ML20238E966

the Cooldown Aspects of the TMI-2 Accident

ML20238E966
Person / Time
Site:	Three Mile Island
Issue date:	08/31/1987
From:	Theofanous T CALIFORNIA, UNIV. OF, SANTA BARBARA, CA
To:	NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
References
CON-FIN-D-1634 NUREG-CR-4978, NUDOCS 8709150313
Download: ML20238E966 (63)

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-

NUREG/CR-4978 The Cooldown Aspects of the TMI-2 Accident

(

Prepared by T. G. Theofanous Department of Chemical and Nuclear Engineering University of California

. Prepared for U.S. Nuclear Regulatory Commission l

kD DOC $ 0320 P PDR

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i NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government rior any agency thereof, or any of their employees, makes any wa'ranty, expressed or implied, or assumes any legal liability of re- ,

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NUREG/CR-4978 R4 The Cooldown Aspects of the TMI-2 Accident Manuscript Completed: December 1986 Date Published: August 1987 Prepared by T. G Theofanous Department of Chemical and Nuclear Engineering University of California Santa Barbara, CA 93106 Prepared for Division of Reactor and Plant Systems Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555 NRC FIN D1634

ABSTRACT The cooldown of the TMI-2 reactor vessel due to high pressure injection that oc-curred at 200 minutes into the accident is re-examined. Flow regimes and condensation heat transfer in the cold legs and downcomer are considered. The presence of nonconden-sibles (hydrogen) and a mechanism leading to its accumulation around the condensation interfaces lead to conclusions that are materially different from those of a previous study that did not consider these effects.

I i

i

$i5

ACKNOWLEDGEMENTS This work was performed under NRC Grant No. NRC-03-003 under the supervision of Dr. J. Reyes. The continuing encouragement of Dr. N. Zuber and Dr. D. Itoss also is gratefully acknowledged. The author is indebted to Mr. K. Iyer for helping with the numerical calculations. We also appreciate the cooperation of Drs. S. Behling and B.

Tollman (EGkG) in supplying information and documents relevant te the TMI-2 accident scenario.

l l

V

TABLE OF CONTENTS Page ABSTRACT ................ . . . . . . . . . . . . . . . iii ACKNOWLEDGMENTS . ..... ................... v LIST OF FIG U RES . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix LIST OF TABLES . . . ................. . . . . . . xi N O M E N C L AT U RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1. INTRODUCTION . . ......................... 1

2. TIIE CONDENSATION TRANSIENT . . . . . . . . . . . . . . . 4 Formulation of the Analytical Model ................... 4 The Choice of Parameters for the TMI-2 Case . . . . . . . . . . . . . . . 9 Numerical Results and Discussion . ........... . . . . . . . 11

3. TIIE DOWNCOMER COOLDOWN TRANS1ENT . . . . . . . . . . . . 14 Direct Contact Mechanisms . ........... . . . . . . . . 15 A REMIX-Type Cooldown Analysis . . . . . . . . . . . . . . . . . . . 19 Choice of Parameters and Numerical Results . . . . . . . . . . . . . . . 21

4. CONCLUSIONS . . . .... ..... . . . . . . . . . . . 25 REFERENCES...... ..... ... . ... ... ... ... . . 26 Appendix A Ilydrogen Absorption in the IIPI . . . . . . . . . . . . . . . . A.1 Appendix B I)egradation of Condensation Rates Due to Noncondensibles . . . . B.1 Appendix C The IIcat Transfer Coefficient in the Absence of Noncondensibles . C.1 Appendix D Parametric Results for the Condensation Transient . . . . D.1 vii

LIST OF FIGURES Page Owner's Group evaluation model 2 Fig. 1 . . . . . . . . . . . . . . .

Flow regime at the injection point . 2 Fig. 2 . . . . . . . . . . . . . . . .

5 Fig. 3 Transient condensation model .. . . . . . . . . . . . . .

Mechanism of condensation in the presence of noncondensibles 7 Fig. 4 . . . . .

i Fig. 5 . Predicted hydrogen concentration transient for base case . . . . . . 12 Fig. 6 Predicted concentration rate transient for base case . . . . . . . . . 12 Fig. 7 HPI temperature at the cold leg exit for base case . . . . . . . . . . . 13 Fig. 8 HPI temperature transient at cold leg exit for a variety of inlet hydrogen concentrations (xgw parametric) . . . . . . . . . . 13 Fig. 9 HPI temperature transient at cold leg exit for a variety of condensation degradation assumptions I(I /2 parametric) . . . . . . 14 Fig.10 Flow regime at 1/2-scale and 1.2 kg/a . . . . . . . . . . . . . . 15 Fig.11 Mechanism for contact with vessel wall . . . . . . . . . . . . . . 16 l

Fig.12 Representation of clip position and geometry (all dimensions in cm) . . 17 Fig.13 Top view of clips in relation to cold legs and downcomer (clip # 1 is under hot leg) .......... . . . . . . 17 Fig.14 Full scale demonstration of the off clip splashing . . . . . . . . . . 18 Fig.15 Cooldown model .... .... 90 Downcomer fluid temperature transient = for base case 94 i

Fig.16 l Fig.17 Downcomer fluid temperature transients for Te = 60*F. . . . . . . . 24 Fig.18 Downcomer fluid temperature transients for Te = 70*F . . . . . . 25 Fig. B.1 Correlation of the Stein, et al. data [B.2) in terms of mole fraction of noncondensibics . . . . . . . . . . B.2 Fig. B.2 Hydrogen concentration transient, xi% = 0.3, xt = 2xi/2 . . . . B.3 Fig. B.3 Condensation rate transient, xim = 0.", rt = 2ry2 . . . . . B.4 Fig. B.4 IIPI temperature transient, xix = 0.3, xt = 2ri/2 . . . . . B4 Hydrogen concentration transient, xim = 0.4, xt = 2ry2 B.5 Fig. B.5 . .

Concentration rate transient, xix = 0.4, x1 = 2xt/2 B.5 Fig. B.6 . . .

ix

/

LIST OF FIGURES (Cont'd) page Fig. B.7 HPI temperature transient, x4x = 0.4, xt = 2xi/2 . . . . . . . . B.6 Fig. D.1 xi/2=0.05.......................... D.2

' Fig. D.2 r i / 2 = 0.2 0 . . . . . . . . . . . . . . . . . . . . . . . . . . D.3 Fig. D.3 z g = 0.0 5 . . . . . . . . . . . . . . . . . . . . . . . D.4 Fig. D.4 z g = 0 .10 . . . . . . . . . . . . . . . . . . . . . . . . . . D.5 .I Fig. D.5 zg=0.30........................... D.6 Fig. D.6 h o = 5, 000 BTU / hr 2f t

• F . . . . . . . . . . . . . . . . . . . . D.7

~

Fig. D.7 ho = 50,000 BTU /hr ft2 *F . . . . . . . . . . . . . . . . . . D.8 Fig. D.8 rhuri = 20 ky/s .................... . . . D.9 Fig. D.9 P = 2,000 paia ........................D.10 Fig. D.10 V = 2.5 m s , , ,,,,,,,,,,,,,,,,,,,,,,,,9,1)

Fig. D.11 c, = 1 BTU /lb*F . . . . . . . . . . . . . . . . . . . . . . . D.12

/

A 4

X

I i

i LIST OF TABLES 1 l

Table 1 Geometric Configuration of OCONEE , . . . . . . . . . . . . 22 l

l l

i 1

i Xi

NOMENCLATURE c concentration cp heat capacity C solubility d diameter D mass diffusivity (molecular) h heat transfer coefficient, or enthalpy K llenry's constant I width of liquid layer rit mass flow rate M molecular weight P pressure g heat flux heat flow rate Q volumetric flow rate R gas constant S surface area f time T temperature T* saturation temperature U velocity V volume w mass fraction x mole fraction

axial coordinate Subscripts e critical

, exit condition fy liquid-t o- vapor xiii

upf high pressure injection 4 inlet condition or hydrogen l

, reference state J n ratio (of molecular weights)

, steam

, turbulent T total 3p defines a constant-see Appendix B l w condition in the reactor vessel Superscripts

]

c condensation Greek a thermal diffusivity or flow fraction entering core, Eq (26)

A length scale of turbulence p viscosity p density i v kinematic viscosity xiv

y z . -

, ----- - q p-1 u

- 1. INTRODUCTION , 'j , .

