ML20212G328
| ML20212G328 | |
| Person / Time | |
|---|---|
| Issue date: | 09/30/1999 |
| From: | Ishii M, Richard Lee, Tinkler C, Wu Q, Zhang G NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES), PURDUE UNIV., WEST LAFAYETTE, IN |
| To: | NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| References | |
| CON-FIN-L-1990 NUREG-CR-6510, NUREG-CR-6510-V02, PU-NE-96-3, NUDOCS 9909290196 | |
| Download: ML20212G328 (94) | |
Text
NUREG/CR-6510, Vol. 2 PU NE-96/3 Corium Dispersion in Direct Containment Heating Theoretical Analysis of the Hydrodynamic Characteristics Purdue University T'd
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U.S. Nuclear Regulatory Commission f 7 '\
Office of Nuclear Regulatory Research i, '
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NUREG/CR-6510, Vol. 2 PU NE-96/3 Corium Dispersion in Direct Containment Heating Theoretical Analysis of the Hydrodynamic Characteristics Purdue University C9 ( / /
U.S. Nuclear Regulatory Commission f 7 '\
Office of Nuclear Regulatory Research i, Washington, DC 20555-0001 % ,,,,,
P YO CR-6510 R PDR ,
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i NUREG/CR-6510, Vol. 2 PU NE-96/3 l
l Corium Dispersion in Direct Containment ,
Heating Theoretical Analysis of the Hydrodynamic Characteristics Manuscript Completed: July 1999 Dat Published: September 1999 Prepared by M. Ishii, Q. Wu, G. Zhang, Purdue University R.Y. Lee, C.G.Tinkler, Nuclear Regulatory Commission Schoolof Engineering Purdue University West Lafayette,IN 47907 R.Y. Lee, NRC Project Manager Prepared for Divisi:n of Systems Analysis and Regulatory Effectiveness Omce of Nuclear Regulatory Research l U.S. Nuclear Regulatory Commission l Wcshington, DC 20555-0001 NRC Job Code L1990
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r L l ABSTRACT l l
The present research at Purdue University addresses corium dispersion during the Direct Containment Heating (DCH) scenario in severe nuclear reactor accident. In DCH l accident, the degree of corium dispersion has not only the strongest parametric effects on l the containment pressurization, but also has the highest uncertainty in predicting it. In view of this, a separate effect test program on the corium dispersion mechanisms in the i reactor cavity and on the subcompartment trapping mechanisms was initiated in 1992 at Purdue University under the direction of the US Nuclear Regulatory Commission. The four major objectives of this study are: (1) to perform a detailed scaling study using the newly proposed step-by-step integral scaling method, and to evaluate existing models and correlations for droplet entrainment, particle size and size distribution, and particle trapping, (2) to design and construct a 1/10 scale Zion reactor model, and to perform carefully scaled experiments using air-water and air-woods metal to simulate the prototypic steam and core melt, (3) to develop reliable mechanistic models for the corium dispersion and transport in the accident scenario, which can be used to predict liquid and gas blowdown, entrainment, droplet size, liquid carryover to the containment, and the subcompartment trapping, and (4) to use the models to perform stand alone calculations for prototypic conditions. In this report, efforts focus on the last two objectives, whereas
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the scaling and experiment parts are covered in a separate report.
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I iii NUREG/CR-6510 1
r CONTENTS l ABSTRACT....................................................................................................................iii CONTENFS................................................................................................................
. LIST OF TAB LES . .. . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . .. . . . . . . . . . .. .. . . .. . . . . . . ..
LIST OF FI GURES .. . . . . . . . . . . . . . . . . . . . . . . . . .... .vii. . . . . .. . .
N OMEN CLATURE. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . .
EXECUTIVE
SUMMARY
ACKN OWLEDGMENTS . . ... . ... ....... .. ... . .. ... ....... . ..... .. .. . .. .. ... . . . .. ...... . . . .. . ... . .. . . '
'l . INTRODUCTION. .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
- 2. MODELING OF THE LIQUID AND GAS BLOWDOWN ........................................ 4 1
\
2.1. Liquid Discharge .. .. ..... . . . . . .. ..... . .... .... . ...... .... ........ . ... . . . .. . ... .. . ... . . .... .. ... . .. . ... .. ... .
2.2. G as Discharge . . . . .. .. . .. . .. . . . . .. . . . . . . . . . .. . . . . . . .. ... 6. . . . .. . . . . . .
- 3. LIQUID FILM FLOW IN CAVITY BEFORE GAS BLOWDOWN........... ............... 8 !
3.1. Film Front Propagation . . . . . . . .... .. .. ..... . . . . .. .. . . . .. ... .. ... . .... .. .. . .... .. ............ . . .. .... .. .. . . . . . . . 8 3.2. Quasi-steady State Film Flow ........................ ...................................... .............. 12 3.2.1. Circular Sector Film Flow on Cavity Bottom Floor..............................12 3.3.2. Film Flow in Cavity Horizontal Section..................................... ..........14 3.2.3. Film Flow in Cavity Chute....................................... .. ........................... ! 5
- 4. LIQUID AND GAS FLOWS IN CAVITY WITH DROPLET ENTRAINMENT.. ..18 3 4.1. Liquid Film Flow in Cavity ............................... ................................................ I 8 4.2. Gas Flow in Cavity .. ... . . .. . .. .... . .. ... .. .. . . . . . .. .. .. . .. . . . . . . ....... . . . . ... . . . ..... .. . ... .. . . ..... . ... . . . .. 21 4.3 . Droplet Flow in Cavity .. .. ... ... .... .. .. ... .... ..... . . . .. ....... . . .. .... . . ... . .. ....... . . .... .. . ... . ... . .. 22
- 5. DROPLET TRANSPORT AND RE-ENTRAINMENT IN S UBCOMPARTMENT. . . ... . .. ........... ........................ .... .. ... ........ ........ .... .. ... ... ... . ... . 25 5.1. Dispersion via Seal Table Exit........................... . ............................................. 25 5.2. Direct Carryover. . . ....... ...... .. . .......... . . ..... .. . .. ... . . .... . . . . . .. .. .... . .. . .. . ...... .. .... . ... . .. ... ... . 2 5 5.3. Re-entrainment in Subcompartment .................................................................. 29
- 6. COMPARISONS WITH THE EXPERIMENTAL RESULTS .................................. 34 6.1. Liquid Flow in Cavity before Gas Blowdown ................................................... 34 6.2. ' Liquid and Gas Flow in Cavity .......................................................................... 44 6.3. Droplet Transport and Re-entrainment in the Subcompartment........................ 54
- 7. APPLICATION TO PROTOTYPIC CONDITIONS ................................................. 57 7.1. Standard DCH Accident . . .. . .... . ..... . . .. .. .. . . . .. ... .. ... . . ... . . . .. ..... ... .... . ..... ... ....... .. . . . . . . . . 5 7 7.2. Vessel Break Size Effects ...... ........................................................................ .. .. 63 7.3. Vessel Pressure Effects . .. .. ... . .... . .... .. ... . ... . .. .. . . ....... . ... ... . . . ..... . . . . .. . ..... .. .. .... . . ... . . .. . 71 t 8.
SUMMARY
AND CONCLUSIONS ......................................................................... 78 REFERENCES.................................................................................................................80 v NUREG/CR-6510
LIST OF TABLES Table Page Table 6.1 Geometric parameters of the PU 1/10 scale test facility................................. 34 Table 6.2 Predictions of the dispersion fractions in the 1/10 scale experinents ............ 55 NUREG/CR-6510 - vi
LIST OF FIGURES Figure Page Fig.1.1 ' Schematic of the corium dispersion process in Zion reactor containment........ 3 Fig. 3.1 Simplified cavity geometry for one-dimensional model................... . ...........13 Fig. 4.1 Simplified liquid and gas flow in the cavity ............. . ...................................19 Fig. 4.2 - Demonstration of the droplet number transient entrained at time t................ 23 Fig. 5.1 Trajectory ofliquid droplet under seal table ................................................... 28 Fig. 5.2 Re-entrainment process in the subcompartment ......... .............. .................... 30 Fig. 6.1 Water film front propagation in the cavity under 1.4 MPa vessel pressure.... 36 Fig. 6.2 Water film thickness and velocity distributions in 1.4 MPa tests................... 37 Fig. 6.3 Water film front propagation in 6.9 MPa tests ............................................... 38 Fig. 6.4 Water film thickness and velocity distributions in 6.9 MPa tests................... 39 Fig. 6.5 Woods metal film front transport under 1.4 MPa vessel pressure.................. 40 Fig. 6.6 Woods metal film thickness and velocity distributions in 1.4 MPa tests ....... 41 Fig. 6.7 Woods metal film front propagation in 14.2 MPa tests.................................. 42 Fig. 6.8 Woods metal film thickness and velocity distributions in 14.2 MPa tests ..... 43 Fig. 6.9 Predicted entrainment fraction in cavity for 1.4 MPa air-water tests.............. 45 Fig. 6.10 Predicted entrainment fraction in cavity for 1.4 MPa woods metal tests........ 46 Fig. 6.11 Predicted entrainment fraction in cavity for 6.9 MPa air-water tests......... .... 47 Fig. 6.12 Predicted droplet :ize in cavity for 1.4 MPa air-water tests ........ .................. 48 Fig. 6.13 Predicted droplet size in cavity for 1.4 MPa woods metal tests ..................... 49 Fig. 6.14 Predicted droplet size in cavity for 6.9 MPa air-water tests ........................... 50 Fig. 6.15 Predicted pressure loss in cavity for 1.4 MPa air-water tests ......................... 51 Fig. 6.16 Predicted pressure loss in cavity for 1.4 MPa woods metal tests.................... 52 Fig. 6.17 Predicted pressure loss in cavity for 6.9 MPa air-water tests ....................... . 53 Fig. 6.18 Effects of discharge nozzle size on the carryover (6.9 MPa vessel pressure). 56 Fig. 7.1 Corium film thickness and velocity distributions along cavity floor.............. 59 i Fig. 7.2 Entrainment fraction F2 in the reactor cavity ................................................. 60 i Fig. 7.3 Volume median diameter of the droplets entrained in the cavity ................... 61 l Fig. 7.4 Cavity pressure resulted from film flow and droplet flow in cavity............... 62 Fig. 7.5 Vessel break size efrects on Fi ........................................................................ 64 Fig. 7.6 Vessel break size effects on the entrainment time t.o in the cavity................. 65 Fig. 7.7 Vessel break size effects on the dispersion fraction F2 in the cavity .............. 66 Fig. 7.8 Vessel break size effects on maximum pressure drop to liquid flow in cavity 67 Fig. 7.9 Vessel break size efrects on the average D in the cavity.......................... .. 68 Fig. 7.10 Vessel break size effects on the dispersion fraction in the containment......... 69 Fig. 7.11 Break size effects on D, of Fa ... .................................................... .. ..... ......... 70 Fig. 7.12 Vessel pressure effects on the entrainment time ten in the cavity.................... 72 Fig. 7.13 Vessel pressure effects on the dispersion fraction F2 in the cavity................. 73 Fig. 7.14 Pressure effects on the maximum pressure drop to liquid flow in cavity....... 74 Fig. 7.15 Vessel pressure cffects on the average D. in the cavity................................ 75 Fig. 7.16 Vessel pressure effects on the dispersion fraction in the containment............ 76 Fig. 7.17 Vessel pressure effects on the maximum droplet size of F3i ..... .................... 77 vii NUREG/CR-6510 i
NOMENCLATURE English .
GreekSymbols A area a constant E entrainment rate C drag coefficient -m dynamic viscosity D diameter. p density d droplet diameter o surface tension F fraction T time f friction factor 0 inclined angle g gravitational acceleration ye lumped parameter H height h film thickness Subscripts K- minor friction factor c Cavity L length cr critical value Ny viscosity number d droplet, dispersion, discharge n - droplet number de droplet at casity exit P pressure disp dispersion R gas constant e entrainment, cavity exit Re Reynolds number en entrainment T temperature f liquid phase, liquid film t- time g gas phase V velocity h hydraulic 1' volume j jet We Weber number s steam, steady state, seal table w width si seal table length x space coordinate v vessel, air-vent y space coordinate vm volume median NUREG/CR-6510 viii
EXECUTIVE
SUMMARY
In Direct Containment Heating (DCH) accidents, one of the fundamental factors in containment heating and pressurization is the degree of the molten corium dispersion.
This is because the intensity of the heat transfer and chemical reactions that may lead to containment over-pressurization are basically proportional to the available surface area of the ejected molten corium. If the corium is highly dispersed and the resultant aerosol particle size is very small, the risk to containment failure can be very high. Therefore, it is important to investigate the corium dispersion process including the mean corium droplet size as well as the dispersal fraction. To understand the corium dispersion phenomenon, a separate effect test program on corium dispersion mechanisms in the reactor cavity and on the subcompartment trapping mechanisms was initiated in 1992 at Purdue University under the direction of the US Nuclear Regulatory Commission. Four major objectives of this study are: (1) to perform a detailed scaling study using the newly proposed step-by-step integral scaling method, then to evaluate existing models and correlations for droplet entrainment, particle size and size distribution, and particle trapping, (2) to design and construct a 1:10 scale Zion reactor model, and to perform the scaled experiments using air-water and air-woods metal to simulate the prototypic steam and core melt, (3) to develop reliable mechanistic models for the corium dispersion and transport in the accident scenario, which can be used to predict the liquid and gas blowdown, droplet entrainment, droplet size, liquid carryover to the containment and subcompanment trapping, and (4) to use the models to perform stand alone calculations for the prototypic conditions. In this report, efforts focus on the last two objectives. The scaling and the 1:10 scaled experiments are covered in a separate report.
In this study, the transient two-phase flow in DCH accident is modeled in step by step method. The entire corium dispersion process as well as the dispersion fraction (Fai,p) of {
the discharged core melt that enters the reactor containment dome is estimated theoretically. The stepwise approach, as proposed by Ishii [5], divides the whole transient into four phases with the dominant mechanisms highlighted in each step. These stages are: (1) the liquid and gas blowdown, (2) the liquid film flow inside the cavity before gas blowdown, (3) the two-phase flow inside the cavity with droplet entrainment, and (4) the droplet re-entrainment and transport in the subcompartment. Simple mechanistic models are developed here in this repon to describe the transport process in every stage.
For the liquid and gas blowdown, analytical solutions are obtained regarding the single phase jet velocity, gas jet velocity, and the discharge characteristic time constants.
