ML20133E489

Cooldown Aspects of TMI-2 Accident

ML20133E489
Person / Time
Site:	Three Mile Island
Issue date:	08/31/1985
From:	Theofanous T PURDUE UNIV., WEST LAFAYETTE, IN
To:
Shared Package
ML20133E494	List: ML20133E489 ML20133G591
References
NUDOCS 8510090412
Download: ML20133E489 (84)

Text

%

3 ..

die C00LDOWN ASPECTS OF THE OdI-2 ACCIDENT by T. G. Theo fancus Scncol of Nuclear Engineering Purdue University West Lafayette, IN 47907 August 1985 Current address: Depart =ent of Chemical and Nuclear Engineering University of California Santa Barbara, CA 93106 951009dflZ m W1

A D i

i I

j Abstract i

r The cooldown of the TMI-2 reactor vessel due to high pressure j injection that occurred at 200 minutes into the accident is re-i

{ .

examined. Flow regimes and condensation heat transfer in the cold legs  !

1 and downconer are considered. The presence of noncondensibles (hydro-i gen) and a mechanism leading to its accumulation around the condensa-tion interfaces lead to conclusions that are materially different frem I

chose of a previous study that did not consider these effects.

I f

i i

l i

i 4

)

i f

I l

i i

(

I i,

m i

i i

l

5 *

]

+

i

INTRODUCTION 4

Previous studies on the Thermal-Hydraulics of the NI-2 accident I

have focused on phenomena leading to core uncovery, associated heacup  !

t i

and eventual degradation. With the recent interest in the Pressurized i

Thermal Shock (PTS) issue [1] it would be interesting to censider, l

4 also, the cooldown behavior, particularly that associated with the actuation of the High Pressure safety Injection (HPI) system [2].

In fact, the B&W Owner's Group (OG) task force on PTS censidered 4

this problem soon after the accident [3]. The phenc=enology invoked in this assessment is schematically illustrated in Figure 1. The basic 4 idea is that the vent valves allowed steam from the rest of the pri-i

1. mary system to flow towards the HPI stream and to condense on it, thus a

i heating it frem the rather low initial temperature of Tg - 10*C (50*F) to a considerably higher level before it reached the cold leg exit 4

j into the downcomer. Based on condensation rates alone this exit tem-perature, T,, was estimated at 207 *C (406 *F) . On the other hand, q

neglecting (conservatively) the quantity of steam already stored within the voided portions of the primary system, an estimate based on available decay heat (i.e. , steaming rate) of 14 l *C (286 *F) was given.

The fracture mechanics analysis for the mI-2 accident was carried out at 141 *C (286*F) .

i 1

In fact within the assumptions of the OG analysis the limit based 1

on condensation rates is conservative, while that based on the decay l

heat is irrelevant. Each part of this statement is clarified,- in turn, j below.

i 4 6 I

4 1

-e e e g-, - . , - , , -r- - - - - - -,-.- - ~ -,-yw -,,,---.-,,.---.-.--.-%-~-,-.-w-g , , --.-~y ,-.------e- ,w-,7,y-.-,, .,y,,~,,gy,,,,,ww,,--..--e-.,., pwr e

o, .

The condensation rates were based on the stratified regi=e (Fig-ure !), and did not consider the jetting / splashing phenomena (Figure

2) at the point of injection. We have estimated that just over the jet length a heatup to !!5*C (249'F) can be expected [4 ]. Considering the increased interfacial area (wall films, entrain =ent of drops into the vapor space) generated as the jet splashes against the opposite wall.

most of the heacup should have occurred prior to the flow's entering the stratified regime. It does not appear, therefore, that condensa-tien rates could have i= posed any limitations.on achieving near saturation temperatures at the cold leg exit (i.e. , 284*C or 543* F at 1,000 psia).

The decay heat is available to generate steam for only so long as the core remains cevered. The fact that a voided cold leg condition is being addressed implies a core already uncovered or well on its way to being so. Thus a portion of the decay heat, equal (rou6hly) to the portion of the core that still is in contact with liquid coolant should be utilized. In fact, at IMI-2 at the time the HPI was turned on, essentially the whole core was uncovered and severely damaged. Any steaming estimates must, therefore, be based upon fuel quenching and water availability to this process, rather than decay power levels. On the other hand, the steam content of the various voided parts of the pri=ary system could be significant but was neglected in the OG analysis. Even the liquid still present in the lower elevations could have been activated into steaming if the already existing steam inven-cory continued to deplete and system pressure decreased. This flashing process could further be sided by energy stored in structures still vetted.

a. . .

s There is another aspect to this problem, however, that dominates the heat-up process to such an extent that any uncertainties associ-ated with the above mentioned ccmplex phenomena affecting steam avai-l I

lability are negligible by comparison. This aspect arises because of the presence of noncondensibles, that is, hydrogen and fission product .

gases, in mixture with the steam. Noncondensibles are notorious in degrading the performance of process condensers. They impose an addi-i tional, diffusional, resistance to the condensation process, and j

because they tend to collect in the immediate vicinity of the condens-ing interfaces, they can be detrimental even in trace quantities. Even

! more importantly, in the present case, we will demonstrate a mechanism 4

l which lesda to continuing accumulation of noncondensibles within the

cold leg and eventaally shuts of f the the condensation process. The rate of accumulation is proportional to the heacup of the HPI (i.e. ,

i i

proportional to the condensation race), yielding a self-regulating behavior whereby condensation shut-off is rapidly obtained indepen-i' dently of the details used in the calculation.

1 The purpose of this paper is to reassess the TMI-2 vessel wall l

i temperature transient, due to HPI, in the light of the phenomena introduced above. The assessment proceeds in two steps. In the first, 1

a simple analytical model is used to quantify the condensation tran-

'1' sient, as affected by the accumulation of noncondensibles, and hence 4

to arrive at the temperature transient of the HPI water entering the 1

downcomer. In the second step, these results are used in conjunction

) with methods adapted from past PTS thermal mixing analyses (5) to l determine the vessel wall temperature.

t 4

I

.,w----. ,, n n - , - - , - - - - . , , . , . . , - - , , .-..--..-.,-e-, , - , . . - - - , ,, anwm.,.~n- n e ~.r..,,--em,-,,.e,a..e . , ,

.w--e-.-w.-mr

o e THE CONOENSATION TRANSIENT Formulation of the Analvtical 'fodel Consider the cold leg /HPI-stream configuration of Figure 3. The cold leg is horizontal, its length is L, its volume is V, and it is initially filled with saturated steam at a pressure P.. The HPI water enters at time t = 0 with a mass flow race E.dPI and a temperature T 1 which is well below the saturation temperature corresponding to the system pressure T*(P.). It for=s a stream along the bottem of the cold leg and exits at the other end with a temperature T,. The cold leg is assumed to coemunicate with an inexhaustible supply of a steam / hydrogen mixture such that any mass loss from volume V, due to condensation, is perfectly compensated to maintain a constant pressure level P., throughout the system. The mass flow race of this supply is denoted by 57 and its hydrogen content is expressed by the mass frac-tion v,

- . The condensation rate over the whole of the liquid / vapor interface (area S = 1, x L) is 5:". The remova[ of hydrogen, frem volume 7, by absorption into the water scream may be assumed to be negligible (see Appendix A) . As a consequence the hydrogen density, c , within the cold leg will increase with time, yielding corresponding tran-sientsonk,E,andT,.Ourtaskistorelatethesequantities through the relevant flow and condensation processes.

As the liquid heats up from I to T,, along its flow path, the potential for condensation decreases. Condensation rates are, there-fore, functions of both time and position, z, and as a consequence we would expect the composition within the gaseous space to vary as well.

o e I

We believe that the essence of the physical behavior may be captured without having to consider this detail. That is, the whole j steamihydrogen space within the cold leg is assu=ed to be well mixed,

, and et is taken to be a function of time only. .

f A hydrogen mass balance, over the gaseous volume of the cold leg (without loss of generality taken as V), yields:

d '

d ,.

(V p,)

= $.,, v, (1) i .

It is convenient to work 'sich mole fractions, x , instead of densi-F e ties, and steam mass flow rates , m S

, instead of total flow races. The transformations can be carried out as follows: We use p =v c = " _

i "i i "i c! x'i (2)

! and p o e,. =c =

i

+ 's =

Pi+P s p

. 1 + c._ R .,. ,.

R,A RT = - ::$-

at

= c onst . (3)

I to express the left hand side of Equation (I), as:

a" d:: ,

d (V O,) .

= V M, c ,t e

.o (l. )

For the right hand side of Equation (1) we use a, P,M,'

• 4 = =

P,M, g . Og

• g [7 . O s RT '

i+ s" = (5)

P, P M

. 3 3

%g = p . X

• 3 p . , and I

w =  % E y* t x,* x,. = 1 (6) e to obtain y -

• ia, i.=

.g + (1 - P3)x,= -

(7) g Clearly,

. . .y

,, = m

. i

+s s

. (.3 )

4

e .

and since steam and hydrogen enter the cold leg with the same velo-city:

O,- 0, c,M, x,  :,

F 0, c ,M , x,Mg (1 - x ?P7 l 9) s therefore,

.y [ 3,

) y Mg * (1 -- M g) X t,

• T " *s ( ' m'F, ) " *s ( 1 -- xim)F'R (10)

Thus, Equation (1) becomes:

t e dx m' x i

L s Ln de V M e, 1 -- x , (11) s$

The steam flow race entering the cold leg, m'T 3, together with the race of mass depletion of steam within the cold leg, cust constitute the c

rate of condensation, m.. That is:

=

dx i

$E s

de eT3sV . ECa (12)

But dx = - 4x, and together with Equation ( !!), Equation ( 12) becomes

$IJ = $"s( 1 -- x , a) .