J 1 Previous studies on the Thermali Hydraulics;of the TMI-2 accident have focuseil on  % T'

. phenomena' leading to core uncovery, associated hbatup and everitual' degradation. .With 4

. the recent interest in the Pressurized Thermal Shock (PTS) issue [1] it would be interesting , j t <

to consider, also, the.cooldown behavior, particularly that associated with the actuatiori y of the High Pressure safety InjectionlHPI) system [2]. m Y

g In fact, the B&W Obner's' Group'(OG) task force on PTS considered this' problem ,j[l o ,

soon after the accident (3]. The phenomenology invoked in this assessment is schematically Illustrated in Figure 1. The basic idea is that the vent valves allowed steam from the rest o;f the primary system to flow towards the HPI stream and to condense on it, thus heating it' (l y from the rather low initial temperature of T4 ~ 10 C (50*F) to a considerably higl$r Ic0el )'

i I

before it reached the cold leg exit into the downcomer. -Based ou condensation rates alone '

this exit temperature, T,, was estimated at 207*C (406 F). On the other hand, neglecI.ing 1

. (conservatively) the quantity of steam-already stored within the voided portio'ns of the  ;

primary' system, an estimate based on available decayhat (i.e., steaming rate) of 141*C a j a

(286 F) was given. The fracture med.mics analysis for the TMI-2 vessel was carried out

at- 141*C (286'F).

-]

In fact within the assumptions of the OG analysis the liniit based on condensation.n rates is conservative, while that based on the decay heat is irrelevant. Each part of tkb '

1p statement is clarified, in turn, below. 3 The condensation rates were based on the stratified regime (Figure 1), and did n6t consider the jetting / splashing phenomena (Figure 2) at the point of injection. We have'

~

)

estimated that just over the jet length a heatup to 115*C (249*F) can be expected [4].

Considering the increased interfacial area (wall films, entra' ament of drops into the va- 4 ti 1

por space) generated as the jet splashes against the opposite wall, most of the heatup should have occurred prior to the flow's entering the stratified regime. It does not appear, therefore, that condensation rates could have imp, sed any limitations ongchieving near saturation temperatures at the cold leg exit (i.e.,284*C or 543*F at 1,000 psia). .

i l

1 p i 1

y<  :

