be seen from the momentum equations interfacial drag provides the coupling that moderates the slip between the three fields-with inertia, buoyancy forces and pres-sure gradient being the other factors influencing the different velocities. For a highly dispersed (locally homogeneous) flow regime as is the case here, the slip depends primar-ily upon which is the continuous phase. Our basic position is that this can be decided on the basis of the volume fractions. Specifically, the phase with a volume fraction below 30% is considered dispersed. The fuel typically meets this criterion and is therefore considered always dispersed, while the gas or liquid are considered as the dispersed phase for void fractions below 30% or above 70% respectively. The intennediate range,0.3 < a < 0.7, is considered as churn-turbulent, a special case of dispersed flow, as described below. The important physics to capture here is that, in the bubbly regime, the gas and liquid are strongly coupled together and their tendency to disengage increases substantially in l churn flow and dramatically in droplet flow. The Ishii-Zuber (1979) approach is used to describe the interactions between each pair of phases, as described in the following. The general expression for the F,j's in the drag terms is: F,j = 3 tdijpj C[o 3 6 l ui - uj l (3.14) The effect of the third phase is approximately taken into account by weighing the interfacial area between phases i and j with the factor 6' dij = 0; + 0 (3.15) I where & is the volume fraction of the third phase. Physically, c,j is the relative volume fraction of phase j in the continuum mixture phase (j+k) and hence is a reasonable approx-imation of the fractional interfacial contact between phase i and phase j. This weighing factor has the correct value in the limits of 6 - O and e - 0. j For droplet and bubbly flow, the gas-liquid drag coefficient is expressed as 2 1/2 2 gap y+37,g7jfgo))c/7 Coi> = 3f (3.16) i a 18.67f(a) I where 1 A-13 I l ? l I

I I i = g, j = (, a 5 0.3 f(o) = (1 - a)25 (3.17) I 3 i = (, j = g, a > 0.7 f(a) = o (3.18) and (v is obtained from I pj l uf - uyl2l _ [ =8 for i,j = g,( (3.19) { = 12 for2,3 = t,g o For churn flow, the drag coefficient is expressed as E Co,j = 8(1 - a)2 (3.20) i I where I i = g, j = l, is = 4 I The F,y and F,i n fuel-coolant drag are again expressed by Eq. (3.14) with i = f, f i f j = ( or g, (, = D, and a drag coefficient given by an expression similar to Eq. (3.16),i.e. l f I 1 + 17.67 [f(6 )]6# l l f Coi, = 0.45 (3.21) g g with i = f, j = g, I, f(6 ) = (1 - O ) (3.22) f f A special case arises in computations where the fuel is allowed to fall and accumulate l at the bottom boundary, i.e., yielding 6 > 0.3. The actual physics here may involve melt f droplet coalescence, local capture of coolant within the melt, or between the melt and g the wall, followed by superheat-driven microexplosions. These processes are outside the current scope of PM-ALPHA. In fact, the latter process is one of the commonly considered triggers of a steam explosion, and hence indicative that the PM-ALPHA-predicted config-uration at this time should be continued with ESPROSE.m simulations into the explosion I A-14 I

1 3 regime. On the other hand, benign accumulation may be allowed to continue if for some reason one wished to pursue the premixing zone at later times. For this situation the user may wish to continue to run PM-ALPHA with an increased fuel length scale (in the accu-i mulation region). In PM-ALPHA, the fuel-coolant drag, when 6 > 0.3,is assumed to be f solely due to gas flow through a densely packed bed. Concepts of laminar and turbulent permeabilities (Sissom and Pitts,1972) are used as follows: j F,f = F,'f + Fjf (3.23) i where g fr e, < 000 F,'f = ( 0 (1 i (3.24) for Re,' > 1000 and

1. '8'
2. '" I"' -"' I F'# =

1.75(2-8 )3 for Re' > 10 / Di 8 (3.25) 8 0 for Re' 510, with

1. ~

Re' = 6f' (3.26) lag Finally, in the bubbly regime the added mass effect is included in the liquid-gas interfacial drag, as given by Wallis (1989) F = 3[9 pip,e l (u, - ut) l (3.27) The schematic of the logic used in PM-ALPHA in deploying the above correlations is pmvided in Figures 3.2 and 3.3. A-15 i

I i I I Ii I U I1 yes droplet flow a > 0.7 Eq. (3.14), (3.16), (3.18) Eq. (3.19) (We = 12) y ) I yes chum flow 0.3 < a < 0.7 Eq. (3.14), (3.20) ~ g' E j f i I y j bubbly flow yes Eq. (3.14), (3.16), (3.17) y a < 0.3 Eq. (3.19) (We = 8) y I U I ) plus added mass effect Eq. (3.27) ~ Y retum i I Figure 3.1. Schematic diagram for the calculation of gas-liquid interfacial momentum coupling. I A-16 I

.... ~ _... - _. _... -......... _. _. _ _ _ _.. _ _ _ _ _ _. I l If I . liquid liquid gas or gas If If N es fuel " droplet" flow o < 0.3 Eq. (3.14), (3.21),(3.22) g ~ If. I yes 0, > 0.3 = dense-fuel regime i Re', > 10 Re' < 1000 if l l Ifyes Ifyes i Turbulent, Eq. (3.25) Laminar, Eq. (3.24) i. l 1 l l. If If 4 = If 1 return i 1 i Figure 3.2. Schematic diagram for the calculation of fuel-coolant interfacial momentum coupling. J A-17

Ii 3.2.2 Interfacial Heat Transfer and Phase Change l The principal, in fact overwhelming, mechanism in premixing is heat transfer from fuel to coolant. This occurs primarily by radiation, but film boiling is also present and it can be important. Phase changes can occur when the liquid / vapor constituents of the premixture find themselves in local thermodynamic non-equilibrium. The main manifes-lI tations of this non-equilibrium is the presence of superheated or subcooled liquid. This leads to vaporization or condensation respectively. Since the void distribution is of major importance in characterizing premixtures, the accurate calculation of these phase change processes is one of the most critical tasks of the calculation. gl In fact, due to the highly dispersive nature of the premixing zone, and the penetrative nature of radiative power, this set of rather complicated processes can be viewed in rather l simple terms. Initially with a subcooled liquid in the bulk, vapor exists only around the melt particles. It is in the form of very thin blankets, and as such of negligible quantity. g The coolant is effectively a " single phase" medium, and heat transfer by both radiation and (subcooled) film boiling is added directly to the liquid. Upon reaching saturation, any further heating leads to a vapor / liquid two-phase mixture, again in a highly dispersive process. There are, initially (upon reaching saturation) ample interfaces for phase change (around the previously thin vapor blankets), and more are created as the vapor generated by boiling detaches and mixes with the liquid. The actual paths for heat transfer in this regime are radiation mainly into the liquid bulk, and convection to vapor and from l vapor to the liquid. The quantity of energy sustained in the vapor due to superheating is negligible, and the liquid cannot sustain any significant amount of superheat-both due g to the extended interfacial area and turbulent mixing conditions that prevail. The whole process, therefore, can be represented quite simply by transferring the energy directly to the liquid and allowing it to produce an equivalent amount of vapor. In the original version of PM-ALPHA this was accomplished by imposing the appropriate phase change rates to drive the mixture to local thermodynamic equilibrium within a very short, specified, relaxation time constant. Presently, we have a more flexible scheme, that accomplishes the same thing within a non-equilibrium framework. Namely, the boiling / condensation l rate is written as: 1 J = h - he [R,(T - T,) + Re,(Tr - T,)] (3.28) y y g where a negative value for J stands for condensation and the R quantities include the in-terfacial area per unit volume of mixture. Changes in pressure are accounted for, through corresponding changes in the saturation temperature T,. Thus, to complete the formu-I A-18

i. lation we need to determine these R's, as well as the rates of energy transfer discussed above. We begin with the latter. 3.2.2.1 Fuel-to-Coolant Convective Heat Transfer i For film boiling we make use of the correlations developed by Liu and Theofanous (1994), specifically for this purpose. All heat transfer goes to the liquid at a rate given by - Nuf6k h 4ft= g} nfQf - T ) (3.29) t g, where nf s the number density of fuel particles given by i 60; nf=1rDj ' } j The film boiling Nusselt number depends on the flow regime, as follows: For subcooled or low void fraction (o < 0.3) liquid, we use Nuf6 = {Nu + [f(Fr)Nuf]5 (3.31) S 1 which can span conditions from low (pool boiling) to high relative velocities. The function of Froude number is defined as M 0.2 = f(Fr) = 1 - (3.32) 1 + l Fr" 6 -1l M where Fr is based on the relative velocity between fuel and liquid and given by. "I - "' Fr = (3.33) gDj i Nuf and Nu are Nusselt numbers based on the forced convection and pool film boiling p respectively. They can be obtained from ? Nu# ( Ar E Mi (3.34) j 1 + k = Kc(d') l S ' ( P t j. and Nuf = 0.5Re}/2g [ PtM + 0.072 Rey 77 Pr 5 E (3.35) S Pg \\ PgSp') pg Sp' p The various dimensionless groups appearing in the above equations are summarized in Table 3.1. Physically, Sp' and Sc' are the superheating and subcooling parameters respectively,and Aris the Archimedes parameter. A-19

I Table 3.1. Summary of Dimensionless Groups Appearing in Constitutive Laws for Fuel-to-Coolant Convective Heat Transfer 4 . (#' ~ #" }. 3 R = Pr = ""k 'P" "P' d' = D Pri = f g ki 0 L ptpt. g I "I - "' I / Ar = # #' ~ #" Ref= 2 po g ut v 'P" f - T,) Sp = [h (T,)- h (T,)]Pr g t y 1 - T,) c Sp' = [h (T,) - h (T,) + 0.5c yg rg (T - T,)] Pr g t f g c i(T, - Te) p Sc = (h (T,) - h (T,)}Pri g t c t(T, - T ) g p i Sc' = (h (T,) - hr(T,) + 0.5cpg (T - T,)] Prf 5 f y c t(T, - Te) g r p Sc* = h (T,) - h (T,) + 0.5cpg (T - T,) E g t f Kc(d') = 0.5d'-E for d' < 0.14 0.86 Kc(d') = r 0.M < d' < 1.25 1 + 0.28d, {4d' 0 Kc(d') = fr