(13)

This result is used in Equation (11) to obtain the final form:

dx $C ce VM c

• La (

s T Next we =ust relate m'c,to the appropriate temperatures and heat transfer coefficients. The role of hydrogen in the condensation pro-cess is illustrated in Figure 4. The steam is assumed to be in thermo-dynamic equilibrium with the liquid at the interface. If there had been no diffusional resistance on the vapor side of the interface the concentration distribution would have been uniform, at x ; the inter-face temperature would have been Tg= T * ( (1 -- x ) P,] (15)

and the condensation rate would have been controlled by the turbulence in the liquid and a corresponding heat transfer coefricient, 5, 3 i.e.,

1 q = h { T" [ ( 1 -- x , ) ? ! -- T37. (:, t) ) (16)

In fact, dif fusional resistance of steam against the hydrogen molecules is extremely important. It gives rise to a buildup of non-condensibles at the interface and a corresponding decrease of the interfacial temperature, as shown in Figure 4. That is, I,. = T * [ (1 -- x,..,) Pm ] (17)

Now the heat flux is J

q = h, { T * [ (1 - >: ) P,}- Igp (a, t} } (18) and a significant degradation in heat transfer is seen if x,t is sig-nificantly higher than xt. The quantities xtt and It can be deter-mined by coupling the mass diffusion process on the vapor side to the heat transfer process on the liquid side of the interface. For laminar flow this can be done exactly [6], but for turbulent flow the process remains poorly understood. The experimental data are scarce and highly non prototypic (steam-sir system, low pressures, film condensation on cooled walls). Our approach is to express the degradation in heat transfer as an exponential function of the hydrogen mole fraction as follows:

X i

y

- =

T"[(1 - xtt) P,l - THPI(*'*} ~~

t/-

=a (19) 11 I"[(1 - x,) P ] - T.dP,.(a , t) .

And in combination with Equation (18) we have

• 1 q = h, e I/*

T* [ (1 -- x ) P 1 - THPI(*' }

The basis for Equation (19) is given in Appendix B.

i

(

t - - -. ... ,. . _ .- -

The heacup of the liPI stream can be obtained frem an energy bal-ance over a differential element, d:, as shewn in Figure 3. That is, dT .

N -

s id?I "? =

h, e *I/: /

T"[(1  : )? -! (21) which upon integration yields,

~

xt.

x e i T* ( (1 - x,) P,] -T, 1 - exp[ - }

(

~ C

'dPI p This heacup may also be related to the latent heat of condensation by:

'hp: C (!, - T, ) = h, E} (23) x, thus the condensation rate may be written as,

• c

~ - [j*,I m =

3 "3P! e h, if .*[(1 - x,) P } -T )*

1 - exp( -

Sh ee e

-=

s =

il 1.dP,. C p ]) (24) and the exit temperature as, I

h,E EC8

=!i+

T e C p d.d PI ( 5)

• he solution, x (c), is obtained by integrating Equation (lt.) with xt(o) = 0,* in conjunction with Equation (24) . The quantities m,(t) *c and T,(t) can then be readily calculated from the last two equations.

The Choice of Parameters for the TMI-2 Case

• he relevant geometric dimensions were taken from the design information from Oconee, which is a B&W reactor similar to TMI-2. From

the cold leg diameter of 0.7 m and its length of 8.15 m, between the reactor vessel and the pump, a volume of 3.I m3 is obtained. The In fact significant accumulation of hydrogen (x, 4 0) vichia che cold leg in which the make up water flow had already been established would be expected.

_ g-volu=e of the upper i m of the downcomer corresponding to each one of the' four cold legs is -1 m 2 Considering that a good fraction of the inclined portion of the cold leg volume may not participate in the mixing process a value of V - 3.5 m was chosen for the calculations.

3 The sensitivity to this parameter was examined by also considering a value of V = 2.5 m . 3 The high pressure injection in TMI is believed to have occurred at -15 kg/s [7]. We bracket this value by choosing :5 ~

I * ""

HPI 5g - 20 kg/s. The inlet water temperature is taken at T = 10*C (50*F). Assuming critical open channel flow at the cold leg exit, the water stream is estimated to attain a depth of 8 cm, e width 1 - 20 cm, and a velocity of u - I m/s (for the 15 kg/s injection rate). The minimum value of the vapor / liquid interfacial area is thus estimated at S - 1 m . '

i As seen in Equation (24) the interfacial area, S, appears only in 4

product with the heat transfer coefficient, h . The effect of higher l

areas, likely to exist due to splashing and entrainment as shown in Figure 2, was covered by considering a generous range in the sensi-tivity analysis for h .OAs discussed in Appendix C a realistic esti-mate for this quantity is h, - 1,300 BTU /hr f t2*F. Accounting for a i

moderate increase in interfacial area due to splashing and associated enhancement of h g (jet condensation, etc.) the icw end of the range for h oconsiderad in the calculation was set at 5,000 BTU /hr fc**F (i.e., nearly a factor of four higher) . The base case value was taken nearly as one order of magnitude higher at h -

10,000 3TU/hr ft27, The upper end, at h, - 50,000 STU/hr f t *F represents an enhancement

10 -

by a factor of x?? and is judged to adequately cover the most extreme behavior.

For the base case the liquid heat capacity was taken at C -

1.3 P

STU/lb *F. Because of the wide temperature range present the sensi-tivity to this parameter was examined by considering also the case of C - 1 BTU /lb* F. The saturation temperatures and latent heat of con-densation (hgg ) were obtained from the steam tables. The system pres-sure, P , was taken at 1,000 psia. Sensitivity to this parameter was examined by considering the case of P, - 2,000 psia. The molecular weight of steam is M, = IS g/g-mole.

4 1 As discussed in Appendix 3 for x , /~, a value of 0.05 is deemed i

appropriate. To generously cover for uncertainties and not to overes-timate the degradation in heat transfer, a base case value of x

f - 0.1 was selected. The upper end of the range was set at x j

- 0. 2.

Finally, the choice of x ,, must be made on the basis of core steaming and oxidation rates at the time of high pressu:e injection l

(around 200 minutes after the start of the accident). It is now known i

that by this time the TMI-2 core had already been severely oxidized I

and partially molten. There seems to be some indication that the mol-

• ten material relocated in the lower portion of the core where it froze forming substantial blockages (8]. At 174 minutes the "B" loop primary coolant pumps were actuated for a short period of time. As a result some loop seal water was displaced into the reactor vessel yielding a vigorous steaming process as verified by the rapid pressurization to

j ll I

i 2,000 psia seen around that time. The details of this process will remain highly uncertain; however, there should be little doubt that 1

the renewed steam availability reactivated the oxidation processes  ;

(hydrogen production). On the other hand, at 142 minutes the pressur-imer block valves were closed, they were opened briefly (-5 minutes) j at 192 minutes and remained closed until 220 minutes. All indications are that the pressurizer remained more than 3/4 full throughout the i

i l

accident; therefore it is unlikely that any venting of steam (and non- l

{ condensible gases) occurred during this brief opening of the pressur-

[

t i:er block valve. Thus at the time of HPI cperation (200 to 217 r i '

minutes) the major fraction of hydrogen already produced and of the fission products released from the disrupted fuel rods, were still l

i present within the primary system volume. The total amounts of gases 4

{ released in the accident are estimated at (9): Kr - 3.5 kg, Xe - 40.6 1 l kg and H2 -510 kg.* The total primary system volume is -10,000 ft3 '

{ Assuming that loop seals (-2,700 ft )3 and lower plenum (-685 ft 8) were 1

still full with water the total steam mass, saturated at 2,000 psia, is estimated at 18,976 kg. A low bound of noncondensibles mass frac-5 j

8 tion, may be obtained by assuming a homogeneous distribution l

l throughout the steam volume. For Kr, Xe, and H, we obtain 0.018%,

i j 0.214%, and 2.68% respectively. Clearly, only the hydrogen is signifi-j cant. Its concentration may be obtained on a mole fraction basis as t

xg -29.7%. On this basis we chose the values x = 0.05, O.I, 0.2, l 0.3 and 0.4 to parametrically cover a broad range around the above >

6

'1 j

) estimated value. For the base case we chose1x . = 0.2. i t .

e t

A quantity of only 25.6 kg of hydrogen would be sufficient to j obtain a mole fraction of 0.4 in all four cold legs.

I  !

I i

e , t l

1 i Numerical Results and Discussion 5 The solutica for the base case is shown in Figures 5 to 7. A rapid buildup of hydrogen in the cold leg and a coneccitant decrease i t n steam condensation rate are predicted. As a result, the HPI water heat up is drastically reduced with cold leg exit temperatures i.

approaching inlet values within a matter of I to 2 minutes. All param-eter sensitivity results lead to the same conclusion. The x g and x

{ 1/2 parametrics are summarized in Figures 8 and 9. The results of the 5 x,a = 0.4 parametric calculation are given in Appendix B. All other '

parametric results are collected in Appendix D.