3

~~~"

l

-Vent Valve

.y> ,, g / HPl(Ti )

1

.- c

-) , .

Steam Condensation ,

, w = . . a.

TTTNT\.,---a--~p' i \

Te I

ah s I

h(-

r -

n- ~;

s-Fig.1. 0wner's Group evaluation model.

l 1 .,.

o i O l

[o

/ , _2

=~4 e HPl

~ ~ ~

o;.,go

. b

}

l 4

Side view Fig, 2. Flow regime at the injection point.

e 2

The decay heat is available to generate steam for only so long as the core remains covered. The fact that a voided cold leg condition is being addressed implica a core alrea iy uncovered or well on its way to being so. Thus a portion of the decay heat, equal (roughly) to the portion of the core that still is in contact with liquid coolant should be utilized. In fact, at TMI 2 at the time the IIPI 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 primary 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 inventory continued to deplete and system pressure decreased. This flashing process could further be aided by energy storea in structures still wetted.

There is another aspect to this problem, however, that dominates the heat-up process to such an extent that any uncertainties associated with the above mentioned complex phenomena affecting steam availability are neglhible 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 additional, diffusicnal, resistance to the condensation process, and because they tend to collect in the immediate vicinity of the condensing interfaces, they can be detrimental even in trace quantities. Even more importantly, in the present case, we will demonstrate a mechanism which leads to continuing accumulation of noncondensibles within the cold leg and eventually to shutting off the condensation process.

The rate of accumulation is proportional to the heatup of the IIPI (i.e., proportional to the condensation rate), yielding a self-regulating behavior whereby condensation shut-off is rapidly obtained independently of the details used in the calculation.

The purpose of this paper is to reassess the TMI-2 vessel wall temperature transient, due to llPI, in the light of the phenomena introduced above. The assessment proceeds in two steps. In the first, a simple analytical model is used to quantify the condensation transient, as affected by the accurnulation of noncondensibles, and hence to arrive at the 3

e

, f. , -

l n

i temperature transient of theHPI water ehtering the downcomer. In the "cond step. th'se e results are used in conjunction with methoils adapted from past PI'S thermal mixing . 7 analyses [5] to determine the adel wall temperature. g

2. THE CONDENSATION TRANSIEN'N Formulation of the Analytical Model 0 l .

> Consider the cold leg /IIPI-stream configuradon of Figure 3. The cold leg is honzont4 its length is L, its volume l's V, and it is initially filled with saturated steanPat a pressure I /

Pw. The IIPI water entebl at time t :- 0 with a mass flow rate thnn and a temperature T4 which is well below the saturation temperature corresponding to the system pressure, T*(Pw). It forms a stream along the bottom of the cold leg and exits at the other end with

,, a temper:;.ture T,. The cold leg is assumed to comunicate with an inexhaustible supply of a Y

stedn/ hydrogen mixture such that t.ny mass loss from volume V, due to condensation, is perfee.lly compensated to tr.aintain a constant pressure level Pw, throughout the system.

] The mass flow rate of this supply is denoted by rhr and its hydrogen content is expressed by the mass fraction ws . The condensation rate over the whole of the liquid / vapor interface (area S = t x L) is rhl. The removal of hydrogen, frorn feiume V, by absorption into the water stream may be assumed to be neglibible,(r.ee Appendix A). As a consequence the i

hydroge7.' density, pg, within the cold leg will increase with time, yielding corresponding  ;

)

transients on rhr, thl and T,. Our task is to reIaie the% quantities through the relevant flow and condensation processes.'

r i As the liquid heats up from T4 to T,, along its flow path, the potentia) for condensation decreases. Condensation rates are, therefore, functions of both time and position, z, and as a consequence we would expect the composition p}hin the gaseous space to v.ry as

-l v e!!. We believe that the essence of the physicil behavior may be captured without baring ' >

teconsider this detail. That is, the whole steam / hydrogen space within the cold jeg is .j r assumed to be well mixed, and pg is takeg to be a function of time only. ,

,J i .

i 4 1 i

Y f  ! ~I j t / ' ___________j

i

! k s :)

I_  : L  :

1;jf by V, p, (t) bs

• W gc ieo 5T 8

% T 3T

}

.7+W {

4

• S HPl 1 T. (t) +- I -""-'*'

• Ti ,

• dz  ;

Fig. 3. Transient Condensation Model.

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

o' d g(Vpi) = rhr wim (1)

It is convenient to work with mole fractions, zi, instead of densitia, and steam mass flow rates, rh,, instead of total flow rates. The transformations can be carried out as follows:

We use pi = Mg ci = Afg cr xi (2) and Pi P, Ps + P, Pw cr = ci + c' RT+ RT" RT " RT ' " * (}

to express the left hand side of Equation (1), as:

d dx-g(Vpi) = V Micrj (4)

For the right hand side of Equation (1) we use l

Pi PMi i P, M, pr , pi = RT , RT , P i+ P, = Pn wi = p, = (5) 5

_ -_ _ ____ _ _ -_ _ - -__-_-___-. . _ _ _ _ _ _ - - _ _ _ - _ _ - - _ _ _ _ _ _ _ _ _ - _ - _ _ - _ - _ _ _ _ - a

l Pi P, M, xi= Pw., x,= Pw, Ma s M, , and x, + xi = 1 (6) to obtain wi (7)

= Mn + (1 - Mn)rix I

Clearly, thr = rh i+ rh, (8) and since steam and hydrogen enter the cold leg with the sarne velocity:

bli pi CiM; x;w xix

-=-= = = (9)

&n, p, c,M, x,Mn (1 - xix)Mn therefore,

. . i . Mn + (1 - Mn)xiw mr = m, 1 + th- = m, (10) m, . (1 - zim)Mn Thus, Equation (1) becomes:

dzi rh, xiw

= (11) dt V M,cr 1-xim The steam flow rate entering the cold leg, rh,, together with the rate of mass depletion of steam within the cold leg, must constitute the rate of condensation, rh!, That is:

rh, dx er M, V = M (12) dt i

Dut dxi = -dx, and together with Equation (11), Equation (12) becomes rh, = rh,(1 - xi ) (13) 1 l

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

dx s rh'*

-= (14) dt V M, c1- xix Next we must relate rhc to the appropriate temperatures and heat transfer coefficients.

The role of hydrogen in the condensation process is illustrated in Figure 4. The steam .

i is assumed to be in thermodynamic equilibrium with the liquid at the interface. If there  :

6

i l

' had been no 'diffusional resistance on th'e vapor side of the ' interface the concentration distribution would have been uniform, at zg; the interface temperature would have been T = T*[(1 - zg)Pw) .

4 (15).

t and the condensation rate would have been controlled by the turbulence in the liquid and .

a corresponding heat transfer coefficient, ho, i.e.,

q = ho{T*[(1 - zg)Pw] - Tun (z,t)} (16) l In fact, diffusional resistance of steam against the hydrogen molecules is extremely important. It gives rise to a buildup of noncondensibles at the interface and a corresponding .

decrease of the interfacial temperature, as shown in Figure 4. That is, Tg = T*[(1 - zig)Pw] (17)

Xi

=

'#######/####/#######/#######A

/

• --- X i.

T *[(1-xn )P ] . T *[(1-xi)P,}

n n X

(z,t)

'##Mu#MHHDM// '###/#######/#/EM T

Vig. 4. Mechanism of condensation in the presence of noncondensibles.

7

l l

.I Now the heat flux is

- q = ho{T*[(1 - zig)P w ] - THPI(2,f)) (18) and a significant degradation in heat ' transfer is seen if zig is significantly higher than s

1x4. The quantities zgg and T4 can be determined by coupling the mass diffusion process on the vapor side to the heat transfer process on the liquid. side of the interface. For laminar flowL this can be done exactly [6], but for turbulent. flow the process remains -

a