1. 5 < d' < 0.6 3.0d, Kc(d') = 0.47d'd for d' > 6.6 E3 M=

1 + 3pfj,,, (RPri p')2 S E = (A + CBS) + (A - CB ) + Sc* E A= Sc' + R'Sp'PrtSc' + R Sp' Prl 3 B = -hSc' + Sp'PrtSc'- Sp'PrtR + Sp'2Prl+ C= R Sp'Pri A-20 I

e - For the two-phase region 0.3 < a < 1, we use Nufs = 0.55 Ref #' Sp'pg (1 - a) (3.36) pg This equation is supported by data up to void fractions of 95%, and it shows that Nuj6 - 0 as o - 1. In this limit the heat transfer from the fuel is due to forced convection to the gas and is appropriately given by (Bird et al.1960) 4fg= nfxDj(T - T ) (3.37) 8 8 f y where Nu, = 2 + 0.6 Rej/2 Prj/a (3.38) with u - uf l Df Re = #a s y (3.39) Vg A smooth transition to this unimportant, limiting regime (a - 1) is provided in the calculation by using the condition Nufs < Nu, to transit from Eqs. (3.29) and (3.36), to Eqs. (3.37) and (3.38). For completeness, the heat transfer between fuel and liquid in the unimportant mgime after rewetting (T - T, <~ 150 *C)is also prescribed. A combined forced convection and 1) f pool boiling correlation (Rohsenow and Hartnett,1973) is utilized. It is 4fr=4fcfl+ (3.40) \\ 9/c / with 4fc and43 being the single-phase forced convective heat flux and pool boiling heat flux respectively. i The correlation for 4fc can be obtained by standard reference (Incropera and DeWitt, 1981) to be 4fc = (Nufch }\\ nfxD}(T - T<) (3.41) i f g, where Nufe = 2 + 0.644 Rey 5 Prj/ (3.42) For the pool boiling heat flux, the familiar correlation for nucleate boiling (Incropera and DeWitt,1981) is u:,ed, up to the condition of critical heat flux, which occurs at T - T, ~ f 50 C. (pr-py) ge(T - T,) f 43= f(h - he) (3.43) y 0.01(h, - he) Prj. a A-21

I' For the transition boiling regime,50 C < T -T, < 150 C, a linearinterpolation between f the film boiling correlation (Eq. (3.34)) evaluated at 150 C and the above nucleate boiling correlation evaluated at T - T, ~50 C (i.e. the critical heat flux) is used to generate the l! f approximate value of the pool boiling heat flux required by Eq. (3.40). The transition to j the vapor dominated regime (a - 1) is applied in the same manner as described above. g Finally, for the special " dense" fuel regime (6f > 0.3) discussed at the end of the previous section, we use Eq. (3.37) for 4fy, but with )

1. ff # l u, - uf l Re" "'51 Pr;2/3 for Re'y' < 50 (3.44) g Nu = 0.91 g

E Nu = 0.61 l u - uf l Re"- Al Pr;2/3 for Re'y' > 50 (3.45) y y where Re" = 8 # " " ~ # (3.46) 9 60jpg Schematics of the logic used in PM-ALPHA in deploying the above correlations are l given in Figures 3.4 and 3.5. El 3.3.2.2.2 Fuel-to-Coolant Radiative Heat Transfer For radiation heat transfer, the objective is to properly estimate the total radiant power leaving the fuel and to deposit it throughout the coolant region. Since a complete treatment j of radiation heat transfer is computationally intensive, two options are provided in PM-i ALPHA. 1 In the first option, the gas phase is assumed to be non-absorbing, i.e. dr,y=0 (3.47) I and, therefore, dr,f = gr., (3.48) E l 5 l The absorption by liquid is assumed to be diffusion-like and occurs only in the local region surrounding the fuel. For a < 0.7, we use dr,r = nf(1 - o)rD m(Tf - T/) (3.49) 2 I A-22 I

i U bubbly flow, single-phase pool / film boiling a < 0.3 Yes Eq. (3.29),(3.31),(3.34), (3.3 5) I ~ or forced convection ) / nucleate boiling Eq. (3.40),(3.41),(3.42),(3.43) i U two-phase film boiling yes Eq. (3.29),(3.36) O.3 < a < 1.0 or forced convection i / nucleate boiling 'l Eq. (3.40),(3.41),(3.42),(3.43: If yes. y l q > = nop q, = 0 V return Figum 3.3. Schematic diagram for the calculation of convective heat transfer from fuel to liquid. A-23

I I I I i 1r yes bubbly flow a < 0.3 q,. o lino yes Or<0.3 l' If no I dense-fuel regime submerged sphere j convection in porous media forced convection 4 l' Eq. (3.37),(3.44),(3.45) Eq. (3.37),(3.38) 1r lf II g 1r u ~ no yes y 4,,- o I = I 3 v return Figure 3.4. Schematic diagram for the calculation of convective heat transfer from fuel to gas. A-24 I

In the droplet flow regime, the radiation heat transfer to liquid drops is approximated by dr,i = min (ntxt,njxDj)Esca(Tj - Tl} (3.50) where Es is an empirical constant accounting for the fraction of radiation that is actually absorbed by the liquid drops and n, is the number density of liquid drops given by 66e nr = (3.51) xi3g The above option, however, is inaccurate at high fuel temperature at which water becomes optically transparent. It also fails to account for the effect of steam absorption, which can become significant in premixing scenarios at high pressure. In such situations, we make use of the zonal method (Hottel and Samfim,1967) which is extended to account for field internal inhomogeneities (Appendix B). In the zonal method, the important physical properties required for the evaluation of radiation heat transfer are the absorption coefficients of the three primary components, water, vapor and fuel. For water, the absorption coefficient is evaluated at the peak wavelength of the blackbody spectrum at the fuel temperature, i.e. C3 Amar= g (3.52) with C3 being the third radiation constant (2898 m K). The absorption coefficient for steam is estimated by evaluating the effective absorption of steam at the fuel temperature and a " typical" steam temperature using the Edwards wide band conelation (Edwards, 1976). For special situations (such as the FARO experiments) in which the domain allows radiation to reach the reflecting walls of the system boundary, the effect of multiple reflec-tions is accounted for by an " effective" absorption coefficient for steam which is generated by a three-zone network analysis (Yuen,1990, Appendix A) of the fuel-steam-boundary configuration prior to the penetration of the water surface. Finally, the " effective" absorp-tion coefficient for fuel is estimated by the expression for a " dispersed" particle cloud in the geometric absorption limit (Siegel and Howell,1992) af = (3.53) The zonal method allows one to compute the radiant energy exchange between any two local regiot's (say, two computational cells) accounting for the absorption (radiative A-25

I attenuation) that occurs in the medium in-between. The approach is based on an exchange factor F(r, r') defined such that if 4,,(r') is the net radiant power density exiting frorn a small volume at location r', the power de,(r')F(r, r')ai(r)dV' is absorbed by component i l (with absorption coefficient a5(r)) at position r. The total energy absorbed by the liquid is g then dr.z(r) = do,e(r) + 4e,(r')F(r, r')ar(r)dV' (3.54) r'p r W where we have included also do,r(r), the absorption by liquid in the immediate neigh-borhood of r due to radiation from fuel within this neighborhood-this separation is convenient in the finite difference representation. Radiation absorbed by vapor is nor-mally not important. However, after evaluating Eq. (3.54), its inclusion involves only a trivial additional effort, while providing flexibility that has proven very convenient under some special circumstances-as in interpreting the FARO experiments where the melt is l allowed to fall through a space occupied by high pressure steam. Similar to Eq. (3.54), g then, we have dr,g(r)=do,y(r)+ 4,,(r')F(r, r')a (r)dV' (3.55) y r'p r Finally, the radiant energy leaving the fuel is obtained from g dr./(r) = nfxDjmTf - do,f(r) - der (r')F(r, r')af(r)dV' (3.56) where the last two terms have the same interpretation as that discussed above. To evaluate these equations we need the local absorption, do.r(r), do,y(r), and do,f(r), W; the exiting radiant power density de,(r) and the exchange factor F(r, r'). Briefly, the local absorption is evaluated on the basis of the emitted radiation, after it has been corrected lI for self-absorption (self-shielding) of fuel particles and attenuation in the coolant within the host computational cell. The exiting radiant power is what is left over after the local absorption. The exchange factors on the other hand embody the geometric configuration (r, r') and the attenuation along the vector Ar = r'- r which depends on the mixture g composition and the absorption coefficient of the three phases along the same path. This already complex situation is further complicated when the code is run in a cylindrical geometry, where a computational cell is actually a ring in three dimensional space - ra-i diation from one part of the ring to another must be accounted for in evaluating " local" I A-26 I

absorption. The detailed treatment, that endeavors to approximately capture all these effects,is provided in Appendix B. 3.3.2.2.3 Phase Change In addressing the R's in Eq. (3.28), the principal consideration is to properly represent convection (turbulence) in the continuous phase. From the point of view of heat transfer the churn regime is dominated by the liquid phase, hence it is lumped together with the bubbly regime. On the dispersed phase we use the simple conduction model Nu~2. For a volume fraction 0 and length scale (, the interfacial area per unit volume of mixture is 60/t, and the dispersed phase R is then 60 2k i i R4, = (3.57) t, ti where i is I or g, whichever is the dispersed phase. When the continuous phase is the gas we have droplets in a gas flow at relatively high relative velocities, thus the usual correlation for forced convection from spheres is deemed appropriate and R,=

1. (2 + 0.6 Rej/2 Prj/a)