I i

THE DOWNCOMER C00LDOWN TRANSIENTS i 4

(

From the above analysis we expect that cold HPI water, nearly at

/

l the injection temperature of -50 F, entered the IMI-2 downconer for 4

the major portion of the injection period. Our task here is to deter-i sine the resulting vessel wall cooldown.

4 The physical situation is schematically depicted in Figure 10. We j

will attempt to look at the problem from two complementary perspec-a tives. First, we examine whether any portion of the HPI stream enter-l ,

ing the downecaer could have come in contact directly with the reactor vessel wall. Second, in the other extreme of phenomenology, the HPI stress is assumed to remain attached (as a film) to the core barrel as

{

1 it falls to mix with the downcomer and lower plenum water contents.

i I

i l

i 1

3 i

i j

i--_ ,,. -- - , , - - - _ _ _ - - .

13 -

Direct Contact Mechanisms The first critical consideration is whether the HPI cold stream coces directly into contact with the vessel wall. An experimental run at the Purdue 1/2-Scale integral thermal mixing facility with an injection flow rate of 1.2 kg/s revealed the flow regime indicated in Figure 11. That is, the stream impinged upon the core barrel side of the downcomer and fell along it as a well-defined attached film. It is our judgment that this flow pattern should also have prevailed at full scale under the 15 kg/s flow race. If there were no obstacles along the path of this film the flow would have continued smoothly until it reached the water level within the downcomer (Figure 10). Unfor-tunately, such obstacles did exist and very likely caused an abrupt deflection, of the downwards flow, laterally, towards the reac-tor vessel wall as illustrated in Figure 12.

The detailed geometry of those obstacles is illustrated in Figure

13. The obstacles are called clips. Twenty of them are attached to the core barrel to support the upper end of the thermal shield. Fecm the design information provided (10), their positions relative to the cold legs could be determined as illustrated in Figure 14. Clearly, nearly one-half of the flow must have impinged upon the upper surfaces of those clips causing it to splasn upon the reactor vessel wall. The other half must have continued undisturbed and been confined between the core barrel and the thermal shield space.

These considerations lead us to conclude that ths resulting upper bound cooling of the reactor vessel wall should correspond to splash-

4 j . .

l -

14 -

1 7

I ing 60*F water at the rate of -7.5 kg/s. For a realistic evaluation  !

I i l the quantitative aspec; of the above-mentioned film-and-splashing flow regi=es and the associated heat transfer need ca be evaluated. Simple, isothermal flev regime experiments of the type mentioned above, but with the presence of the thermal shield support clips, would be the j necessary first step in such evaluations. Based on the results of f these experiments some condensation experiments run at the appropriate flow regimes, and in the presence of noncondensibles would also be i

useful to quantify any additional heating due to condensation in the ,

j film-and-splash ficw regime within the downcomer. However, unless an l r j unforseen phenomenon strongly mitigates the condensation inhibition i i ,

a i

effect of the noncondensibles (see Appendix B), our parametric calcu- '

i  :

J 1

lacion with h =

$0,000 BTU,hr f2 t *r indicate, that cur present 0 y

results will not be materially altered.  ;

[

! A REMIX-Type Cooldown Analysis I

If direct contact did not occur, the vessel vall cooldown was controlled by the fluid temperature as it filled the dcwnecmer. The J

j most benign flow regime that could have occurred in this case is that j

illustrated in Figure 15. Except for a thin thermal plume which is

confined between the core barrel and the thermal shield and mixes i i

4 quickly as it descends, the rest of the fluid volume would be well  ;

i j mixed. This situation is very similar to that of a portion of the REMIX procedure utilized in the usual HPI charmal-mixing analyses i dealing with a liquid-full cold leg situation (5}.

4 Let Vg (t) be the volume of the fluid within the lower planum and b

i

\

t I

i

.- -_-,_-,.--,,-----.----,_-...,c---..- - , - . . - ~. , , - _ - - .-, - . _ - - ,. , , - - - - - - - - -

e .

the downcomer corresponding to each of the four cold legs as shown in Figure 10. The density of this fluid is denoted by 03 The cold stream enters at a volumetric flow rate Q , and a density a,. A fraction, a, of the flow, Q ,, which would have to exit if the control volume was

fixed in time is assumed to enter the core, while the remaining, (1 - a)Q,, is utilized to increase the fluid volume within the downco-mer. Based on available flow areas within the core and the downcomer, '

the maximum value of a is 0.6. For a fully obstructed core c = 0.

i Since the degree ci lower core blockage in TMI is not known, the quan-i tity a is treated as a parameter within the above range.

An overall mass balance may be written as d

, (Vg o)=Q p -- c Q, o, (26)

The rate of change of the control volume is given by dV,

' = (1 - 3) Q, (27)

The erergy balance accounting, for the thermal energy conducted out of the metal structural components, as they become submerged, Q , is written as 4 -

(V, . momh)=Q p h -- a Q p h de e e e o m m +Q v (28)

Together with the equations of state c = f (h) and T = g (h)

(29) we have a closed system of five equatlons in the five unknowns, namely, p,, h , T,, Q, and Vg .

For an approximate estimation of Q, the downcomer was discretized j axially into four equal segments. When the level of fluid volume V f

l i

16 -

i 1

reached the lower end of each axial segment, the conduction calcula-  !

i ,

tion for that segment was initiated and continued to the end of the calculation. The total heating was obtained by su= ming up the contri-I bution of all the thus-setivated segments, t t

j i

Solutions were obtained by marching out, numerically, in time '

j from specified initial conditions.

h y Choice of, Parameters and Numerical Results f

'Jith the exception of the initial fluid volume, V g(o), and of the initial temperature of the non-submerged portion of the structures, '

r the choice of parameters in this rather basic analytical model is i

straightforward. The relevant geometric quantities were taken to be those of the Oconee reactor. (See Table 1.) The cold water was taken to enter at T - 30 F with a mass flow rate of Q,0, - 15 kg/s.

i l Parametric calculations with T, - 60*F and 70*F also were performed. i i

f 2

As mentioned earlier the value of a was considered parametrically t within the 0.0 to 0.6 range.

f The possibility that additional condensation upon the core barrel

} {'

film which would increase T, prior to contact with the downconer water i j

level should also be mentioned here. From the thermal shield length i (Table 1) and an assumed lateral spread of - 13 we obtain an addi-u i 2 tional condensation surface area of -$.3 m . The downconer volume is

} -6.3 3 8. Employing the results of the condensation parametrics we see l that the additional area (a factor x$.3 from base case) is amply covered by the h, - 50,000 BTU /hr f 2t *T parametric calculation (factor of x37). Also as we can see from Equation (14) the increased volume (a i

I i .

1

17 -

factor of x1.3 from the base case) may be thought of as compensated by x, - 0.4 parametric (i.e. , a factor of x2 from the base case) . Thus ,

.a again, unless an unforseen phencmenon strongly citigates the condensa-i tien inhibiting ef fect of noncondensibles the values of T, utilized in this analysis would not be materially altered.

The initial fluid volume within the downcomer/ lower plenum region is uncertain. Prior to the "B" loop pump actuation the downcomer was essentially empty. There have been some estimates, however, that the pu=ps displaced nearly 1,000 fe l of water from the cold leg piping into the reactor vessel. This would have been suf ficient to fill the downeceer ecmpletely if the core had been completely blocked, or to fill one-half of the core and downcomer volumes if free flow into the core had been possible. However, the HPI occurred nearly one-half hour later, and in all likelihood this was adequate time to allow, again, downcomer deplacion. The value of gV (o) was, therefore, taken equal to the lower plenum volume (divided by four to account for the four cold legs). The effect of any larger initial fluid volume would have been to decrease, somewhat, the cooldown race.

The initial temperature of the downcomer structures is also un-certain. The water diaplaced, by the "B" pumps, from the cold leg pip-ing (loop seal volumes principally) had been stagnant for a consider-able length of time and it could have cooled somewhat from its normal operating temperature of -530'F. We ignore this effect and take all structures (core barral, thermal shield, vessel wall) as well as the fluid within v fto be initially at $30*F. In addition, a parametric calculation was run assuming a core barrel temperature of 1,000*F to t

l re flec t , approximately, consistency with the highly degraded core con-2 ditions at that time.

The results are shown in Figures 16 to 19. The sensitivity to parameter 3 is seen to be rather small. The effect of the overheated core barrel is also seen to be small. For the maximum duration of high pressure injection quoted [7], temperatures of -200*F are being i

predicted. The breaks in the curves are due to the discreciaation of 4

the structural heat input. They are useful in indicating the time-wise progression of the water level in the downcomer. In particular the last break, which has been marked in the Figures, indicates the time l

] that the downcomer is 100* full.

4 CONCLUSIONS If the high pressure safety injection that was initiated at -200 minutes took place for -15 minutes at 15 kg/s, the TMI-2 vessel wall temperatures reached levels below 200*F. The principal factor in this cenclusion f.s degradation of heat transfer due to the presence of non-condensibles (hydrogen, fission product gases). A mechanism leading to 4

accumulation of noncondensibles within the TMI-2 cold legs has been described and indicates that the above conclusion would be true even t

if the noncondensible concentration in the upper plenum area was rather low. Furthermore the HPI water is predicted to have entered the empty downcomer at -60'T and a mechanism for direct contact of a por-tion of this flow with the reactor vessel vall has been identified.

Thus, restricted areas of the vessel wall could have rasched tempera-

! rures close to 60 *F. These results have been obtained through the 1

s . .

i .

judigious use of available knowledge and a broad range of parametric evaluations attempting to cover uncertainties. Still, several areas, 4

particula-ly of an experimental nature, which have been identified for further study must be addressed before these results can be considered final.