The process is assumed to be isothermal. For the second stage, the liquid film propagation and the subsequent quasi-steady state film flow in the cavity before gas blowdown are modeled analytically. The models estimate the film front propagation time ,
as function oflocation, the film velocity and thickness distribution along the cavity floor, and the fraction ofliquid that flows out of the cavity without dispersion. These results i supply the necessary initial and boundary conditions for the entrainment process in the I cavity. For the entrainment process, the liquid flow, the gas flow, and the droplet flow are modeled individually. By combine all the field equations, numerical solutions are ,
obtained for the entrainment time duration, total entrainment fraction in the cavity, and j ix NUREG/CR-6510 a
the volume median size of the droplets entrained in the cavity. After the liquid film and droplets have entered the containment, three paths are assumed for the droplets to be transported to the upper containment based on the observation in the Purdue University 1:10 scale simulation experiments. The first path is the carryover (F21) of the droplets entrained in the cavity through the seal table room. This fraction of carryover is assumed to be mainly determined by the view factor of the seal table exit to the cavity exit. The second path is the direct carryover (F22) of the very fine droplets that are entrained in the cavity and able to follow the gas stream all the way to the upper containment. Here a trajectory analysis is imposed to obtain a critical droplet size; droplets larger than this critical size would impinge on the seal table bottom wall and thus are trapped in the subcompartment. The final path is the carryover (F3i) from the re-entrained droplets in the subcompartment. The trajectory analysis is used a;,ain to determine the fraction of the re-entrained droplets that can survive the subcompartment trapping and follow the gas stream to the upper contamment. Eventually, the total corium droplet carryover (Fa;,p) is obtained from the summation of fractions, F 21, F 22, and F3i.
Comparisons have been made between the predicted values and the experimental data obtained from the Purdue University 1:10 scale simulation tests. Reasonable agreements are obtained for the major flow parameters, including the film front propagation time, the film thickness and velocity in the test cavity before gas blowdown, the entrainment fraction and mean droplet size in the cavity, the cavity pressure rise due to friction loss of the gas flow to the liquid flow, and the total droplet dispersion fraction in the upper containment. According to the model, the dispersion fraction in the upper containment is mainly contributed by the re-entrained droplets in the subcompartment and by the droplets that are entrained in the cavity and can pass through the seal table room. By applying the models to the prototypic cases under typical DCH accident conditions (i.e.,
reactor pressure of 6.2 MPa, vessel break size of 0.35 m, core melt mass of 54 ton), the predicted total droplet dispersion fraction in the upper containment is only 1.4% of the discharged core melt. However, this fraction can be as high as 10% if the vessel break size increases to 0.58 m (about 1.7 times the typical size). The maximum dispersion fraction measured in the experiment was about 6% for vessel break size equivalent to 54 cm at reactor pressure of14 MPa.
Since the models are based on an isothermal assumption and the chemical reactions and possible corium-water interactions in the reactor cavity are neglected, the numerical results presented in this report can only be treated as a first order estimation of the hydrodynamic behavior of the corium dispersion transient. For very high vessel pressure or for the case of very large break size, the gas flow in the cavity would be choked. In such a situation, the model can not be applied for the entrainment analysis in the cavity because the transient choking phenomenon is not included in the present models.
Although several simplifications have been made in developing the present models, the dominant mechanisms in each phase are accounted, allowing for better understanding of the corium dispersion problem in DCH accident scenario. The approach would also be valuable for a complete analysis of the DCH accident.
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! i ACKNOWLEDGMENTS The authors would like to express their gratitude to Dr. S.T. Revankar, Mr. S. Kim, Mr. D. Zheng, and Mr. K. Sato for their participation in acquiring the experimental data employed in this work. Sincere appreciation is also due to Dr. F. Eltawila for his valuable I
discussions and support to this project. 1 This work was funded by the US Nuclear Regulatory Commission under contract number NRC FIN L1990. l 1
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t xi NUREG/CR-6510
- 1. INTRODUCTION In Direct Containment Heating (DCH) accidents, one of the fundamental factors for containment heating and pressurization is the degree of molten corium dispersion. This is because the rate of heat transfer and the chemical reactions that may lead to containment over-pressurization are basically proportional to the available surface area of the molten corium. If the corium is highly dispersed and the resultant aerosol particle size is very
- small, the risk to containment failure can be very high. Therefore, it is important to investigate the corium dispersion process including the mean corium droplet size as well as the dispersal fraction of the total discharged corium. To understand the corium dispersion phenomenon, extensive experimental studies have been conducted at SNL [1],
ANL [2], and Purdue University [3,4,5] for the Zion reactor geometry, which provided a large data base for analytical modeling. Some theoretical analyses have been carried out with approaches based on empirical correlations [6, 7], which yielded reasonable results when compared with the existing experimental data. However, some of the mechanisms are still unclear due to the complexity of the dispersion process. To study, both experimentally and analytically, the corium dispersion mechanisms in the reactor cavity and subcompartment, the following four major scopes of the DCH project at Purdue i University were defined:
(1) Perform a detailed scaling study with the newly proposed stepwise integral scaling method [8] to identify the mechanisms governing the transient of corium dispersion, and evaluate the existing physical models for each individual mechanism [9].
(2) Design and conduct simulation experiments using air-water and air-woods metal in a 1:10 linear scale Zion reactor model, collecting dispersion information such as the film flow transient in the cavity, the entrained droplet size and size distribution, and the dispersion fraction of the total discharged !! quid.
(3) Develop or select reliable mechanistic models and correlations for the corium
' dispersion phenomenon. i (4) With the models, carry out stand alone calculations for prototypic conditions.
The scaling study and the 1:10 scale separate effect experiment have been carried out, which were covered in a previous report [5]. In this report, the main efforts focus on the modeling of the hydrodynamic characteristics of the corium dispersion process neglectmg the chemical reactions and the possible corium-water interactions in the reactor cavitv.
With isothermal assumption, the whole accident transient is simplified into several phases, including the liquid and gas discharge, the liquid film flow in the cavity before gas blowdown, the liquid and gas flow in the cavity with droplet entrainment, and the liquid transport and re-entrainment in the subcompartment. In each phase, the dominant driving mechanisms are considered for practical modeling. These mechanisms were ;
initially identified in scaling studies by Ishii [8] and were verified in the Purdue University 1:10 scale separate effect simulation experiments [3,4,5]. With the stepwise approach, the model gives reasonable results when compared to the experimental data.
By applying the model to the prototypic Zion reactor condition, a stand alone estimation
- of the general trend of the corium dispersion process is presented, and thus a better understanding of the DCH phenomenon is obtained.
From the separate effect experiments [3,4,5], the sources that contribute to the final dispersion fraction (Fai.,) in the reactor containment dome are summarized in Fig.1.1. 4 Initially, part of the liquid corium rushes out of the cavity as a fihn flow before gas blowdown. This fraction of the corium (F )i cannot participate in the entrainment process, and thus does not contribute to Fai.p. With the steam blowdown from the primary coolant system, the corium in the cavity is subjected to the entrainment process. Part of the
]
. corium is then dispersed into droplets (F 2 ) with the remaining portion (1-F2 -F i ) flowing {
out of the' cavity in the form of a liquid film. Of the entrained particles, some small i droplets (defined as the fraction F22 of the total discharged liquid) follow the gas stream, I bypass the seal table, and finally enter the upper containment building through the four air vents. Meanwhile, a small fraction (F 21 ) of the dispersed droplets enters the seal table room and reaches the containment dome through the seal table exit. The remaining droplets and the liquid film impinge on the seal table walls, partly being re-entrained as aerosols (F 3 ). Afterwards, the particles (F 3i ) that can follow the gas flow will survive from the wall trapping and enter the contamment. Consequently, the total dispersion 1 fraction (F4i.,) in the containment dome is the summation of F2i, F22, and F3i.
In the scaled experiment, the liquid transport transient lasted less than one second.
The flow was complicated such that no single mechanism can thoroughly dominate the entire process. Therefore, a stepwise approach, as proposed by Ishii [9], is applied here to model the whole transient with one mechanism being highlighted in each step. The entire j
transient process is divided into four stages:
(1) liquid and gas blowdown (2) liquid film flow inside the cavity before gas blowdown (3) two-phase flow inside the cavity with droplet entrainment (4) droplet re-entrainment and transport in the subcompartment i For these stages, simple analytical models are developed with isothermal assumption to describe the whole corium transport process and to predict the corium canyover fraction to the containment dome. It should be emphasized that the efforts focus on the hydrodynamic characteristics of the corium dispersion phenomena. The heat transfer 1 between the hot corium and the steam stream is simplified as an isothermal process. This assumption does not necessarily mean neglecting heat transfer, because maintaining the temperature of a high speed gas flow needs significant heat transfer from the hot corium
[10]. There would be two other choices for the practical modeling, i.e., isentropic process and equilibrium process. Due to the existence of the hot corium and the moisture in the steam stream, isentropic assumption is not feasible. As for the second choice, long time frame (~10 s) is needed for the blowdown steam to reach equilibrium with the hot corium according to the prediction of the CONTAIN code (7]. The corium dispersion and transport in the transient lasts about 2 seconds, which is too short for the equilibrium assumption. However, due to the isothermal assumption, our numerical results can only i be treated as a first order estimation resulted from the hydrodynamic behavior of the corium dispersion transient. Although several simplifications have been made in l developing the present models, we believe that the dominant mechanisms in each phase are accounted, which result in better understanding of the dispersion problem in DCH ;
accident. I NUREG/CR 6510 2
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4
- 2. MODELING OF THE LIQUID AND GAS BLOWDOWN To predict the prototypic dispersion, it is necessary to have a reasonable estimation for the corium and steam discharge rates, i.e., the upper boundary conditions of the accident transient. The objective of this section is to formulate the liquid and gas jet velocities under the prototypic conditions. For the scaled tests, the blowdown came through a discharge line located under the test vessel to control the initiation of the discharge transient. Therefore, the relation between the blowdown rate and the vessel pressure is quite different from the prototypic case. The liquid and gas jets velocities in the experiments are obtained directly from the measurements [5].
2.1. Liauid Discharge Before the reactor vessel failure, molten corium with total volume 1,'n accumulates in the lower head of the vessel. The primary coolant system of volume 1; is pressurized with saturated steam under a pressure Po. Once the vessel bottom is breached, the core melt is immediately ejected into the reactor cavity by the pressure force of the steam.
Because the corium is incompressible, the volume discharge rate Q,n of the molten material should equal the rate ofincrease of the vessel free space 11, i.e.,
' = Q, = Vjj A, (2-1) where Vj is the jet velocity and A; is the discharge break area. By assuming a potential liquid jet flow, Bernoulli equation is applied to relate the corium jet velocity to the vessel i pressure in the form of I P-P,=1 pf Vj + -Kp,Vl , 1 (2-3) where Paan is the cavity pressure in the process of the liquid discharge, and K is the minor loss coefficient of the flow through the breach. Due to the very high vessel pressure in DCH accident, the ambient pressure P.on is negligible, and thus the liquid jet velocity is approximately given by I
2P V=
j .
(2-4) pf(1+ K) i On the left hand side of Eq. (2-1), the volume of the primary coolant system, vi, is also a function of the vessel pressure P. In the liquid discharge transient, the steam in the coolant system experiences an isothermal expansion because of the existence of the hot core melt and the heated structural mass [10], which leads to:
P1,' = const.= P 1,'o o . (2-5)
By substituting Eq. (2-4) and (2-5) into Eq. (2-1), an ordinary differential equation governing the vessel pressure P is obtained:
' ~
d 'Po%' 2
_ ,' {
(-6)
~
dtr P> < pf(1 + K),
with initial condition:
P(t = 0) = Po . (2-7)
Eq. (2-6) is analytically integratable, which yields the solution of P as p _- Po 2/3 , (2-8)
T=3 2 A, P"'
o
=
3V,o A, 2 pf(1 + K) % (2-9) 2%'
where Vjo is the initialjet velocity under vessel pressure Po. By substituting this pressure solution into Eq. (2-4), the jet velocity transient becomes:
2 Po"* V,o y#
_yf}P (1+ k) (yt(gi+1)"8 f+1)U$ '
Consequently, the time needed to discharge the core melt, termed as the liquid discharge time, to, is controlled by the following equation:
y '
'r 3
2f3 l
d
%= VAdt= jj %< t,+1 -1 .
(2-11) o _ s A, V,o , _
By rearranging this equation, ta is solved explicitly in the form of t, = D +1 -1 .
(2-12) 3 < A,V,o, If the volume of the core melt % is much smaller than the initial steam volume in the primary coolant system as in the case of the prototypic accident, Eq.. (2-12) is reduced to 2Y t, = -
d 1 + =3 Y" + . .= .' f"
- 1' .
(2.13) 3 A, V,o _ < 2% >
A,V,o This solution indicates that the liquid discharge time can be approximately obtained from l the initial vessel conditions. Throughout the liquid discharge transient, the jet velocity is nearly a constant, the initialjet velocity.
6 2.2. Gas Discharge The steam blowdown follows the molten corium discharge. For the elevated primary system pressure, the steam flow through the breach is choked. The steam undergoing ,
rapid depressurization expands isentropically unless sufficient energy is transferred to the flow. According to Henry [10], the expanding steam would receive heat from both the deposited and the entrained high temperature corium. In view of the large heated capacity of corium, it can be assumed that the steam expands isothermally, in which case the steam would receive sufficient energy to remain at a constant temperature. With this assumption, the steam jet velocity at the breach is given by:
V, = JR,T, , (2-14) where R. is the steam gas constant and T is the steam temperature. For the isothermally expanding steam, the specific kinetic energy comes from the work done by the expanding steam per unit volume, i.e.,
yo
-V,2 = IPd v. (2-15) 2 ;,
The notation P and v are the steam pressure and the specific volume, respectively, while subscript t and v refer to the breach and the vessel respectively. By applying the gas state equation and substituting Eq. (2-14) in Eq. (2-15), one obtains:
f % f 1 = v,'dA v = In 1 = In .
