ML031410212
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| Issue date: | 05/20/2003 |
| From: | Wang A NRC/NRR/DLPM/LPD4 |
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Text
.~~~~~~~~~-
- .- 9
~.
INSURGE PRESSURE RESPONSE AND HEAT TRANSFER FOR PWR PRESSURIZER by HAMID REZA SAEDI B.S. Mechanical Engineering University of Miami (1981)
Submitted in Partial Fullfillment of the Requirements for the Degree of MASTER OF SCIENCE IN MIECHANICAL ENGINEERING at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY November 1982 Massachusetts Institute of Technology Signature of Author:-,k (j
/-4-a# [g-Department of Mechanical Engineering November 30,1982 Certified by:
"Accepted I Thesis Supervisor by:---.-
a Chairman, Mechanical Engineering Department Committee ENCLOSURE 1
.1 I.
I I
6/
-e-ACKNOWLEDGEMENTS I owe a debt of gratitude to Professor Peter Griffith for taking me as one of his students and his guidance throughout the research.
I thank Mr. Joseph Caloggero, Mr. Bill Finley, Mr. Fred Johnson, and Mr. Dan Wassmouth for their continuous help in keeping the test facility intact; and Ms. Sandy William Tepper for her kindness and administrative advice, and Ms. Karla Stryker for typing this thesis.
Cooperation of Dr. Sang-Nyung Kim is acknowledged.
I would also like to thank my friends, Warren Davis, Robin Baines, Chan-Young Paik, Doug Reitz, and others in the heat transfer lab, for making the last year so enjoyable for me.
Finally, I wish to thank Northeast Utilities and the Yankee Atomic who sponsored the research.
.VW II
TABL OF-S TABLE OF CONTENTS Page TITLE PAGE........
I ABSTRACT.
2 ACKNOWLEDGEMENTS.
4 TABLE OF CONTENTS 5
LIST OF FIGURES 7
LIST OF TABLES.
9 LIST OF SYMBOLS 10 CHAPTER 1:
INTRODUCTION.......
13 1.1 Issues and Recent Events.
13 1.2 Some Important Transient Processes.
13 1.2.1 Loss of Secondary Steam Load.
14 1.2.2 Pressurized Thermal Shock.
14 1.2.3 Small Break Loss-of-Coolent Accident.
14 1.3 Summary 14 CHAPTER 2:
EXPERIMENTAL INVESTIGATION.
16 2.1 Experimental Apparatus.
16 2.2 Instrumentation 21 2.3 Experimental Procedure.
23 2.3.1 Insurge Experiments.
23 2.3.2 Loss of Heat Experiments 23.
CHAPTER 3:
EXPERIMENTAL RESULTS..............
24 3.1 Insurge Into Partially Filled Tank.
24 3.1.1 Radial Temperature Gradient.
24 3.1.2 Liquid Region and Mixing of the Jet.
26 3.1.3 Vapor Region.
31 3.1.4 Wall Temperature Response..
31 i'3.2..Insurge Into Empty Tank
..i 31 3.2.1 Liquid Region.
31 3.2.2 Vapor Region.
32 3.2.3 Pressure Response.
32 Page 3.3 Summary 35 CHAPTER 4:
ANALYTICADLMODEL........................................
36 4.1 Previous Works....
36 4.2 General Discussion.
36 4.3 Mixing of the Subcooled Jet.
37 4.4 Wall Condensation 42 4.5 Heat Transfer to the Wall
- ... 43 4.6 Interface Heat Transfer Model 47 4.7 Comparison Between Different Modes of Heat Transfer.
52 4.8 Overall Model 55 4.9 Comparison Between Model Prediction and Data.
58 CHAPTER 5:
CONCLUSIONS
.a.....
63 REFERENCES.
64 APPENDIX A:
EXPERIMENTAL DATA.....
65 A.1 Experiment B84.
65 A.2 Experiment TR8.
78 A.3 Experiment FF1.
90 A.4 Experiment ST4.
100 A.5 Experiment EM9..
112 A.6 Miscellaneous Experiments 127 APPENDIX B:
COtISERVATION EQUATIONS FOR A THERMODYNAMIC SYSTEM.
128 APPENDIX C:
ORIFICE PLATE AND ITS CALIBRATION.
130 APPENDIX D:
DETAILS OF A WESTINGHOUSE PRESSURIZER.
132 I
Z LIST OF FIGURES Figure Page 1
Schematic Diagram of Apparatus.
17 2
Schematic Diagram of Main Tank.
18 3
Baffle Assembly.
19 4
Schematic Diagram of Primary Tank.
20 5
Top Flange of Primary Tank.
22 6
Plume Geometry.