7 t

.s ACKNOWI.EDCMENTS This work was performed under NRC Grant No. NRC-03-003 under the supervision of Mr. J. Reyes. The continuing encouragenent of Dr. N.

Cuber and Dr. D. Ross also is gratefully acknowledged. The author is indebted to Mr. K. Iyer for helping with the numerical calculations.

We also appreciate the cooperation of Des. S. Behling and B. Tollman (EG&G) in supplying information and documents relevant to the TMI-2 i

accident scenario.

i REFERENCES

!. PTS Rule, USNRC.

i

2. Reyes, J.,

i Ltr. to T.C. Theofanous

Subject:

HPI Mixing in Steam,

, February 25, 1985.

3. B&W owner's Group Report on TMI-2 PTS.

4. Theofanous, T.G. , Ltr. to J. Reyes on "TMI-2 Downcomer Tempera-

. tures with HPI," April I, 1985.

$. Iyer, K. and T.G. Theofanous, " Decay of Buoyancy Driven Strati-fled Layers with Appilcations to PTS: Reactor P*edictions,"

Proceedings of National Heat Trans fer Conference of 1985 held in Denver, Colorado, August 4-7, 1985.

6. Theofanous, T.G. and M.K. Fauske, "The Ef fects of Noncondensibles on the Race of Sodium vapor Condensation from a Single-Rising MCDA Bubble," Nuclear Technology, 19, 132 (1973).

7. Sehling, S.R., " Computer Code Calculations on the T:iI-2 Accident:

Initial and Boundary Conditions," EGG-TMI-6859, May 1985.

8. Tollman, 3., " Thermal Hydraulic Features of the IMI Accident,"

Draft EC&G Report, June 1985.

I j 9. Behling, S. EG4G, Private Communication, August 9, 1985.

l

10. Skillman, G., Metropolitan Edison Co, Private Communication.

August 4, 1985.

1 0

,. - , - - - - --- -- , - +- , , -

,m. .

. - - . . . _ _ . . -_- . . - . . _ . . _ . _ . .. - _ = ~ ~ .

t 6 ,

t 1

f Table 1 j Geometric Configuration OCONEE 1

1 j Injector diameter: 0.177 f t 2

1 4

l Cold Vessel / I. owe r 1.oop Core Thersaal

, t.e g Downcomer Plenum rump Seal Barrel Shield  ;

i Inner Diameter 2.33 14.22 14.22 --- --- --- ---

l (ft) i 1

1.ength (ft) 24.5 18.6 --- --- ---

18.6 16.0 Base Hetal l

< Wall thickness 0.21* 0.703 0.36* --- ---

0.19* 0.167 (ft) -

i.,

Clad Thickness O.0 l* 0.016 0.016 --- --- --- ---

., (ft) I Insulation Thickness 0.30 0.30 0.30 --- --- --- ---

(tt) i l Wall lleat Tr.

Area to Water 0 179.3 208.I 69.2 --- ---

176.8 311.7**

I (ft 2)

.) Internal Structures:

l Ileat Tr. Area (ft 3) --- --- --- --- --- --- ---

Tleichne s s (ft) --- --- --- --- ---

$ F1uid Volune" 104.5 169.9 153.3 --- --- --

! ( f t *)

j

• Assumed

} ** Both sides j o Per cold leg 1

UENT UALUE HPI (Ti)

/

=o, STEAM CONDENSATION /

_ b_ h h_ h b h-

~.

hb- '

(\ e T

El Figura 1. OG Evaluation Model E HPI s

n --

Figure 2. Flow Regime at the' Injection Point

l 1

l L >

6 ,(t),i at w.,

[(t) U'4 N )

4 => . c '

B gggg 3

< g 3g _-g g_ , --

v Te(t) #,

g

--* gd:g 4 ,

et4 Ti Figure 3. Transient Condensation Model X.. t

_s _/ 1 4 9' ) / _A S / _/ J l l -

%t a- -

T )-( 1 - xu.) P , T * -( 1-x;, )Py

- \- _ . ,

,,,,// .,u- is //////

T,[z,t)

T Figure 4. Mechanism of condensation in the presence of noncondensibles.

a ..m

- L w. _.. _, - . - > s_a-- , __. . _ - ~ .aw-a w ,.,oauw a 8 9 O

C.

l I l $ i j b 4 l

' i

. o O

v1 1

O N C. U h

- 3 W1 8

.Jlt C O C. w C g C

• 4 u_ -

n C Z c 10 b,j - o ~I L

, D- a LL.J C E E z - _

r o

.e3 C M C. L to .e3 C

' D O

E

^

O e u o

E D

I:13

' 0

"" _ b

• t3 3

i - O =

o.

m .

LO D

6 3

e M i i I I I I I I C.

l O 6

c c O O O O

_ c 2HX

_ sa M _.mm._,.R+J __.AhI_ 4 a -o__. .=_ w A_a-. _ '

_.,_..J. 4m,.--,- A. - . . + .,A , .-.

• A m - -

9 e I

C C.

O h l l 1 -

i "t j C

. I -=

I i

C i O

• e b

- 0 0

W j u e

1 - o. m O ] C

~

.2 I .

l u_ _

, s I

Z C,i -

cz c a a

O r e w w U 4 (j-) I a

- a b

.oa C

e e a M

h L ,

C

-e e

i C* o2 C --

M C

S

_ m E

O C O C

. N

• W 8

6 3

c E I  : e . . -

, , o

• I -

6

' o Q =

- C C C C C. , 9 o e e C

C C E d o' (S/S)4110GW

, - ' , , - = .-cw---- e m . ~ r-w.-iw

• T--+- --'T-------*e'-

+ - *a== "

• 6- ~m-e-,- aA- -- L 4m e s- -r---Wa------*<.- '

--.dLA* *kL---A'lL1J3 A+- - - - = ^--- -k 44W,-r. bk k4 u -s -AA-----a 4

O

> C.

h j h

4 C

C*

~

l S

i g

a e O E N "

o. u l - S i

e M

_ - * =G l

C C

. - ." C. *=.

! C

~

.e.3 I

• l -

M

)

1

- a 1

cC *2 M O "* O cE g -

L tu e E -

H _

O l H- u M

1

~

C 0 i ~

cc i

G 6

- 3

.es R

C b 1

o G E

O 1

o 2 C

f .

! b

'l -

O 4

- k I 3 I

C ,M l t f i '

i l 9 s

O 6

i

c. O. O. O. O. O.

O O C C C C C O O C C v3 = (T) Cu -*

l .O ) c'W A l.

i

-.ew+, e e,,-- ,

.-.n. - - u-,w,r., _ ---,. --,- .e~-m - .-- - - - - , .r--- t-m-r ,,ew - e -

w, m. - , ,-

e e C

I C*

1 i j I O

e 1  : C O

O.

.4 t

a w

! o 3 i O*

, to .+3 C. =. N. LT). N e CCCC M

~

o >- S 4

m&S3S9Si H ~

==

X X X X

- tn i

> c u

F- c d d N fl f

g

! D -

- Z Q tu -

u fD ,

g g 4 ,.

y C ~ A O" C- E O - - .e3 p-c -

g 1

O () g '

LD .4 2

~

C  %- el

, - Z -

~

c L 1 H 4 I ld Q b

>- _.,j C. 4 C j.

c (M G N Z b +

s -

O v (\j 3

3 k) l ~ -

.e8 =e i,

~

ML i c -

, A .ea c 33 D a Z l -

A3 p._ _

24 il ak I b8 c- _ _ &

5 CL 3

- g

• x es

) -

a GB O

-e b 3

- CD e i i _ __ - - sg i

C. 6 i

C. C. C.

t C O. O.

O O C O.

3 C C O

.a  : .m  :

. ~

, . m-- , ,, - -

s 4 m ,e #1 m

. _ _ . . _ _ . _ . . . ~ . - _. . . _ _ _ . _ _ __ . ,. . - _ . . _ . _ _ . . _ . - - _ _ . _ , , _ . . _ _ . , . _ , _ _ - .

C o

l t

6 a a a t i a a i d

l i o i

I -

c. .

l -

"s bc

, Oc C C Ln

l. c * *) w l\ a. a p' 97 O  ; - a g OOO  ! MW LLL eo J u 6 5 E E" e tln e RRR C -c C. O c

t3 w

-4

-f M '*l O2 U "U

- c z 4L

> a a ta U W c v D o

~

C 4 *C c

a ec

- w MO ew n m -

z .a s.

CL-- LL! 9 bO p

w .

~

w

. aa l e U +

(L w I D 'ts ^

_J '. bCU N c-- i 30*

g --

+ .*3 UL r X 8 d a kwC a -

o OOE

_ . v -

• E e a Q I E 3%

_ D .e3 m gi HC&

_ - w et b

l -

g y

- 1eM C C  ::c :> -

F -

o.

N m

O n n - b 3

I:n i #

• i

• i i c. L i

1 1

C. C. C. C. C. C. i C C C C C C C C C C C  :- (O Cu -

(i S20) EMniSE3dW21

\

[ HEAT STRUCTURES l . .. N

/ \

, \

3

( s -

/

j I

/

.- e -  !