(3.58) g where the Reynolds number is based on the relative velocity and droplet length scale. A similar approach can be taken, and is provided as an option to the code, when the liquid is the continuous phase, i.e., Re, = ' (2 + 0.6 Rel/2 Prl/3) (3.59) 9 However, the situation here can be more intricate, especially at the very low void fractions characterized by low interfacial areas and relative velocities. Under such conditions, Eq. (3.59) will underestimate heat transfer, as heat transfer is actually dominated by turbulence created by the melt particles. An approach that accounts in a direct way for liquid turbu- { lence at the liquid-vapor interface, as used by Liu and Theofanous (1994) for subcooled film boiling, yields 106ht ut - uf Re, = 0.25 pfcpr Pr,-1/2 (3.60) Recalling that the physics of the process dictate thet liquid superheat is very limited, the coding in PM-ALPHA chooses the higher value among the two apprcaches. A-27

I Finally, we have to be concerned about special and extreme cases that may lead to i highly non-equilibrium cases, whose relaxation cannot be captured by the above formu-l lation. Such situations include rapid changes in pressure that produce superheated liquid l l and/or subcooled vapor. PM-ALPHA allows a mechanism to handle these situations through a formulation that drives the system to local equilibrium with a specified time g constant. Namely: R, = P'g(I,'o - I ) g when T, > T (3.61) g g (T, - T )r g g and Re, = #' when T > T, (362) i (T - T,)rt t I Physically, the boiling / condensation rate should decrease as the liquid approaches saturation. While this effect is implicit in the definition of J, it can lead to severe time step restriction, particularly in regions with high heat transfer coefficients. To improve the robustness of the code while maintaining the correct physics, the phase change rate is B assumed to be limited by a characteristic rate given by W Jm = p'g 5 p, (Tt) -1 (3.63) 7e P Physically, the above expression is the estimated boiling / condensation rate which will cause the liquid to become saturated in a characteristic time r. 7, is assumed to be e proportional to the computational time step. Experience shows that this restriction in J improves significantly the robe.stness of the code and its effect diminishes in the limit of 5 small time step. The corresponding limits on R's are W R,,m = R, (3.64) y g Re,,m = Rt, (3.65) I whenever lJl > lJml. A schematic of the logic in PM-ALPHA deploying the above correlations is provided l in Figures 3.6,3.7 and 3.8. A-28 I

1 U yes enhanced heat transfer T,> To for subcooled vapor Eq. (3.61)' No 9 } yes droplet flow I } a > 0.7 = submerged sphere Eq. (3.58)

• l Eq. (3.19)(Weer = 12)

U chum / bubbly flow U - yes a < 0.7 conduction limit Eq. (3.57) Eq. (3.19)(Weer=8) l V return Figure 3.5. Schematic diagram for the calculation of vapor-interface heat transfer coeffi-cient. [ A-29

I l i-I I v i E yes enhanced heat transfer T i>T for superheated liquid g s Eo. (3.62) 3 { No y l 4 g yes droplet flow W a > 0.7 = conduction limit Eq. (3.57) -=-- Eq. (3.19)(Weer = 12) E yes V a < 0.7 E V y churn / bubbly flow ' churn / bubbly flow submerged sphere submerged sphere Option 1 Eq. (3.59) Option 2 Eq. (3.60) Eq. (3.19)(We = 3) Eq. (3.19)(We er = 8) er select maximum of 2 options ~ V return I Figure 3.6. Schematic diagram for the calculation of liquid-interface heat transfer coeffi-l cient. E A-30 I

If mass transfer from interface energy balance, Eq. (3.28), U Exceed no Bounding Rates? yes use maximum mass transfer rate, Eq. (3.63) If If adjust heat transfer coefficients, Eq. (3.64), (3.65) V return Figure 3.7. Schematic diagram for the calculation of the mass transfer rate between liquid - and gas. ' A-31

I 3.3.2.3 Fuel Breakup and Fragmentation The processes of breakup and fragmentation, as introduced in Section 2, are respon-g sible for the two source terms that appear on the r.h.s. of the fuel length scale transport 3 equation (Eq. 3.13). In order to relate physically to these source terms, and to obtain their lI general form, it is best to begin with the interfacial area transport equation, written in conservative form, per unit volume of the total flow field, as BA f g, + v - (A uf) = $} + S{ (3.66) f In this equation $} and ${ correspond to interfacial area source / sink terms due to frag-mentation and breakup respectively, again, per unit volume of mixture. Fragmentation l leads to a loss of mass from the fuel field, hence its effect would be to reduce the fuel par:icle (assuming the same shape) surface area. Breakup, on the other hand, is due to subdivision of a fixed mass, hence it should produce an increase in surface area. The above 4 equation can be derived, in the usual manner, by using the Reynolds transport theorem and Green's theorem for a " material" volume in the fuel field, including the source terms El in the statement of conservation, and letting the volume shrink to infinitesimally small B dimensions. Now, assuming that the interfacial area of the fuel can be characterized by that of a cloud of spherical particles with a single, effective length scale, the A can be written as f I A = njxD} (3lG7) f where nf s the number density of particles and, therefore, relates to the particular volume i fraction and length scale by f (3.68) h 6 = nf f xDj From these equations we obtain l A = G6f f (32) Df In the material volume mentioned above, the changes in A (and hence the source terms) f can be obtained by simple differentiation for fragmentation and breakup respectively as: dAf G d61 66f dDj ( dt

• iT'di ~ Dj di i

I f f l and dAf 66f dDf Ss, m 6$s ( m ~ Dj dt di s I A-32 I

1 l Since the fragmentation is assumed to be occurring without affecting the particle number density, but only their size, the first term on the r.h.s. of Eq. (3.70) can be written (using Eq. 3.68) as: 6 d8f 180f(dDr\\ ( } D ' di Dj \\ dt j f f and collecting Eqs. (3.69) to (3.72) into Eq. (3.66) we finally obtain: e(S)~ (A ') = 4 {2(":'),- C' '),} <8 '8) The first term on the r.h.s. (negative) can be seen to produce a reduction in interfacial area (sink), while the second term produces an increase due to particle subdivision (reduction in length scale). To complete the formulation we need to express the derivatives on the r.h.s. in terms of field variables, and this is done next. Fragmentation is the fundamental mechanism that drives the steam explosion, after it has been triggered, and it has been, therefore, mainly discussed in this context (Yuen et al., 1994, Theofanous and Yuen,1994). In premixing, the flow field is characterized mainly by low pressures, relatively low relative velocities, and fuel particles that are separated from the liquid by vapor-at subcooled conditions this is as thin vapor blankets; after saturation the vapor occupies a significant fraction of the flow field and is able to flow, especially where a > 0.3, macroscopically through the mixing zone. None of the available data are appropriate for these conditions--they primarily address two phase, gas-liquid systems, although some liquid-liquid data are also available (Patel and Theofanous,1981; Yuen et al.,1994; BQrger et al.,1993). Moreover, all data are for drops with small millimeter length scales, while in premixing the length scales begin orders of magnitude larger than that. Recognizing this limitation, the treatment is considered, at this stage, as parametric in purpose, and we follow the instantaneous Bond number formulation of Yuen et al. (1994). It consists of defining a total fragmentation time, t}, correlating it to the instantaneous Bond number, and assuming that the instantaneous fragmentation rate is given by the ratio of the current droplet volume to the instantaneous breakup time. Namely,

1. ~ "'

-1/4 t},E

1. 'c-1/2 = gfgg (3.74) with Bog =_ 3CapcD l uf - ui l2 c=f t = f, s (3.75) f p

16o and 'd xD (' ) .dt 6tf l A-33

I The derivative we are looking for can be obtained from the last equation as /dDT =1D f f a (3.77) g i( dt )f 3tfi The two-phase character of the coolant is then approximately taken into account by weight-l' ing the above result by the vapor and liquid volume fraction to obtain the fina! result: (dD ), = 1 Dfa f 1-o -+ (3.78) i dt 3 f (tfg tft ) I! For breakup, the limitations due to lack of experimental evidence are even more severe, for here we are looking for the splitting up of large masses. The operative mecha-g nisms are Rayleigh-Taylor instabilities at the interfaces, but also bulk phase motions and associated inertia. The latter aspect has not been discussed previously; it requires some further explanation, which can be made in terms of the following key observations:

1. At large length scales surface tension forces are negligible and macroscopic bulk motions can lead quite readily to breakup.

2. Coherent melt masses of macroscopic scale can lead to macroscopic vapor blankets, g

which can be unstable, especially under subcooled conditions. The collapse of such blankets is a dynamic phenomenon accompanied by macroscopic collisions, of melt and coolant masses, with significant energy to affect the bulk flow behaviors. Under highly subcooled conditions such phenomena can supply effective triggers to initiate g steam explosions. E

3. Under the conditions mentioned above, and with the possible participation of local fragmentation phenomena, a premixing zone can provide an effective medium for multi-length scale interactions; that is, flow oscillations from one region of the zone to another, with associated breakup and fragmentation phenomena that continue to feed the dynamics.

I As a consequence, a parametrics-oriented approach is utilized at this time. For an order of magnitude, the breakup process is taken to be controlled by the melt length scale, D, f g with a characteristic time constant obtained from the melt velocity, through a specified fall 3 distance, taken as the smaller of the actual fall distance or AD. f I I I" = max l uf l (3.79) I A-34 I

where 03 s an input-specified parameter greater than unity, and L is the total available fall i distance. Physically, the breakup should cease when the length scale has reached the so-called capillary length. Accordingly, the breakup process is terminated in the calculation by the condition (dD I a =0 when D~ (3.80) f dt s g(pf-pt) By varying #3 as a constant we can explore wide ranges of breakup behavior. By making do to vary in space, or with flow conditions, additional dimensions of these phenomena can be explored. Because of the compensating effects discussed by Theofanous et al. (1995) these parametric evaluations can be quite focused and fruitful. The source terms in the fuel / debris continuity equations, Eqs. (3.5) and (3.6), can be obtained in a similar fashion. We begin by recognizing that Fr is the fragmentation rate per unit volume of mixture, and in a material volume it can be obtained by simply differentiating the macroscopic fuel density, p'. That is: f dp'f = pfdef = pf a 1-a Fr s -+ (3,81) dt dt tfg tje where we have made use also of Eqs. (3,68), (3.77) and (3.78). A-35

I

4. REFERENCES

1. Amsden, A. A. and E H. Harlow (1970),"The SMAC Method: A NumericalTechnique for Calculating Incompressable Flows," Los Alamos Scientific Laboratory Report LA-4370.