25 7
Axial Temperature Distribution of Experiment: TR8 at t = 50 sec.
28 8
Axial Temperature Distribution of Experiment: KK1 at t = 10 sec.
29 9
Density Variation in Liquid Region.
30 10 Pressure Response of Experiment: FF1.
33 11 Pressure Response of Experiment: EM9.
34 12 Schematic Representation of Flow Establishment.
39 13 Plot of C2 as a Function of Froude No..
41 14 Vapor Temperature Response for Experiment: ST4.
45 15 Wall Heat Transfer for Experiment: FT5.
48 16 Interface Heat Transfer 50 17 Temperature Distribution Used for the Simple Analysis.
51 18 Configuration of the System.
56 19 Comparison of Data and Model for Experiment: FT5.
59 20 Comparison of Data and Model fpr Experiment: FT2.
6Q 21 Comparison of Data and Model for Experiment: ST4.
61 22 Comparison of Limiting Cases.
62 Experiment: BB4.
Experiment: TR8..
Experiment: FF1..
Experiment: ST4..
Experiment: EM9.
9 9
- . 9 9
9 9
9 9
a S
9 9
9 9
9 Pressure Vs. Mass Flow Rate for Orifice..
General Arrangement for Westinghouse Pressurizer Outline of Westinghouse Pressurizer.
Total Heater Output.
Figure A.2.1 through A.1.11 Page 65 A.2.1 through A.2.11 A.3.1 through A.3.9 A.4.1 through A.4.11 A.5.1 through A.5.14 78 90 100 112 C.1 D.1 D.2 D.3 131 134 135 136 J
-O ABLE LIST OF TABLES Page Order of Magnitude for Different Types of Heat Transfer for Insurge Experiments.
53 Order of Magnitude for Time Constants of Different Types of Heat Transfer for a Westinghouse Pressurizer.
54 Output of the Heaters..
133 Table 4.1 4.2 D-1
lz -
-C.
z E -
-" '-': ""I "
", Z. -7U-
I -
I
!, 4'.
, -.1, -
. -, 6 - LIST OF SYMBOLS Constant used in equation (22)
Constant used in equation (22)
Constant used in equation (22)
Area Concentration (used in Section 4.3)
Heat capacitance Dimensionless coefficient used in equation (11)
Diameter Specific energy Froude Number (modified)
Gravitational constant Enthalpy Condensation coefficient of heat transfer Coefficient of heat transfer Averaged coefficient of heat transfer Conductivity Constant of Gaussian distribution used in equation (12)
Length Mass Rate of change of mass Momentum Pressure Heat flux Heat transfer rate Total heat flux aO al a2 A
C C
C2 D
e Fr 9
h hcond hz hayg K
K L
m m
M p
qU Qu is' --
...~~~~~~~~~~~~~~~~~~~~~~~~~~-
-.. Coordinate in transverse direction (used in 4.3)
Reynolds number Time Temperature Specific internal energy Velocity Volume Specific volume Vertical distance from nozzle of jet Diffusivity Density Viscosity Constant of Gaussian distribution used in Equation (12-ii)
Depth of penetration of heat Subscipts cond Condensation e
Zone of establishment of jet f
Saturated liquid g
Saturated vapor int Interface n
Spatial coordinate m
Evaluated at the axis of jet 0
Insurged fluid s
2ambient-fluid t
Transition zone of jet r
Re t
T u
v u
z p
1.1 1'
6 A
v Vapor
- I w
I Wal Superscript i
Time coordinate
",=
- --, -r-
.,r CHAPTER 1 INTRODUCTION 1.1 Issues and Recent Events During the past few years, prediction of the pressurizer transient response has become an important factor in the licensing of pressurized water reactors (PWR's). A transient can be caused from a simple loss of secondary steam flow l] to more complicated accidents such as pressurized thermal shock (PTS), steam generator tube rupture (SGTR), or small break loss-of-coolent accident (SBLOCA) [2]. In the next section the processes taking place during the above transients will be briefly discussed.
Experiments run on Loss of Fluid Test (LOFT), series L6-3 and L6-5
[3], have shown substantial deviations between calculated and measured pressurizer level and system pressures. These calculations were based on the RETRAN computer code [5].
Recently, an attempt was made to make prediction of transient response to the reactor trip of Millstone Point Unit 2 and Connecticut Yankee power plants [4].
Predictions for the system pressure response were made using RETRAN 2 and RELAP-MOD 6 [16] computer codes.
Both codes overestimated the pressure by a significant amount. The primary conclusion in both cases was that the pressurizer model used in the above codes, and most possibly others, needs improvement.