_ poorly understood.' The experimental data are scarce and highly non-prototypic (steam.

air system, low pressures, film condensation onLcooled walls).'Our approach is to expreso the degradation in heat transfer as an exponential function of the hydrogen mole fraction-

. as follows:

q T*[(1 - zgg)Pw] - THPI(2, f) - Ti

-=

0

= exp - .(19) 9- T*[(1 - xg)Pw) - Tu Pi(z, f) zi/2 And in combination with Equation (18) we have q = h, exp - zg {T*[(1 - zg)P] - TRPI(z,f)} (20) 2 /2 1

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

The heatup of the HPI stream can be obtained from an energy balance over a differ-ential element, dz, as shown in Figure 3. That is, thMPI Cp = lho exp ( x1,2 ) {T*[(1 - zg)Pw) - TnPf } (21)-

dz which upon integration yields,

- hoS exp { *""'* [

T - T = {T*[(1 - zg)P ] - Tv} < 1 - exp 4

r (22)-

rilnPlcp 6 . . s This heatup may also be related to the latent heat of condensation by:

thnPic,(T, - T4) = hf ,th; (23)

Thus the condensation rate may be written as,

' ho s exp { _*xi th' = "###

h,

1. {T*[(1 - x4)Pw) - T,} < 1 - exp -

rhnpicp

"' } ' '> (24) f 8

and the exit temperature as, Ta = Ti + I*

. '(25)

~

cp m npi The solution, xi(t),is obtained by integrating Equation (14) with zi(o) = 0,in conjunction with Equation (24). This ignores some initial accumulation due to condensation already occurring' on the makeup flow but does not affect the conclusions of the study. The quantities thl(t) and T,(t) can then be readily calculated from the last two equations.

The Choice of Parameters for the TMI-2 Case The 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 0.7m and its length of 8.15m, between the reactor vessel and the pump, a volume of 3.1ma ;c obtained. The volume of the upper Im of the downcomer corresponding to each one of the four cold legs is ~ Im 3 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 = 3.5m8was chosen for the calculations. The sensivity to this para neter was examined by also considering a value of V = 2.5m a, The high pressure injection in TMI is believed to have occurred with ~ 15kg/s [7).

We bracket this value by choosing thHP1 = 10kg/s for the base case and thHPI = 20kg/s for a sensitivity case. The inlet water temperature is taken at Ti = 10*C(50*F). Assuming critical .open channel Bow at the cold leg exit, the water stream is estimated to attain a depth of 8cm, a width t ~ 20cm, and a velocity of u ~ Im/s (for the 15 kg/s injection rate). The minimum value of the vapor / liquid interfacial area is thus estimated at S ~ im2, As seen in Equation (24) the interfacial area, S, appears only in product with the heat transfer coefficient, ho. The effect of higher areas, likely to exist due to splashing i and entrainment as shown in Figure 2, was covered by considering a generous range in  !

the sensitivity analysis for ho. As discussed in Appendix C a realistic estimate for this quantity is ho ~ 1,300 BTU /hr ft2 "F. Accounting for a moderate increase in interfacial area due to splashing and associated enhancement of ho (jet condensation, etc.) the low l J

end of the range for ho considered in the calculation was set at 5,000 BTU /hr ft2 *F (i.e.,

9

l l

.nearly a factor of four higher). The base case value was taken nearly as one order of

].

2 magnitude higher at h, ~ 10,000 BTU /hr ft *F. The upper end, at ho ~50,000 BTU /hr I I

ft *F represents an enhancement by a factor of x37 and is judged to adequately cover the 2

nio::t extreme behavior.

)

For the base case the liquid heat capacity was taken at cp ~1.3 BTU /lb F. Because of the wide temperaf.ure range present the sensitivity to this parameter was examined by considering also the case of cp ~1 BTU /lb*F. The saturation temperatures and latent heat of conservation (h f,) were obtained from the steam tables. The system pressure, Pw, was taken as 1,000 psia. Sensitivity to this parameter was examined by considering the case cf P. ~ 2,000 psia. The molecular weight of steam is M, = 18 g/g-mole.

As discussed in Appendix B for 7 /2 a value of 0.05 is deemed appropriate. To 1

geretously cover for uncertainties and not to overestimate the degradation in heat transfer, a base case value of ri/2 ~ 0.1 was selected. The upper end of the range was set at I /2 i ~ 0,2.

Finally, the choice of rim, must be made on the basis of core steaming and oxidation

,- rates at the time of high pressure injection (around 200 minutes after the start of the

}

accident). It is now known that by this time the TMI-2 core had already been severely oxidized and partially molten. There seems to be some indication that the molten material relocated in the lower portion of the core where it froze forming substanital blockages (8).

Eventually some 20 to 30 tons of core material made it into the lower plenum where it was found in a solidified debris form. 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 2,000 psia seen around that time. The details of this process will remain highly uncertain; however, there should be little doubt that the renewed stearn availability reactivated the oxidation processes (hydrogen production). On the other hand, at 142 minutes the pressurizer block valves were closed, they were opened briefly (~5 minutes) at 192 minutes and remained closed until 220 minutes. Allindications are that the pressurizer remained more than 3/4 fuli throughout the accident; it is unlikely, therefore, that any 10

venting of steam (and non-condensible gases) occurred during this brief opening of the pressurizer block valve. Thus at the time of IIPI operation (200 to 217 minutes) the-

. major fraction of hydrogen already produced and of the fission products released from the disrupted fuel rods, were still present within the primary system volume. The total amounts of gases released in the accident are estimated at [9): Kr ~ 3.5 kg, Xe ~ 40.0kg and H2~ 510kg.* The total primary system volume is ~10,000 ft3 . Assuming that loop seals (~ 2,700ft 3) and lower plenum (~ 685fta) were 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 fraction may be obtained by assuming a homogenous distribution throughout the steam volume. For Kr, Xe, and H we 2 obtain 0.018%, 0.2147o, and 2.68% respectively.

Clearly, only the hydrogen is significant. Its concentration may be obtained on a mole fraction basis as zi ~ 29.77o. On this basis we chose the values xix = 0.05,0.1,0.2,0.3 and 0.4 to parametrically cover a broad range around the above estimated value. For the base case we chose xiw = 0.2.

Numerical Results and Discussion The solution for the base case is shown in Figures 5 to 7. A rapid buildup of hydrogen in the cold leg and a concomitant decrease in steam condensation rate are predicted. As a result, the llPI water heat up is drastically reduced with cold leg exit temperatures approaching inlet values within a matter of 1 to 2 minutes. All parameter sensitivity results lead to the same conclusion. The xix and xy2 parameterics are summarized in Figures 8 and 9. The results of the xix = 0.4 parametric calculation are given in Appendix B. All other parametric results are collected in Appendix D.

i i

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

11

i I

L 1

1.0 , , , , , , , , , , , , ,

3 j

0.8 - - j 0.6 - -

5 - -

1 0.4 - -

0.2 - -

0.0 i 0 2 4 6 8 10 12 14 16 1 t (min)  ;

i Fig. 5. Predicted hydrogen concentration transient for base case.

10 , , , , , , , , . 7 , , , , ,

l 1

L 0 - -

l 6 - -

a lib - -

5 o.

.E 4 - -

2 -

0 O 2 4 6 8 10 12 14 16 I 1

t (min) i i

Fig. 6. Predicted condensation rate transient for base case.

12 I

.i

_. . . _ . _ . _ . . _ . _ _______.____.._______ _ U

500 , , , ,. ,

400-- -

300 - -

C t, ..

F*

200 -

100 - -

0 ' ~' ' ' ' ' ' ' ' ' ' ' ' ' '

0 2 4 6 8 10 12 14 16 t (min)

Fig. 7. HPI temperature at the cold leg exit for base case.