A CORE UESSEL

/ \ BARREL UALL 80* F THERMAL c6 SHIELD T T ' : : '.'~ ill-M)Q ~

to build up level

,v - -

s *m d% .%-

+ - ~

,U p (t) . ^

- ~

~ s ~

j , ,

. , ~ ~ . ~

- s,"

l Figure 10. Cooldown Model 1

_m if//

h

- -FILM ON CORE BARREL [{

Yfa

, , I 3 l

s.

Figure 11. Flow Regime at 1/2-Scale and 1.2 kg/s

% 30cs- ~~+

7// ///// _ _,12. 7cz top view of clip 7 g 7cm I 100cm / / ~I 15.24cm L - SPLASH OFF A / /

N '

CLIP clip D 2'

+. -5.08cm f

core '

-barret ~

dthermal shield I

side view Figure 12. Mechanism for Figure 13. Representation of contact with vessel wall. clip position and geometry.

! COLD LEG VESSEL UALL l 31, *2', *3, or 34 1 . _ _ _ _ _ _ . _ _ _ _ _ -

(

r  :

$4 or $14 l$3or$13 i L

L CORE BARREL OR

• 7 or *17 $6 or *16 1 1 CORE BARREL SCALE 10cm l Figure 14. Top view of clips in relation to cold legs and i downcomer. ( clip *1 is under hot leg )

FALLING THERMAL FILM / 7 VESSEL SHIELD / UALL

/l ;

/l.

/

,i

/

CORE / i /

BARREL '/ /

/

/1/ _

/

/

MIXING /' /%// UELL MIXED /

\ / /  % '

/ / '

46 ( -

Figure 15'. The most benign mixing mechanism as HPI film enters volume Uc.

=

h

. ..- r w _,

h a

, 2 LA.

2 o

~ ~

C

= Ln

, :I, 1 3

\

.; i 4 C

\

i -l < l t=

i

! 7 L

- - _ C O

i f l

- -=~ = .~ N. r t.C ef o

a w l

w c

=, = .

I.. i e

, a s a u=~

I I ,I e -

l &

, e eer r 1 C

l

--. ---  !) h l s

n Q

=

-  ;=-.=s_ = = ., I i 1

'l 1 - -

8'l

- = g

, ; , 3 c

m. r 7;

i.  !

L i .

4

)

i_ , ~*

i

; , , e i

t

,' 1 - , 6 4

. , j 3

't

)

.J,.

a i

- .I![ l ,,

5 ~

tti

f ,'i/ lI s -

l ,

, m. . . ,

i

;

= 0

,i t l

< - i 4- c,

- .i*  ; - - -

E I.

t i i - I n

-  ;[j U l

t L i #'

/ f / -

! c .e2 l

== ',!' / j ~ -

--- >i .l

/

j/ '-

3 T

i .. .f , / . m -.