(2-16) 2 ;, v < v, s < pas Accordingly, the pressure and density at the choking location are related to that in the reactor vessel, i.e.,
A'- = E = e*' = 0.60653. (2-17) p, P, With this relation, the steam mass flow rate is readily obtained in the fonn of P' P' se, = p,V, A, = A, R,T, }R,T, = 0.60653A, (2.18)
R,T, With the initial steam mass M,o in the primary coolant system, the vessel depressurization process is modeled from the mass balance equation:
d M' = -dr, , (2-19) dt or 1l dp' = 1l dP' = -0.60653A P' (2-20) dt RT, di jM.
l By direct integration, the vessel pressure transient is solved as:
P, = P,oe -" , (2-21)
{
where Y' l r' = (2-22)
O.6%53A M.j The corresponding steam mass flow rate transient is given by:
0.60653AJ P[
rh, = e -d'> .
(2-23)
< [T, ,
To this point, the liquid and gas blowdown transient is modeled completely. The liquid jet velocity, liquid discharge time, gas jet velocity, gas mass discharge rate, and the vessel pressure transient are all related to the initial conditions before the accident occurs.
These results define the initial and upstream boundary conditions of the corium dispersion transient in a DCH accident, which make it possible to model the corium dispersion and transport in the reactor cavity as presented in the following sections.
I; 1
i 7 NUREG/CR-6510
- 3. LIQUID FILM FLOW IN CAVITY BEFORE GAS BLOWDOWN The focus of this section is on developing a model for the amount of corium which flows out of the cavity before the gas blowdown and a model for the film thickness and velocity along we cavity floor when the gas flow begins. The film thickness and velocity 4 are needed as the initial conditions for the next step modeling of the entrainment process.
In reality the film flow is a three-dimensional, two-phase transient process in an complicated cavity geometry. It is impractical to seek a detailed analytical or numerical solutions without simplifications. Based on the flow visualization performed in the 1:10 scale simulation tests, the whole film flow process can be simplified into two levels. l These are the film front propagation and the followed quasi-steady established film flow.
When the liquid jet impinges on the bottom floor of the cavity, part of the film flow propagates towards the cavity exit. In this stage, the time needed for the film front to reach the exit is of great importance for the prediction of the amount ofliquid that flows out of the cavity without dispersion. After the film front reaches the exit, the flow can be treated as quasi-steady. The amount ofliquid that does not participate in the entramment process is estimated from the time duration of the film flow at the cavity exit before gas blowdown initiation.
3.1. Film Front Propagation To obtain the transient behavior of the film front propagation, a one dimensional model is developed using a constant friction factor f on the floor and the lumped gravity force effects with constant lumped inclination angle 0. The governing equation, the boundary condition, and the initial condition are given below.
Momentum equation:
BV BV Bh f, 2
+V -gcose = -- V - g sin 6, (3-1) at Bx 8x 2h Boundary condition:
V(x = 0) = V j , t 2 0. (3-2)
Initial Condition:
V(t = 0) = 0, 0 s x s x, , (3-3) where V, h, t, and x are the film velocity, film thickness, time, and the axial coordinate in the flow direction from the jet center, respectively. The jet velocity, Vj, reaches a steady value Vp in a very short time period, hence, it is treated as a step function.
t<0 V, = ,[ 0, (3-4)
Vjo ,t20' In the momentum equation (Eq. (3-1)), the term representing the gradient of the film thickness, h, with respect to x is neglected since it is very small compared to the other terms. Furthennore, it is also assumed that the gravity force term can be omitted because the dynamic head variation of the film flow is much larger than the change of the static pressure head. By assuming a constant flow rate for the step change jet velocity, the original momentum equation is reduced to:
BV BV f*
+V =- V, ,
(3-5) at Bx 2% V,,
where V;o is the steadyjet velocity and ho is the initial liquid film thickness at the jet edge location. This equation can be solved with the characteristic method [11]. First, the characteristic line is defined as:
dx
-=V, (3-6) dt l and the compatibility equation along this line is:
dV f* 3
=- V. (3-7) dt 2(%V,,)
The velocity solution on the characteristic line is:
i 1 1
- = - + A (t - r), f*
V A = (kV,,) , (3-8)
V,o By substituting this velocity solution into the differential equation of the characteristic line, the characteristic line from the origin at time T is thus given by:
x t- r = -+ $x .
(3-9)
V, 4 The lines for different t have no intersections. It implies that the later discharged liquid can never catch up with the film front, and the film front location xr is governed by:
t= I+ 4
= I + !",o x'2t 2 0. ,
(3-10)
V,, V,, 4%V This solution is a first-order estimation in which the gravity force can be neglected, which is rather true for the prototypic DCH case with a, vessel pressure over 6.2 MPa.
For the case of 1.4 MPa air-water experiment triggered by a solenoid valve located under the test vessel, the valve opens gradually within 0.2 seconds, and the corresponding jet velocity increases linearly with respect to time to a maximum value:
' 0, t<0 Vj =< At, O s t 5 t, , (3-11)
. A t, , < > t, where A is a constant and t, is the time when the jet velocity reaches steady state. With constant film thickness assumption and neglecting gravity effects, Eq. (3-1) is reduced to: l BV
+V BY = f* V2 , (3-12)
Bt ax 2ho From the method of characteristics, the characteristic line of the film flow should satisfy:
b= V. (3-13) dt Along the characteristic line, the relevant compatibility equation is given by:
dV 1 2
=- f.pfV, (3-14) dt 2h o which has analytical solution of:
1 1
-= + p(t - r) , (3-15)
V V(t = r)
!" (3-16) p = 2h, ,
where t -is defined as the time when the characteristic line initiates from x = 0. i Subsequently, the film velocity V(t = t )= V(x = 0 ) = At. Substituting Eq. (3-15) into the characteristic line Eq. (3-13), an first-order ordinary differential equation for a characteristic line is obtained:
dt 1
-= + p(t - r), x(t = r) = 0, (3-17) dx Ar which has a solution:
x = -In(1 + AA r(t - r)) . (3-18)
This solution represents a set of characteristic lines with respect to different t. Since the film velocity becomes larger and larger, the later characteristic line will catch up with the NUREG/CR-6510 10
former ones, resulting in an envelope line at the intersections that is, physically, the film front location. To obtain the film front location, x ,r it is necessary to find the condition at which the derivative of x with respect to t is zero, corresponding to the maximum distance the characteristic lines can reach at time t. This condition gives:
t = 2r, (3-19) which suggests that the time for the film flow started at (x = 0, t = t) will reach the film i
front within a time period of T. By substituting this relation into Eq. (3-18), the film front location, xr, is obtained as a function of t: {
~
l 2-1 xf = -In 1+ bat ,
(3-20)
)
0 4 -
or vice versa, the film front propagation time is presented as a function oflocation:
r 8ho exp " -1 4'exp(p xf )-1 s 2 h, s
=1 -
,Ostst #. (3-21) t=k PA l AL Here, tst is the time for the steady velocity to reach the cavity exit. After the liquid jet becomes steady with speed V. = At, at time t , this signal takes 2t time to propagate to the film front. Thereafter, the characteristic line solution should be:
x = 11n[1 + pV,(t - r)]. (3-22) 0 These lines have no intersection points, and thus liquid discharged later cannot reach the film front. Accordingly, the film front location is governed by:
i x =1 1n[1+BV,(t-t,)], t 2 2t, = t,, (3-23) 0 In the scaled test cavity, the time for the liquid film front to reach the cavity exit is much smaller than ter. Hence, Eq. (3-21) is applicable for the actual film front propagation in solenoid valve control case.s. It should be emphasized again that these solutions are valid only for larga jet velocity such that gravity force can be neglected, which is rather true for the prototype DCH case with a vessel pressure over 6.2 MPa. With low jet velocity, which applies to the low pressure woods metal tests with mpture disc control, a substitution for Eq. (3-10) is the integration of the later quasi-steady state solution that considers gravity effects at the chute section. This is because the upstream film flow can not catch up with the film front with an initial step change of the jet velocity, and the propagation problem is identical to the one under steady state. However, in the case of the prototypic accidents, Eq. (3-10) is suggested due to the negligible grasity effects.
y 11 NUREG/CR-6510
3.2. Ouasi-steady State Film Flow Following the film front propagation, the flow towards the exit is treated as a quasi-steady state process until the gas blowdown. From the jet center, a circular film spreads at the bottom floor with a portion of the flow towards the exit. For the geometry of the Zion reactor cavity, deter:nined by the view factor of the circular film flow to the path leading to the cavity exit, about 1/3 of the circular film flows directly towards the cavity exit and constitutes the steady state film flow part. The rest of the film flow climbs on the vertical wall up to the ceiling area around the jet nozzle, and eventually falls down to the bottom floor with a significant time delay. Once this portion of liquid impinges on the bottom, it splits into two equal parts. One part goes towards the exit and the other towards the opposite direction, resulting in a net 1/3 of the total flow moving forward with a slightly less initisi velocity. To model the quasi-steady film flow, three distinct ,
sections are considered along the flow path (Fig. 3.2), which are the circular sector section, horizontal section with variable periphery, and the inclined section.
3.2.1. Circular Sector Film Flow on Cavity Bottom Floor In the circular sector, the film flow is axisymmetric and horizontal. A one dimensional steady film flow model in the circular sector is developed with frictional effects. The boundary conditions are obtained from the potential flow theory of a liquid jet impinging on a solid wall vertically. The gradient of the film thickness is omitted in the momentum equation due to the large Froud number of the film flow.
Momentum equation:
V = 1V , D /2sxsx i.
2 j (3-24)
Bx 2h Continuity equation:
8xhV
= 0, D j/ 2 s x s xi . (3-25) 8x Boundary condition:
V(x = Dj /2) = V, , (3-26) h(x = Dj /2)= Dj /4. (3-27) xi is the distance from the jet center to the nearest vertical wall, and D; denotes the jet diameter. From the continuity equation (Eq. (3-35), we have:
xh V = cons tani1 = D* V, . (3-28) 8 NUREG/CR-6510 12
jet center x4 circular sector section x
I W, horizontal section w(x)
W2
/ xs Ws inclined section 5
1 i i k (
l I
n7
\'/ x3 cavity exit x
Fig. 3.2, Simplified cavity geometry for one-dimensional model 1
13 NUREG/CR-6510 i I
By substituting this relation into Eq.(3-24), the momentum equation is reduced to:
dV =- ' 4f" xV . 2 dx (3-29) s D*Vu By direct integration, the solution of V with respect to x is obtained as:
V= Y" (3-30) l 1+b -1 2 < D, / 2, and the corresponding film thickness is:
h=V oD,' .
(3-31) !
8xV It is clear that the film velocity decreases due to friction effects. Without wall friction, the film velocity persists and the film thickness decreases inversely with respect to the radius of the circular film flow field.
3.2.2. Film Flow in Cavity Horizontal Section In the horizontal section, gravity effect is neglected. The horizontal channel is unfolded as a flat plate with variable width w(x), involving only 1/3 of the circular film flow that enters this section. The steady state governing equation is in the following form with boundary conditions coupled to the circular sector section.
Momentum equation:
l dV f
= - , V, x 3s x s x2 . (3-32) dx 2h Continuity equation:
hw(x)V = 3hi wi V , ix 5xsx 2 (3-33)
Boundary condition:
V(x = xi ) = Vi , (3-34) h(x = xi ) = hi . (3-35)
The subscript 2 refers to the end of the horizontal section. The width w(x) of the flow path increases linearly along the flow direction, which is determined by unfolding the horizontal channel:
w(x)= w i + W - w' (x-x 2
i
), x, s x s2 x , (3-36) x 2 -X i where wi equals one third of the periphery of the circular film flow at the end of section one, and w2 is the periphery at the end of the horizontal channel. With this explicit relation, the momentum equation (3-32) can be integrated using the method of variable separation.
dV y2 = -82(w- k2 (X-x i))dr , (3-37) f*
- 2 = 2(hi iwiV), (3-38) k=2 ' ~ '. (3-39) x 2 -X i The final analytical solutions for the film flow in the horizontal section are given by, V= Y'
., xi 5xsx 2 , (3-40) 1+ wi (x -x i)- os (x-x,)2 b*
h = E(x)V(x), x, s x s x2 . (3-41) 3.2.3. Film Flow in Cavity Chute In the inclined chute section with constant channel width we , flow visualization shows that the film flow merges at the bottom floor and does not climb on the side walls before gas blowdown. This observation greatly simplifies the governing equation with both friction and gravity effects, making analytical solution achievable. The governing equation is one-dimensional and steady with a constant friction factor. However, the film thickness shows a discontinuity between the two sections due to the sudden change in the flow path width.
Momentum equation:
V = b ' -gsine, V x s x s x,.
2 (3-42) i dx 2h j Continuity equation: I dhV
= 0, x i5 x s x, (3-43) ax I
15 NUREG/CR-6510 ;
Boundary condition:
V(x = X2 )" V2 . (3-44) h(x = x ) =w,lh2 .
2 (3-45)
The subscript e denotes the cavity exit. By substituting the continuity equation into the momentum equation, the film thickness term is removed, resulting in an ordinary differential equation for the film velocity V:
dV V = -p V - a ,
8 (3-46) dx
!" (3-47) p= 2V h ,
23 a = g sinB, (3-48) h = h(x -+ x3 ) = *1 h2 ,
3 (3-49)
W, where h3 is the film thickness at the beginning of chute section. I' rom the integration table, the solution of V is obtained implicitly from e
V - k' 3 x3 s x s x, ,
0.51n , (3-50) x-x2 = 3pk (k + V)' + dtan~' ( dk s, V3 where, k= -
(3-51)
P.
The film flow models presented above give all the characteristics of the film flow before gas blowdown. These include the film front transport time in the cavity, the film velocity, and the film thickness along the cavity floor. To carry out the computation, the liquid jet velocity and discharge rate are needed as the initial and upstream boundary conditions, which are available from the previous section. From the film front transport time, the amount ofliquid, Mi, that flows out of the cavity before gas blowdown can be estimated. By subtracting the film front transport time from the liquid discharge time
. obtained in section 2, the liquid film flow duration at the cavity exit is obtained Thus the amount ofliquid that does not participate in the entrainment process in the cavity can be given by the product of the liquid flow rate at the cavity exit and the flow duration, i.e.,
M i = (t, - t,)p,, V,w,h, . (3-52) i NUREG/CR-6510 16
l' This part of discharged liquid will not be subjected to the latter phase of entrainment process in the reactor cavity, and therefore should be excluded from the dispersion process. Furthermore, the film thickness and the velocity distributions in the cavity before gas blowdown supply the necessary initial conditions for the modeling of the entrainment transient that will be discussed in the next section.
1 l
l l
l 17 NUREG/CR-6510
- 4. LIQUID AND GAS FLOWS IN CAVITY WITH DROPLET ENTRAINMENT After the gas blowdown, the flow pattem in the reactor cavity is rather complicated.