500 , , , , , , , , , , ,

400 - -

300 l

g v x, - 0.05 .

f--

200 1 0.1 I .

0.2 0.3 100 -

t i e f e f a f f i i Q a n e e 0 2 4 6 8 10 12 14 16 t (min)

Fig. b. HPI temperature transient at cold leg exit for a variety ofinlet hydrogen concentrations (ziw parametric) .

13 6 .I - . - -. .. . . . . . -. . . .

I, i; .

500 i i i i . . . i > i . i i

i. .

g >

'400 - -

300 --

w - .

• ~

200 - -

l- ~ ~

0.1 0.05 .

100 -

0 O 2 4 6 8 10 12- 14 16~

t (min)

Fig. 9. HPI temperature transient at cold leg exit for a variety of condensation degradation assumptions (x172 parametric).

a. THE DOWNCOMER COOLDOWN TRANSIENT From the above analysis we expect that cold IIPI water, nearly at the injection tem-perature of ~50 F, entered the TMI-2 downcomer for the major portion of the injection period. Our task here is to determine the resulting vessel wall cooldown.

We will attempt to look at the problem from two complementary perspectives. First, we examine whether any portion of the HPI stream entering the downcomer could have come in contact directly with the reactor vessel wall.' Second, we consider the downcomer fluid temperature transient as it fills with the llPI.

14

= _ _ _ _ - - _ _ _ _ _ _ - _ _

1 i

Direct Contact Mechanisms 1

The first critical consideration 'in whether the HPI cold stream comes 'directly into contact with the vessel wall. An experimental run at the UCSB 1/2 Scale integral thermal mixing facility with an injection flow rate of 1.2 kg/s revealed the flow regime indicated in Figure 10. 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 rate. If there were no obstacles along the path of this film the flow would have continued smoothly until it reached the .l water level within the downcomer. Unfortunately, such obstacles did exist and very likely - ,.

caused an abrupt deflection, of Die downwards flow, laterally, towards the reactor vessel Jwall.as illustrated in Figure 11.

l l

\ l L __i Film on core barrel =_:g.d s h se r a ni in  !

l 1

U u .

i i

Fig.10. Flow regime at 1/2-scale and 1.2 kg/s.

15

i p ,

L i<

l f W _ ##

N 1

I -Splash off a clip Clipy y ifJ

+

Fig.11. Mechanism for contact with vessel wall.

The detailed geometry of those obstacles is illustrated in Figure 12. The obstacles are called clips. Twenty of them are attached to the core barrel to support the upper end of the thermal shield. From the design inforrnation provided (10), their positions relative to the cold legs could be determined as illustrated in Figure 13. Clearly, nearly one-half of the flow must have impinged upon the upper surfaces of those clips causing it to splash upon the reactor vessel wall. The other half must have continued undisturbed and been confined between the core barrel and the thermal shield space.

This behavior was actually. demonstrated by means of a simple model experiment.

The open air arrangement involved a horizontal acrylic tube positioned opposite a vertical I wooden wall fitted with a model clip as illustrated in Figure 14. The relative positions, dimensions (except for the tube' diameter), and flow rates of tap water were at 1:1 (full) j scale. The flow regime is illustrated, from several perspectives in Figure 14. The vigorous splashing and flow diversion away from the core barrel observed in this experiment leave no doubt that the areas of the TMI-2 vessel under the cold leg nozzles were exposed directly l to near 50*F water.

16 -l

~ 30 -

8 8. .I 12 7 V//////////d 1 Top view of dip n

~

100 12;3,,

Clip-2 5,

+ s.De

/  %

! Tnermal Core!

Barrel Shiek!

Side view Fig.12. Representation of clip position and geometry (all dimensions in cm).

COLD LEG Vessel Wall _ _ _ _ _ _ _# 1J2,,__#3, or_#4, _ _ _ _ , _ s g

1. 4 or #14 #3 or #13

\

\

Core Barrel OR

1. 7 or #17 #6 or #16 s

1 Core Barrel Scale ;

10cm Fig.13. Top view of clips in relation to cold legs and downcomer (clip #1 is sinder hot leg).

17

Y$ .

w; y.

Y

=

R;

.h ..;Lp

= . %f p"K

, ]S  %* '-

.j,J!.l g

a y fj$

+

h fhYf ,

ll mi m e> ..

1 x

.v a 3

et ; .

b 4: s o

.** ' ]. N@dI*hh- d

. i: :.--.%os $&T y;;.g;;m  ; f, 4; .; N Nf :r1 . i j .. g p < , ,. ,

. y}

::7.

~

I c.. . ,

4  :$ nr

, li;:

a g

. s/h,E . . $$

+

• *g g fy,y.f G t: s

?

a ggla j tvXe" (19g

$ *, lF Ke@w. 3,; ps v *iR;l g '

t ,rB l

. pre ,

ic p> - .

,'e, ;.

-7 y )

,; , a:n,; f

% O!

{ s;pc.md! $!%

4.9J.1. kG  ;} r%{ ' i 4

l w ,3 l -

u, ,.

4g:n N%d y 4:

y].i&n.q,,

_ !1 .  ; ,, ,..

k'$ i JJ i -

p ,? ,, . .. h

.?.

I Fig.14. Full scale demonstration of the of clip splashing.

18 i

i k

. . . . .. l

1 t

i, A REMIX-Type Cooldown Analysis In addition to the direct contact of cold water discussed above the TMI-2 vessel wall was gradually exposed to the fluid filling up the downcomer. The situation is illustrated in Figure 15. Except for the thin thermal plumes (created as the falling films enter the fluid volume) which mix quickly as they descend, the rest of the fluid volume would be well mixed. This situation is very similar to that of a portion of the REMIX procedure utilized in the usual IIPI thermal-mixing' analyses dealing with a liquid-full cold leg situation (5h Let Vf(t) be the volume of the fluid within the lower plenum and the downcomer corresponding to each of the four cold legs as shown in Figure 15. The density of this fluid is denoted by pm. The cold stream enters at a volumetric flow rate Q, and a density p,.

A fraction, a, of the flow, Go, which would have to exit if the control volume was fixed in time is assumed to enter the core, while the remaining, (1 - a)Qo, is utilized to increase the fluid volume within the downcomer. Based on available flow areas within the core and the downcomer, the maximum value of a is 0.6. For a fully obstructed core a = 0. In the presence of vent valves any steam binding would be insignificant. Since the degree of lower core blockage in TMI is not known, the quantity a is treated as a parameter within the above range.

An overall mass balance may be written as d

g(V pm) f = Qepe - oQopm (26)

The rate of change of the control volume is given by dV di " ( ~ "N ( }

The energy balance accounting, for the thermal energy conducted out of the metal struc-tural components, ar they become submerged, w, is written as d

3(V pmhm) f = Qapaha - aQopmhm + Qw (28) 19

i ;.L l

l l,

l I,

l l .. ~~M:1 & ~E5 ?S=E=2 M'~B?'

l l: [ Heat Structures '

Clip --+

l {? i d -

3

' s 1

l

' ql  !  ; i I L- I f-g i

.l ,

~

. r i Core h I, Barrel I 4's Vessel

[

Wall .

l' aQo "p[

fl/jh I Thermal L _ _ _ _ _ _ _ _ _ _ _ _ _ _> - shield (1.a)Octo build up level i

~ ^

^ ^ V (t) ^

~ _ ~ _ _ _

.._~ ~~ _ ~ . ~

.A A O i

e e Fig.15. Cooldown model.

20

T$gether with the equations of state p = f(h). and T = g(h) '(29) we have a closed system of five equations in the five unknowns, namely, pm,hm,Tm,Q, and V. f For an approximate estimation of Qu, the donwcomer was discretized axially into four j equal segments. - When the level of fluid volume Vf reached the lower end of each ' axial' segment, the conduction calculation for that segment was initiated and continued to the ,

l end of the calculation. The total heating was obtained by summing up the contri'aution of all the thus. activated segments.

Solutions were obtained by marching out, numerically, in time for specified initial conditions.

Choice of Parameters and Numerical Results. l 1

With the exception of the initial fluid volume, Vf (o), and of the initial temperature of .j the non-submerged protion of the structures, the choice of parameters in this rather basic analytical model is straightforward. The relevant geometric quantities were taken to be 'l those of the Oconee reactcs (see Table 1). The cold water was taken to enter at T, = 50*F-with a mass flow rate of Q,p, = 15kg/s. Parametric calculations with T, = 60'F and 70'F also were performed. As mentioned earlier the value of a was considered paramterically within the 0.0 to 0.6 range.