l n j

• P p l-ll { m

(

-  ?// i;;/ / / L l -

w

/

/ f -

!ll 4 m 1 j r

~-

s t

n

- .I, a,

• I /j //

a

~~~

l . O

,m e

'l'1 /ja / '

E

'~

i

- i' O l

i

//// / l U

]'

/#/'/ -

I C

3

, ./<//

o b y. l C3

,; v

0

( .. f  ; e

, f

• W

%J Q l - -

I H , o s L 1

3 1 t:0 l

C, .

4 l t t I a 1

Q c.

N

=. c. e. c. 0 N

C C C C C C

• n  :- m N ~

( e ^ . la, j 3 a. s.a.,

ge[ im ge n y -

k m ] e %.d m %em Ws. 'his .W i

im I

I l

l l

c

- i t

C

.. , 5 i C l ',I^'I fI t = Lt.

a k

I E l: &

' l S

% {. w

{.

w

- !J l' ll

. +

l Q jbl

.")

) -

e

a tI, t-u  ; -

{ [fj . L

- = o

), O. C . OJ. r. c. .;! ,;;

f j- 4 6

, c.. c,, o,, o., c,, =.i l l n ---- g

- SS5f2g l .j p l  :: ~ : : : L

/fi I l

c

! aa .

! 5 5 cs c c 5' lll l l

, c U

i- o'yll l

.\  :

• 1

.' ll l

• I ~' '= c M *: "I *1 m t l1l5 j *: 10

. :l I

' j! l I s

I -

a

']

l l

,, o L  %

I!I:/ l l - , . .

I 7 -

g" r i C / jl tn c ~

a j/ -Z t

E 80 a L

~ e ,l/ ' t 2 l- 5: e a

/'l ,/ '

ii ~ ~

{ ~

f- 1 E

i -

. w O._ l 0 6' --

il / C ( O, *'

- 2 el . . . .

i .. ,/,,/

i' 2

e -i, 5 m e

rn .il 3

g /// ,

- -, [ _ 1 -

l/// '/

3

~ / ~

• a llll; ~ '

' ,e,  ; ,  %

/

, . U

,' a / / JC I

_ / IE o u

/! ~

= /.

5  : .

u

' l

• 6'

/- JB -

c-e

/

l I L

5

, C c)

, i , , i .

i i

-e g

a. o. a. o.

M #'mh M M

a. =.

m C C C C m

(D .O r m C C ca -

i , ang gn,.33. ,,3 -

2 COU) "Li l.CCCCn O I '

9 9 1

1 J

l C

l $ g I

, t 4

• WTD.

l

.;!},l I ,

, u.

f Q

I \ l C p

r i l

) l n

,'ll q; q

i H

o

n j j i e

L ll , , i IC= s.

2-4

• o m:c  :

1 '

%e Oi C.ccc i -re=

• i i

i is 4

_ scc er -

s r

{

J t

3 I

a O

" - $ ( "Y P

,'t ,h 1

i

- W

l q 1.f I l J. x~* ~_

C n

.u m; y*. w ~

b i

i l'll

,f>

5

. It -

C l'

z s.

> c - C

$ . E i * -

- to W I x L k

T C

uJ Z

C A

II , A - G

-~

6

- l H C

<> 4 O w \

O 2 - **"*

C

/

/ =, -

m

,, r ,/ . - ,

ws n :r D i N -# ' '

a

/

C.O i

/ "  %.

E l '/ --

L C .' '/ / /

~

~

C, D

3

z /

l- UO g #

~ o U

\ T h.99)',Y i C_

- /

o i

y

~

C3 C ' C~

L. 7-' C -

- CO l Cd w

- I O J b D

D i t I f '  %

I I k

C. O. O. C. O. O.

O Cma C t.C .n C C C m N ~

m-( s

~\ e. .s ~

.,nm

( 2 U 2(=d) O w.! 1 C d a d rN C

Appendix A Hvdrogen Absorption y the HPI The mass flux of hydrogen into the turbulent HPI stream may be estimated from [A.I3 0"'

In

• C M (A 1) il, A )

where D is the molecular diffusivity of hydrogen in water, u' and A are the velocity and length scales of the turbulence energy-containing eddies, C is the solubility of hydrogen in water, and M is the =olecu-lar weight of hydrogen.

The diffusivity, D, in 20*C water is given [A.2] as 5 x 10 -5 cm /s. For any other temperature, I, the diffusivity may be obtained by

,. U j D' = 0O I o

2

! (A.2) 1 where ; is the viscosity of water at T. For example at 160*C the i

viscosity is 0. !74 cp [A.3] and D - 4.2 x 10 ~ cm 2/s .

The solubility may be related to the partial pressure of hydro-l t

gen, Pg , through Henry's law by p

i i x=

1 t

K (A.3)

!* For 100*C water the Henry's law constant K is given [A.3} as K = 5.73 x 107 anHg. At a hydrogen partial pressure of I bar we can

thus calculate an equilibrium hydrogen mole fraction of 1.32 x 10- s, For a partial pressure of ~100 bar (assuming a high value of xg) we have x . - 1. 32 x 10 - 3, which corresponds roughly to C - 7.3 x 10-3 g-3 moles H /cm H ,0.

9 The turbulence length and velocity scales are chosen as S cm and 30 cm/s respectively (see Appendix C) .

'4ith the above esti=stes Equation (A.1) yields

$=5.76x 10-' g/cm

/s. The exposed area within the cold leg is of the order of I m . 2Thus a hydrogen mass of ~3.5 g could be absorbed

! per minute, or -52 g for the 15 minute duration of the high pressure injection. On the other hand, a steam volume of 3.5 m 3 at 105 bar at hydrogen mole fractions of 0. 2 and 0.4 would contain -3,200 and

~6,400 g respectively. Clearly the dissolution of H into the water cannot provide an effective mechanism for countering the hydrogen e

3 accumulation caused by condensation.

References i

i A.1 Theofanous, T.G. et al. , " Turbulent Mass Transfer at Free Gas-1 Liquid Interfaces, with Applications to Open-Channel, Bubble and Jet Flows," Inc. J. Heat Mass Trans fer, Vol. H, pp. 613-614 (1976).

A.2 Kreich F. , Principles of Heat Transfen Int. Texthcok Co. 1966.

A.3 Handbook o,f,f Chemistry and Physics, 47th Edition, Chemical Rubber Publishing Co. , Cleveland, Chio ( 1961) .

i

,i

, t Appendix B r I Degradation of Condensation Rates Due to Noncondensibles 1

j No directly applicable experimental data could be located in this j area. Our approach is, therefore, based on cautious utilization of

! available data, in low pressure steam / air systems.

6 First, let us consider how the binary diffusivity in the hydrogen / steam system compares with that of the air / steam system. At l Icw pressures the diffusivity may be related to the critical pres-l sures, temperatures and molecular weights of the components [3.13

,/,

8 3 = 3.64 x 10-

' )2*334P )I/8(T T . -

j P9 12

/Tg f (P I #I #I #2 )8/lf1 s% +1l yj a

(3.1) oo 2 u - 4.91 atm em /s. This value may be con-i At 533*K this yields P D i

4 .

verted to high pressure using the critical properties of the 'nixture P'=Ix c

P and T' = E x T c

, 3 j ej j j cj and a graphical representation of the ratio e

l PD , g- ,

i pa pa <

l given by Bird et al. [B.13. For example for x = 0. I we have ,

i t i

T' = 585.3 *K and P' = 197.3 bar. Thus K = 0.6 and with the previously i

.' obtained value of P CD0 we obtain, for P = 102 bar, f 0 - 2.9 x 10 ~* cm2/s. At 373 K the same procedure yields i

! D - 1 x 10 -2 c, 2/s. Very similar results are obtained also for x1 = 0.2. At the other extreme of xg = 0.8 we have T' = 155.S*K, I P' = 54 bar, and K - 1. Thus the 0 - 4.8 x 10-2 c, 2/s and 2 x 10 -2 c, 2/s values are obtained for the high and low temperature l

I  ;

cases respectively. These values are to be contrasted with a value of

D - 0.239 es /s for an S*C air / steam system and a value of 2 = 0.634 cs /s for the hydrogen / air system st0*C and I bar. At 100 *C the above values are =ultiplied by a factor of x2. It is clear there-fore that the high pressure steam / hydrogen system (present applica-tion) would give rise to considerably higher diffusional resistance to l

4 condensation than the low pressure steam / air systems which havebeen previously studied experimentally.

Stein et al. [3.23 carried out experiments of steam condensation in the presence of air. Condensation took place in the underside of a

<, horizontal cooled copper place, at system pressures of 3.1, 6.2 and

]

12.4 bar. 'Je have correlated these data in the manner shown in Figure B. I. An exponential decay with x f = 0.05 is indicated. This is con-sistent with much older data obtained in vertical condensing place geometries [3.3].

4 On the other hand, Stein et al. [3.2] have argued that natural convection effects were important in mitigating some of the d

condensation inhibition effects of the noncondensibles. If this were

, true in the air / steam system it would be even more important in the hydrogen / steam system. Unfortunately, the information available does not allow the reliable evaluation of such effects, which are therefore left outside the scope of the present study.

In an effort to cover such uncertainties the slower exponential decays with x. = 0.1 and 0.2, as shown in Figure B. ! were also con-i i

1

-. -- . - - ,- . ,- n - _- . ,-- - - - - - - -

sidered in the parametric evaluations. Further= ore, if natural convec-tion effects are i=portant their onset should take place at low enough condensation rates where the suction due to condensation is somewhat diminished. Indeed the deviation seen in the data at q/q - 0.I say be due to this type of behavior. To cover this possibility and ack-newledging the absence of data for q/q - 0.1 ve have also carried out additional parametric calculations whereby for x, > 1x, = x the q/q .