1.2 Some Important Transient Processes In order to understand and model an accident, one should recognize the processes that take place during a transient. In general, these processes are insurge, outsurge, and empty pressurizer refill.- This thesis will address the two possible insurge processes; i.e. insurge to partially filled and refilling of empty pressurizer. In the next few paragraphs, the processes involved in particular accidents will be discussed.
1.2.1 Loss of Secondary Steam Load In a typical accident of this kind, a series of insurge/outsurge maneuver are made. This is due to a variation in the steam load which causes expansion of primary coolant. Therefore, the only processes involved are insurge and a partial outsurge of a partially filled tank.
1.2.2 Pressurized Thermal Shock This accident involves a combination of all processes. In a typical PTS, the secondary pressure drops very rapidly causing the primary to overcool.
At this point the pressurizer can be emptied at which the Emergency Core Cooling System (ECCS) comes on, and refills the pressurizer.
The system is then overpressured.
1.2.3 Small Break Loss-of-Coolant Accident This accident involves system refill and repressurization, since the primary refills with subcooled liquid from the High Pressure Injection System (HPIS).
1.3 Summary As the recent events have shown, the ability of the present codes to accurately calculate transient responses in which multiple failure occurs is questionable. In order to find the range of the pressure respbnse, one may solve the upper and the lower limit cases; i.e. adiabatic and equilibrium models. But, there is a substantial difference in magnitude between these two limits; therefore a realiable operational limit cannot be estimated from this method.
Until a justifiable model is introduced NRC recommends calculations based on adiabatic assumption for all kinds of transients including PTS.
The proper calculation of primary system pressure response depends on accurate modeling of phenomena such as heat transfer and condensation on the wall, spray operation and effectiveness, and nonequilibrium between the vapor and liquid in the pressurizer. Though models do exist for calculating pressurizer transient performance, they do not all consider all of the important processes and even if they do, the adequacy of the elements constituting the models has not been tested. Therefore, a systematic, analytical study accompanied by experimental work is needed to investigate the true behavior of important processes occuring in the pressurizer. This thesis is intended to fulfill the above objective for some cases of insurge transients.
CHAPTER 2 EXPERIMENTAL INVESTIGATION 2.1 Experimental Apparatus The apparatus is shown schematically in Fig. 1. It consists of two cylindrical stainless steel tanks:
the primary tank, 45 inches high and 8 inches ID, and the storage tank, 57 inches high and 8 inches ID. The main tank has six windows and is equipped with six immersion heaters totalling 9 KW, Fig. 2. The baffle at the inlet pipe of the primary tank was made of a 3 inch diameter stainless steel, 1/4 inch plate and was welded to the bottom flange by four legs, 1-1/4" x 1/8" x 1/8", Fig. 3. As shown in the Fig. 1, the line connecting two tanks consists of two quick-opening valves for rapid inputs, an orifice to measure mass flow rate and a control valve.
The storage tank was pressurized with bottled nitrogen.
For the first set of experiments, three 5/16" brass rods were welded to the top flange of the primary tank, Fig. 4. A 3/32" hole was drilled every one inch in each of the rods in order to hold the thermocouples inside the tank.
The rods were placed at 1200 from each other and at different radial positions. A cap made of cast iron was welded around each rod, each having six drilled holes, Fig. 5. In order to accomodate each thermocouple, compression fittings were welded in the drilled holes and Buna-N o'rings were used to prevent any leakage.
For the second type of experimental runs, a new type of flange was built.
In-this case one 5/16" x 42" heavy walled stainless steel tube was used as the thermocouple housing.
The flange was drilled and tapped to accomodate one 1/2" NPT compression fitting (for the tube) and sixteen
COMPUTER N2 STORAGE PLlR/.
CELL PIMARY TANK
~~~~~~~~~~~~~TANK WATER STEAMGCEL lg~~~WATER /
DRAIN DRAIN ORIFICE CONTROL VALVE SCHEMATIC DIAGRAM OF APPARATUS FIG. I
~~~
-=-- -~-
-a I /,W I"
f-l F,6 i'-.
A
-2II Stainless Steel Sleeves w
2 2 'Diameter Glass Wirdow.
IuN Schematic Diagram of Main Tank FIG. 2 A yt )
u t
..J;
,k
, il a
-m :
14L-
-i -_' _'l -, -: -':
'.
-:_ . - '
- -
- '-, i- .
-14 I~~
~~~~~~~
I If r ~
~
~
1 l
31 16
'8 if 11 -
BAFFLE ASSEMBLY FIG. 3 It 4
U. -..
SIGNALS TO COMPUTER THERMOCOUPLE HOUSING BRASS RODS-6 IMMERSION HEATERS-DIFFERENTIAL PRESSURE TRANSDUCER GLASS WINDOW LINE STEAM TO DRAIN SCHEMATIC DIAGRAM OF PRIMARY TANK FIG. 4 TO i -
I 1/16" NPT compression fittings, for the thermocouples. As before, the rod was drilled every bne Inch along its length.