The major concem here is to predict the mass dispersed fraction (F2) of the discharged liquid, as well as the mean droplet size at the cavity exit. Due to the inertia of the film flow and the shear force of the high speed gas stream, the film flow rushes toward the cavity exit along with droplet entrainment. 'Dierefore, it is expected that the model should involve three flow types: the film flow on the cavity wall with droplet entrainment, the gas flow subjected to the liquid film interfacial friction and the drag force for the entrained droplets to accelerate, and f'mally the droplet flow.
4.1. Liauid Film Flowin Cavity The liquid film flow after gas blowdown is the source for the droplet dispersion.
Driven by the high speed gas stream, the liquid film accelerates towards the cavity exit.
Meanwhile, the film flow becomes thinner because of droplet entrainment. This entrainment process persists until the film completely moves out of the cavity or the film thickness reduces to a degree that no further entrainment can occur. Here, the duration of the entrainment process inside the cavity is defined as the entrainment time t . To practically model this film flow transient, the following simplifications are employed.
First, the cavity is treated as a horizontal channel with a hydraulic diameter Dn. This simplification allows us to neglect the gravity force effects. In reality, the liquid film velocity is very high and accelerates immediately after gas blowdown, resulting in a large film Froud number. Thus, the gravity force plays a relatively minor role in the liquid film transport transient. Secondly, based on the flow regime transition criterion, the flow regime in the cavity belongs to annular mist flow. The liquid film is thus assumed to cover the entire cavity wall with uniform film thickness. As gas blows over the film surface, the film moves towards the cavity exit, and its thickness reduces continuously due to droplet entrainment. Furthermore, the entrained droplets take certain time (or travel length) to deposit on the cavity wall again Because of the large channel size Mh " 8), there is little chance for the entrained dropleis to deposit in the cavity. ,
Accordingly, it is assumed that no droplet deposition occurs inside the cavity. With all
' these assumptions, the one-dimension film flow model is developed in the following way.
The mass change rate of the film block equals the total droplet entrainment rate on the film surface illustrated in Fig. 4.1:
(xD,pf) = -(rD,L)t,(t) , (4-1) where L and h denote the film block length remaining in the cavity and the thickness of the liquid film sheet, respectively, i:, is the droplet mass entrainment rate per unit film surface area. A correlation for this term given by Kataoka and Ishii [12] is:
i 1 i
i 1
i Cavity Channel ee
. O Liquid Film . Q Droplet Flow - *
- Dh e' wpe:4U
- i r 9 e ~ Gas Flow. sisse.
e e -
, . kg i
.. . { ;
su.u v'9 h P LpW l bh?hhh$h' Nhhhb 'fhhhi.
L(t)
=
Le Fig. 4.1, Simplified liquid and gas flow in the cavity I
l l
l 1
1 19 NUREC,/CR-6510
i i, = 6.6 x 10-7(Re f We)" (4-2)
<ps <Du, 4p,Y,h We = p,V,'D, ' hp'
Ref= ,
0
, (4-3)
Pi < Pz >
This correlation is subjected to the following entrainment onset criteria:
> \
- ' ' <#' #' l 2135Ref N, = , y, 2 > 15 (4-4) 0 < Pi >
pgjal(gap) r >
b 211.78RefN' / , N, s1 (4-5) )
G upts 15 r 31/2
- ' ' b 21.5Refi2, Ref< 160 -(4-6) J G < Pi >
By assuming that the droplet horizontal velocity is the same as the film velocity at the moment of entrainment, the momentum change rate of the film block equals the total force acting on the fihn:
_ d' L y f, 'p,' 'y' dL_ E,dL _ L ' d L' ' ,
dt* L 2h ypf, g dt , hp, dt 2h s dts where AP is the pressure difference between the film tail and the cavity exit. The wall friction factor, f., is expressed in terms of the film Reynolds number (Wallis [13]): ,
i f, = 0.079Re725 Ref> 2000,
, (4-8) !
16 f, = Re , Re fs 2000, (4-9) f While the interfacial friction factor, f,i is given by (Wallis [13]),
f, = 0.005 1 + 300 h ' .
(4-10) 1
( D,s The initial conditions for Eq. (4-1) and (4-7) are: l L(t = 0) = L, = cavity length , (4-12)
- 1
= -Vf(t = 0), (4-13) d t ,,,
NUREO CR 6510 20
i i
l i
h(t = 0) = (4-14) xDA .
The cavity length, Le, is the total cavity length along the flow path including all sections.
Once the two differential e:piations (Eq. (4-1) and (4-2)) are solved, the entrainment time ;
t.o is obtained whenever L becomes zero c.r h reduces to a degree that the entrainment onset criteria cannot be satisfied. However, these equations contain three extra variables, 1 i.e., M, pg, and V,, which are coupled with the gas flow and the droplet flow. To seek j complete solutions,- the gas flow and the droplet flow in the cavity have to be investigated together.
4.2. Gas Flowin Cavity l The gas flow over the film surface is averaged over the entire length of the film remaining in the cavity. The flow is assumed to be quasi-steady, thus the gas mass ficw l rate is equal to the discharge rate formulated in section 1: '
zD"2' = 0.60653Aj P,[ '"
p,V, e .
(4-5)
<4> < )R,T, , !
The right hand side of the above equation is for prototypic isothermal blowdown conditions. For the case of scaled simulation tests, experimental data indicate that the l exponential dependence on time is still true, but the time constant as well as the coefficient are altered with regard to the adiabatic blowdown process and the discharge breach geometry. Here, the gas density ps is related to the pressure loss through the isothermal gas state equation:
P,,, + 0.59 _ P""
(4-6) p, Pe l The factor 0.5 of the pressure loss term is from the consideration that the gas density is l averaged over the entire liquid film flow in the cavity. Finally, the pressure loss is
- balanced by the interfacial friction force and the drag force (F 4) acting on the dispersed droplets:
1 xDf y= f, ' p ,' 'y d L' '
<4> 2 rpf, s dt s With these three equations coupled to the liquid film flow model, the extra variable p.,
V,, and & can be solved if Fa is successfully related to the flow parameters. That brings up the following part concerning the droplet flow in the cavity.
4.3. Droolets Flow in Cavity To ir.vestigate the total drag force acting on the droplets remaining in the cavity at any ,
time t, two factors need to be considered. First, since the entrained droplets fly out of the cavity continuously, it is important to consider how many droplets remain in the cavity at time t. Secondly, at any moment, the drag forces are different for the droplets entrained at different times in the past. It is thus necessary to study the entrainment in step by step method to obtain a meaningful time dependent drag term.
By assuming that the droplets entrained at time t in di interval have the same diameter d (volume median diameter), the number of droplets entrained in this time intervalis:
dn(r) = mass endnment rak per d areax tow Sm sMace area dr mass of one droplet i,(r) (4-8)
= , s (xD,L(r))d r Pt where d is given by (Kataoka and Ishii [13]),
/ S r 3 -1/3 r 32/3
- Pr d = 0.028 g p,(V, - V,)2,
/ 2 Re- Re,/3 rPr>
- s
<Pts
, (4,9)
At time t (t > t), some of the droplets entrained at time t have already flown out of the cavity and thus contribute no drag force to the gas flow in the cavity. As shown in Fig.
4.2, the remaining number of the droplets entrained in the (t, t+dt) time interval is given by, dn(t, r) = L(r)-s(t,r) dn(r), (4-10)
L(r) where s(t, t)is the distance traveled by the dn(t) droplets from time t to t:
d '# ' '#
s(t,r) = (4-11)
L(r), L(r)<s(t,r)
Here Va (4, t) is the velocity (at time 4) of the droplets entrained at time T. When L(t) is smaller than s(t, t), no droplets entrained in the (t, t+dt) time interval remain in the cavity at time t, and thus dn(t, t) should be zero (s(t, t) 2: L(t)). The drag force acting on the remaining dn(t, t) droplets is thus given by, NUREG/CR-6510 22
l Le I
l l
l t
\ !
_ Gas Flow \ i
?
i >
\ dn(t-r, t) l
, J. U. .<. ;
I
, ,; p W
..%',,,u eee ee e ee
. g+. \
f,g.;pp.7
- fi .P TS;-Q:cy*MANilisip ?.e.:nd ik. i,58?? - $:s*
- 7U W97h
- ,%n; , ; ff; 'u c' %;p. -
+
er e t s mnk rn. sm,,;cdy:Hy?,[Np!W+[g;qfqx:n%rnq;
?;1. n r' e 4 - g 3
,r-
< w ay A :. ?,t_,u. % e,e.a y;)b'!yTw c -8, i ;;h_wg
- ." m;: vas; wwqgsgah:??e.3:
i i j i I j l
L(t) l f
I I I I I i f
l i I l l l l 1 1 I l l y;g;,Q3q,t~;
o Wm Mingunp:,,u.:aq,aa+&m..agiine a 3v ,W:: .g;;9% # s;
- a:1, c
- c w
, ,,s ty y p ,;,7y,:; a Q.,:p ; %;ev.c , j. wl %
" 5
, ;;;Q ;c j; g
i r ..
~-
l f. ..[ 'i .
,s l ca I
g i _e - a :.n I ylii.) '. l l
l ,?. 4 i i
__. Gas Flow g
. p; y s'
.; e-
~ '
~- l $ ff dD(1, T) li i I
sb9 pg:,
,e e i e; dM I, aw l
,rv . p l r'y c.s
- p a;re gw , . .
- >
9 x, gr mA y(1* .N
.r e
., ls?
i Q,EN:p']?3 Y4 ^myja:+%c t
jriYNYEn mu mm:T#'d?@[w'd}M;u eb-L:wnry t%:. d k. m$j U Ng x ~
f204J a w. 3 ew w@ann n sF'dhMdD l I I l
i_
4t) l Mt)-Mt) l 1
l l t
- I l l
l 3 l
l,-_ S(t, t) _
l Figure 4.2, Demonstration of the droplet number transient entrained at time t 23 NUREG/CR-6510
I dF,(t,r)= C,p,(V,(t)-V,(t,r))* dn(t,r), (4-12) and the total drag force on droplets in the cavity is simply the integration of Eq. (4-12):
F,@ = ,p,f,(t)4,(t,r))' '
(L(r)-s(t,r)) dr. (4-13)
Here, another variable Vo(t, t) appears. Considering a single droplet entrained at time t and accelerating in the gas field, Newton's second law is applicable:
dV,((,r) = 3 C p!- -V,(()-V,(f,r) -
2 (4-14) 4d ,<pp-df where the drag coefficient Co is given by (White [14]),
24 6 s C,= + +0.4, 0 s Re, = Ps(V -V u s 2)d 5
x 10 . (4-15)
Re, 1 +]Re, p, While the initial droplet velocity upon entrainment is assumed to be the film velocity:
V,((= r,r) = Vf (r). (4-16)
At this point, the model for the liquid and gas flow in the cavity is completely closed.
Although there are many simplifications and assumptions involved, analytical solutions are still impossible. To solve these equations. a numerical approach is inevitable. The key parameter to couple the film flow to the droplet flow is the gas density or the pressure loss & over the liquid film flow. Once & is determined, all the equations can be solved by simple numerical methods. In the numerical code, an iteration technique is applied to the & transient. Initially, a constant AP is imposed on the problem. After a complete calculation loop, a new pressure transient in the cavity is obtained. Using this AP information as the new input, the numerical iteration begins. Once AP comerges, the solution of the problem is obtained. The entrainment fraction in the cavity is then given by:
t, F= (4-17) 2 Pf % 6 {i,(r)nD,L(r)}dr.
- 5. DROPLET TRANSPORT AND RE-ENTRAINMENT IN SUBCOMPARTMENT After the liquid film and the entrained droplets enter the subcompartment, three mechanisms are considered to be responsible for some small droplets being transported into the upper containment dome. The first mechanism is the carryover of the droplets entrained in the cavity through the seal table room located right above the cavity exit. 1 The second mechanism is the direct carryover of small Jroplets by the gas stream due to drag forces. This part of droplets is originally entrained in the reactor cavity and does not deposit in the subcompartment. The final mechanism is the re-entrainment of the film flow with some large droplets deposited in the subcompartment due to the shearing of the high speed gas flow. These three mechanisms were observed in the 1:10 scale simulation experiments (3].
5.1. Discersion via Seal Table Exit After the entrained droplets fly out of the cavity exit, a small fraction of them goes into the seal table and rushes out into the upper containment dome. The maximum fraction, F21, traveling through is assumed to be limited by the view factor of the seal table exit to the cavity exit, i.e.
4 F u= F 2"" , (5-1)
A, where An is the area of the seal table exit, Aw is the area of the cavity exit, and F2 is the droplet entrainment frac on in the reactor cavity, which can be obtained from the previous analysis of the corium dispersion and transport in the cavity. For the geometry of the Zion reactor containment building (5], the area ratio of An to Au is about 3.5%.
Besides the entrained droplets, a fraction of the liquid film may enter the seal table room, j and part of it would rush out of the seal table exit. However, since only the droplet ]
carryover is a concern, this fraction is excluded.
]
5.2. Direct Carrvover The direct carryover comes from the small droplets entrained in the reactor cavity. Of the entrained droplets with total volume fraction (F2-F2i) in the cavity, part of the small droplets, F22, can follow the gas stream and bypass the subcompartment structure without i deposition. This portion of droplets then enters the upper containment through the air l vents that . simulate the path of the steam flow from the subcompartment to the containment dome. As shown in Fig. 5.1, the droplet and gas flow from the cavity exit impinge on the seal table bottom wall and spread around. Based on the experimental l parametric study (3), this flow can be treated as a circular film flow on a flat plate of the same width as the seal table bottom floor (I4 ). By assuming that the wall friction to the gas stream is negligible because of the relatively small geometry and that the gas velocity i
I 25 NUREG/CR-6510
V, is the sam 9 as at the cavity exit (V,), the mean gas film thickness on the plate is f approximately:
f D ,,'
S,=I -
'1 + D *'
(5-2) 2<4>< Ls> i Inside the gas flow, a droplet with an initial velocity V at the cavity exit will move towards the seal table wall in the x direction as shown in Fig. 5.1. Meanwhile, driven by the gas stream, droplet gradually turns to the gas flow direction (y direction). Large J droplets with high initial velocity impinge on the seal table wall before being convected out of the wall area. To determine the diameter of the droplets that deposit on the seal table bottom wall, a droplet trajectory analysis is applied.