I

2. Bird, R. B., W. E. Stewart and E. N. Lightfoot (1960), '&ansport Phenomena, Wiley, New York.

3. Burger, M. S.H. Cho, E.v. Berg and A. Schatz (1993), " Breakup of Melt Jets as Pre-Condition for Premixing: Modeling and Experimental Verification," Proceedings, CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8, NUREG/CP-0127, March 1994.

4. Edwards, D. K. (1976), " Molecular Gas band Radiation," Advances in Heat Transfer, 12,115-193.

5. FletcherD.E and A. Thyagaraja(1991),"TheCHYMESCoarseMixingModel," Progress in Nuclear Engineering,26,31-61.

6. Haar, L., J.S. Gallagher and G.S. Kell (1984), NBS/NRC Steam Tabies, Hemisphere Publishing Corp.

l

7. Harlow, EH. and A.A. Amsden (1971), J. Computational Physics,8,197.

8. Hottel, H.C. and A.E Sarofilm (1967), Radiative Transfer, McGraw Hill Book Co.

New York. I

9. Incropera, EP. and D.P. DeWitt (1981), Fundamentals of Heat Transfer, John Wiley and Sons.

ang.

10. Ishii, M. (1975), "Thermo-Fluid Dynamic Theory of Two-Phase Flow," Eyrolles.

11. Ishii, M. and N. Zuber (1979), " Drag Coefficient and Relative Velocity in Bubbly, l;

Droplet or Particulate Flow," AIChE Journal 25,843.

12. Liu,C.and T.G.Theofanous(1994)," Film BoilingonSpheresinSingle-andTwo-Phase Flows," DOE /ER/12933-3, Final Report, December 1994.

13. Patel, P. D. and T. G. Theofanous (1981), " Hydrodynamic Fragmentation of Drops,"

Journal of Fluid Mechanics 103,207-223.

14. Rashid, Y.R., T.G. Theofanous and H. Foadian (1995), " Failure Assessment of Reac-tor Vessel Support Structure Subjected to Ex-Vessel Steam Explosion Loads," 1995 I

A-36 I

ASME/JSME Pressure Vessel and Piping Conference, Honolulu, Hawaii, July 23-27, 1995. '1kans. of the ASME, J1. of Pressure Vessel Tecimology(submitted).

15. Rivard, W. C., O. A. Farmer and T. D. Butler (1974), "A Computer Program for Mul-ticomponent Chemically Reactive Flows at All Speeds," Los Alamos Scientific Labo-ratory Report LA-5812.

16. Rivard, W.C. and M.D. Torrey (1977) "K-FIX: A Computer Program for Transient, Two-Dimensional, Two-Fluid Flow," LA-NUREG-6623.

17. Rohsenow, W.M. and J.P. Hartnett (1973), Handbook of Heat Transfer, McGraw Hill Book Co., New York.

18. Siegel, R. and J. R. Howell (1992), Thermal Radiation Heat Transfer,3rd. Ed. Hemi-sphere Publishing Corp.

19. Sissom, L. E. and D. R. Pitts (1972), Elements of Transport Phenomena, McGraw Hill, New York.

20. Theofanous, T. G., W.W. Yuen, S. Angelini and X. Chen (1995), "The Study of Steam Explosions in Nuclear Systems," DOE /ID-10489, January 1995.

21. Theofanous, T. G., C. Liu, S. Additon, S. Angelini, O. Kymnlhinen and T. Salmassi (1994), "In-Vessel Coolability and Retention of a Core Melt," DOE /ID-10460, Novem-ber 1994 (peer review version).

22. Theofanous, T. G. and W. W. Yuen (1994), "The Probability of Alpha-Mode Contain-ment Failure Updated," Proceeding of the CSNI Specialists Meeting on Fuel-Coolant Interactions, NUREG/CP-0127, March 1994,330-342.

23. Wallis, G. F. (1989), " Inertial Coupling in Two-Phase Flow: Macroscopic Properties of Suspensions in an Inviscid Fluid," Multiphase Sci. Technol. 5,239-261.

24. Yuen, W. W. (1990), " Development of a Network Analogy and Evaluation of Mean Beam Lengths for Multi-dimensional Absorbing /Isotropically Scattering Media," J.

of Heat Transfer 112 408-413.

25. Yuen, W. W., X. Chen and T. G. Theofanous (1994), "On the Fundamental Microinter-actions that Support the Propagation of Steam Explosions," Nuclear Engineering and Design 146,133-146.

26. Yuen, W. W. and A. Ma (1992), " Evaluation of Total Emittance of an Isothermal Nongray Absorbing, Scattering Gas-Particle Mixture Based on the Concept of Ab-sorption Mean Beam Length," ASME J. Heat Transfer 114,653-658 A-37

I

5. NOMENCLATURE speed of sound, also absorption coefficient a

A dimensionless constant, Table 3.1, also area Arnn coefficients defined by Eqs. (4.28) to (4.31) Ar Archimedes number, Table 3.1 B dimensionless constant, Table 3.1, constant in radiation model, Appendix A Br coefficients defined by Eqs. (4.32) and (4.33) Bo Bond number, Eq. (3.75) E specific heat 3 cp C dimensionless constant, Table 3.1, also normalization factor, Eq. (B34) l C3 third radiation constant Ca drag coefficient C& coefficients defined by Eqs. (4.34) and (4.35) l Co drag coefficient, Eqs. (3.16), (3.20), (3.21) d radiation model parameter, Eq. (A4) d' " modified" fuel diameter, Table 3.1 D diameter, also residue g E dimensionless constant, Table 3.1 5 Ea empirical constant, Eq. (3.50) F(F,F) radiative exchange factor, also dimensionless function, Appendix B Fo drag due to the added mass effect, Eq. (3.27) F interfacial friction factor, also dimensionless function, Appendix B F' laminar component of F F' turbulent component of F Fr fragmentation rate Fr Froude number, Table 3.1 g gravitational constant g gravitational vector gb exchange factor between a volume element and an area element at the base wall l gg exchange factor between volume elements gs exchange factor between a volume element and an area element at the side wall gt exchange factor between a volume element and an area element at the top wall G dimensionless function, Appendix B h specific enthalpy i he convective heat transfer coefficient from fuel to liquid A-38 I

.H dimensionless function, Appendix B H[J] Heaviside step function I specific internal energy J rate of mass transfer from liquid to gas (positive for evaporation) Jm characteristic mass transfer rate, Eq. (3.63) -k thermal conductivity, absorption coefficient Kc(d') empirical function defined in Table 3.1 ( length scale L total available fall distance, Eq. (3.79), also mean beam length mf mass of one fuel particle M dimensionless constant, Table 3.1 number density n Nup Nusselt number for forced convective film boiling Nu Nusselt number for pool film boiling p p pressure Pr Prandtl number Q scaler quantity 4 interfacial convective heat transfer 4,. radiative heat transfer do radiative self absorption r radial coordinate R dimensionless viscosity density ratio, interfacial heat transfer function Re Reynolds number Re' effective Reynolds number, Eq. (3.26) Re" effective Reynolds number, Eq. (3.46) s source term for interfacial area transport Sc dimensionless subcooling parameter, Table 3.1 Sc' modified dimensionless subcooling parameter, Table 3.1 Sc* modified dimensionless subcooling parameter, Table 3.1 Sp dimensionless superheat parameter, Table 3.1 Sp' modified dimensionless superheat parameter, Table 3.1 t time tf characteristic time for the complete fragmentation of one fuel particle t} dimensionless complete fragmentation time of one fuel particle, Eq. (3.74) T temperature I' estimated advanced temperature A-39

Ii i radial velocity (or horizontal in Cartesian coordinates) u u velocity vector v axial velocity (or vertical in Cartesian coordinates) l l V volume We Weber number axial coordinate Greek a void fraction o* void fraction to switch from liquid iteration to vapor iteration ll correlation constant in fuel fragmentation model, Eq. (3.74), also Eq. (3.79) i also angular variable br grid size in radial direction i 6t time step Bl 6: grid size in axial direction 5 density ratio (pf /pi, i = f or g) or convergence parameter c 7; dimensionless integration variable, Appendix B 6 volume fraction, also angular variable A wavelength ll

Amo, wavelength at which the Planck function is a miximum at T, Eq. (3.52) f y

viscosity kinematic viscosity, also wave number in Appendix A v p microscopic density g p' macroscopic density, Eq. (3.1) Wl o Stefan-Boltzman constant, surface tension optical thickness, Eq. (B.45) l r time constant to bring the liquid to saturation, Eq. (3.63) re time constant to bring the gas to equilibrium, Eq. (3.61) rg rr time constant to bring the liquid to equilibrium, Eq. (3.62) 6 " correction" factor to two-phase correlations due to presence of a third phase, Eq. (3.15), w wave number I Subscript absorption a b breakup, also boiling db debris A-40 I

e emission exiting quantity er f fuel, also fragmentation fc forted convection g vapor (steam) i instantaneous value ij between components i and j i,j grid location i,j t liquid m minimum s interface, saturation w wall Superscript time step n n A-41