2.2 Instrumentation Steam pressure and pressure drop across the orifice were measured by using variable reluctance type transducers.
The transducers were calibrated before the run by a dead-weight gage tester.
Temperature measurements were made by using copper-constantan thermocouples.
The thermocouples that measured temperature inside the tanks were insulated with magnesium oxide and shilded by a stainless steel metal sheath. Steam and water temperatures were measured by the two different sets of thermocouple arrangements mentioned earlier.
Originally, eighteen thermocouples were arranged radially. They were intended to measure temperature at centre line, half way to the wall and 1/4 inch close to the wall, Fig. S. For the second type of runs, 13 thermocouples were arranged axially inside the tank while 8 thermocouples were used to measure temperature on the outside wall.
The thermocouples on the outside were attached to the tank by means of thin layers of mica and were strapped with wire to assure their position.
The signals from the pressure transducers and the thermocouples were recorded on floppy disks using a Perkin-Elmer mini-computer. The computer was furnished with an Interface, hence making t a Real Time Data Acquisition System (RTOAS). The DAS was able to record up to 8000 data points per second using 24 channels.
-4 1- '101 DRILL -
19DI 64DIA.
DRILL 2 5 "DIA.
1-2 DIA.
MILD STEEL ThermocOLVe supportrg cap THERMOCOUPLE.
POSITION
-CAP Top Flange of Primary Tank FIG. 5 2.3 Experimental Procedure 2.3.1 Insurge Experiments The primary tank was filled partially with water. In order to heat up the water quickly, live steam was bubbled into the water. This caused the tank pressure to raise up to 75 psia and a temperature increase to 3030F.
After the water began to boil, the tank was deaerated by opening the relief valve. This was done until most of the non-condensible gas was driven out.
The pressure and temperature were maintained at a constant value so that equilibrium would establish.
Meanwhile, the storage tank was filled with water and pressurized with nitrogen. After steady state was reached in all components, the two quick-opening valves were thrown open. The rate that water was charged to the primary tank was adjusted for different runs by controlling nitrogen pressure, which was around 300 psi, and the control valve.
2.3.2 Loss of Heat Experiments Each time the insulation was changed, a set of heat loss experiments were run.
After the tank was deaerated, it was brought to steady state condition leaving only vapor at approximately 75 psia.
The steam supply was then closed and pressure and temperature signals were recorded.
J CHAPTER 3 EXPERIMENTAL RESULTS I
3.1 Insurge Into Partially Filled Tank Two types of experiments were run, using the two different arrays of thermocouples. Tests were run using wide range of insurge rates for both cases. Typical insurge rate for the experiments were from 0.2 inch/ sec to 0.8 inch/sec (based on the pressurizer inside area). In order to obtain the same jet to ambient density ratio for the experiment and a pressurizer, insurged water temperature was maintained at 70°F while the initial pool temperature was at 3030F.
A complete discription of experiments involving insuroe to a partially filled tank is given in Appendix A. Sections A.1 and A.2 are data for insurge rates of 0.5 in/sec an 0.24 in/sec using three different radial thermal thermocouple locations in the pool.
Section A.4 contains the data taken using only pool center line temperature easurements for an insurge rate of 0.4 in/sec.
N 3.1.1 Radial Temperature Gradient The experimental runs using the three radial TC locations were intended to detect the radial temperature distribution in the liquid and vapor regions. Results of all the experiments performed indicated that no significant radial temperature gradient exists in any of the regions.
The only exception to this was during the insurge when a plume was shed at the entrance due to the baffle (Fig. 6).
The thickness of the region which there was a radial temperature variation as found to'be pr6portional: to-'-
the insurge rate, since radial temperature differences of 10°F to 500F were L ~~~~
~~~~~~~
I I.-
.I
--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% D_,
- t.
I I
I
i U
V
-I
- VAPOR REGION MAIN-LIQUID REGION SUB-COOLED LIQUID REGION PLUME FIG. 6 PLUME GEOMETRY observed depending on how rapid the insurge was. See Figs. 7,8. As the insurge was stopped, the plume and along with it the radial temperature differences faded away. Throughout the insurge and after, the vapor region showed no sign of a radial temperature difference (see Fig.
A.1.2 through A.1.11 in Appendix A).
3.1.2 Liquid Region and Mixing of the Jet For the cases of an insurge when the tank was initially one-third full, the insurged liquid failed to break through the interface.
This was observed to be true for all the allowable insurge rates.