The possibility that additional condensation upon the core barrel film which would i increase T prior to contact with the downcomer water level should also be mentioned here. From the thermal shield length (Table 1) and an assumed lateral spread of ~ 1 i m .we obtained an additional condensation surface area of ~ 5.3 m2 . The downcomer volume is ~ 6.3 m a. Employing the results of the condensation parametrics we see that the additional area (a factor x5.3 from base case) is amply covered by the ho ~ 50,000 J BTU /hr ft2*F parametric caculation (factor of x37). Also as we can see from Equation (14) the increased volume (a factor of x1.8 from the base case) may be thought of as 21 I 1

i compensated by the zg. ~ 0.4 parametric (i.e., a factor of x2 from the base case).- Thus, again, unless an unforseen phenomenon strongly mitigates the condensation inhibiting effect of noncondensibles th'e values of T, utilized in this analysis would not be materially.

altered.

Table 1 - GEOMETRIC CONFIGURATION OF OCONEE Injector diameter: 0.177 ft Cold Vessel / Lower Loop Core Thermal I2g Downcomer Plenum Pump Seal Barrel Shield

-Inner Diameter /

Width (ft)' 2.33 14.22 14.22 --- --- --- ---

length (ft) 24.5 18.6 --- --- ---

18.6 16.0 Base MetalWall Thickness (ft) 0.21* 0.703 0.36* --- ---

0.19* 0.167 Clad Thickness (ft) - 0.0l

• 0.016 0.016 --- --- -- ---

Insulation Thickness (ft) 0.30 0.30 0.30 --- --- --- ---

Wall Heat Tr. Area 2 69.2 304.1**

to Water (ft ) 179.3 207.7 --- ---

17.6.8 i

Intemal Structures:

2 Heat Tr. Area (ft ) ... ... ... ... ... ... ...

Thickness (ft) --- --- --- --- --- --- ---

1 3

Fluid Volume (ft )* 104.5 176.3 153.3 --- --- --- ---

l

• - Assumed l-

• • Both sides Per cold leg 22

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 bem some estimates, however, that the pumps displaced nearly .,s00 ff a of water from the cold leg piping into the reactor vessel. This would have been sufficient to fill the downcomer completely 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. Ilowever, the HPI occurred nearly one-half hour later, and in all likelihood this was adequate time to allow, again, downcomer depletion. The value of Vf (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 rate.

The initial temperature of the downcomer structures is also uncertain. The water l

displaced, by the "B" pumps, from the cold leg piping (loop seal volumes principally) had been stagnant for a considerable length of time and it could have cooled somewhat from its normal operating temperature of ~ 530"F. We ignore this efffect and take all structures (core barrel, thermal shield, vessel wall) as well as the fluid within fV to be initially at 530*F. In addition, a parametric calculation was run assuming a core barrel temperature of 1,000*F to reflect, approximately, consistency with the highly degraded core conditions at that time.

The results are shown in Figures 16 to 18. The sensitivity to parameter a 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 predicted. The breaks in the curves are due to the discretization of the structural l 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 that the downcomer is 100% full.

23

q -

1 r...

i i

i 1

)

L ,' 600 . .. , , . . .. , , , , , , , .

l oowncomer rus . -

3 500 -- - i 1

J 1

I 400

[ a-0 C

'v Ag 0.2 .

.1 )

i h 300 - '

Z.:~iM?~- ..,... .

0.4 0.6 -

,'-:.~~....~~.~....

~.-

. _~ - :w: -. .. . ..

-m-- - .- . = = x ~;D'c-200 -

~;

' ' ~' ' ' ' ' ' ' ' ' ' ' ' ' '

100 0 2 4- 6 8 10 12 14 16 t (min)

Fig.16. Downcomer fluid temperature transients for base case.

600 . , , , . , , , , , .. . . . .

500 - -

a = 0.0 (also a = 0 A core barrel at 1.000* F) 400 -- N -

C N.

v 'I. 0.2 -

IE Mg; ,, ,, . ,, ,,,

300 -- -

0

~ e ~' ' -K -.,' .'" .~.'; . . .

f* -

~

_ ~--. -~ . ~;; -. . .. . .

- : :.  ;.p~;.:-.... _

~~-

200 -

100 '

0 2 4 6 8 10 12 14 16 t (min)-

Fig.17. Downcomer fluid temperature transients for T, = 60* F.

24

m 600 i i . , , , . . . . . . . .. .

500 - -

400 . -

9. C. ,s 300 -

D.!

~ ~

7'. . ~ . .

,,7 4- a . :.. .e . ,

o.s n.n 200 -

100 ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

O 2 4 6 8 to 12 14 16 t (min)

Fig.18. Downcomer fluid temperature transients for T, = 70* F.

4. CONCLUSIONS

l. 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 1cvels well below 200*F, The principal factor in this conclusion is degradation of heat transfer due to the presence of noncondensibles (hydrogen, fission product gases). A mechanism leading to the accumulation of noncondensibles within the TMI-2 cold legs has been described and indicates that the above conclusion would be true even if the noncondensible concentration -

in the upper plenum area was rather low. Furthermore, the IIPI water is predicted to have

. entered the empty downcomer at ~ 60*F and a mechanism for direct contact of a portion of this flow with restricted areas of the reactor vessel wall has been demonstrated.

25 l

i REFERENCES

1. PTS Rule, USNRC.

2. Reyes, J., Ltr. to T.G. 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 Temperatures with HPI,"

April 1,1985. ,

5. Iyer, K. and T.G. Theofanous, " Decay of Buoyancy Driven Stratified Layers with Applications to PTS: Reactor Predictions," ANS Proceedings of the National Heat Transfer Conference of 1985 held in Denber, Colorado, August 4-7, 1985.

6. Theofanous, T.G. and H.K. Fauske, "The Effects of noncondensibles on the Rate of Sodium Vapor Condensation from a Single-Rising HCDA Bubble," Nuclear Technol-ogy,19,132 (1973).

7. Behling, S.R., " Computer Code Calculations on the TMI-2 Accident: Initial and Boundary Conditions," EGG-TMI-6859, May 1985.

i'. Tollman, B., " Thermal Hydraulic Features of the TMI Accident," Draft EG&G Re-port, June 1985.

9. Behling, S., EGkG, Private Communication, August 9,1985. 1

10. Skillman, G., Metropolitan Edison Co., Private Communication, August 4,1985.

1 l

i 4

d 26

_ _ _ _ _ _ ._ ____a

'],\

' Appendix A

' Hydrogen Absorption in the HPI I

The mass flux of hydrogen into the turbulent HPI stream may be estimated from [A.1]

( r 1/2 th ~ CMg y{ pu (A.1) .l where.D is the molecular diffusivity of hydrogen in water, t? and A are the velocity and 9 i

' length scales of the turbulence energy-containing eddies, C is the solubility of hydrogen in 1

. water, and M is the molecular weight of hydrogen, i

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

' D = Do To p ( A.2) .

where p is the viscosity of' water at T. For example at 160*C the viscosity is 0.174 cp [A.3].'

and D '~ 4.2 x 10-4cm2 j,,

The solubility may be related to the partial pressure of hydrogen, Pg, through Henry's '

law by-P-

z=A (A.3)

For 100*C water the llenry's law constant K is given [A.3] as K = 5.73 x 307 mmHg.

At a hydrogen partial pressure of 1. bar we can thus calculate an equilibrium hydrogen mole fraction of 1.32 x 10-5 For a partial pressure of ~100 bar (assuming a high value of rg) we have z ~ 1.32 x 10-3, which corresponds roughly to C ~ 7.3 x 10-5 g-moles 3

H2 /cm H 2C.

The turbulence length and velocity scales are chosen as 8 cm and 30 cm/s respectively (see Appendix C).

With the above estimates Equation (A.1) yields th = 5.76 x 10-6p/cm2s. The exposed area within the cold leg is of the order of im 2. Thus a hydrogen mass of ~ 3.5g could be absorbed per minute, or ~ 52g for the 15 minute duration of the high pressure injection.

A.1

On the other hand, a steam volume of 3.5m3 at 105 bar at hydrogen mole fractions of 0.2 and 0.4 would contain ~ 3,200 and ~ 6,400g, respectively. Clearly the dissolution of H 2into the water cannot provide an effective mechanism for countering the hydrogen accumulation caused by condensation.