o decay is specified to linearly approach zero at xt = 1. Except for using x , = 0.3 or 0.4 all other parameters were fixed at the base case values. The condensation transient for this kind of behavior is shown in Figures 3.2 to 3.7. Again a rapid shut-off of condensation is observed, although in this case the hydrogen mole fraction continues to increase approaching values close to unity.

In summary, unless strong natural convection effects due to the rather icw density of hydrogen compared to that of steam become effec-tive to stir up the diffusion inert gas boundary layer in the vicinity of the condensing interface, the choice of an exponential decay with x ~

0.1 should not be particularly overrestrictive.

Re ferences 3.1 Sird R. et al., Transport Phenomena, Wiley Publishing Co. 1961.

B.2 Stein, R.P. et al., " Condensation on the Underside of a Horizon-tal Surface in a Closed Vessel," HTD-Vol. 47, ASME 1985.

3.3 Langen, E., Forschung a.d. Geb. d. Ingenieurwes, 2:359 (1931).

l l

B 1.0 i

$\

0.3 --

Data of Stein, et al. (B2)

• 3.1 bar,A 6.2 bar,a12.4 bar A

Exponential decag functions:

9/q, 0.6 -

x ,,2 = 0.05

. x,,,= 0.10 x.,,= 0 . 2 0 ,

0.4 -

\

m A

i

• 0.2 ..

l e 1

e.0 i . . ,

0.0 e.1 0.2 93 0.4 AIR MOLE FRACTION Figure B.1 Correlation of the Stein, et al. data in terms of mole traction of noncondensibles.

5 e n ,

T

'I 45 w -

t 2

1

- 1 I i t  !

N .

. { ~

6. -

s

{ -

~ -

c:

- l ,

I

% r i 1 -

i l

t i

\

' 2

, . , a -

A U_ i \. ~  ;

l \  ;

C u \ l r-i

%w ~

w

\ u r

A l

\4

[

~^

& l I- ' >. l q P

• , "y i I M

~.-

y ,

)s . -

c I

t s }- !O

! C

? .-m C .

L i

\ .

J

~

IL C m - C 5 , _.

%d 4

W m

~

, t C.

ca O

N

\

W e

O t i t i i '

e t C, C C C

=

~

C C C C 6 C C C C C. C. OJ.

ease C.

meeP l

• bis \

O

• e m-

9 F L_

~

9 ,

m al

'e

~

A le *s h

w .

g - M J

~

~ - ,,l l

a

=

o

-g

)

,e L -

.s ,i f i s -

(- , -*

% =

1 l, "

k s - L-N 1.

m e -

% i =b

.- W-m .

le l ,

," Z

.- r to =

L QJ w ~

\ l *

. t l 6 l t -

k i  :

x

, lI .",

l c  !

%s y D l

% I i c 4 __ '

L _

e

.9 E

O .-

\ ' -

=

l _ .

, 4 and w ,

i i i '

i ,

O C c

C C C

. . . . =. 5 (2/SM!iCGA'

1. 9 w'

l $

l, ,

i t r 4 h

I  ! n

- I i C.

~

i i  !

l l I

. l l O i i 1 -

I I A- l- 1 9 d

sN

~

le e

""% -e l

. - i 9

0 c 9 -

l j

<* C 4

- c_.  ;

t y *

[

l

• ~

b Id f W C- F-- -

Z I _

C 4 o

_ , v *

- D 1 b-i .

D l

% l r q i C n e e

e.m r

w 4

h C. -

C.

% a L

@. ~

r i i i .

a.

• g ,

iL e 8 $ $ i d

• o = m m =

l

(,), e l

W 9 I i -

. l~ l 1

s ls l8.:

n' -

N ~

9 CJ

'4 h .

\ '

i s 1  :

I g ~

d

( (J . .

7 C

$ C e c-Lu _

C. W-:-

.O O W

T 4 X -

N>'

- 7-e -

l- l 3

- ,4

\ -

O k l l ..

% w i l

y 7%.

• "a.

n O

- C*

L ,

N -

y i i f I i O

e i C, C C C C C C.

4 m a r.  ; e 2HX l

l I

I I

4 9 C

i l s t i , -2 t

i LJ N - C A  ! - .

u -

M _

i o

• L- a

• N C_J S

9 O -

.h f

,n ~

e l c_

- il I+

N _

z . - .

s Z e Z D E -

0 o.?_

ss H h G,s - l c

k c i l

\ l bl H ll' =

Hi Q -

a q -

o C*

4 - _

b

. N z -

C k c

~ c

~

05 9 .

g -

@ i i i , i i d i 5 k:>

=

c'

=

C. C. C. O. O. C.

e  %

o

[C wA w / A\ ' J' .1 U I' W

1. 9

?o

'ses'

$ Q l

! i

)

- I l l .-

[ . r -g

-  ! i 9 l . r I -

s C-oy -

is ca 4

h -

M Q ~ 5

• si -

~

i j

e i 1 -

7

% = C

=

I v h I

-< s-

• w

\ lt l

~

m [=e

~

\ -

C H-C

4. -

=.

f N

I

• w l- l _

M  !

l l

s I l5" I

t ~ .

k, I e Q OJ C. -

~ -

C I i ' '

, O N - C Q e. e. e. a. "

9

- 9 9 u

o a a e'

'O

.~- n N a

% , i m

A Appendix C The Heat Transfer Coefficient in the Absence of Noncondensibles i

In the absence of noncondensibles heat transfer is conqrolled by the turbulence in the liquid stream. A formulation developed for mass absorption by Theofanous et al. [C.1] about 10 years ago was found also appropriate for condensation by the experimental work of Bankoff j

[C.2] and Thomas [C.3]. For heat trans fer, using Pr - 1, the equations

! are St = 0.25 Re" c I" for Re c > 500 (C.1)

$t for Re < 500 (C.2)

=C.70Re{ll The turbulence Stanton and Reynolds numbers are given by:

h I = "

St: u, o c and Re =

(C.3) t V i

The u' and A, also called integral velocity and length scales have

)t been related to the mean flow velocity, U, and hydraulic diameter. D, I

in a couple of different ways. Theofanous et al. [C. l] used the rela-

}

tions known to apply for pipe flow: u' - 0.05 U and A - 0.03 D . Bank-h 4

off [C.2] suggested that for stratified flow of depth 6: u ' = 0.3 U and A - 6.

)

Assuming open channel critical flow at the cold leg exit (Fr - 1) we can estimate a liquid depth 6 - 8 cm and a velocity U - I m/s. With the Theofanous et al. choices for u' and A and for 100*C vater z

(v = 0.0029 en /s) we obtain Ret - 826, the choice of Bankoff yielding i

even higher values. Thus, the regime of Equation (C.1) is applicable.

We will first show that both choices for u' and A lead to very similar 1

results.

i

-,,w., -

,,.w. .,, , , - . , - ., - ,.- - - .. --,_ -- -... .

1 We can define a mean flow Stanton number by J

h o - N h UpC Re Pr Re ( *

'l and in combination with Equations (C.I) and (C.3) we obtain j St = St c U = Or.25 tRe-l'"' U (C.5) or

?

a y! / 'u'3 / "

4 /

h = 0.25 p C (C.6)

C

! ,gt/s l

I

- T l Denoting by h, and h,3 the heat transfer coefficients based on the 1

Theofanous and 3ankoff choices of turbulence parameters respectively 4 we have:

hj -

5

' 100 ' I!'

B 30 3

= 0.62 (C.D i h - ' - -

o I

That is a difference between the two predictions of only 38%.

Using Re g = 826 in Equations (C.I) and (C.2) we obtain St - 4.66 t

x 10 -2 and 2.43 x 10-2 respectively. Let us choose the value Stg-3x 10 ~*. In combination with Equation (C.5) we obtain St - 1.5 x 10 - 3

) '

i

T r

which utilized in Equation (C.4) finally yields h , - I,004 f

BTU /hr ft2.F. ,The Bankoff prediction would then be I h - 1,620 STU/hr ft **F. An in-between value of h, - 1,300 BTU /hr ft2.F will be considered as a best estimate.

j These predictions should be viewed, however, with a certain degree of reservation. The reason is that the limited experimental j data available in this area were obtained at icw pressures. The con-4

cern is that at the high pressures, high subcoolings and high heat i

i e

r-- , - - , , - +v. -- >-we w-ve- ,m - , - - , , , , _g n-- - - - - - - - - - - - - - - - - - - , , - - ------,----.,.,--,-w,-n. - , , , , , , - + - - , , - ,

. _- . _ _ . _ . . . - _ = . _ . _ . - . . .. --

~

fluxes of interest here the condensate fluid may be difficult to dis-sipate by turbulent mixing, yielding stratification and hence a signi-i ficant reduction of the heat transfer coefficients from the values predicted above.

References C.1 Theofanous, T.G. et al. , " Turbulent Mass Trans fer at Free, Gas-

., Liquid Interfaces, with Applications to Open-Channel, Bubble and Jet Flows," Inc. J. Heat Mass Transfer Vol. 19, pp. 613-624 4

(1976).

C.2 Lee, L.,

R. Jensen, S.G. Bankoff, M.C. Yuen and R.S. Zankin, 1

] " Local Condensation Races in Cocurrent Steam-Water Flow," in

.I Non-equilibrium Interfacial Transient Processes, Ed. J.C. Chen and S.G. Bankoff, ASME 1979.

C.3 Thomas, R.M.,

! " Condensation of Steam on Water in Turbulent

• I Motion," Inc. J. Multiphase Flow Vol. 5, I-15 (1979).

1 I

i 4

i i l r

.1.1

Appendix D Parametric Results for the Condensation Transient Each case is represented by three figures, a, b, and c, depicting the hydrogen mole fraction, the condensation rate, and the HPI exit temperature, Tq , respectively. Each case is identified by the parame-ter value varied from the base case, All other parameters remaining the same.

Fig. I (a),(b),(c) x = 0.05 1/2 2 x = 0.20 t/2 3 = 0.05 x,.

4 0.10 x,1

=

5 x g, = 0.30 6

b, = 5,000 BTU /hr f t**F 7

h, = 50,000 BTU /hr ft2 *F "HPI

= 20 kg/s 9 P, = 2,000 psia 10 V = 2.5 m3

!! C =

! BTU /lb *F

-mm m

= e 1 1

1 C

C.

h h l h l euluul C

- C

_i w -

S L -

C

~ C

.O ~

C C .

CG _

LO 8-

_j O

er-I _

'r

_ 8 C

_ C C

C.

C 1 i f i I I f f i 9

C C

C C C C C C C C C C C:3  ::-. C C.

c. Cu. C.

C 2HX l - . - - . .

C i i O.

i i i i i i i e C

_ e

~d -

m _

M b =

, - o d

w -

~ _

Z -

O O _

C i

U_. _

E C -

C5 LLJ gr 1-- l 03 (f3 _

l r

< w C

_ e 5 -

I l

_ t I e

_  ! o g

C

_ i c.

m .

C

, i i i i . -

i C.

C c c c C C C C C C C O C,

d e e -

m o (S/SM)10GW

lf C

C.

k k h h C

C.