For a droplet of diameter d in the gas flow field, the major force acting on the particle is the drag force imposed by the gas flow, and the gravity force is neglected due to high droplet velocity at the cavity exit. Accordingly, the equations of motion for the droplet are:
/1 'dV 1 f
1 g d 'Ps, g ,y = 2 s3 C pf f, A,)2 s , H
( >
f 1 'dV 1 / 1 g&'Ps, g ,* = gCs 4 d , p,Q , %
- Y V, = V,s = .
(5-5) dt, dt The corresponding initial conditions are:
y(t = 0) = 0, x(t = 0) = 6, , (5-6)
V,,(t = 0) = 0, V,(t = 0) = V, . (5-7)
By assuming constant drag coefficient, analytical solutions of the particle trajectory are y = V,t
- ' In ##' V,t + 1 (5-8) 3 gp,, Cs <4dpf x = S,
- ' In ##' V,,t + 1 (5-9) 3 g p,, Cs <4dpf ,
the two equations can be combined together to eliminate the time variable. The particle trajectory then depends only on the droplet size and the initial velocity Va. Within the seal table length, Ls, any droplet that has a trajectory (y < Ls/2, x = 0) will impinge on the seal table bottom wall and thus should be excluded from the fraction of direct carryover, Fu. Thereafter, the problem is reduced to finding the initial droplet velocity Ve of a specific droplet with diameter d.
1 i
In reactor cavity, the velocity of a entrained droplet is governed by the following I equation of motion:
91 g s
, Pt fu -Ys f - W
.On average, the droplet entrained in the cavity accelerates by the drag force of the gas l
j stream within about a half of the cavity length. For constant gas velocity in the cavity and j
. zero initial droplet velocity upon entrainment, the solution for the droplet velocity at the
{
cavity exit is given by:
l V'
I'4. = V, - e s .
(5-11) 3p,Cs 1+ V,t*
<4Pi, d L,
' 4pfd~
-=
2 b (V s
)dt = V,t,s3-P,C s> In ~1 + 3p,Cs' V,t,~
(5-12)
< 4pfd, _
where t. is the time interval for the droplet to travel through the half cavity length. For a droplet of size d, Ve is obtained by combining the above two equations. If Ve is greater
, than Yea, droplet velocity for critical size droplets, this droplet will impinge on the seal table wall. Subsequently, it is expected to find a critical droplet size do when Ve equals Vey. Droplets smaller than da will be convected out of the wal table wall region, contributing to the direct carryover fraction Fn. With a log-nonnal droplet size distribution [15], we have:
'0.884 y ,(g _ y ) J, 3.13d.
(o.mrp d(313d.,, - d)s dd (5-13)
- )
2.13d Y = In .
(5-14)
(3.13d,,, - ds The d. is the volume median diameter of the droplets entrained in the cavity, which can i be obtained from Eq. (4-9). To solve all these equations, simple numerical iterations can yield the critical droplet size, da, as well as the liquid fraction of the direct carryover to the containment dome (Fn).
l 27 NUREG/CR-6510
i Ls/2 i
{
4 5
N i
\ ! :N'N
.\ i N
- . SealTable
, t., x x x x x s x x x N x x x s. x x x s, xx\
8
- ~er-
.i Gas J l Flow Cavity Exit
/ /
/ ; ,,/
/ i /
/ ! /
/ '! ,/
/ ! i Fig. 5.1, Trajectory ofliquid droplet under seal table
' NUREG/CR-6510 28 1
5.3. Re-entrainment in Subcomnartment Among the total discharged liquid, only a small fraction of liquid droplets of diameters less than der is directly carried over to the containment dome. The remaining liquid deposits on the seal table bottom and the subcompartment structure walls, resulting in a new film that is subjected to a re-entrainment process from the high speed gas stream.
The flow visualization in the 1:10 scale simulation experiment shows that re-entrainment occurs mostly around the seal table bottom wall where the gas flow is still strong [3].
Away from the seal table, gas velocity reduces significantly because of the expansion and mixing in the large subcompartment free space where re-entrainment is thus considered to be insignificant. Of the re-entrained droplets in the seal table area, certain droplets that can follow the gas stream will be eventually convected to the upper containment dome through the air vents, and the rest is trapped in the subcompartment structure. To determine the liquid fraction that is convected to the containment, a two-step model is developed concerning the re-entrainment process and the trajectory of the dispersed droplets. A schematic illustration of the model is shown in Fig. 5.2.
The first step is to find out how much liquid is re-entrained in the seal table area. It is assumed that the film flow on the seal table bottom wall is in the form of a circular film flow analogous to a flat plate investigated in the experimental parametric studies [3].
Only the liquid film in a sector that is towards the front air vent has the chance to be both re-entrained and transported into the containment dome. Furthermore, the film velocity and the gas velocity are assumed to be the same as that at the cavity exit, and the entrainment duration is equivalent to the entrainment time t.n in the test cavity. This is because the entrainment duration in the cavity is mainly determined by the liquid film transport time as shown in the latter sections. When the entrainment process is terminated in the cavity, the film flow source is also exhausted. Therefore, within the total entrainment time ircerval, t , the re-entrainment fraction on the seal table bottom wallis given by:
F, = '#" A (5-15)
(1-(Fu+ F22))%Pt where As is the area of the film sector that faces the air vent. Since there are two front air vents, a factor 2 is proposed here. For the simplified Zion reactor subcompartment, the sector length is half of the seal table width, L., with an angle span of roughly 30'.
The key parameter here is the entrainment rate 6,, which is a function of the liquid film Reynolds number and the Weber number based on the gas velocity according to Kataoka et al. ([13], Eq(4-9)). With all the assumptions, the only unknowns to determine 6, are the film velocity Vr and the film thickness h on the seal table bottom wall. By neglecting the friction force on the seal table bottom wall, the film velocity is equal to the average liquid velocity at the cavity exit, Vr., obtained from the model of the corium dispersion in the cavity. Thereafter, the average film thickness on the seal bottom wall is approximated in the following way from the continuity equation:
Ld Lv
- = == =
l s
i ) . , a
! / , .
- N i / * '
N l' / _
, / 8 '
N i / $ Yh N l / *iii *
's i
-/ Vdy
- N
! /- droplet **
s Seal Table / '
.~
/ / ,/ / / / / ,/ / / // .* *' , y 5
....* N
! 6g '
N N
i Gas Flow
! N i
= .
! h
-]
m x N
Cavity Exit N
Figure 5.2, Re-entrainment process in the subcompartment NUREG/CR-6510 30
5 i
h = 1 '(1-(F u+ F u))% V 1 D' ,
(5-16) 2 _
xD,Lc 3p+ 2Ls>
where L is the seal table width. Thereafter, the re-entraim2ent fraction F3 in the subcompartment can be obtained explicitly with Eq. (5-15). l The remaining problem is to decide the fraction of the re-entrained droplets that are convected to the upper containment dome through the air vents. It is observed that most of the fine droplets enter the upper containment dome through the two front air vents. '
Therefore, the following investigation is confined to the region directly connected to the t two front air vents. Here, droplet trajectory analysis is applied again to determine the fraction of the droplets that can follow the gas stream all the way to the containment. A droplet re-entrained in the seal table region has its lateral velocity towards the subcompartment side wall. Meanwhile, due to the drag force from the gas flow, this droplet gradually gains a vertical velocity towards the air vent. Certainly, there must be a critical droplet size deri. Droplets with sizes larger the de,i can not follow the gas stream !
to the containment dome and will then be trapped in the subcompartment structure. For a droplet traveling in the vertical gas flow field with gravity effects as shown in Fig. 5.2, its ,
trajectory is obtained in the similar way developed in section 5.2.
_ _ y gd' '_y gd ' e .2,g, x= V' # t - --In (5-17) m _
m 2.)gdlm
( s d
y = -In "- V,ot + ,
(M) m ud dA8 m= (5-19) 4p, ,
where, x is in the vertical up direction and y is in the horizontal direction towards the side wall. The Voo denotes the droplet velocity at the moment of entrainment, which is assumed to be the film velocity Vr. In these equations, care should be taken for the drag coefficient Ca because the vertical velocity of the gas in the vent area is relatively slow with a small Reynolds number particularly for the fine droplets. This implies that C4 could be much larger the 0.4. Hence the following correlation for drag coefficient [14] is used in the computation of the critical droplet size:
6 C, = 24 +0.4, 5 Re, s 2 x 10 . (5-20)
Re, (1+[Re)
Let the notation Lv stands for the distance from the seal table edge to the subcompartment wall in the film flow direction, and Hy equal the air vent height measured from the seal table bottom. If the trajectory of a droplet of size d satisfies (x < H,, y = Lv), this droplet 31 NUREG/CR-6510
will impinge on the subcompartment wall and thus be trapped. By substituting x and y in Eqs. (5-17) and (5-18) with Hy and L,, the critical size dai of the droplet that can barely make its way to the containment is obtained if the gas velocity V, in the air vent area is known.
i There are four air vents that connect the subcompartment to the upper containment dome. The two front ones at the both sides of the seal table are identical in terms of their flow path from the cavity exit. The other pair have longer flow paths compared to the front ones. Gas flow comes out of the cavity is then separated into four paths and the flow rate Q, in each path is solely determined by the pressure loss from the cavity exit to the containment dome. For the i-th path with incompressible gas flow assumption:
R Q,':
AP= R' Q= z ,
(5-21) 2Ps 2Ps where Qz refers to the total gas flow rate of all paths and Ri is the " resistance" of the i-th path, which is the summation of the major and minor losses along the flow path divided by the cross sectional area, whereas the total " resistance" Rz is defined as:
K = [, d . (5-22)
For the simplified geometry of the Zion reactor containment building, and from the estimation of the " resistance" of each path, the flow rates in these paths are calculated as
[15]:
Op = G,2 = 0250,,, Q,3 = 0320,,, Q,4 = 0.180,,, (5-23) where Qs1 and Q,2 are the gas flow rates in the two front air vents. Subsequently, the gas speed V, in the air vent is obtained by dividing the mass flow rate with the gas density and the path cross sectional area. With this gas velocity, Eq. (5-17) and (5-18) can be solved for the critical droplet size dai. Using dai as the upper limit, the fraction of the re-entrained dmplets that enter the containment is obtained from the log-normal droplet size distribution:
7 , 7' '0.884 ,-(os:4rp 3.13d. dd. (5-24)
- J D(3.13d, - d)s The parameter Y is defined by Eq. (4-9).
As a summary, the total carryover fraction is simply the summation of F 21, F22, and F3i. These results are basically obtained from the droplet trajectory analysis. For droplet re-entrainment in the subcompartment, only a small area around the bottom wall of the seal table room participates. This assumption is valid according to the 1:10 scale experiments and to the estunation to the gas flow velocity in the prototypic subcompartment. If the vessel pressure is very high or the vessel break size is quite large as will be discussed in the section 7, the gas velocity in the air vent area might reach the NUREG/CR-6510 32 J
entrainment onset condition, and the carryover would thus be much higher due to the re-entrainment process in the vent area. In such a case, the model should be extended to include the extra fraction of re-entrained droplets, which is rather far from the interests of the present study. Moreover, the trajectory analysis can only yield the final result of the carryover regardless of the time transient. For a more sophisticated investigation, the heat transfer between the hot corium and the steam flow should be considered, which may result in smaller gas density than what is employed based on the isothermal assumption.
As a rough estimation, the drag force imposed on the re-entrained droplets could be smaller and thus less droplets would be convected to the upper containment. From this .
point of view, the present model is conservative. Beside all these concerns, the liquid film flow entering the seal table room might contribute to the total carryover to the upper containment. However, if only the droplet carryover is the concern, this fraction may be excluded.
l 1
1 I
l 33 NUREG/CR-6510 1
- 6. COMPARISONS WITH THE EXPERIMENTAL RESULTS To evaluate the presented model, comparisons are performed with the experimental data obtained in the Purdue University 1:10 scale DCH tests [3,4, 5]. The Purdue University separate effect experiments were carried out at wide range of pressure conditions with water or molten woods metal to simulate the core melt in the prototypic accident. A 1:10 scale Zion reactor model was designed and constructed to investigate the blowdown liquid dispersion and transport. Various instruments were employed to capture the parameters that are important for understanding the corium dispersion phenomenon in the accident. These parameters include the film front propagation, the liquid film velocity and thickness in the cavity, the entrainment fraction and droplet size distribution in the cavity, and the total carryover in the upper contamment. Here, the data for the comparisons include the time transient of the film front in the cavity, the film -
thickness and velocity in the cavity before gas blowdown, the fraction ofliquid that does not participate in the entrainment process, the entrainment time and fraction in the cavity, and the total carryover to the upper containment. Table 6.1 shows the geometric parameters that are employed in the estimation calculation. In all these comparisons, the jet velocities are obtained from experimental measurements [3,4, 5] rather than from the discharge model developed in section 2, because the friction loss of the discharge line in the tests differs from that of the prototypic blowdown.
Table 6.1, Geometric parameters of the 1/10 scale PU test facility Dn(m) xi(m) x2 (m) Le(m) A /A., L. (m) Hy(m) A,(m) 2 g,(m) 0.25 0.15 1.04 2.0 3.5% 0.5 0.73 0.172 1.02 6.1. Liauid Flow in Cavity before Gas Blowdown In the air-water experiment under a 1.4 MPa test vessel pressure, the jet discharge is actuated by a solenoid valve with maximum velocity of 13 m/s and a 0.2 seconds linear rising edge due to the gradual response of the valve opening. The liquid discharge lasts 0.55 seconds, followed by air blowdown. The theoretical prediction of the film front location versus time is compared with experimental data as shown in Fig. 6.1. The difference between prediction and experimental data is less than 5%, where the measured data is obtained from film thickness signals when the film front reaches the probe. The film flow takes 0.43 seconds to reach the exit, which is termed as the film transport time te before gas blowdown. Since there is only one third of the circular film flow toward the cavity exit, the non dispersion fraction F is given by:
F,=Q,,(t,-t,,) .