APPENDIX B THE MIXING OF PARTICLE CLOUDS PLUNGING INTO WATER by S. Angelini, T.G. Theofanous and W.W. Yuen Proceedings, NURETH-7 Saratoga Springs, NY, September 10-15,1995 NUREG/CP-0142, Vol. 3,1754-1778 B-1

l THE MIXING OF PARTICLE CLOUDS PLUNGING INTO WATER S. Angelini, T.G. Theofanous and W.W. Yuen ABSTRACT This work addresses certain fundamental aspects of the premixing phase of steam explosions. At issue are the multifield interaction aspects under highly transient, multi-dimensional conditions, and in presence of strong phase clunges. They are addressed in an experiment (the MAGICO-2000) involving well-characterized particle clouds mixing with water, and detailed measurements on both external and internal characteristics of the mixing zone. Both cold and hot (up to 1500 C) particle clouds are considered in conjunction with saturated and subcooled water pools. The PM-ALPHA code is used as an aid in interpreting the experimental results, and the exercise reveals good predictive capabilities for it. B.1. INTRODUCTION This paper describes certain fundamentally-oriented experiments with particle clouds plunging into water. Of special interest are the dynamics of the (transient) interaction, the multidimensional behavior, and, in the case of hot particles, phase-change phenomena and the resulting void fractions in the mixing region. While in a broad sense the subject could be classified under the well-established field of "fluidization," it is, for the most part, outside the main realms investigated previously. That this is so is not immediately obvious, but it will be demonstrated by the results of the present work. Our present interest derives from the study of steam explosions. It is known that such explosions propagate through coarse-scale mixtures (the "premixtures") of a " hot" liquid (usually a melt) into a coolant (typically water). In the metastable state of a pre-mixture the hot liquid is surrounded by vapor blankets (film boiling), and depending on the particulars of the interaction (size of mixing zone, temperature of melt, coolant sub-cooling, etc.) it may contain more or less voids (that is, vapor as the third component). It is now possible to compute this propagation, and the resulting shock pressures to the surrounding structures (Theofanous and Yuen,1994) provided the spatial distributions of the premixture constitutents are known at the instant that an explosion is triggered. Thus, the study of " premixing" as a phenomenon provides the key link between the inde-pendent variables that characterize a melt-pour scenario (i.e., pour geometry, quantities, water pool geometry and subcooling), and the resulting explosion itself. B-3

I Clearly, the use of particle clouds limits the context, for even if a melt was to enter the water not as a coherent mass, but in a more-or-less broken-up state, under most conditions, additional break-up would be expected during premixing. Still, this limited context (one that may be called " idealized premixing") is extremely attractive. The reasoning can be summarized as follows:

1. Absence of break-up allows complete characterization - a "must" for deep under-standing of the phenomena, and unambiguous testing of analytical / predictive capa-ll bilities.

2. Collective-particle (cloud) behavior is of central significance, even in the presence of break-up-deep understanding of such behavior is an essential prerequisite to 4

understanding the whole process (including break-up). l

3. Deep understanding of idealized premixing can provide important insights, if not quantitative bounds (such as on the degree of voiding) on the behavior of real pre-mixtures.

4. Finally, the approach can lead to the creation and study of liquid-particle clouds, as a means of getting to the fundamentals of propagation-i.e., the study of propagation under well-defined premixture conditions and triggers.

l, This line of inquiry has begun already with the MAGICO experiments (Angelini et al.,1994a), involving mostly hot particle clouds, and the Berkeley Nuclear Laboratory (BNL) program (a portion actually carried out at Oxford University), involving mostly isothermal, two-dimensional clouds (a flow field as slice with thickness slightly larger than l the particle diameter) (Hall and Fletcher,1994), while related efforts have been announced (and are probably underway) also in France (Berthoud and Valette,1994) and in Germany (Jacobs,1994). In the same context, the MIXA experiments (Denham et al.,1992; Fletcher and Denham,1994) in Winfrith, UK, and the ALPHA experiments (Yamaro et al.,1994) g in JAERI, Japan, should probably also be mentioned. They both involve melts broken up 5 into particle clouds prior to entering the water, although complete characterization of the melt particle sizes has not been made available. At the other extreme we have the more " integral" type experiments, FARO (Magallon et al.,1994) and ALPHA being currently the more prominent,in which more-or-less coherent melt masses are let to fall into water. l The present work is an outgrowth and continuation of the MAGICO experiment just mentioned. In a related effort, the PM-ALPHA code is being developed (Amarasooriya and Theofanous,1991; Yuen and Theofanous,1995), and we make use of it here to aid in the interpretations. B-4

The MAGICO experiment involved liter quantities of steel particles at temperatures up to 900 C, plunging with velocities of ~ 2 m/s into saturated water pools of 0.25 and 0.5 m in depth. The major thrust in the new experiment is to achieve particle temperatures of up to 2000 C, hence the name, MAGICO-2000. At this temperature level radiation heat transfer becomes rather significant and leads (according to the PM-ALPHA calculations carried out in the design phase) to extensive voiding of the premixture-well above the ~60% value reached in the original MAGICO tests. Another key objective in the d esign was - to increase the duration of the interaction (i.e., advance from small scale to intermediate scale behavior). This was achieved by increasing the total volume of the particulate and the pool depth, which also allows much higher inlet velocities. Finally, around these two main anchors, we built an experimental prcgram covering wide ranges of particle density, particle sizes, and water subcooling. Experiments were carried out in both axisymmetric and Cartesian (2D) geometries. Following the description of the experimental apparatus, procedures and measure-ment techniques (Section 2), the test program and results are given in two main parts, covering the isothermal and high temperature runs, in Sections 3 and 4 respectively..A summary of key findings is given under concluding remarks in the last section.

2. EXPERIMENTAL APPARATUS, PROCEDURES, AND MEASUREMENT TECHNIQUES The principal experimental objective was to generate uniform particle clouds at tem-peratures approaching 2000 C, and it was met by a special purpose " furnace" designed and built in our laboratory. The central element of it is a graphite block, machined into a matrix of parallel holes and slots, as illustrated in Figure B.1. The holes are to contain the particles during heating-an arrangement of miniature doors (a total of 5 doors, one door per row of particles) are used for this -and the particles are released on command by simultaneously opening all the doors. Heating is accomplished by passing a high electri-cal current through the graphite " resistor," formed by the combination of holes and slots, from one end of the block to the other. The total power available by the transformer is 12.5 kW, and it is sufficient to reach the 1500 to 2000 C range in 7 to 10 hours. The heating is gradual, to minimize thermal gradients / stresses and allow time for thermal equilibration between the graphite and the particulate load.

Major development work was required (for details see Angelini,1995) to support such a " hot" block, to build and properly operate the miniature doors, to thermally insulate the whole structure, and to create the necessary inert containment for it. Both the thermal B-5

I! Il =- o a g

2. _

O o i N ' u 200 mm I O % d \\ N 3' 203 mm \\i I g 196 mm I Figure B.1. Heating element in MAGICO-2000. Il insulation barrier and the outer inert containment are provided with mechanisms to allow the particle cloud through, while still protecting the hot graphite block from atmospheric air, and from the steam generated when the particles plunge into the water pool beneath. 4 The overall arrangement is illustrated schematically in Figure B.2. The various particulate materials utilized in the experiments, and respective densi-ties, sizes, and shapes are listed in Table B.1. This table also shows the melting points and g maximum temperatures attained so far with each one of them. At still higher tempera-uj tures the particles tend to " stick" to each other in such a manner as to prevent the full and reproducible release needed to form a uniform cloud. Recently, we have developed tech-niques that inhibit these surface interactions and thus allow us to achieve temperatures of l ~2000 C. Experiments were conducted in two series. One, addressing momentum interactions, l involved isothermal (room temperature) pours-the " cold" runs. The other included phase change effects and was carried out with high temperature pours-the " hot" runs. Experimental conditions are summarized in Tables B.2 and B.3 for the " cold" and " hot" l runs respectively. In addition, we have carried out cold single-particle runs (they are not included in this table) for the purpose of testing experimental techniques and PM-ALPHA in the " dilute" particle limit, under conditions for which an analytical comparison is possible. These runs will be mferred to by the particle size and the material used. B-6 I

transfarnwrx ee = \\ r 1C E7 IC a s [ ".'f 2 so. amo se 12em 1 i. I I X, 1500 Figure B.2. Schematic of MAGICO-2000. All dimensions are in mm. TC indicates the thermal containment, IC indicates the inert containment. In loading the particles into the graphite block we found a packing fraction of ~60%. From the overall geometry (fraction of hole area to the total), we can compute that an ideal, frictionless, pour should produce a cloud of dimension similar to the graphite block with a particle volume fraction of ~26%. Accelerating under freefall this cloud would arrive at the pool surface (normally ~1.4 m below) with a velocity of 5 m/s. The freefall was confirmed from the experiments; the cloud, however, was found to be considerably elongated (see Tables B.2 and 3) as compared to the ideal height of 20 cm (the height of the holes). Moreover, the elongation was significantly greater in the hot runs as compared to that in the cold runs. Since frictional resistances, between the particles and graphite wall, are responsible for this elongation, the above trends indicate that the high temperatures aggravate this friction. Alternatively, it may be that this frictionallimitation is aggravated by the same surface interactions that yield at higher temperatures the particle " sticking" mentioned above and is responsible for introducing a " delay" in the flow of each particle once the support has been removed. More work is being done to better map the particle volume fraction within the cloud, but for the time being from the dimensions of the cloud prior to impact we can find a value of average particle volume fraction, and this is given for each run in Tables B.2 and B.3. A ZrO2 Particle cloud pouring at 1500 C is shown in Figure B.3. B-7

th I E ~ l 1 S e 0 4 A i I T- ., gpg ~ Figure B.3. Zirconium Oxide pour at 1500 C. B-9

i Even though both the graphite matrix and the water tank have a square cross-section this geometry is referred to as "axisymmetric." This is to indicate our view of it as approx-imately axisymmetric, since via slight redistribution during the freefall the cloud cannot really be distinguished from a cylindrically shaped one (also note in Fig. B.1 that with the 4 corner holes missing, the equivalent cross section is already quite round), r.nd more importantly, its interaction with the water is "all around" (largely axisymmetric). This is to be distinguished from the " Cartesian" geometry tank in which the width in one direction is reduced to be approximately equal to that of the pour, forcing the interaction with water to be two-dimensional on a " plane." The main reason for this second geometry, which was employed only for some of the cold runs, was to be able to see j clearly "behind" the mixing region-after the tail end of the cloud had entered the water. In addition, it was interesting to distinguish experimentally this effect of geometry-we would expect the 2D cloud to penetrate more slowly than the axisymmetric one-and provide another test point for computer codes. The designations "AX" and "CR" are used in the name of the cold runs for the axisymmetric and Cartesian geometries respectively. The interactions were recorded on video at the rate of 30 frames per second, and j at selected instances by X-ray radiographs. The video records were scanned and made i available as electronic files into the computer for further processing. From these we could i easily extract histories of the interaction penetration front, evolution of the interaction zone shape, rise of water (surrounding the interaction zone) level, and heights of the two-phase spray (" dome") forming above the interaction in the hot runs. Both local (covering the water tank) and global (including the elevation of cloud formation immediately below the furnace) videos using Sony Hi8 camcorders were obtained. The flash X-rays were J generated by a Hewlett Packard model 43734 generator equipped with a soft X-ray tube with variable energy capability of up to 360 kV. We optimized the energy level and position of the tube relative to the film (see Fig. B.4) for the purposes of each type of run. For the cold runs our interest was to be able to delineate any regions of high particle concentration, created through the interaction of the high-velocity cloud with the water. Such regions were predicted by the numerical simulations (PM-ALPHA), but certainly they could not be detected in the video records. The other interest in this part of the investigation was in exploring the possible existence of a " hole" predicted to form immediately behind the submerged particle cloud, and an interesting dynamic of " closing in" a short time later. To maximize clarity, these runs were conducted in what we referred to as the Cartesian geometry. B-11