Failure of the jet to break through the interface resulted into the stratification of the liquid region in the bottom of the tank.
This stratification was caused by the negative buoyancy due to the density difference and because of the baffle at the inlet pipe.
Two distinct liquid regions, Fig. 6, were observed to exist:
one being the main liquid region which refers to the original amount of the liquid. Throughout the transient this region maintained its original temperature. The other region consists of the subcooled liquid which was insurged. This region is further subdivided in a few stratified layers of subcooled liquid.
This can be readily seen from Figs. A.4.4 through A.4.11 in Appendix A.
These stratified layers of liquid proved to be quite stable because after the insurge was stopped they retained their temperature profiles. At each instant of time, the region which separated the main liquid from the subcooled region was observed to be a mixing layer at approximately two to three inches in height.
A rough sketch of the density variation in the liquid regfon i-given In Fig. 9.
It should be noted that this type of stratification should be expected LEGEND D
0 CENTRE LINE 1/4" AWAY FROM WALL OUTSIDE WALL WATER LEVEL SATURATION TEMPERATURE
,,.*-ws
-bltS EXPERIMENT
- [r8 T I ME: 50 SEC I
I
~~~I I
0 I-o I
0 I
I
~~~~~I I
150 200 250 300 350 TEMPERATURE RADIAL AND AXIAL TMiPERATURE DISTRI3UTION: INSURGE RATE=0.25 i/sec 45 40 35 1-4A
- T1 0i
-J 30 25 20 15 Lii C. )
$--I 5
0 100 I,
9 f
25h 20[
10 0
100 EXPERIMENT: KK1 TIME 10 SEC U
0 a
a
~~~~~~~-
k/
0 I
300 I
150 I
250 TEMPRATIJRE 350
/F RADIAI, AND AXIAL TIMV'ERATURE DISTIRIBUTION: INSURGE RATE=0.5 in/sec 45 40 35 30 I
C..)
In wi I-0a 1S J1 I
I I
I to I
I
VERTICAL DISTANCE FROM NOZZLE I
I I
I I
I H
I(a CD J
z.
Cl) 3 Z.
F.
I I
I 1
I, mz U) 0 c
/
I I
I I
I I
I I
I I
I I
I I
I in an actual pressurizer. This is again due to the negative buoyancy on the jet and the baffle at the inlet. Furthermore, some pressurizers such as B W are equipped with a horizontal bank of heaters which further block the axial mixing.
3.1.3 Vapor Region As it was pointed out earlier (3.1.1),
no radial temperature gradient existed in the vapor region except in a boundary layer on the wall.
Furthermore, no axial temperature gradient was detected in the vapor region except very close to the interface. The temperature signals also indicated a few degrees of superheat to exist in the vapor.
See Fig. 7 for instance.
3.1.4 Wall Temperature Response As Figures A.4.6 through A.4.11 show, wall temperature changes at two locations, at the liquid-vapor interface and at the hot and cold liquid interface. The former acquires the same temperature as the vapor after a time lag, while the latter cools down very rapidly to a temperature close to the ajoining liquid temperature.
3.2 Insurge into the Empty Tank As before, two types of experiments were run for the case of the insurge into the empty tank. The range of the insurge rates were from 0.4 inch/sec to 0.7 inch/sec.
Temperature of the insurged liquid was at 700F.
3.2.1 Liquid Region The experimental runs using the radial TC's showed that the only radial.teperature gradient was because-of the plume. As before-, this gradient faded away as the insurge was stopped. The radial temperature difference was observed to increase as the insurge rate was increased.
Using the centerline TC's, it was observed that complex pool temperature profile was produced, see Fig. A.5.5 through A.5.14 in Appendix A. After the transient was stopped these layers tended to maintain their last temperature and remain stagnant.
3.2.2 Vapor Region Regardless of the insurge rate, no radial temperature gradient was observed.
Furthermore, no axial temperature gradient was detected, Fig.
A.3.3 through A.3.9, except very close to the interface. A few degrees of superheat was detected in the body of the vapor.
3.2.3 Pressure Response In this case, the jet was able to break through the interface. This gave rise to direct condensation on the subcooled liquid interface. As a result of this the pressure dropped severely during the first few seconds and then it started rising, Fig.
- 10. At this point, the liquid level was sufficiently high so that the jet no longer break through the interface.
This height at which the jet was no longer able to break thru was observed to be roughly equal to the baffle height.
Different types of pressure responses were observed for different insurge rates, Fig.
- 11.
It can be safely postulated that the pressure response depends on variables such as the insurge rate, baffle geometry, tank and other components geometry, etc.