(6-1) 3T{,
Here, the fraction Fi is estimated to be 15%, which agrees with the experimental measurements [3,5]. The predicted film thickness and velocity distributions before air blowdown are plotted in Fig. 6.2. The flow velocity, measured with hot film probe placed right above the cavity floor, is reduced to 4 m/s at the exit as a result of friction and gravity effects. The film thickness is very small in the horizontal section because the j liquid spreads all over the walls including the upper ceiling. In the chute section, the film flow merges at the bottom floor, resulting in a much thicker liquid film. Since the model captures the major characteristics of the physical phenomena, reasonable estimations are obtained especially for the trends of change along the floor to the exit. In the case of the 6.9 MPa air-water tests, the water discharge is triggered by breaking a rupture disk. The film front propagation is thus govemed by Eq. (3-21). The measured waterjet velocity is 75 m/s (3,5]. The model predicted and the measured film front locations are compared in Fig. 6.3, which demonstrates fairly good agreements. In Fig. 6.4, the measured film velocity and thickness are compared with the model predictions.
In the woods metal tests under 1.4 MPa vessel pressure, the liquid jet velocity is 11 m/s with a sudden step jump when the rupture disk breaks [4, 5]. The jet lasts for 0.7 seconds that was measured with a conductivity probe. Because the initial velocity is small, the film front loses all its momentum near the cavity exit and the model gives zero film velocity at the cavity exit, (Fig. 6.6), resulting in an infmite transport time te. This i result agrees with the flow visualization conclusion and no liquid flows out of cavity l before air blowdown. Consequently, the film front traveling time is initially proportional to the traveling distance (Fig. 6.5). As the front proceeds, the analytical solution, Eq. (3-10), departs from the later stage transient due to the neglect of the grasity force.
However, because of the unique characteristics of the step change of the jet velocity, the film front location can be estimated from the integration of the quasi-steady state solution with the gravity effects (the upper curve in Fig. 6.6). This is because there are no intersections among the characteristic lines originated from the jet edge. Nevertheless, i for the case of 14.2 MPa woods metal tests [4], the measured liquid jet velocity is much faster (about 31 m/s). As shown in Fig. 6.7, the measured film font locations match the predictions of Eq. (3-10). Fig. 6.8 presents the comparisons for the film thickness and velocity distributions.
In conclusion, to effectively apply the analytical solution for the film front propagation, the jet velocity should be sufficiently high so that the inertia of the film flow can overcome the wall friction and gravity effects. If the jet velocity or volumetric flow rate is too small, the discharged liquid cannot reach the cavity exit before gas blowdown, and all the liquid is subjected to the later stage dispersion process. This condition may be quantified by evaluating the film velocity at the cavity exit with the quasi steady film flow model. Under the prototypic conditions, due to the high vessel pressure and the small friction loss along the discharge path, the film front propagation solution Eq. (3-10) is expected to be applicable without significant discrepancies.
1 0.4 e experimentaldata l
- model 0.3 -
E 0.2 -
0.1 -
O i- ' - . .
0 0.6 1.2 1.8 x(m)
Fig. 6.1, Water film front propagation in the cavity under 1.4 MPa vessel pressure l
1 NUREG/CR-6510 36
n l
10.0 15.0
- O measurement ,
l 8.0 model -
12.0
^ 6.0 -
velocity E o ~
9.0 m E - ,
e )m v
c 4.0 -
v g -
6.0 =
~
thickness 2.0 - =
3.0 R-0.0 * ' ' ' '
O.0 0 0.6 1.2 1.8 x(m)
Fig. 6.2, Water film thickness and velocity distributions in 1.4 MPa tests 37 NUREG/CR-6510
f I
4 0.040 , , , ,
. experimental data: 0.032 s . .
\
0.030 -
0 0.020 -
0.010 -
0.000 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
O.000 0.500. 1.000 1.500 x (m)
Fig. 6.3, Water film front propagation in 6.9 MPa tests i
NUREG/CR-6510 . 38 l
l
, 80.0 i 1 e measured film thickness '
70.0 0.008 -
60.0 l
. _ _ - - _ _ _ _ _ _ _ _ measured
_ _ _ _ _ avera _ _ge v______
elocity: 50 m/s 50.0 e
film velocity -
40.0 -2 E x o
5 0,004 -
30.0 flim thickness E 20.0
~
0.002 -
10.0 9
~
4 0.000 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
O.0 0.000 0.500 1.000 1.500 x(m)
Fig. 6.4, Water film thickness and velocity distributions in 6.9 MPa tests 39 NUREG/CR-6510
I 0.6 e experimental data integration of steady solution 0.4 _ Eq. (3-31)
?
v .
w-0.2--
00 ' ' ' ' '
0 0.6 1.2 1.8 x(m) l Fig. 6.5, Woods metal film front transport under 1.4 MPa vessel pressure 1
i NUREG/CR-6510 40
oa measurement 15.0 .
model -
9.0 l
m velocity R I U
l 10.0 -
l
~-
6.0 U
[
.c '
5.0 -
3.0 thickness o O 0.0 - - - -
0,0 0 0.6 1.2 1.8 j x(m)
Fig. 6.6, Woods metal film thickness and velocity distributions in 1.4 MPa tests ;
i 41 NUREG/CR-6510
0.080 , ,
experimental data: 0.065 s O.070 -
0.060 -
0.050 -
0 0.040 -
0.030 -
0.020 -
0.010 -
,0.000 ' - ' - ' ' - - ' - - - - ' - -
0.000 0.500 1.000 1.500 x (m)
Fig. 6.7, Woods metal film front propagation in 14.2 MPa tests NUREG/CR-6510 42
_ = _ _ J
i i 40.0 i
e measured film (Nekness 0.008 30.0
.'- - - - - - - - - - - - - - - - measured
- - - - geavera velocity:2 6 m/s 0.006
^ e E flim velocity -
20.0 -3 E 0,004 -
film tNekness X: <,
10.0 0.002 -
1 o
' {
0.000 ' '
O.0 0.000 0,500 1.000 1.500 x(m)
Fig. 6.8, Woods metal film thickness and velocity distributions in 14.2 MPa tests 43 NUREG/CR-6510 1
6.2. Liould and Gas flow in the Cavity In Figs. 6.9 to 6,11, the total entrainment fraction transients are plotted against the entrainment time under different experimental conditions. In general, the entrainment fraction increases rapidly at the beginning of the gas blowdown due to the large film j surface area in the cavity. As time approaches the entrainment time, ten, when the liquid film tail moves out of the cavity completely, the entrainment fraction is flattened, reaching the limit F2 that refers to the total entrainment fraction in the test cavity.
Compared with the experimental data, the predicted total entrainment fractions are quite accurate except for the low pressure air-water tests operated with solenoid valve control
[3,5], which shows a 23% difference. As the vessel pressure increases to 6.9 MPa [4,5],
the liquid film velocity becomes much faster so that the entrainment time (about 0.1 seconds) is significantly shorter than in the low pressure test.
In Figs. 6.12 to 6.14, the predicted mean droplet sizes are presented under different test conditions. For the rupture disk actuated tests (the low pressure woods metal tests and the high pressure air-water tests), the difference between the measured and the predicted mean droplet sizes using the original droplet size correlation of Kataoka and Ishii is within 15%. However, for the low pressure air-water tests actuated by solenoid valve, good agreement is achieved if the coefficient (0.028) of Eq. (4-9) is replaced with 0.082. Careful comparison shows that the only difference is the test actuating mechanism: one is controlled by solenoid valve and the others are triggered with breaking rupture discs. For the case of solenoid valve control, the closing of the solenoid valve is automatic after liquid discharge with certam time period that is overlapped with the gas discharge time [3, 5]. Although this time interval is very short (about 0.06 s), the gas flow from the auxiliary pipe line blows the liquid jet apart and generates some large droplets. This argument also explains the reason why the measured entrainment fraction in Fig. 6.9 is about 23% larger than the predicted value. The by-product of the model is the pressure loss to the friction between the gas flow and the liquid flow (both film and droplet flows) in the cavity. In Figs. 6.15 to 6.17, the pressure loss to the liquid flow in the test cavity is presented as function of time. The maximum pressure loss is lower than 100 kPa.
The model predicts the total entrainment fraction reasonably well, when compared to the experimental data. 'Ibe predicted droplet size with the original mean droplet size correlation of Kataoka and Ishii is about 15% lower than the measured value. From the point of conservative prediction, this discrepancy is acceptable because it yields a larger total droplet surface area and hence a slightly more severe containment heating and pressurization. In addition, the pressurization of the reactor cavity caused by the liquid flow can be predicted. It should be mentioned that the model for the gas flow in the cavity may not be directly applied to the case when the gas flow is choked at the cavity exit as in the 1:10 scale tests with 14.2 MPa test vessel pressure [4, 5]. In such a process, choking occurs for a short period of time after gas blow down. However, the results of the tests operated under high vessel pressure also showed that the cavity pressure peaked in a relative longer time frame compared to the very short entrainment time duration.
i NUREG/CR-6510 44
i Therefore, using the initial gas velocity in the cavity may yield reasonable estimation of entrainment. But the cavity maximum pressure could not be predicted due to the exclusion of the choking mechanism. In spite of the possible applicability of the model to high pressure case, the model has its limit in handling the transient choking phenomenon in the cavity, especially when the entrainment duration is comparable with the choking time. In order to justify the model in this situation, further effort is needed that considers the choking process.
I i
. Enperimental data: 0.43 in 0.2 seconds .
5ca 0.40 -
0 .
8 0.30 -
Ti y .
u.
EO 0.20 -
E .
.5 .
1
- 2. 0 10 15 0.00 ' ' ' ' ' ' ' '
O.00 0.05 0.10 0.15 Time ( s )
Fig. 6.9 Predicted entrainment fraction in cavity for 1.4 MPa air-water tests I 45 NUREG/CR-6510
I 3 -
g .
5: -
i j 0.15 -
1 -
c - Enperimental data: 11% in 0.25s '
C ~
.9 -
\1 13 i -
g 0.10 -
i -
u.- -
g -
I .
'O .
I E . n C
- g 0.05 -
g i
w -
3 .
l 0.00 ' ' ' ' -
0.00 0.10 0.20 0.30 Time (sec)
Fig. 6.10 Predicted entrainment fraction in cavity for 1.4 MPa woods metal tests
}
I NUREG/CR-6510 46
i '
1 '
4
~
Enperimental data: 33% in 0.2s ~
g 0.40 -
0 .
.5 8 0.30 -
=0 m -
Eco 0.20 -
E ~
.5 m
y 0.10 -
tu 0.00 ' ' ' ' ' ' '
O.00 0.02 0.04 0.06 0.08 Time ( s )
Fig. 6.11 Predicted entrainment fraction in cavity for 6.9 MPa air-water tests I
j 47 NUREG/CR-6510
8 E-4 . . . .
i . . .
m E 6E-4 -
y -
5 .
f .
.5 4E-4 -
m h! ^
m .
E Experimental data: Dvm=4E-4 m o.
o m
2 E-4 -
O -
OE0 - ' - - ' ' ' - '
O.00 0.05 0.10 0.15 Time ( s )
Fig. 6.12 Predicted droplet size in cavity for 1.4 MPa air-water tests t
2 E-3 .
i .
i -
~
E ~
A
.' Experimental data: Dvm=0.001 m .
- g. -
o
.5 1 E-3 -----___________________________
e y-g . __
-E -
~e a .
8 o .
-0E0 ' ' '
0.00 0.10 0.20 0.30 Time ( s )
Fig. 6.13 Predicted droplet size in cavity for 1.4 MPs. woods metal tests 49 NUREG/CR-6510
F l
l 3E-4 .
_m Experimental data: Dvm=1.84E-4 (m) -
E b 2E-4 -
3, ------------------- ----------.
o
.5 e (" -
.ti
. tn
-g 1 E-4 -
a.
2 O .
OE0 ' ' - ' - ' -
0.00 0.02 0.04 0.06 0.08
, Time ( s )
Fig. 6.14, Predicted droplet size in cavity for 6.9 MPa air-water tests NUREG/CR-6510 50 1
l 8E4 . . . .
. Pressure peak in the tests: 3.5E4 Pa n ,
as 1 6E4 -
.'9 m .
H 3 4E4 -
8 2 .
E m
8 2E4 -
e c.
I OE0 * ' '
O.00 0.05 0.10 0.15 Time ( s )
Fig. 6.15, Predicted pressure loss in cavity for 1.4 MPa air-water tests 51 NUREG/CR-6510
1 s
\
8E4 .
. Pressure peak in the tests: 5.5E4 Pa .
m Cl.
m 6E4 -
-5 m
g o
- 4E4 - -
8_ ~
E a
g 2E4 -
iC OE0 O.00 . 0.10 - 0.20 0.30 Time ( s )
Fig. 6.16, Predicted pressure loss in cavity for 1.4 MPa woods metal tests 1
)
)
I NUREG/CR-6510 52
1ES ,
Pressure peak in the tests: SE4 Pa m
m 8E4 -
c.
32 m
.5_r 6E4 -
2 ~
8 S 4E4 -
8 8
m 8: 2E4 -
- c. i
.0E0 ' ' ' '
O.00 0.02 0.04 'O.06 0.08 0.10 Time ( s )
Fig. 6.17, Predicted pressure loss in cavity for 6.9 MPa air-water tests j
6.3. Droolets Transoort and Re-entrainment in the Subcomoartment In the case of air-water experiments, the predicted dispersion fractions in the l containment compare well with experimental data (Table 6.2). The discrepancies are within 15%, and the predictions are slightly higher. However, for woods metal tests, the measured Fais, is about 1.6%, while the predicted value is 0.86%. In the experiments, about 1.4% woods metal is collected around the seal table exit area [3], including some large pieces. Only 0.2% woods metal comes from the two front air vents in the form of fme droplets. Here, the liquid that travels through the seal table room might be under-predicted by about 1% due to the involvement of the liquid film flow through the seal table. Since the total dispersion fraction is small, this difference appears to be significant.
For the purpose of modeling the total dispersion fraction, the exclusion of the film flow that passes through the seal table is tolerable. From this point of view, the model is still conservative and slightly over-predicts the dispersion fraction.
Of the total dispersion fraction, the direct carryover (F 22 ) is extremely small in all cases as shown in Table 6.2. Only the droplets smaller the 14 m can be convected out of the seal table area without deposition. This is because the droplet velocity at the cavity exit is so high that most of the droplet entrained in the cavity will impinge on the seal table bottom wall. For the case of the air-water tests, the maximum diameter of the droplets re-entrained in the subcompartment is smaller than the critical diameter of the droplets that can be transported to the containment. Therefore, all the re-entrained water droplets in the seal table area and toward the front air vents are counted in the total dispersion fraction. On the other hand, the critical size for woods metal droplets is much smaller than the maximum diameter of the droplet re-entrained in the seal table area, and a small fraction of the re-entrained droplets contribute to the total dispersion fraction Fai.p.