I X-ray beam \\ / (] i f % film X-ray source gf windows Figure B.4. Top view of X-ray arrangement in hot runs. For the hot runs, our major interest was to measure the void fractions within the in-teraction zone. Fortunately this became possible because, as discussed above, the particle volume fractions obtained in the hot runs were sufficiently low to allow, in between the particles, regions providing sight lines from the X-ray source to the film, involving only steam or water. The average void fraction along such lines (regions) could be measured using calibrations, obtained in situ, with known quantities of void. The approach is simi-l. lar to that developed in the original MAGICO experiment (Theofanous,1993). To further optimize discrimination here, without significantly affecting the geometry, we make use of the two " windows" shown in Figure B.4. They are simply empty beakers,7.5 cm in diameter and 7.5 cm long, used to remove a total of 15 cm of water from the X-ray path, thus enhancing the sensitivity of the measurement. The uncertainties in this measure-ment will be discussed together with the presentation of results. The same applies for the uncertainties in the measurement of the rise of the water level and of the heights of the two-phase spray. The advancements of the fronts in the pool involve determination of position and time, and they are made with an accuracy of 3 cm and 0.015 s respectively. These are small, for our purposes, and they are reflected in the size of the symbols used in the figures. Temperatures were measured continuously during heatup, using both K-and C-type i thermocouples, positioned at various locations within the particulate and the graphite matrix. The maximum temperature difference is shown in Table B.3, and it is indicative of the uncertainty in initial cloud temperature. Code predictions will be shown alongside the presentation of the experimental results. The code is the version documented by Angelini et al.,1994b, and the inputs for each rtm are according to the specifications given in Tables B.1 through B.3. Only the following additional clarifications are necessary: B-12

1. The axisymmetric geometry was modeled by matching the cross-sectional area of the tank. The pour area was modeled by matching, to the closest integer number of computational cells (of size 3 x 3 cm), the cross-sectional area of the experimental pour as obtained from the videos prior to impact on the water (the cloud appeared to expand slightly during the freefall); this involved a differencebetween actual pour and simulated pour of about 16% for the cold runs and 12% for the hot runs. Accordingly, the particle volume fraction has been adjusted from the average value listed in Tables B.2 and B.3 in order to conserve the total particle mass; sensitivity studies showed little or no effect due to this small change in particle volume fraction.

l

2. Calculations in the dilute limit, for comparison with the single-particle runs, were carried out by releasing a " mini-cloud" (a packet of particles covering just one com-putational cell) with a particle volume fraction of l%. That the single-particle behavior was approached was confirmed with calculations using 0.5 and 0.1% particle volume fractions that yielded the same results.

l

3. To determine more precisely the position of the fronts in the Eulerian calculation, we superposed Lagrangian tracer particles, made to move with the local (cell) velocity of the particulate field.

4. For the hot runs, the code calculations were carried out with a particle temperature at the middle of the range shown in Table B.3. The results were not sensitive to any specification within the respective ranges.

3. RESULTS FROM THE COLD RUNS All the front-propagation results from the axisymmetric cold runs are summarized in Figures B.5 through B.10. Figures B.5 and B.6 refer to single-particle runs and calculations, and they include the analytically determined terminal velocities (sphere in Newton regime, j

constant drag coefficient Co = 0.44). These comparisons are indicative of the accuracy of the experimental and data reduction procedures and the appropriateness of the analytical approach. The small deviation in terminal velocities seen for Al 0a may be due to micro-2 bubbles trapped on the surface of the highly porous particle--such an effect appearing more pronounced given the low density of Al O. The next three figures (B.7 through B.9) 2 3 show the collective particle effect in producing a faster-penetrating front and the influence of the particle density on this phenomenon. The faster-penetrating front is the result of the prolonged inflow of particles into the mixing region which causes an overall alteration of the velocity fields. This will be discussed more in detail later. There is some discrepancy r B-13

I between experiment and calculation, and this appears to increase as the particulate density decreases, and from the visual records it also appears to be associated with instabilities on the cloud front. These results are highly reproducible. Remarkably, a relatively small l reduction in inlet velocity (from 5 to 4 m/s) is sufficient to suppress these instabilities, as shown in Figure B.10. p 70 i i i E 6dI-

• • P. 2.9 mm E
• "p. 6 3 mm O

a pred. 2.9 mm J g O prod. 6.3 mm oo Ca .n iyticai. 2.9 mm. ,6 40- o ..... an.iyt,c.i, e 3 mm - E 30-O 'A -9 e' A n 2

• o A1 k

20-O g

E k 10[- .a o E A 4 o 0 0 0.2 0.4 0.6 0.8" 1 Time (s) Figure B.5. Advancement of single particles, ZrO. 2 I p 70 S 9 exp., steel 2 4 mm E [ A exp. Ai 2.o mm o O pred. ste 2.4 mm g 50 a prod.. Al,0 2.0 mm 3 m o analytical. steel 2.4 mm ) i e 40 o' enetyticat. Aip3 20mm - E f *o "A h E 30r o g 1 O 7 d 6 I 20 3 8 i T[3'Nd j10F 4 $Of I d E O 0.4 O 8 1.2 - 1.6 2 E' Time (s) Figure B.6. Advancement of single particles, steel and Al 0. 2 2 The morphology of the front in all four cases discussed here is shown in Figure B.11. This figure, representing a two-dimensional projection of the three dimensional fronts,is not very powerful in depicting the extent of the instabilities, although it allows to discern the difference in behavior between the " stable" steel and the " unstable" lighter materials. B-14 I

~_ l f y 70( 4 i u steel j6D ~ o sinow porticie exp. o --=-- single porticle, prod. y 50,.,, . tuii pour. exp. A 1 full pour, prod.

409 of.

S'.* a g 30h o= e o 5;- , 2 0e of. H I a 30-o., e. 5 0; 4 i.. 0 OI2 0.4 0.6 0.8 1 Time (s) Figure B.7. Comparison between full pour (MF.AX) and single particle, steel. y 70 4 i i i a LO2 j 60L o o single porticle. cxp. 5 50'.

• • --- 8'a9 P*'5c'* Pd-2 9 full pour, exp.

l 3,5' a 0 '""'"Pd' 2

• 4Da 00 5

g 30[l,.%gD = e% 20-2 5 b,. 30 g N,. 5 or 0 0.2 0.4 0.6 0.8 1 Time (s) Figure B.8. Comparison between full pour (MZ.AX) and single particle, ZrO. 2 7 70, i i o Al2O3

• 60 2

E o

• 9'8 P*c*
• "P.

s t - ---.'"ngie peri,cie. prod. i i s 50j og0 om eui, poor, exp. 1 full pour. pred. 4 30l-0.9o ?.o 2 2 o o0og

20-

.,o 8 i 10-3 i 0 0 0.'6 0.' 8 O 0.2 0.4 1 Time (s) Figure B.9. Comparison between full pour (MA.AX) and single particle, Al 0. 2 2 B-15

i 7 140 i i 1 3 l120 o O fun pour, exp. g100,- o fun pour, pred. m a 8 0,- g 60F l! o O 40h 2)0'- +,,, - a o 0.2 0.4 0.6 0.8 1 Time (s) i Figure B.10. Advancement of full pour of ZrO particles in 1.2 m pool (MZD.AX). 2 1 I llU 120 cfr j U 60 cm 3. l' Al,03

ZrO, Steel ZrO,,1.2m tank Figure B.11. Front morphologies in the cold runs in axisymmetric geometry. Contour lines are 0.033 s apart in the 60 cm runs and 0.066 s apart in the 1.2 m run.

l The radiographs from two Cartesian geometry runs employing a full pour of ZrO 2 particles (MZ.CR), taken at 0.15 and 0.25 seconds after the first contact with water, are shown in Figures B.12 and B.13 respectively. These figures show the formation of a " hole-gj in-the-water" behind the cloud and the dense packing produced at the front. Both of these El phenomena were predicted by PM-ALPHA during our work with the axisymmetric runs and motivated our investigations in the Cartesian geometry. According to our calibration, the quantity of water present in the hole region is negligible, but a few particles can be ) identified in it. The various regions are much more clearly identifiable in the original g; X-ray (than in the reproduction given here), and outlines of them are shown superposed with the PM-ALPHA results in Figures B.14 and B.15. Note that the essential features, such as hole shape, including the necking-in phenomenon shown in Figure B.15, and the position of the densely-packed region of particles are well-captured in the computation. B-16

I a p. b e g fr f 7,nx c' pc 3 },% 'y gby.a '4.: w*; gt1 yk ~'T,M . c ~. l',,, 7 -l'!i , 0.., ,_..a" I t Figure B.12. Reproduction of X-ray images taken 0.15 s after impact of a pour of ZrO 2 particles on water (MZ.CR). The white area is given by the boundaries of the cassettes containing the X-ray films. B-17

1 i i l l i i. i ~ g i 3 i i ~ 4 i i l l l l i i 1 i y~2, j = l e. a .u ' n w.' .n l {' 7 y, \\ 2h 1 ,e t. f

• VX?{k(g',',

"Ly

wn:

, _, "? } v /m % <r y ' :a L l 1 l Figure B.13. Reproduction of X-ray images taken 0.25 s after impact of a pour of ZrO2 particles on water (MZ.CR). The white area is given by the boundaries of the cassettes 4 containing the X-ray films. l B-18 i - - - ~

Boundary of [" Y- - c-~=._r_ X g X-ray titm I 3 } {f ' 1- + Initial water level i N qui re 10 (from X-rays) Boundary of highly-packed particles (from X-rays) k ~ ' ' Figure B.14. Superposition of contour lines from X-ray films onto predictions from PM-ALPHA. ZrO cold run (MZ.CR),0.15 s after impact of particles on water. The prediction 2 shows the void fraction contour lines at intervals of 10%, starting at 10%. The dots are representative of particle location (Lagrangian tracer particles). Particle volume fraction is about 18% in the zone of the red dots and about 2% in the zone of the dark blue dots. B-19

M _-m M Boundary of '-y9 / X-ray film 'y Y /(P ! I 1' initial water level if / $ U( )M lh' Boundary of ?. l - liquid region ~ (from X-rays) f'!? [ I \\\\. Boundary of 4 hi / ghlypacked particles g (from X-rays) p. Wy.s..;gg l Figure B.15. Superposition of contour lines from X-ray films onto predictions from PM-ALPHA. ZrO cold run (MZ.CR),0.25 s after impact of particles on water. The prediction 2 shows the void fraction contour lines at intervals of 10%, starting at 10%. The dots are representative of particle location (Lagrangian tracer particles). B-21

-a. e.sm.--+a-_s ..s-u-.eaa-- e.wr ---n-----.m. s - ma a mma. - - -... -n.~-.-~.-n.~ n+ -. - am a ...a..---- 1 I l 0 I l I I y 5 i i I i f i l l i 1 i J 1i 1 'l 1 r i i 1 4 4k ,i i I 1 g--

Also in Figure B.15, we can see the presence of the instability that is responsible for the experimental front overtaking the calculation, as discussed already for the axisymmetric runs. These instabilities are indeed present also in the Cartesian geometry. That the behavior in this geometry is closely related to that in the axisymmetric one is demonstrated in Figures B.16 through B.18, which compare directly the two behaviors. In Figures B.16 and B.17 (steel and ZrO, respectively) the basic behavior that the planar geometry slows down 2 the penetration is quite evident in both experiments and the computations-indeed, the agreement with the degree of reduction is quantitative. These figures also show that the - degree of discrepancy between experiments and computations due to the instabilities is quantitatively similar in the two geometries. However,in the Al O case, Figure B.18, the 2 3 instabilities overwhelm the whole behavior to such an extent that the " constraint" of the planar two-dimensionality cannot be felt.' This relates to the smaller wave length (found in this case) as compared to the depth of the flow field. The front morphologies (again projections) in the Cartesian runs are mproduced in Figure B.19. - 70 i i i 60 O Axisymmetnc geometry, exp. 8 50-O Cartesen geometry. exp. 2 4,, symmetric pred. g 40{ ..... ce, en preo. 0 g 30-g ~ E

• 20-8

= j 10}' g0' c 0 O.1 05 2 0.3 0.4 0.5 Time (s) Figure B.16. Comparison between front advancements in MF.AX and MF.CR. The X-ray images are useful in explaining the above-mentioned alteration of velocity fields. The continuous transfer of momentum from the particle cloud to the water results in large displacements of the water itself and the generation of a hole in the region behind the front. The presence of this hole implies that, aside from the first ones, the particles are falling through a gap, therefore not decelerating until they reach the front. Here their momentum is dissipated in further displacing the water (" pushing" it away) and aiding the front in its advancement, which thus results to be faster than that of a single particle. This behavior is quite diffemnt from that observable in a sedimenting bed: in this case, B-23

- 70 i i b 6 - E

• Axisymmetre 9aom*iry. *xp-Sg O Cartesian gesmetry, exp.

5*g Axisymmetre prod. a t

• • • • • Cartesian prod.

I 407 E E 30i g 20{: o'.... 2 o i 106 2 e e k 0.1 0.2 0.3 0.4 0.5 l Time (s) Figure B.17. Comparison between front advancements in MZ.AX and MZ.CR. I y 70 sPDA S E e Axisymmeir,. pometry, exp. S h O Cartesian Geometry, exp. g g 5 0-Axisymmetric prod. a

• • • • • Cartesian pred.

e 40-5 G '*..**. E 30a 20[- 2 o e O l e p E 10-2 2 I .,2 m5 o-0 0.1 0 0.3 0.4 0.5 0.6 0.7 0.8 Time (s) = Figure B.18. Comparison between front advancements in MA.AX and MA.CR. l 30 cm 3 g L O e w 60 Cm W w U I T Al O ZrO Steel 2 3 2 Figure B.19. Front morphologies in the cold runs in Cartesian geometry. Contour lines g are 0.033 s apart. I B-24 I 1

from an initial uniform suspension of particles in a liquid, gravity starts a downward motion of the particles, but the achieved terminal velocity is always lower than that for a corresponding single particle (Mirza and Richardson,1979). This is due to the increased resistance that the liquid finds in moving upwards through the sedimenting particles in the one-dimensional geometry. It is interesting to note, however, tha t even in our experiments, once the inflow of particles ends, such a sedimenting behavior is asymptotically reached, as Figure B.20 clearly shows: here we compare the advancement of the particle front for runs MZ.AX (already in Fig. B.8) and MZD.AX (already in Fig. B.10). Initially the two cases behave very similarly, the difference in slope being due to the lower impact velocity in the 1.2 m run; however, shortly after the inflow of particle ends, the front in run MZD.AX undergoes a deceleration, with a velocity quickly approaching the terminal velocity of a corresponding single particle, represented by the continuous line (the front in run MZ.AX reaches the bottom before any deceleration can be detected). PM-ALPHA very effectively captures this aspect of the flow, c

• O

. uzu i - 2 0-

• o o MZDAX g7 f,o anaiyt., 2.9 mm

.- 3 4 0_ o !z

• o

-60~

o j 80 C oo 100[- .E 8 0 Q ~ 0.2 0.4 0.6 0.8 1 Time (s) Figure B.20. Sedimenting behavior in deep pools.

4. RESULTS FROM THE HOT RUNS The penetration behavior and instabilities in these runs were found to be quite similar to those observed in the cold runs. The results are summarized in Figure B.21. The behavior for run Z1500/0-2 is very similar to Z1500/0-1, which is not included in Figure B.21. We note that subcooling appears to aggravate, somewhat, the instabilities. These are responsible for the apparent disagreement in the figure: " waves" of particles stretching past the bulk of the cloud, the latter being closer to the prediction. We also note an indication of reversal in trend, compared to the cold runs: here the light cloud (sic) is B-25

I not nearly as unstable! Under strong vapor flux due to intensive boiling the light cloud decelerates rather quickly and comes almost to a halt (both in the experiment and in the calculation). The front morphologies for runs Z1500/0-2, Z1500/3-4 and Z1500/18-5 are l illustrated in Figure B.22, from which one can see the different behavior of the instabilities due to subcooling. p100 i i S E 8 E oA 60*Q, 'Y-. E 40- $o [** i / 0: O :,%^ g 8 20-

• O O

on,,,,, o,0 o mstabihties e o Oc o'1 o!2 o 03 0.4 0.5 0.6 Time (s) Figure B.21. Advancement of the front in hot runs. Experimental data (predictions): o (dotted line) is Z1500/18-5, x (dash-dot line) is S1200/0-6. 60 cm A ( Y U f 80 cm l M i Y Z1500/0-2 Z1500/3-4 Z1500/18-5 Figure B.22. Front morphologies in the hot runs. Contour lines are 0.066 s apart. g While the instabilities express a local behavior, albeit an interesting one, of much greater significance for our purposes are the overall mixing zone development, the void fraction in it, and the related flow behavior around it. In particular, the water level around g, it provides a measure of the overall void history as a result of phase change phenomena, g while the spray dome above it provides an indication of the steaming rate resulting from I B-26 .I! ]

I the interaction. These key behaviors are presented below. Only a small sample of the results is possible within the space available; complete details have been documented and discussed by Angelini(1995). Void fraction measurements The measurement of void fraction is limited to the chordal average through a small region 15 cm below the initial water level. It is the only " local" measurement among those presented here and thus strongly depends on the characteristics of the evolution of the interaction in its detail, rather than on a global behavior. As such, the measurement not only provides insight into premixing, but represents probably the most important test for computer codes. The local void fractions found experimentally in runs Z1500/0-2 and Z1500/3-4 are compared to the predictions in Figure B.23; the experimental value has been taken 0.35 s (+0.05 s uncertainty) after first impact of particles on the water. The analysis of the X-ray film is based on 8 calibration films in which steps of void of known length were placed in the tank. Comparison between these films and those taken during the hot runs is facilitated by the presence of witness marks and allows us to place the uncertainty within the range shown. 1 1 i-i i Z1500/0-2 Z1500/3 4 0.8 0.8 8 5 5 0.6 5 0.6 5 5 g0.4 .] 0.4 0.2 0.2 0 0 O 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) Time (s) Figure B.23. Comparison between void fraction measured in runs Z1500/0-2 and Z1500/3-4 and corresponding PM-ALPHA predictions. i As expected, the prediction suggests that the effect of 3 C subcooling is to introduce a delay time in the onset of voiding. After this delay extensive voiding of the mixing region is reached, somewhat more grndually, but at even higher levels (up to 100%) than the saturated case, temporarily. This is confirmed by the experimental measurements. B-27