It should be noted that the sudden drop in pressure at time, t = 14-sec, (Fig. 11), s probably due to the presence-of the window; see Fig. 2. It is postulated that due to an area Increase, a new surface is formed hence an increase in the interfacial
EXPERIMENT : IF1 20 30 TIME
/SEC PRESSURE RESPONSE FOR INSURGE TO EMPTY TANK: INSURGE IZAT3=o.s in/s 68 66 U) a-C, LUJ U)cc U)
LiJ 0IC 64 62 60 58 56 0
10 40 50 60 i
I LA lI I,
__I_
1 EXPERIMENT 20 30
- EM9 40 50 IJ 60 TIME /SEC l'RESSURE IESPONSE FOR INSURGE TO EMPTY TANK: INSURGE RATE=0.7 in/s A
74 73 V) a-C, 72 71 70 69 68 U)
I U)
LLJ
- ,J QL-
. Xz 0:
Cl 67 66 0
10 heat transfer and a drop in pressure.
It's not clear why this disturbance is'not evident in Figure 10.
3.3 Summary Experimental observations indicated that the liquid region s divided into two distinct regions.
One being the main liquid region wich corresponds to the original amount of the liquid in the tank. This region remains at its original temperature during the insurge with no radial temperature gradient. The other region is the insurced subcooled liquid which itself is consisted of small layers of liquid at different temperatures.
The vapor phase becomes superheated by a few degees during the insurge and has no radial or axial temperature gradient.
As the experiments showed, the only regions of wall which responded to the transient were the parts adjacent to the vapor and to the subcooled liquid region.
Insurge experiments to the empty tank showed that a complex condensa-tion phenomena takes place at the interface.
It was seen that the latter and hence the pressure response could be a function of the insurge rate and surge line and sparger geometry.
J
L ~~~~~~~~~~~~~~~~~~~~~~~
- CHAPTER 4 ANALYTICAL MODEL 4.1 Previous Works Lack of adequate experimental work could have played a major role in the failure of the previous models, as has been pointed out by Nahavandi
[6) in late 60s and by Bonaca [4) more recently.
One of the earliest models made the assumption of an adiabatic compression of vapor.
This kind of crude modeling which neglects any kind of heat transfer results in an erroneous response.
Later, a series of models were developed which considered saturation line process along with heat transfer to the vessel
[7].
In some other pressurizer analysis, some workers [8,9,1) came up with calculation methods involving several isothermal control volumes.
Such a model needs a method of evaluating heat transfer between control volumes, a method which we don't yet have.
In recent years, new digital programs, such as RETRAN or RELAP-5 are being used to describe the overall behavior of the system. The latter and the previously mentioned models were ntended only for slow transients and they have proved to be unsuccessful for more complex and faster transients.
4.2 General Discussion To describe all the phenomena occuring in the pressurizer during a transient, the following processes should be considered:
(1) Mixing of-the subcooied jet below the free-surface (2) Condensation or natural convection on the walls of the pressurizer in the vapor
L.
-.-~.
I. (3) Heat transfer to and from the wall in the liquid (4) Condensation heat transfer at the free surface (5) Condensation on the spray entering from the top of the pressurizer In the next section, individual points relevant to the insurge transient which are mentioned above will be discussed in the light of these experimental observations. As it will be shortly discussed, 4.7, the only dominant process, for insurge duration of order of wall conduction time constant, is the wall heat transfer. Later they will be put toqether into a pressurizer model suitable for calculating the peak pressure during an insurge transient.
4.3 Mixing of the Subcooled Jet One of the most significant observations in the pressurizer experi-ments is the stable stratification which is produced when there is an insurge of subcooled liquid. This stratification was detected in the experiments reported earlier (§3.1.2).
The existance of the stratification can be understood analytically by considering mixing in an ideal case. Let us imagine a dense jet enterina a large pool of less dense liquid.
Dimensional analysis shows that the local velocity, v, and the local density, p, depend on the other variables as
[10):
v z
r Ps Po D =
P7
, Fr, Re)
(1)
Vo D D Po and Ps P
z r
-Ps Po 2
= f(-
,Fr, Re)
- (2)
PSP D
D Po
. - -::,: ~~~~~~~~~~~
- -: ~~~~~~~~K
~ ~ ~ ~~ k -
'4
".~~.... where 2
vO D vo Re =-
- Fr =
v Ps Po gD PO Near the ceiling level; i.e., the highest level reached by fluid of the jet (Fig. 12), Jet fluid leaves the upflow region and enters the down flow region.
Thus, near the ceiling level the vertical flux of the jet decreases with height.
The jet can be thought as three zones:
zone with positive entrainment near the jet entrance, zone with negative entrainment near the ceiling level, and transition level between zones, zt [ll (see Fig. 12).