W 7

em a

C

. O.

^

N N

w _

w C k _

e M

gZ c_ _

c-r la.]

l L1 E 6 "

pa 8

m C

C.

m

~

C.

m h

m O

t t ' ' ' C-e 9 s

~

C C- O C H R O.

8 d a

e e

a e

c e

o o -

m ~ -

( J } dW3.l w

__. . . __ .-. . _ . ---- ,-, -_o.

C i i i i , ,

c.

e.

C

- =

~

%e. O o - o 6~ _

C C

o -

s G-e -

u_ -

uJ C=

ci a _

CE O

I _

E w

C

- C g

1 8

C

- C C

i i t I i i t i =

C C

C C g C g C 8 8 e. 9 8 m.

2HX 1

A. ~ -

n O

C, .

I 8 I i i e i i C m

as.

e

_ C*

• ~

N h

8

,W C\1 1

g -

c L -

duuu%

C,,

C. - C ,I-W .

C-W

(.O I 8

I O

C C

C g

t I t t '

i I s

O.

C 8 8 8 8 8 8 C C C =* Cu Q

~

(S/SM)100W r

1 e

h

+ e.

C C.

I i e i 6 e i e i CO eu, C

- . C*

C C.

Cu A ,,,.

D C C*

m O

~

U '

r

~

s

{ w._.

_ C, Y

{ _

C=w LLI r _

E C

- C*

O

- C*

4 O

C g

C

! I t '

s t i  !

O C

C. C. C. C. C. C.

C C C C C C C C C C it3  ::" C t in Cu -

(didW31 l

i

% S C

C. l 8 i i a i e , , , e ,

man m

C

- C m

G C N -

C.

• g a -

e O

C C O_

N C .Z -.

cE I

i r _

n 8

g 1

- 8 h

C

- C a

4 f f f I f '  ! I i < 9 C

C C g C a.

M 8 $. 9 m. 8 2HX 1

4

• -._4...

. - . _ _ _ .=

9 9 C

1 C.

e C

- C t -

P q =

b .

N 8

g T ~

-i -

Z o -

S

__I LL _

O C _

Lu _.

1-- *[Ir 03 _

~

w

- 8

-. g 1

C g

O

- C a

i e

C 9 i t I t t t t .

C C C C C C C C, C. C. C* C*

C.

C C C T N C (S/SM110GW

9 e C

I 4 C.

1 1 1 4 1 6 C 1

C

- C*

W C

A - C M

d

\

M -

~~

W C

- C

(.a. -

d m

i C ,Z C- _

y _

Cz L'J.

t' ~"* _

W C

- C*

I C

- C*

b m

M f

i m

m 8

it f I I i i t t 1 8

C C. C. C. C. C. C.

C C C C C C C C C us .. CJ -

t, (didW31 E

.- 9

e .

1 i

C C

1 8 I I a i I l d W

C

- C

_J

~

. A ~

k C

T -

cu d -

8 o -

d C ~

i -

LL. -

biI. -

8.~Z

._j "'I C g C') W X -

E n

~

8 (C

8

=-

i 8

OJ f I I I I  !

• I 8 C

o 8 8 8

~

e. =. $. $.

C 2HX

• ,,g e .-

b -

I 4

a a O o O

l

- C*

I 3 I I i i j g I g met G.IS O

_ C*

4

~

O -. .

y k

o

~

..m -

Z 8 c3

.m g

_i

, t.

~

r= .

- A u . .

gr H tu

-(f) _

r 8

~

8 W

4 8

W l

m

! f f I +

9

, 9 8

C 8 8 8 8 8 8 s - - e a s (S/SM1100W i

l

• '*~= . .. L. .

l l

-. - . . ~ . -- , . . , . . . , - - - - . . _ - . _

C i , , . ,

C.

e_.

J C

_ e i

s C

- C l

n a.

t _

+ _

C 6 _

c.

ks _

C- 8.z i r e.

u_!

E

~

w

. - 8 g

8

_a 8

1 C

t i i

• I t I t o C

1< c. o. O. O. C. C.

o 8 8

=

9 m 8 8 o

~ -

l (3IdW31.

l w

- ,.,.m-- - , -

y- - ------,-w -------w v. y -

A e * ._L L>4 -m__ . , . _ . a .- - - - - - - - - -.---m- i_

6 e i

1 c

C '

I I 8 8 1 6 i g e m

i M

f C

C.

=

4 s L c O.

t

.

• W 4= -

b 8

U e

c -

K -

, L -

oz W -

CC r

_ @w O

y U

z

- 8 8

40 g

8 N

i

' C I

?  !  !  !  ! I 9

Q

1. .

8 8

. . . m. .

l 2HX 1

l l

l f

i I

O o

i i i , , , , , ,

d_

O C.

n -

\

L

• 8 m m 4

1

. k. -

z 8'

, o -

1 d

u- _

I cz C

ua

}--

xr

o. ~

tu cn _

5 9 -

o

! C.

1 t -

, 5 I

8 i i i , . . .

, 8 i

C

,^

8 8 8 8 8 8 -

b @ @ "

b C

! ~

. (S/SM)100W l

l I

i t

t <

l

e e o I g i 4 6 -

L I g i O.

C C.

mum aus.

s g .

e use

~

e I

gr c_

O__ _

t1!

E r d

o Q.

W mum 8

elu.

8 emu i '

8 I l I d

C- C.

a e e. c. e c g b -

( 5 }dNd i t

L

1

. e l

-1 8

i i i , . i , i , d M

W m .

C.

?

d C

w -

o.

~ cu gy ,

P -

C O

] U -

d g

i g, _

A LL.) c *2 -*

_]

~ c.m I c

CD tu 4 -

r 1--

_ 8 i

_5 i

1 1

t 4 $

8 f

! t l I l f l f . ,

C 7

C

2HX l

l I

l 0 O E l I

O 4

Q.

e_

0.

1 2 -

C

_ C.

=.

M I !o i

C.

,* ~

.a i

i A I

Z - i 8 o,

c i

u_ _ r 1 r t y

C. - _

8.z

= _x w w z

U3 _ -

8

=

e v.

8 m

. 8 c

- 8 8 8 8 8 8 a

l (S/9M)100W 9

l

• *pg yw , - _ r-, . - . - . y- _ - -c y ..,- ,y- --- y _ - , - _ . _ _ ,

--,, s___j

---9 ,.__.7 y y

- 4... __ _ _s- ._ _2 _._.__2_i.__. 4 m..4 ..u.. _.4 m __o__

e t 8

h h h I $ l 2

4 mIul 8

es.

- 8 -

a m

y -

.b .

• 8

@r g

M 4

1 n

4 -

Z

_ 8r C-W $

8 g

I k

1

! C

- C g

l

, 8 i

g

=

i , , , , , , , , 8 C

l C C. C. C. C. C.

! 8 S 8 8

= m ~ -

t ( J ' C'I J 'C In--

. - - - -..-. - ..--. ..- .- . - . - - ---- - - - - - - - - - - - - - - - --l :

A 4 -r- ,- +- z-- - u, - - 4 A I

O C.

k l l t

B.m C

C.

m b 54 C

O.

e

• 9 i

e -

, _ 8 b ~

C C ~

K -

g -

C U - Q".g

._,,) -

em O u.:

Z r 8

] c 8

- 8 1

i l "

O

! l  ! 8 '

!  !  ! O, O

r- .

eS C

2HX

- - --r - - - - ,- -

---

-- y - p . , , , -

,e-----r---

a a e

C*

$ 3 4 i g g I i i @

C C

- J, -

e i

• =d

& _ 8 m

a

, b _

2 8 g _

c -

u_ _ -

I -

C ez y _

e- 2

& ua G3 _ z

- 8

, i 8

8 a

, , , 8 e

8 8 8 8 8 i e e e -

8 l

. m e i

i (S/SM)10GW l

i i

_ fl

6 6 C

C 4 3 I i t i i i d._

C C

8 g .

A

! o 8

m

~

d

.I J

i

' 8Z

• z CZ

! LLJ F- -

e 8

g 8

(i

~ ~

8 N

I 1

, , , , 8 C

C. C. C C. C. C.

8 8 8 *

$ _- m -

( .J 3 dWB1 f

l I

f r

I t

i .

e .9 C

I e C.

6 s 4 a t t i C C

- C*

L 1 -

=

C

~

C.

, @ ~

N

~~

W C -

i C

- C*

C i ec - -

i U._ -

N g

8Z e _Z C

z -

E

- 8 i.

g s

8 i

j 8

N I I I f I  ! 1  !

8 .

C M

2HX t

a

- - - - - - - -- - ~ ' ~ '

a ~ a - w - n s e o

C.

l k l 4 -

I C

C a

~

e ~ ~

-4 b I e

! Qqr C 1

~

d

. W '

~

J z 8 o -

~

ci.

4 L:_ -

M 1-C 8z L,,j cI -

H I e - _

+

c3 C*

e C*

.e W

. 8 g

O i I e i * . 9 C, C

8 8 8 8 8 8 1

C CD C  :" N C (S/SM1100W l

i

. .av- Aw . m $ - _ - - __s n 1s- r- -.L- --,--..a S, -4 -p = a ut

_ -4 s I

8 0 0 h

6 6 t 8 4 -

6 C

C' M

8

' - m N

8

_ C e

i W N

gZ L _

c.x m E W U, r

~

w ,

8 m

i 8

m E 1

4  :

i e

" l I

8 5 m i,

~

), - i i.

8 f I j l 1 C C O c c c C,

~

> g 8 .

[ $ a -

[ .J } c'W .3. .l I c 1 e t

i

.. , 7

., --- - , .~.- . _ _ .,. , - - - ,... - , . _, . . , , _ , , - _ , _ _ _ _ , , , ,. _ _ _ .. . , . . , , _ , _ , _ . . , , _ _ , , _, .. __ , I

4___ , A ..__m ,---u--- -s _ . - - A 24-. _ . - - - _ _ - _ ..-J . , _ . . . .

O >

C C.

• h k h l l

- =.e I

C C

T

\@ 8 e _ -

cu I

4 i

8

~

o -

d Cd _ _

i

> gz .

i Lu _ _

• r .

i J l C E i I _ _

+

8 g

l 8 -

i --

l 1

t I

8 4

l 2

0 I f I t I i t I 8 ,

C

.t

~ C l, -

cHX l

l l

I l

. ~ . . - . . .-.- ._.- -.- .- - - , , _ - . , ,, ., - , . . - - , . , . . - , _ - - - - , _ . - , . ,-.

4 D.

3 8 1 i i i i i , , .

i. e_

1 4

i C  !

- C* -

4

_ 1

=

1

,t

.P -

N e -

, 8 e a t

, . L4. -

i i

2 8 i

g -

C 1 -

, .l u_ -

, I gz C

y ex .

W W z

l C - ~ i w

i '

1 i

1 - 8 l

}

t l

i 1

8 x

8

{

4 i.

1 i #

1 , . . .

, , , 8 l C

! 8 8 8 8 8 8 C

G3 @ 7 N O i

(S/SM1100W i .

i i .. - - . . - - . - - . - , . . _ _ t

-- - ,____ . . . ,.. -. - _ , . . - , , . . . . . , . - _ , , . _ , , . ,_.n- . _ , - - - ., . - - . , - . _ - . , - _ - - - , _ - - - , .

_ m- A e _ w c C.

l l h h m

W C*

M m.

M 8

m 4

C -

kC C _

L _

- 8r d

Z tu W -

I

l- - H 8

a a

} M ,

I I

8 -

3 1

amm e

8 m

l 4

m i

, , . , , , , 8 I C C C C O. .

2 d 8 8 4

% 8, 9 ~ -

( J } dW3 l.

s s.

O i i i o.

e a i i i C e

O

_ C" W -

Q -

C m

W 8

o -

~

d i

c-CC _

Il -

-7 L'] C~

__J _ C "r C "G r I -

i--

c

- C d

1 --e 5

7 1

4

~

8 N

e t t I i t i 8 8 C

7 en.gz . .

cHX f

.- . . . - - . - --, ~

,-, n, ,,

aA ^

C l

C.

l h umme e

O

- C

~

O C C

g w \ -

. I Z 8 O

J o -

i

-J 1  !

E i

C a * @t -

LL3 F- - [

I U3 -

~

w 8

g WM C

_, C-4m 8 -

. 8 C .

3 8 8 8 8 8 8

. h e (S/SM110GW i

l

C C.

4 1 e i i I e i i O C

C.

7 m

8 g

A

- Q C

• M -

8 C

Q_ C C "Z E _

C ~r LL.! u.i

& I

~

i--

8 g

4 C

C.

7 8

Cu C

f f I e ' s t C.

C C, C. C. C. C= C C c C C C C C C C C w o = m ~ -

(d)dW31 9

--ene+

• 4 O

i O.

e i i i i  ! 6 C 6

=

C

• O.

~

.="

A -

N

- - 8 u-C O

O O.,,,,

C k- -

LLJ J

8.z c _I O

Z -

E r

- 8 3

C

- C

+ C Q

g O

t i f 4 I I I l - O.

C C C C C C C C C C C G3

• C. us. .

c.1 C

I l ...

5. -

. . . . . e l

_ i l

=

- C a

n -

_I M

i

\%

O

~ l

_ C.

m

+ i -

. C. -

l l

2 I 8 a -

g

_i  !

~

u_ _

_i C

G-LJ c- E g tu U3 -

I w

- 8

- 8 C

C g

, , i i i . , i a C

c c c c C. 8 C. C. C.

C C.

O e e  :- a e (S/SM1.LOGW

o h -

8 i i i i i i i , , s-e e

- o -

C c.

m_

4 -

= c

• C*

w -

O L -

z e

I

- 8.x e_

LU W r

c c.

e 1 -

8

=

8 m

t

, , , 8 o

O. C. C. C. c. c.

l 8 e

8

= 5 8

~ 8_

C l

1

( d ) dW7. '.

1 1

(

l

.