For different sizes of the discharge nozzle at a test vessel pressure of 6.9 MPa, the predicted total carryover is shown in Fig. 6.18. The predictions are about 20% higher than the experimental data (the solid rectangular symbols in Fig. 6.18). This trend is expected since the gas velocity is faster for larger discharge nozzles. It results in stronger re-entrainment and smaller droplet size in the subcompartment.
NUREG/CR-6510 54 w
Table 6.2 Predictions of the dispersion fractions in the 1:10 scale experiments Conditions F2 da F22 dai dm.xi F3: Foi,p Foi,,
(%) ( m)- (%) ( m) ( m) (; . t (%) (measured)
(%)
1.4 MPa 1.5 14 7E-5 340 102 1.80 3.2 2.7 water 1.4 MPa 0.53 4 IE-14 184 553 0.33 0.86 1.6 woods metal 6.9 MPa 1.26 14 SE-5 228 93 1.64 2.9 2.4 water l
i 1
55 NUREG/CR4510
l 10 . .
1 m Model results Test data 8 -
n h . .... ..........................................
m . .
U 0 . .
4 c.
U ................l.................!................_
.- un u m 2 - - - - - - - -- - -
0 3.5 4 4.5 5 Dj (cm)
Fig. 6.18 Effects of discharge nozzle size on the carryover (6.9 MPa vessel pressure)
1
- 7. APPLICATIONS TO THE PROTOTYPIC CONDITIONS The models developed in the previous sections are based on major mechanisms, and the correlations employed in these models for entrainment rate, mean droplet size and size distribution, and drag coefficients are well established. It is expected that these models are applicable to the prototypic Zion reactor DCH process. Several sample estimations of the corium dispersion transients in the Zion Reactor Power Station are presented in this section, including the parametric studies concerning the effects of the vessel break size and the vessel pressure change. It should be emphasized again that the model assumes isothermal process without chemical reactions and possible corium-water interactions in the reactor cavity. However, these predictions can only give the general trends of the corium dispersion process with the modeling of the fundamental hydraulic mechanisms, resulting in understanding of the DCH phenomenon.
7.1. Standard DCH Accident The standard DCH accident is assumed to occur under the following conditions:
vessel pressure: 6.2 MPa breach size: 0.35 m core melt: 54 t (7.0 m')
steam temperature: 600 K These reference parameters are based on the probabilistic analyses [8] of the postulated DCH accident. With the minor friction loss coefficient (K) equal to 0.5 in Eq. (2-4), the corresponding corium jet velocity (Vj) is 32.8 m/s, and the blowdown process lasts 2.22 seconds (the liquid discharge time ta). Following the corium flow, the steam discharge starts at an initial mass flow rate of 972 kg/s, which decreases exponentially with respect to time.
From the moment of the initiation of the corium discharge, it takes about 0.57 seconds for the liquid film flow to reach the cavity exit (Eq. (3-10)). This time interval is termed the film front propagation time t . Accordingly, the time duration for the quasi-steady liquid film flow at the cavity exit before steam blowdown is estimated to be 1.64 seconds. Since there is only one third of the discharged liquid flowing towards the cavity exit, the amount of corium that flows out of the cavity before steam blow-down is estimated to be:
r 23 M=3 i V,xD pf(t, -t,)= 133x10 (Kg),
- 8 (7-1)
I which is (F i ) 24.7 % of the total discharged corium. This part of corium will not participate in the latter dispersion process after steam blowdown. Based on the modeling of the quasi-steady. state film flow in the cavity, the distributions of the liquid film 57 NUREG/CR-6510
58 l velocity and thickness along the cavity floor before the steam blowdown are shown in l
Fig. 7.1. In the cavity pedestal section, the minimum corium film thickness is about 6.3 mm due to the film spreading over the walls. However, the film thickness in the chute section is much larger because the film flow is mainly on the bottom floor. At the cavity exit, the thickness reaches 6.6 cm. On the other hand, the liquid velocity decreases along the cavity floor because of the wall friction and the gravity force. At the cavity exit the corium film velocity is about 8.0 m/s.
After the steam blowdown from the primary cooling system, the flow in the reactor cavity consists of three parts, i.e., the corium film flow, the gas flow, and the entrained droplet flow. According to the model, the entrainment process here is determined by the film transport time, the time interval for the film flow to completely move out of the cavity after steam blowdown, which is about 2.8 seconds. As shown in Fig. 7.2, during this time period the total entrained droplet volume amounts to 28% of the discharged corium. The corresponding volume median diameter of the entrained droplet is about 3.75 mm (Fig. 7.3). The pressure increase in the cavity due to the friction loss to the droplet flow and the film flow is shown in Fig. 7.4, which presents a maximum of 0.12 MPa pressure peak at about 0.3 seconds after steam blowdown. Although this pressure peak is much larger than twice the atmospheric pressure, the Mach number of the steam flow is less than 0.7, and there is no choking at the cavity exit due to friction loss.
Of the total entrained droplets in the reactor cavity, about 529 kg corium droplets with a volume median diameter of 3.75 mm travel through the seal table, entering the upper containment dome. This part of corium (F 21) amounts to 0.98% of the total discharged core melt. Almost all of the remaining entrained droplets along with the film flow deposit on the subcompartment structure and are subjected to the re-entrainment process.
Only droplets smaller than 20 m can be directly carried over to the containment.
However, its mass fraction (F22) is so small (~ 3.78x 10-is) that it is negligible. Therefore, besides the droplets through the seal table exit, the other portion of the total dispersion fraction in the containment comes from the re-entrained droplets that survive the subcompartment trapping. By the proposed trajectory analysis, the re-entrained droplets that are smaller than 675 m can be convected to the upper contamment dome. This part of droplets amounts to 243 kg, about 0.45% (F3i ) of the total discharged core melt.
Consequently, the total dispersion fraction (Faisp) in the containment is 1.43%, and the corresponding corium mass is 772 kg. About 68% of the dispersed droplets come from the seal table exit with a volume median diameter of 3.75 mm, and the remaining 32%
have a diameter smaller than 675 m.
0.100 , , ,
40,0 0.080 film velocity 30.0
_ 0.060 _
20.0 0.040 - >
film thickness -
10.0 0.000 ' ' ' o,o 0.000 5.000 10.000 15.000 xfm)
Fig. 7.1, Corium film thickness and velocity distributions along cavity floor 59 NUREG/CR-6510
m d
l l
l
- l -
0.400 , ,
1
. Po =6.2 MPa .
- > Dj =0.35 m 8 0.300 V,=7.0 m* -
.E C
.9 U
g 0.200 -
Eo .
E .
C 3 0.100 -
E 0.000 ' - - - ' . . . - t . .
0.00 1.00 2.00 Time ( s )
Fig. 7.2, Entrainment fraction F2 in the reactor cavity s
NUREG/CR-6510 60 '-
1 1
i ,
Po=6 2 MPa
~
- D,=0.35 m -
E
- V,=7.0 m*
3 0.004 -
.s -
8 m
g 0.002 _
~6.
e Q .
i 0.000 - - - - ' . . . . , . .
0.00 1,00 2.00 Time ( s )
Fig. 7.3, Volume median diameter of the droplets entrained in the cavity 61 NUREG/CR-6510 i
2E5 , , ,
^
m .
Po =6. 2 MPa o-
. D,=0.35 m .
] -
V =7.0 m' -
E.-. 1ES - -
o . .
g .
O b - .
m 8 SE4 -
e .
a.
y -
5 .
m o -
OE0 - - - ' - - - ' - - \' - -
0.00 1.00 2.00 3.00 Time ( s )
Fig. 7.4, Cavity pressure resulted from film flow and droplet flow in cavity NUREG/CR-6510 62
7.2. Vessel Break Size Effects The effects of the vessel break size on the corium dispersion is investigated at 6.2 3
MPa vessel pressure with 7.0 m of core melt. First, the fraction of corium that flows out of the cavity before steam blowdown is plotted in Fig. 7.5 with respect to different break sizes. As the break size increases, the fraction (F )i approaches zero due to the reduction of the corium discharge time to. For instance, if the reactor lower head drops to the cavity, the discharge process ends instantaneously. Subsequently, no corium flows out of the cavity before steam blows down. As shown in Fig. 7.5, the critical break size is calculated to be 69 cm. For a vessel break larger than this diameter, all the discharged corium is subjected to the entrainment process after steam blowdown with Fi equal to zero.
After steam blowdown, the dispersion duration (t., the entrainment time) becomes shorter and shorter as the vessel break size increases as shown in Fig. 7.6. This is mainly because of the larger gas velocity and density that drive the film flow faster and quickly terminate the entrainment process in the cavity. In Fig. 7.7 and 7.8, however, the total dispersion fraction F 2and the maximum cavity pressure grow due to the increase of the liquid friction force for larger vessel break size within the studied range. This implies that the entrainment rate plays a dominant role in spite of the reduction of the entrainment duration, resulting in a larger dispersion fraction in the reactor cavity. Moreover, the volume median diameter of the entrained droplets in the cavity decreases for larger vessel break sizes due to the stronger steam flow (Fig. 7.9).
In the subcompartment, the fraction (F21) of corium travels through the seal table and increases gradually as the break size changes from 0.3 m to 0.54 m as shown in Fig. 7.10.
For larger vessel break sizes, the re-entrained droplets that can survive the subcompartment trapping become significant. In Fig. 7.10, this fraction of corium (F3i )
resches 8.2% of the total discharged corium at the break size of 0.54 m. The corresponding maximum droplet size is about 720 m. Fig. 7.10 also shows that the direct carryover fraction F22 is virtually zero regardless of the vessel break size. It is interesting to note that the critical size of the re-entrained droplets that can follow the gas stream to the containment decreases eventually as the vessel break size increases, as shown in Fig. 7.11. It suggests that the lateral velocity of the re-entrained droplets in the air vents rises along with the growth of the vertical steam flow velocity. As a result of the two competing factors, i.e., the vertical drag force and the lateral droplet inertia, smaller droplets can impinge on the subcompartment wall for larger vessel break sizes.
The model developed in section 3 cannot handle the situation when the gas flow chokes at the cavity exit. The investigation of the vessel break size effects is thus limited to the break diameter of 0.54 m. Beyond this upper-limit, a more sophisticated model is needed to deal with the transient steam choking phenomenon.
0 0.40 . .. ..
_ Po = 6.2 MPa .
V.=7.0 m*
O.30 -
l 1 0.20 -
0.10 -
0.00 ' .i .f . . . . . . . i . ...
0.400 0.500 0.600 0.700 D, ( m )
Fig. 7.5, Vessel break size effects on Fi s
4.00 , , , ,
3.50 [
Po = 6.2 MPa --i E
V,=7.0 m' i
^ 3.00 E- -
- 0) .
- 3
.i i.
g 2.50 F -
i :
C) :
E 2.00 -i O !
- 5 C :
1.50 L 3 E ! !
C
- g 1.00 .E-
-i D E C 3 W 0.50 E- i i
i 0.00 ~ ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
0.30 ' 0.35 0.40 0.45 ' ' .50 0
D, ( m )
Fig. 7.6, Vessel break size effects on the entrainment time ten in the cavity 65 NUREG/CR-6510
-- - - - ~ ~
Po = 6.2 MPa 5 -
V, =7. 0 m * -
0.40 -
1 l n 1 0.30 -
0.20 -
0.10 -
0.00 ' ' - ' ' ' ' a ' - '-
0.30 0.35 0.40 0.45 0.50 0.55 D (m) i Fig. 7.7, Vessel break size effects on the dispersion fraction F2 in the cavity NUREG/CR-6510 66
^
d 6E5 -
6 i i i -
c.
~ : i
> : Po = 6.2 MPa y SE5 P Vm =7.0 m' i:
. m :
o :
c 4E5 :- 2 3: i i O
c
. 3E5 .-
a . d o- -
O :
2 E5 m
y) - :
O : :
0 u 1 E5 -'
. 2 a - .
m :
m .
a) : :
6 ggg - , , . , I . , , , t ,,,, t , , . . t , , . -
- n. o.30 0.35 0.40 0.45 0.50 D, ( m )
Fig. 7.8, Vessel break effects on maximum pressure drop to liquid flow in cavity 67 NUREG/CR-6510
0.00s , ,
l Po = 6.2 MPa V =7.0 m' -
1 l
E 0.004 - -
v A
.t l d - -
O
.E E
g 0.002 - -
0.000 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
O.30 0.35 0.40 ' 04
.' 5 ' 05
.' 0 .
D (m) i Fig. 7.9, Vessel break size effects on the average D in the cavity NUREG/CR-6510 68
0.150 , ,
~
c -
Po = 6.2 MPa Q) .
E C
. V,=7.0 m' .
- 0.100 -
O -
O - F.disp -
/-
.C.
C O 0.050 F, -
- - 3 O '
g 6
,- p21 -
C _______,
=t'- ----------
~~~~~:
.O_
.o.00 ---=r:_ _
L')
O p .
- a. 22 -
v>
0 .
0.05 ' ' ' ' ' ' '
O.30 ~0.35 0,40 0.45 0.50 D (m) i Fig. 7.10, Vessel break size effects on the dispersion fraction in the containment 69 NUREG/CR-6510
/
/
SE4 ,
E ,
t 8
. M N 7E 4 -
m d .
8 .
t .
e -
e -
B 6E-4 -
n .
a E .
e o SE4 -
e= .
Po = 6.2 MPa -
5n
- Vm=7.0 m ' -
s .
4E 4 ' ' - ' - t .,, , i O.30 0.35 0.40 0.45 0.50 D (m) i Fig. 7.11, Break size effects on Der ofF3 NUREG/CR-6510 70
7.3. Vessel Pressure Effects With the standard break size (0.35 m) and total core melt volume (7.0 m3), the vessel pressure effects on the corium dispersion phenomenon is presented here. Within the pressure range of 3.5 MPa to 9.0 MPa, the fraction of corium that flows out of the cavity before steam blowdown is constant, about 24.7% of the total discharged corium. This is because the duration of the quasi-steady film flow at the cavity exit is inversely proportional to the square root of the vessel pressure, while the corium discharge rate increases linearly with the square root of the vessel pressure. Therefore, the effect of the vessel pressure change is canceled in Eq. (3-10), resulting in a constant Fi . However, this conclusion is not valid for the case when the film front cannot reach the cavity exit, which corresponds to a condition when the vessel pressure is very small (less than 1.7 MPa).