The following conditions have to be satisfied for the above zones:
dZ fA vdA =o z =
(3) d vcdA =
Z <
(4) dcz dZ = O ;
Z > Zt
~~~~~~~(5)
Ps -
P where concentration, c Ps -
Po and subscript, m, means value at the axis of jet.
The momentum equation in vertical direction is, z~~~~~~~~~~
fA pv2 dA = Ef p2 dA]
+ g fZ dz A(ps p)dA z > zt (6)
1-
. ~ m...,sa SCHEMATIC REPRESENTATION OF FLOW ESTABLISHMENT FIG. 12 II
-e
! - ~ -
Ir,
,1 I
La and pV2 dA = [fPv2 dA
+ gf dzf (ps-p)dA
- Z<zt (7) fA A
Z=Ze Ze A
where Ze = length of zone of establishment (see Fig. 12).
Momentum at zone of establishment can be expressed as:
Ze Me = Mo + 9 dxf A(ps - p)dA (8) and according to Albertson et al; JfcdA A
{(2w)1/2 -
z} z
{3 -
(2w)1/2l z2
~~= 1+
+
-2 (9)
-1+
C2 Dnozzle C2 2 nozzle 2
nozzle 4
From the last two equations, Me can be written as,
{6 + (2X)1/2} C2 Me = ME1 +
-]
(10) 6 Fr where C2 is a dimensionless coefficient given in Fig. 13. The case considered here involves a negative buoyancy which corresponds to a negative Froude number.
So, the left hand plane of Fig. 13 applies to this analysis.
Finally, value of zone of establishment can be found as, ze = C2Dnozzle (11)
For the zone with positive entrainment, the velocity and concentration profiles can be regarded to be similar at all heights. Using the Gaussian distributions; iu Is
-L,
ASMTTCVALUE I
ASYMPTOTIC ALUE
-30
-20
.1 020 30 VI.
-3o
-20 -
-5 ASYMPTOTIC VUE ASYMPTOTIC 5-r
.1 C2 AS A FUNCTION OF FROUDE NO.
1 FIG. 13 I
I X-
f-I I
v
= e-kXr/z v2 (12-i)
-k(r/z)2 vm and P
PS
- e-"K(r/z)2 (12-ii)
Pm Ps where and K are numerical constants. Using equations (12-i), (12-ii) in (8) and noting that ceiling level occurs when Um = 0; one can solve for zL; ZL
= 1.94jFril/2 (13)
Dnozzle Using numerical values, it can be seen that the ceiling level will never reach the free surface for the operational range of insurge rates.
Therefore, if the jet cannot make it to the free surface without the presence of the baffle, it definitely will not reach the interface in the actual case.
4.4 Wall Condensation During an insurge transient, the vapor temperature increases corresponding to an increase in the pressure. Due to the wall heat capacitance, there will be a time lag in temperature response. The temperature difference between wall and vapor causes condensation to occur on the wall. It should be noted that less wall condensation can occur during accidents in which a considerable pressure drop is followed by a rapid system refill (repressurization).
In order to obtain the heat transfer to the wall, an expression for
.the condensation coefficient of heat transfer shouldbe arrived at.
Nusselt's theory based on laminar film condensation can estimate the coefficient of heat transfer within reasonable accuracy. The following assumptions should be made for this model:
- 1) neglecting effect of non-condensible gases present in the pressurizer
- 2) neglecting any shear stress at the condensation interface
- 3) assuming a fully developed laminar flow.
The resulting coefficient of heat transfer can be expressed as:
havg = l L hz dz (14)
(hcond)
= 0.943 g (p (15) avg where L is the instantaneous length of vapor region plus the equivalent length of the top flange, i.e.
L(t) = L(t) +
P (16) d 4.5 Heat Transfer to the Wall The wall heat transfer in the vapor space turns out to be the most significant heat transfer in the problem.
This heat transfer was evaluated in the following manner. The heat diffusion equation can be regarded as the governing equation for wall temperature distribution, aTw 32Tw (17) at Bx2 B.C.
() Condensation on the inner face q (x = ) = hcond (T - Tw (x 0
O))
(18)
(ii) Perfect insulation on the outside u
aTw q (x = xo) = K ( -
)
= 0 (19) ax x=xo where x is wall thickness, and hcond is condensation coefficient of heat transfer calculated as described n the previous section.
Using the observations from insurge experiments to partially filled tank, it can be deduced that vapor temperature increases in an approximately linear fashion (see Fig. 14).
Mathematically this can be written as; 2
2 dTv) d T
(&t)
Tv - Tv(t=0) + (
At + (-
+ *..