I The highly subcooled run, Z1500/18-5, produced, in agreement with the calculation, an insignificant void (as judged by the level swell to be discussed shortly below). It was below the detection limit of the X-rays (~ 25%). In run Z1500/0-1 void fractions by X-rays were not measured. In run S1200/0-6 the combination of low particle density and intensive vapor gener-ation causes the particles to undergo a strong deceleration, as already seen in Figure B.21. The ensuing particle accumulation, below and around the detection region, is responsible for essentially complete voiding of that region, and a measurement of 100% void fraction is obtained. The low particle density in this case, synergistically with the vapor production and associated momentum interaction produces quite different axial particle distributions than in the ZrO runs. This is illustrated in Figure B.24. Note in particular that in the 2 ZrO runs the X-ray is taken well behind the front, and in the trailing side of the descend-2 ing particle cloud (behind the concentration peak) while in the sic run the front has just passed through this location, the particle concentration is low, and on the rise as the main l portion of the descending cloud is approaching. The peak in this cloud is narrower and quite high. Due to this singular behavior the comparison with the prediction is rendered l in the form of Figure B.25. Note that within a few centimeters away the prediction gives a rather broad voided zone with a void fraction of ~ 90% as compared to the measured ~ 100%. 120 S1200/0 6 100i

---

Z1500/0 2 -

[ - - - Z1500/3 4 f 8y 9, -4 '" 8 x-ray ostection f 60- [ '%, ' ~ 2 ( 7.*Y ^ " 40 20 bottom of pool 0.02 0.04 0.06 0.08 0. Particle volume fraction Figure B.24. Predicted particle volume fractions in hot runs at time of X-ray trigger. The black dot identifies the location of the front according to the prediction. By contrast, as can be seen in Figure B.26, the X-ray in run Z1500/0-2 was obtained away from the front and the associated (singular) high-sensitivity region. In run Z1500/3-4 the presence of subcooling is responsible for three distinct singular regions the void I B-28 I

12C i i S1200/0 6 _100. h vo'd fracten measured 80-5 60 g 40 20 void traction particle volume fraction *10 k 02 0.4 06 0.8 1 Volume fractions Figure B.25. Volume fraction distributions in run S1200/0-6. distribution presents a maximum which is lagging the peak in the particle cloud because of the time required for the water to reach saturation first. At an even higher location, the void fraction collapses temporarily because of recirculation of subcooled water that is being displaced by the front. Incidentally, the X-ray happens to have caught the region of high void fraction. 120 120 i i i i 21500/0-2 Z1500/3-4 100-100-h h measured measured ~ 80- " "'o tracten ~ 80- -/ "'d tracten h g 60-7 / _g 60g % 40- % 40 ( 20 voia traction 20-voto traction particle volume fraction *10 particle volume fracten*10 k O.2 0.4 06 0.8 1 b 02 0.4 0.6 0.8 1 Volume tractions Volume fractions. Figure B.26. Volume fraction distributions in ZrO runs. 2 Water level swells The level swells for runs Z1500/0-2 and Z1500/18-5 are shown in Figure B.27. The uncertainty in measurement is in locating the somewhat disturbed (and disrupted) inter-face. For the calculation the upper and lower limits shown correspond to the 50% and 90% liquid fraction contours at the interfacial region-they are indicative of the water r B-29

I level. The important trends in this figure are that 18 C subcooling suppresses voiding almost completely, and that the void in the uang zone for the saturated run peaks out and contracts. This latter effect is indicative of the flow reversal phenomenon (in the wa-l ter surrounding the mixing zone) and the ETHICCA phenomenon described previously (Angelini et al.,1994b). l In run S1200/0-6 because of the shallow penetration these phenomena are less dis-cernible, especially since the interface broke sufficiently to make measurements impossible l beyond 0.3 s (the comparison up to this time with the calculation is similar to that in Figure B.27). For runs Z1500/0-1 and Z1500/3-4 the behavior is very similar to that of Z1500/0-2. 100 .i. i-i- i-i- i 95-2 W E 90-8 f 2 T 85L -.......N j f, g ~~ -f E D R -- ..j ..w. g e E 75-

• • P '*"98 - 215" d

===== exp. range, Z1500/18-5 70' p'et range. 21500/0 2 _l prod. range. 21500/18 5 b.1 U.2 b.3 04 0.5 b6 b.7 0.8 = Time (s) Figure B.27. Water level swells for runs Z1500/0-2 and Z1500/18-5. Predictions refer to 50% and 90% liquid contour lines. I Heicht of sprav dome Ii The heights of the spray dome above the initial water level for runs Z1500/0-1 and 1 Z1500/18-5 are shown in Figure B.28. The experimental data are represented by bars g: which incorporate the uncertainty in their measurement, and the prediction corresponds 5 to the position of the 2% liquid volume fraction contour line (contour lines between 1 l and 5% form a rather narrow band). Results similar to those of Z1500/0-1 are obtained in runs Z1500/0-2 and S1200/0-6, while for run Z1500/3-4 these data were not available. From this figure we see that in the presence of 18 C subcooling the spray dome is alrr.ast nonexistent and forms only after all the particles have entered the tank (~0.4 s), again suggesting that for this run evaporation is almost completely suppressed. The calculation predicts the same behavior. On the contrary, in saturated water large amounts of vapor are produced that escape the tank dragging liquid along with them from early in the mixing B-30 I

(note that the computational grid in the simulation of Z1500/0-1 is limited to 60 cm above the initial water level). It is worth pointing out the difference in scales between Figures B.27 and B.28: the water level grows by a maximum of 15 cm, as opposed to 70 cm and more for the spray dome. Although both behaviors are linked to the vapor generation in the mixing region, they are completely distinguishable. 70 i y - ----- 21500/18 6 S. 60' 2 .}' l50F 2 / 40F 2 e 4 S 30- /

• 20l

/ 2 . 10 . ~ ' --- 0 0.'2 0.4 0.6 0.'8 O 1 f Time (s) Figure B.28. Height of spray dome above initial water level for runs Z1500/0-1 and Z1500/18-5.

5. CONCLUDING REMARKS The MAGICO-2000 facility and the associated measurement techniques provide a unique capability to produce uniform particle clouds of temperatures up to 1500 C, cur-l rently, for the study of detailed interaction with water pools. Interesting phenomena identified under isothermal conditions are the formation of densely packed regions at the penetrating front, the formation of a " cavity" behind relatively dense clouds (10+14%

volume fraction), the development of instabilities (finger-like) at the penetrating front, and the slowing-down effect of a motion restricted to planar symmetry. Interesting phe- { nomena quantified in hot pours include local voiding in the mixing zone, global voiding through the level swell, the formation of a two-phase spray dome about the mixing zone, [ and the effects of slight (3 C ) and moderate (18 C ) subcooling on the above. Calculations with the PM-ALPHA code helped to interpret and probe in much greater detail than is feasible experimentally into these phenomena, and showed the importance of the details for the correct simulation of the process. Only the front instability was not captured by the numerical model. All these comparisons are expected to contribute significantly to an overall scheme of code verification appropriate for the intended applications. B-31 f

ACKNOWLEDGEMENTS This work was funded by the U.S. Department of Energy's Advanced Reactor Severe l Accident Program (ARSAP) through ANL subcontract No. 23572401. We are very grateful to Mr. Tony Salmassi, who was instrumental in the design and the construction phases g of the MAGICO-2000 facility. We would also like to acknowledge the contribution of Mr. Sam Ameen (Aweto Custom Printing) in the development of X-ray radiography for void fraction measurements. Messrs. Steven Sorrell(DOE) and Stephen Additon (TENERA) played a key role in programmatically supporting this project. REFERENCES

1. Amarasooriya, W.H. and T.G. Theofanous (1991) " Premixing of Steam Explosions: A Three-Fluid Model," Nuclear Engineering & Design 126,23-39.

i

2. Angelini, S. (1995), "The dynamics of hot particle clouds plunging into water," PhD thesis, University of California at Santa Barbara.

l

3. Angelini, S., E. Takara, W.W. Yuen and T.G. Theofanous (1994a) " Multiphase Tran-sients in the Premixing of Steam Explosions," Nuclear Engineering & Design,146, 83-95.

I,!

4. Angelini, S., W.W. Yuen and T.G. Theofanous (1994b) " Premixing-Related Behavior of Steam Explosions," Proceedings CSNI Specialists Meeting on Fuel-Coolant Inter-actions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994,99-133.

I

5. Berthoud, G. and M. Valette (1994) " Calculations of the Premixing Phase of an FCI with the TRIO MC Code, Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, 27.

i

6. Denham, M.K., A.P. Tyler and D.E Fletcher (1992) " Experiments on the Mixing of Molten Uranium Dioxide with Water and Initial Comparisons with CHYMES Code Calculations, Proceedings of the Fifth Intemational Topical Meeting on Reactor Ther-mal Hydraulics (NURETH-5), Salt Lake City, UT, September 21-24, Vol VI,1667.

] i l 1

7. Fletcher, D.E and M.K. Denham (1994) " Validation of the CHYMES Mixing Model,"

Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994, 89. I B-32 J

8.' Hall, R.W.and D.E Fletcher (1994)" Validation of CHYMES: Simulant Studies," Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/ CP-0127, March 1994,70. ~

9. Jacobs, H. (1994) " Analysis of Large-Scale Melt-Water Mixing Events," Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG/CP-0127, March 1994,14.

10. Magallon, D. and H. Hohmann (1994) "High Pressure Corium Melt Quenching Tests in Faro," Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8,1993, NUREG /CP-0127, March 1994,1.

11. Mirza, S. and J.E Richardson (1979) " Sedimentation of Suspensions of Particles of Two.

or More Sizes," Chemical Engineering Science,34,447-454 = 12. Theofanous, T.G. (1993) "The Study of Steam Explosions in Nuclear Systems," In-ternational Seminar on Physics of Vapor Explosion, Tomakomai, Hokkaido, Japan, October 25-28, pp. 5-26.

13. Theofanous, T.G. and W.W. Yuen (1994) "The Prediction of Dynamic Loads from Ex-Vessel Steam Explosions," Proceedings, International Confemnce "New Trends in -

- Nuclear System Thermohydraulics," Pisa, May 30-June 2,1994,257-270.

14. Yamano, N., J. Sugimoto, Y. Maruyama and K. Soda (1994) " Studies on Fuel Coolant Interactions during Core Melt Accident of Nuclear Power Plant," Proceedings CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8, 1993, NUREG/CP-0127, March 1994,271.

15. Yuen, W.W. and T.G. Theofanous (1995) "PM-ALPHA: a Computer Code for A.ddress--

ing the Premixing of Steam Explosions," DOE /ID-10502, May 1995 f B-33}}