After steam blowdown, the dispersion duration (ten) decreases when the vessel pressure increases, as shown in Fig. 7.12, due to the larger gas velocity, liquid film velocity, and the gas density. In Figs. 7.13 and 7.14, the total dispersion fraction F2 and the maximum pressure loss in the cavity grow due to the increase of the liquid friction force under larger vessel pressure condition. Similar to the vessel break size effects, the enhancement of the entrainment rate plays a dominant role in spite of the reduction of the entrainment duration, resulting in a larger dispersion fraction in the cavity. Moreover, Fig. 7.15 shows that the volume median diameter of the entrained droplets in the cavity decreases for higher vessel pressure due to stronger steam flow.
In the subcompartment, the fraction (F2i) of corium aerosol particles that travel through the seal table and enter the containment dome increases slightly as the vessel pressure changes from 3.5 MPa to 9.0 MPa as shown in Fig. 7.16. With higher vessel pressure, the re-entrained droplets that can survive the subcompartment trapping becomes important. This fraction of droplets (F3i) reaches 2.3% of the total discharged corium for the vessel pressure of 9.0 MPa. The corresponding maximum droplet size is about 810 m (Fig. 7.17). Moreover, the direct carry-over fraction F22 is extremely small regardless of the vessel pressure, and the total dispersion fraction Fdisp is the summation of 2F and F3i. Similar to the previous section, the investigation of the vessel pressure effects is limited to the case where no steam choking occurs at the cavity exit. For a vessel pressure higher than 9.0 MPa, steam choking is inevitable.
In general, the increase of both the break size and the vessel pressure will enhance the degree of corium dispersion. However, the break size effects are much stronger because the steam discharge rate is proportional to the area of the breach. For the case of 0.54 m vessel break size, the amount of the dispersed corium in the containment reaches 10 % of the total dispersed core melt, which comes mostly from the re-entrainment process in the subcompartment. Moreover, as mentioned before, the model developed in section 3 can not handle the situation when the steam flow chokes at the cavity exit. If the vessel pressure is over 9.0 MPa or the vessel break size is larger than 0.54 m, the steam choking phenomenon is inevitable at the cavity exit. Therefore, a more sophisticated model is needed to deal with the transient steam choking problem.
e 5.00 ' - .
8 s i , ,
D =0.35 m 1
4.* .
- V,=7.0 m' -
n .
VJ v : }
g .
3.00 --
c) .
- i E
j C 2.00 '-
e !
E :
.C .
~
cc .
D 1,00 ~ -
C "
W : :
0.00 ' ' ' ' - - t . , ,
,,,,,,,,,,,,,,,[
4E6 SE6 6ES 7E6 8E6 9E6 Po ( Pa )
Fig. 7.12, Vessel pressure effects on the entrainment time to in the cavity NUREG/CR-&*iJ 72
L l
i l
0.50 , , -
u" ; D,=0.35 m .l 3_ 0.40 ..
E V,=7.0 m* j cd ; -
o .
C : :
'h 0.30 h 2 O - "
"O : -
o . -
CU : -
- t. -
- . 0.20 --
2 C -
G) : -
E : :
.E :
i
@ 0.10 h .
C -
- (
1.u :
0.00 ~- - - ' - - ' - - - - ' - '-
4E6 SE6 6E6 ' 7E6 8E6 9E6 P. ( Pa )
Fig. 7.13, Vessel pressure effects on the dispersion fraction F2 in the cavity 1
1 73 NUREC/CR-6510
2.5E5 , i i i i
m .
ca : :
- c. :
D l =0.35 m -
v .
V =7.0 m 3
> 2.oes _ ;
.=y (U : :
O : :
C : .
1.5 E5 - - -
.O_ . .
- a. - .
0" : :
m .
- O 1.oES "-
2 u) : :
O - .
q) : :
w 5.oE4 - -
a : : '
- v) -
~
U) :
q) . .
w -
o.oEo 4E6 SE6 6E6 7E6 SE6 9 E6 i
P ( Pa )
Fig. 7.14, Pressure effects on the maximum pressure drop to liquid flow in cavity i
I I
e 8.0E 3 ; , , ,
i !
7.0E 3 -
D,=0.35 m j i
V =7.0 m' i 6.0E 3 F :
e : i E. ! i v 5.0E 3 j-i
> i i
.4 : :
> L i es 4.0E 3 : :
O i i C i 3
, 3.0E 3 E- -i
- n. : :
O i
- i 2.0E 3 F .:
i 1.0 E-3 E-
-2 i
0.0E0 ' ' ' ' ' ' ' ' ' ' ''''''''''
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75 NUREG/CR-6510 L
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- 8.
SUMMARY
AND CONCLUSIONS i The transient two-phase flow in the DCH accident is modeled in step by step method. i The entire corium dispersion process as t ell as the dispersed fraction (Fdisp) of the total !
discharged liquid that enters the reactor containment dome are estimated theoretically.
The stepwise approach, as proposed by Ishii [5], divides the whole transient into four stages with one mechanism being highlighted in each step. These stages are (1) the liquid and gas blowdown, (2) the liquid film flow inside the cavity before gas blowdown, (3) the two-phase flow inside the cavity with droplet entrainment, and (4) the droplet re-entramment and transport in the subcompartment. Simple mechanistic models are thus developed to describe the transport process in every stage.
For the liquid and gas blowdown, analytical solutions are obtained for the single phase liquidjet velocity, gas jet velocity, and the discharge characteristic time constants.
The process is assumed to be isothermal. In the second stage, the liquid film front propagation and the following quasi-steady state liquid film flow in the cavity before gas blowdown are modeled analytically. The models yield the film front propagation time versus location, the film velocity and thickness distribution along the cavity floor, and the fraction ofliquid that flows out of the cavity without dispersion. These results supply the necessary initial and boundary conditions for the entramment process in the cavity. For the entrainment process, the liquid film flow, gas flow, and the droplet flow are modeled individually. By combining all the field equations together, numerical solutions are obtained for the entrainment time duration, total entrainment fraction in the cavity, and the volume median size of the droplets entrained in the cavity. After the liquid film and droplets have entered the containment, three paths are assumed for the droplets being transported into the upper containment based on the observation in the Purdue University 1:10 scale simulation experiments. The first path is the carryover (F21) of the droplets entrained in the cavity through the seal table room. This fraction of carryover is mainly
- determined by the view factor of the seal table exit to the cavity exit. The second path is the direct carryover (F22) of the very fine droplets that are entrained in the cavity and can follow and gas stream all the way to the upper containment. A trajectory analysis is proposed here to obtain a critical droplet size. Droplets larger than this critical size would impinge on the seal table bottom wall and thus be trapped in the film flow. The final path is the carryover (F3i) form the re-entrained droplets in the subcompartment. Again, a trajectory analysis is used to determine the fraction of the re-entrained droplets that can survive the subcompartment trapping and follow the gas stream to the upper containment.
Eventually, the total corium carryover (Fais,) is obtained from the summation of the fraction F2i, F22, and F3i.
Comparisons have been made between the predicted value and the data obtained from the Purdue University 1:10 scale simulation experiments. Reasonable agreements are obtained for the major flow parameters, including the film front propagation time, the film thickness and velocity in the test cavity before gas blowdown, the entrainment fraction and mean droplet size in the cavity, the pressure loss to the liquid flow in the cavity, and the total dispersion fraction in the containment. According to the model, the NUREG/CR-6510 78
l i
dispersion fraction in the containment is mainly dominated by the re-entrained droplet the subcompartment and the droplets entrained in the cavity that can pass through the s
{ table room. When the models are applied to the prototypic accident at the standard DCH conditions, the predicted total dispersion fraction in the containment is only 1.4% of the 4
discharged core melt. However, this fraction can be as high as 10% if the vessel break size increases to a halfmeter. {
Since the model is based on the isothermal assumption and the neglect of the chemical reactions and the possible corium-water interaction in the cavity, the numerical l
results can only be treated as the a first-order estimation of the hydrodynamic behavior of the corium dispersion transient. Moreover, under very high vessel pressure or for the case i of very large break size, the gas flow in the cavity would be choked at the cavity exit. In such a situation, the model could not be applied to the entrainment analysis in the cavity because the transient choking phenomenon is not included in the present model.
Although several simplifications have been made in developing the present models, the dominant mechanisms in each step are observed, which allows for better understandings of the corium dispersion problem in the DCH accident scenario. The approaches would also be valuable for a complete analysis of the DCH accident.
i I
REFERENCES
- 1. M.D. Allen, M.M. Pilch, T.K. Blanchat, and R.O. Griffith, " Experiments to investigate Direct Containment Heating phenomena with scaled models of the Zion Nuclear Power Plant in the SURTSEY test facility", NUREG/CR-6044, SAND 93-1049(1994).
- 2. J.L. Binder, L.M. - McUmber, and B.W. Spencer, " Direct containment heating experiments in Zion nuclear power plant geometry using prototypic materials",1993 ANS Winter Annual Meeting, San Francisco, CA, Nov.,1993.
- 3. Wu, G. Zhang, M. Ishii, and S.T. Revankar, " Experimental simulation of corium dispersion phenomena in Direct Containment Heating", Accepted for publication in the Journal ofNuclear Engineering and Design (l 995).
- 4. Q. Wu, S. Kim, M. Ishii, S.T. Revankar, "High pressure simulation experiment on corium dispersion in Direct Containment Heating", Presented at the ANS Winter Meeting (1995).
- 5. M. Ishii, Q. Wu, S.T. Revankar, S. Kim, and G. Zhang, "Corium dispersion in Direct Containment Heating, Part I: Separate effect experiments with water and woods metal simulating core melt under Zion reactor conditions", NUREG/CR-6510, PUNE-96/02 (1999).
- 6. D.C. Williams and R.O. Griffith, " Assessment of cavity dispersal correlations for possible implementation in the CONTAIN code", Draft Report of SNL (1993).
- 7. K.E. Washington, " Direct Containment Heating models in the CONTAIN code",
SAND 94-1073 (1994).
- 8. "An Integrated Structure and Scaling Methodology for Severe Accident Technical Resolution", Edited by N. Zuber et al., NUREG/CR-5809, EGO-2659 (1991).
- 9. M. Ishii, H.C. No, and G. Zhang, " Stepwise Integral Scaling Method and its Application to Severe Accident Phenomena", NUREG/GR-0009 (1993).
- 10. R.- Henry, "An evaluation of fission product release rates during debris dispersal",
Proc. ANS Intemational Topical Meeting - Probability, Reliability and Safety i Assessment 1, April 2-7, p. 375-383 (1989)
- 11. G.B. Whitham, Linear andNon-linear Waves. Wiley, New York (1974).
12.I. Kataoka and M. Ishii, " Mechanism and correlation of droplet entrainment and deposition in annular two-phase flow", NUREG/CR-2885, ANL-82-44 (1982).
- 13. G.B. Wallis, One Dimensional Two-phase Uow. McGraw-Hill, New York (1969).
- 14. F.M. White, Viscous Fluid Flow, McGraw-Hill, New York, (1991).
- 15. G. Zhang, " Studies if droplet entrainment and dispersion in two-phase flow", Ph.D.
Thesis, School of Nuclear Engineering, Purdue University (1994).
81 NUREG/CR-6510 ;
J
NRc FORM 3as U S NUCLEAR REGULATORY Commission 1. REPORT NuheER
, aan Aempnea er mRc, Ana va., supp., Rev.,
l
! EE BIBUOGRAPHic DATA SHEET ""*"""""**"'"*""
NUREG/CR-6510, Vol. 2 j 2. TITLE AND SUBTITLE PU NE-96/3 l Codum Dispersion in Direct Containment Heating l 3. DATE REPORT PuBUSNED Theoretical Analysis of the Hydrodynamic Characteristics
( McNN l YEAR i September 1999
- 4. F1N OR GRANT NLASER L1990
- 5. AliTHOR(S) 6. TYPE OF REPORT
)
M.1shi, Q. Wu, G. Zhang, Purdue University .
R.Y. Lee, C.G. Tinkler, U.S. Nuclear Regulatory Commission Technical
- 7. PERIOD COVERED (h:dusae Deses) 3/92-10/95
- 8. PERFORhaNG ORGANIZATION NAME AND ADDRESS (FNRC. svavase oman once or Asgem u3 Nuedser Anguisery commessn and memng edeess; scontecer, provsee name end manno ed*ess)
Schoolof Engineering Purdue University West Lafayette,IN 47907
- 9. SPONSORING ORGANIZATION . NAME AND ADDRESS (FNRC, type 'Same es abovei #contactr, Arevase NRC Dveson. Omco er Augsn yS. Mmeser Asguistry commasam and menne ed*ess }
Division of Systems Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research l
U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 {
- 10. SuPPLEnt.NTARY NOTES R.Y. Lee, NRC Project Manager
- 11. Aa6 TRACT (210 wense or auss)
The research at Purdue University addresses corium dispersion during'the Direct Containment Heating scenario in a severe nuclear reactor accident. The degree of corium dispersion has not only the strongest parametric effects on the containment pressurization, but also has the highest uncertainty in predicting it. In view of this, a separate effect testing program on the corium dispersion mechanisms in the reactor cavity and the subcompartment trapping mechanisms was initiated at the Purdue University.
The four major objectives of this study are: (1) to perform a detailed study using a step by-step integral scaling method, and to evaluate existing models and correlations for droplet entrainment, particle size and size distribution and particle trapping, (2) to design and construct a 1/10 scale Zion reactor model, and to perform carefully scaled experiments using air water and air-woods metal to simulate the prototypic steam and core melt, (3) to develop reliable mechanistic models for the corium dispersion and transport in the accident scenario, which can be used to predict the liquid and gas blowdown, entrainment, droplet size, Equid carryover to the containment, and the subcompartment trapping, and(4) to use the models to perform stand alone calculations for th3 prototypic conditions. In this report (volume 2), efforts are focused on the last two objectives, whereas the scaing and experiments are documented in volume 1.
- 12. KEY WORDS/DESCRIPTORS (List wonfs orpfwases ehet waar esses sesearchere m Joce6ag Ine report.) 13. AVAa.Aan.nYSTATEMENT direct containment heating unlimited c:rium dispersion u sEcuRrrYNN scaling * *>
severe accident unclassified separate effect experiments (rn. Asparo unclassified
- 15. Nuh2ER OF PAGES
- 16. PRICE NRC FORM 335 a49)
i i
Printed :
on recycled paper 1
Federal Recycling Program l
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