References A.1 Theofanous, T.G. et al., " Turbulent Mass Transfer at Free Gas-Liquid Interfaces, with ,

Applications to Open-Channel, Bubble and Jet Flows," Int. J. Heat Mass Transfer, 19, pp.' 613-614 (1976).

A.2 Kreith F., Principles of Heat Transfer, Int. Textbook Co.1966.

A.3 Handbook of Chemistry and Physics,47th Edition, Chemical Rubber Publishing Co.,

Cleveland, Ohio (1961).

1 i

I A.2

q y

y Appendix B Degradation of Condensation Rates Due :o Noncondensibles No directly applicable experimental data could be located in this area. Our approach is, therefore, based on cautious utilization of available data, in low pressare steam / air systems.

P' First, let us consider how the binary diffusivity in the hydrogen / steam system esm-pares with that of the air / steam system. At low pressures the diffusivisity may be related to the critical pressures, temperatures and molecular weights of'the components [B.})

1 1 V2 PD 2 = 3.64 x 10-4 4 - (p,1)

M }2.334 (Pc3 Pc2)2/ (T Tc2)s/12 c3 Af1 hf2 At 533*K this yields P D? 2 ~ 4.91 atm cm 2/s. This value may be converted to high pressure using the critical properties of the mixture Pl=[xjPci and Tl = [ xjTci j j i

and a graphical representation of the ratio PD pg go = A, given by Dird et al. [B.1]. For example for xi = 0.1 we have Tl = 585.3 K and Pl = 197.3 br.r. Thus K = 0.6 and with the previously obtained value of PODy 2 we obtain, for P =

102 bar, D ~ 2.9 x 10-2cmd/s. At 373 K the same procedure yields D ~ 1 x 10-2cm2/s.

Very similar results are obtained also for xi = 0.2. At the other extreme of zi = 0.8 we have Tl = 155.8*R, Pl = 54 bar, and K ~ 1. Thus the D ~ 4.8 x 10-2cm2 /s and 2 x 10-2 cm2/s values are obtained for the high and low temperature cases respectively.

2 These va!ues are to be contrarted with a value of D ~ 0.239cm /s for an S C air / steam ,

system and a value of D = 0.634em2 /s for the hydrogen / air system at 0 C and 1 bar. At 100*C the above values are multiplied by a factor of x2. It is clear, therefore, that the high pressure steam /hydrogei, system (present application) would give rise to considerably higher diffusional resistance to condensation than the low pressure steam / air systems which have been previously studied experimentally.

B.1 i

l

s;"

S.'

k.,'

4 Stein et al. [B.2) carried out experiments of steam condensation in the presence of air.

m.

Condensation took place in the underside of a horizontal cooled copper plate, at system pressures of 3.1,'6.2 and 12.4 bar. We have correlated these data in the manner shown in Figure B.1. An exponential decay with zip = 0.05 is indicated. This is consistent with much older data obtained in vertical condensing plate geometries [B.3].

.Q 1.0 '

Data of Stein, et al.

h 3.1 bar 6.2 bar .

0.8 - \ *\, 12.4 bar

. \. 9 9/ o- exp { x ,x,, }

X 0.6 -

g in

'o gI . ~~ 0.05 L e tr \ -- 0.10

'tr *

- - 0.20 fi . L' O.4 -

I l 8 l

t (i 0.2 -

• \.\'\ .N ~

L N 0.0 ' ' ' '

O.0 0.1 0.2 0.3 0.4 0.5 l AIR MOLE FRACTION l  !

l Fig. B.1. Correlation of the Stein, et al. data (B.2)in 1 terms of mole fraction of noncondenss,bles.

+

t

On'the other hand, Stein et al. [B.2) have argued that natural convection effects j were important in miiigating some of the condensation inhibition efffects of the noncon-

-densibles. 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 effecta, which are therefore left outside the scope of the present study.

B.2 qhlk '

In an effort to cover such uncertainties the slower exponential decays of 22 /2 = 0.1 and 0.2, as shown in Figure B.1 were also considered in the parametric evaluations. Fur-

.j- thermore,if natural coavection effects are important 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 9/g, ~ 0.1 may be due to this type of behav.

. ior. To cover this possibility and acknowledging the absence of data for 9/q, < 0.1 we

?

have also carried out additional parametric calculations whereby for zi > zt (where zt in some specified, limiting value) the g/q, decay is specified to linearly approach zero at zg = 1. Except for using zgm = 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 D.2 to B.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.

1.0 ,

0.8 -

0.6 -

E -

0.4 - -

0.2 -

0.0 i ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

O 2 4 6 8 10 12 14 16 t (min)

Fig. B.2. Hydrogen concentration fransient, 24. = 0.3, zt = 2xt/2 B.3

,.y .

' ;:n fp,, e ' [.

4 .[! t/ , A ,

s>

(-

7 g , ,

,q .

-/ n .

,.A ' tr fi 10 j '

f

. . . . . i gr , . . . . . . . .

[

a _ _

+ .. t

. o.

6 - ..- F> -

e ,

f .

,sr

. .u w .-

on. .

E 4 / -

'l c ,,

It N, c> s t 2:1 4 >-

f < <

s- i a' ,

g T

s. p

) ' ' ' ' '

.- 0 ' '

, 0 2 4 6 8 , 10 ' 12 14 16-t (min)

Fig. B.3. Condensation rate fransient, rg = 0.3, zz, = 2x2/2-

f. F r.-

'y  !

i 4

' , ,d e o7 p e 500 ,

g s ,

1 i

J' 1

,. 400 ,

, +

300 ' 4' . <

g >

t 4 i i -

t*

200 6 -

I L

~

100 -

k -

ol . i , . .e..

, , , i .

a . . .

.)f 2 4 / ' '0 8 10 '12 14 16 fjV.> '

t (min)

r ,s ,

Fig. B.4. IIPI temperature transient, sg m %3, ir. = 2xi/2 i gg ..( a'

,1) __ ek

. . , .,a -

h

1.0 ' , , ,

0.8 --

1

. 0.6 -

X -

0.4 .

0.2 -

l -

0.0 ' ' ' ' ' ' ' ' ' '

l ' '

p 0 2 :4 6 8 10 12 14 16 t (min) l Fig. B.5. ' Hydrogen concentration transient, xiw = 0.4, xi, = 2x s12 10 , , , , , , , , ,

.i 8 .

6 -

e ih -

x_ -

um E 4 .

2 -

0 ' ' ' ' ' ' ' ' '

O 2 4 6- 8 10 12 14 16 t (min)

Fig. B.G. Concentration rate transient, x4, = 0.4, x1, = 2xi/2 B.5

1'

(

i .

590 . , , , , , , , . . . i i 400 - i

- i 300 C,

O l t* -

200 100 -

0 14 16 o 2- 4 6 8 10 12 t (min)  ;

l Fig. B.7. HPI temperature transient, zw = 0.4, xt = 2xi/2 1

References B.1 Bird R. et al., Transport Phenomena, Wiley Publishing Co.1961. ')

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

i 13.3 Langen, E., Forschung a.d. Geb. d. Ingenieurwes, 2:359 (1931).

13.6

Appendix C The Heat Transfer Coeficient in the Absence of Noncondensibles 1

In the absence of noncondensibles heat transfer is controlled 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 7

of Bankoff [C.2] and Thomas [C 3]. For heat transfer, using Pr ~ 1, the equations are St, = 0.25 ret 2/4 for Ret > 500 (C.1)

St, =- 0.70Ref i/2 for Ret < 500 (C.2)

The turbulence Stanton and Reynolds numbers are given by:

h" u'A l

1 St, = U'pc and Ret =v- (C.3)

The u' and A, also called intergral velocity and length scales have been related to the mean flow velocity, U, and hydraulic diameter, D,in a couple of differc at ways. Theofanous I et al. [C.1] used the relations known to apply for pipe flow: u' ~ 0.0. U and A ~ 0.03Da.

Bankoff [C.2) suggested that for stratified flow of depth 6:u' = 0.3UandA ~ 6.

Assuming open channel critical flow at the cold leg exit (Fr ~ 1) we can estimate a liquid depth 6 ~ Scm and a velocity U ~ Im/s. With the Theofanous et al. choices for u' and A and for 100 C water (v = 0.0029cm2 /s) we obtain Rc, ~ 826. The choice of Bankoff yields 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 results.

We can define a mean flow Stanton number by

h. Nu Nu

~

St = Up s RcPr Re (C.4 )

and in combination with Equations (C.1) and (C.3) we obtain C.1

h St n St, U = 0.25Re,~'/4U (C.5) or p /4g t3/4 l

ho '= 0.25p j, (C.6)

Denoting by h!' and hf the heat transfer coefficients based on the Theofanous and Bankoff  ;

choices of turbulence parameters respectively.we have:

3r 5

'/4 '100' '/4 g= R 3

= .62 (C.7)

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

Using Re, = 826 in Equations (C.1) and (C.2) we obtain St, ~ 4.66 x 10-2 and 2.43 x 10-2, respectively. Let us choose the value St, ~ 3 x 10-2 In combination with Equation (C.5) we obtain St ~ 1.5 x 10-8 which utilized in Equation (C.4) finally yields h[ ~ 1,004 BTU /hr ft2*F. The Bankoff prediction would then be hf ~ 1,020 BTU /hr ft2*F. An in-between value of h, ~ 1,300 BTU /hr ft2*F will be considered as a best estimate.

These predictions should be viewed, however, with a certain degree of reservation. The

~

reason is that the limited experimental data available in this area were obtained at low pressures. The concern is that at the high pressures, high subcoolings and high heat fluxes of interest here the condensate fluid may be diflicult to disipate by turbulent mixing, yielding stratification and hence a significant reduction of the heat transfer coefIlcients from the values predicted above.

References C.l' Theofanous, T.C. et al., " Turbulent Mass Transfer at Free, Gas-Liquid Interfaces, with Applications to Open-Channel, Bubble and Jet Flows," Int. J. Heat Mass Transfer 19, pp. 613-624 (1976).

C.2

C.2 Lee, L., R. Jensen, S.G. Bankoff, M.C. Yuen and R.S. Zankin, " Local Condensa-tion Rates in Cocurrent Steam-Water Flow," in 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 Motion," Int. J.

Multiphase Flow 5,1-15 (1979).

f I

C.3

Appendix D Parametric Results for the Condensation kusient

Each case is represented by. three figures, a, b, an'd c, depicting.the hydrogen mole

' fraction, the condensation rate, and the HPI exit temperature, T., respectively. Each case is identified by the parameter value varied from the base case. All other parameters remain r ' the same. '

i.

l-I J

l

)

l 1

i i

i 4

D.1 s

_ __._ i

' 1.0 , . . . , . , , , , , , .

0.8 - -

0.6 .

x - .

04 - -

1 02 -- .

0.0 '

O 2 4 6 8 10 12 14 16 t (min) 10 . . . , , , . ... , , . , , , ,

e s. .

g 6 - -

a -

.E. . ,

'*E 4 - . 1 1

,1 2 -

o . . , . . . . . . . . . . i 0 2 4 6 8 10 12 14 16 )

t (min)

$00 i i i i '

. , , , . i . . . i 400 -

300 -

C -

o_

200 -

300 .

f 1  % a I 1 i I 0

0 2 4 6 8 to 12 14 16 t (min)

Fig. D.1 (a), (b), (c) 7 p = 0.05 3 D.2

i. I I i I

10 . , , , . , , , , , , , , , ,

l 0.8 - .

0,6 - .

M -

0.4 - . 1 i

(. .

0.2 .

0.0 ' '

O 2 4 6 8 10 ' .12 14 16 8 (min) 10 , , , , , , , , , , , , , ,

e - -

1

~

.6 - -

7

,Eh . .

.g. 4 .

2 - .

0 2 4- 6 8 10 12 14 16 I(min) 500 , , , , , , , , , , , , , , ,

400 - -

300 -

c t

s' 200 -

ioo .

o .

0 2 4 6 8 10 12 14 to t (min)

Fig. D.2 (a), (b), (c) ri/2 = 0.20 D.3 1

p.

' l

..,; 'i i .0 , , . , , , . , , , ,

, . .i 08 -

06 - -

x_ ,

l 0.4 _

0.2 .

i 0.0 0 2 4 6 8 10 12 14 16 t (min) i 10 , , , , , , , , , , , , , , , 'j 4 e i

8 -

1 n 6 - l a -

.s.

• E 4 .

0 2 4 6 8 to 12 14 16 t (min) 500 400 - -

300 - -

c-t.,

n-200 -

100 -

0 O 2 4 6 8 10 12 14 16 1 (min)

Fig. D.3 (a), (b), (c) zw = 0.05 D.4

__,_--_,.__--..--.___-.,__--___m.__ - - - . , - . _ . _ _ _ _ _ _ _ _ m _ _ _ _ __

' i i E g i g a g s g i g I s 4

, 0.8 - -

0.6 - -

J - .

0.4 - -

t' .

. j 0.2 - -

0.0 O 2 4 6 8 10 12 14 16 t (min) to , , , , , , , , , , , , , , ,

l' 8 -

l l-

.g 6 - -

'ch

-6

• E 4 --

2 0 ' ' '

O 2 4 6 8 10 12 14 16 i(min) 500 , ,. , , , , , , , , , , , , ,

400 -

N) *-

C t.

200 -

100 -

0 ' ' ' ' ' ' ' ' ' ' ' ' ' '

O 2 4 6 8 10 12 14 16 t (min)

. Fig. D.4 (a), (b), (c) .r = 0.10 D.5

_ _ . _ _ _ . _ _ _ _ __ z __ J

l s

4 1.0 , , , ,. , , , , , , , , , , ,

0.8 - .

0.6 .' __

'A - .

I 0.4 - .

0.2 .

I 0.0 0 2 4 6 8 10 12 14 16 i(min) i 10 , , , , , , , , , , , , , , ,

1 8 -  ;

- (

. I

-- 6 -

1 e

ik j e.

• E 4 -

2 0

O 2 4 6 8 -10 12 14 16 i (min) 500 ,

, , , , , , i , , ,

i i 400 300 C

L F* -

200 100 O 14 10 O 2 4 6 8 10 12 t (min) i l

Fig. D.5 (a), (b), (c) xx = 0.30 l

r D.6

I n

in . , , , , , . . . , , , . . .

0.8 -

0.6 -

a 0.4 -

i...

OP .

0.0 ' ' ' ' ' ' ' ' ' ' ' ' ' '

O :2 4 6 8 10 12 14 16 t (min) 10 , , , , , , . . . . . , , i .

I i .

a .

l 6 y -

.e. ,

• E 4 . .

2 -

l 4

o 0 2- 4 6 8 10 12 14 16 t (min) -

500 , , ,

3 i i . , i i . i . 6 400 - -

300 - -

i t., . . .

e 200 -

i

{

100 - -

i 1

0 0 2 4 6 8 10 12 14 16 t (min)

Fig. D.6 (a), (b), (c) ho = 5,000 BTU /hr ft2 .7 i

i D7 l

i .0 , , , , , , , . 6 4

m 08 -

0.6 -

0.4

~

0.2 ..

t i i r t t i 1 1 0.0 16 0 2 4 6 8 10 12 14 t (min)

I 10 . , , , , , , , , , , , . . .

8 2

• Th 6

• E 4 -

i p -

0 O 2 4 6 8 10 12 14 16 t (min) 500 , , . , , , , . . . . . . i .

400 -

300

.c r' 200 Ioo .. -

0 2 4 6 8 10 12 14 16 t (min) 2 Fig. D.7 (a), (b), (c) ho = 50,000 BTU /hr ft .7 D.8

I \

~!

1.0 , , , . , , , . , , , , , ,

0.8 -

0.6 -

M 't- .

0.4 -

~

v. ~

0.2 -

0.0 '

O 2 4 6 8 10 12 14 16 t (min) 10 . , , , , , . , , , , ,

8 - -

g 6 - -

. ' .j. -

• E 4 - -

2 .

0 2 4 6 8 10 12 - 14 16

);

t (min) j 500 ,

400 .

300 c .

a.-.

J 200 .

100 .

0 ' ' ' ' ' ' ' ' ' ' ' ' '

O 2 4 6 8 10 12 14 16 I (min)

Fig. D.8 (a), (b), (c) thnef = 20kg/a D.9

1.0 , , , , , , , , , , . , ,

i , i

- 0.8 -

)

0,6 - .

)

' ~

~

0.4 . -

1 i

0.2 -

00 0 2 4 6 8 10 12 14 16 l t (min) .,

10 , , . , , , . . . . . i i e i i

8- -

g s -

b e.

E 4 2- -

0 O 2 4 6 8 10 12 14 16 i (min)

,, 500 , , , , , , , , , , , i , i .

400 -

300 -

g r*

200 100

. , , , , i . , , . . . .

o 0 2 4 6 8 10 12 14 16 i (min)

Fig. D.9 (a), (b), (c) P, = 2,000 psia D.10

l 1.0 ' I i 3

i  ; i g , g g i 0.8 -

0.6 -

s.

^

0.4 .

z 02 ,

0.0 ' ' ' ' ' i - i i i 0 2 4 6 8 10 12 14 16 1 (min) 10 , , , , ,

8 -

l l

6 g - .

ik 6

un

• E 4 .

.2 *

'O ' ' A ' ' ' ' =

0 2 4 6 8 10 12 14 16 i (min) 5% , , , , , , , , ,

400 -

. W 300 -

C L .

200 -

.i i

100

^

0 ' ' ' ' ' ' ' ' ' ' ' ' ' '

0 2 4 6 8 10 12 14 16 j t (min)

Fig. D.10 (a), (b), (c) V = 2.5m 8 i

?

D.11 i i

l i.;' .:

f f

E. 1 b ' s l 4 4

' i ' 6 6 & I i 8 8 I

{. . =

0.8 - . -

, 0.6 - -

M = .

0.4 - .

3 0.2 - -

e 0.0 O 2 4 6 8 10 12 14 16 t (min) ,

l 1

l i i .

10 , , . . . . . i i i i i 1

l 1

~ l 8 -

6 -

.bis "

ea -

• E 4 -

2 -

t t 0 14 16 0 2 4 6 8 10 12 t (min) 500 , , , , , , , , ,

400

- i 300 C

o_ -

h -

200 Sw -

l t I i g a a a t a 1 a 1 s i a t 0 2 4 6 8 to 12 14 16 I (min)

Fig. D.11 (a), (b), (c) c,, = 1 BTU /lb'F i

D.12

l wRc.,to1M u s Nuctaan xsovLatoav commission i a 6' cat Nuuse R ,4uc,a e, rioc. saa v. No. .r mire o.

7fo',"JM' . BIBLIOGRAPHIC DATA SHEET su ,NirRuctioNs 3

,,,,m.....,

Rivers.

NUREG/CR-4978

, mA...L._

l 1he Cooldowr spects of the TMI-2 Accident

. oAre n oRipereo MONin T&AR

. aut oam December / 1986

. oApnuoRt ,ssveo

1. G. ofanous "*' ' " / l August I 1987 [

7 PEHF DRMsNG ORGANi2 AllON NAME ) M AILING ADDR E 5s itric'une l's C ':dW 6 PROJECi r T A WWQHK UNII NUMBt R 'I Department of Chem al & Nuclear Engineering I , ,,,,

University of Cali rnia Santa Barbara, CA 9' 06 1

(- D1634  ;

10 SPONSORING ORGANIZATION NAME AND MA1L ADDRE5S Hwspa#I,p coder ' siiT vet OF f*t POR T Division of Reactor and ant Systems Office of Nuclear Regulat ny Research Technical j U.S. Nuclear Regulatory C nission a "' a '* w" a t o "~ ~ ~' "

Washington, DC 20555

,, supra M.. OAR ,No,..

)i A

IJ ABST H ACT 000 we,as e, > ens lhe cooldown of the 1MI-2 reacto vessel du to high pressure injection that occurred at 200 minutes into the accident re-ex ined. Flow regimes and condensation '

heat transfer in the cold legs and 'own r are considered. The presence of noncon-j densibles (hydrogen) and a mechanism ading to its accumulation around the condensa- 1

( tion interfaces lead to conclusions. at are materially different from those of a previous study that did not consi rt se effects.

i i

s y

1. DOCUMt NT AN A L Y$t$ - e K E VWO DE SC R iPT ONS i 16 A w AIL A9:Li f

• j ST A TE YENT 1MI Noncondensibles ,'

Cooldown Condensation '

Henry's Const t hydrogen . ted

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,r,,,,,e,,,,,

17 NUMB 6h O' P AGt$

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