(20) dt dt2 t
t 2 Tv(t=0) + (-
At (21) t For mild transients the dependancy of wall temperature on time and position can be approximated by a fully developed parabolic profile [13],
x x ~2
= a + a1
(-) + a2 ()
(22)
Tw(x=o) xo xo where a ; i = 1,2,3 are constants.
Invoking the boundary conditions,
~dTw Kal q =- K (t Tw (x=o)
(23) and 0d2T-(w) 2
- K[al a]:
-a K)K
+ 2 --
ITw(x=o' (24) dx x=xo xo x
EXPER-IMENT 30 TIME
/SEC VAJ'OR TMPEItA'rUIR RSPONSE: INSUIRCGE IATE=0.44 in/sec 320 318 316 ST4
-1 a)
NY Li LU LU Hl-314 312 310 308 306 0
.t.
qj,
.I 10 20 10 60 I
Heat transfer to the wall can be also expressed as, to lim Ax+o d
pCp dt n
I Tw x n=1
= p Cp d f Tw(x=o)Eao p
10 x
xo + a2(-)
dx xo Tw(x
=
therefore, Using equations (23), (24), (27) and (18), equation (26) reduces to, go dTw q = pcpxo 3K (Tv equating (18) and (28) results into an ordinary differential equation with Tw(x=o) as the dependant variable, xo hcond (1 +
)
3K (Pcpxo) d
+ hcond Twi xo hcond
= t 3K dTv (p cp xo)J -
+ hcond Tv The right hand side of equation (29) is simply a function (linear) of time (invoke equation (21)),.e.
R.H.S.
E X hcond )(pcp 3K dTv dTv
+
x0))
+ hcond Tv(t=o) + ()t) d t
~~~~~~t (25)
- and, (26) a0=1 (27)
(28)
(29)
(30)
-L~~~~~~~~~~~~~~~~~~~~~~
7 1
o
=
=
L
-1
--?--
-- ~,_*._ Solving for homogeneous and particular solution, Tw(x=o) = Tv +
-P
) (ebt
(
1)(dTv 131) hcond dt where b = hcond/[(Pcpxo)( +h 3K The accuracy of this model was checked against data by evaluating equation (6) at x=xo. The discripency was found to be negligible within thermocouple's accuracy. The overall utility of this model will be shown shortly.
Using equations (15), (18) and (31), one can easily calculate the vapor wall heat transfer. A typical calculated wall heat transfer rate is shown in Fig.
- 15.
From the above analysis it can be deduced that thicker walls simply mean a longer time constant and a larger percent error in the final result. This is due to a possible "hot region" in the wall.
4.6 Interface Heat Transfer Model When the heaters are not in use; the only heat source to the main liquid is the vapor region. The heat and mass transfer from vapor to the main liquid region occurs at the interface. Due to the low thermal diffusivity of water, depth of pentration of heat below the interface is very small.
In view of this short penetration, the main liquid region can be considered as a semi-infinite body.
In order to find the importance of this phenomena, i.e. by comparing values of the different kinds f heat-transfer, the heat diffusion equation must be solved.
-----
ONE DIMENSIONAL MODEL OF EXPERIMENT: FT5 9E3 I-m N
ILL CO) z 0-
.I I-hi I
8
'7 6
5
£1 3
2 1
0E3 0
5 10 15 20 25 TIME
/SEC WALL EA'T TRANSFER: INSURGE RATE=0.78 in/sec
-1 tn 0,
The constitutive equation is; aT a2T (32) at aX2 With conditions, T(x,o) = Tv(o) 0 x T(o,t) = T(t) t >
This equation was solved by finite difference technique using an implicit relationship (Crank-Nicolson);
Tni+1 = rTn + (1 -
2r)Tni + rT1n+1 (33) n-1 for r = aT/(Ax) 2 and 0 < r 1/2 using conditions, Tl =
So, (q/A)i+l _ (Tli+l -
T3+1 )/2&x (34)
/
The result of this calculation is shown in Fig.
16 for the experiment FT9 As it can be seen, the interface heat transfer is negligible.
The same result was obtained using a simple order of magnitude analysis. In this case, the energy equation at the interface was considered (Fig. 17):
q = KA (T)
(35)
Total heat-transfer, Q, can be written as:
QT Q = (A6) -
(36) 2
800 F-M~~~~~~~~~~~
N 700 600 LUm
'500
<:300
-n
- ~cr
,,, 200
- 1t 100 IcJ 0
(*
0 5
10 15 20 25 30 TIME
/SEC IN'ElRFACE I IEAT TRANSIER INSURGE RATE=0.78 in/sec T
1-TL TEMPERATURE DISTRIBUTION USED FOR THE SIMPLE ANALYSIS FIG. 17
,I iI. I v
VAPOR LIOUID l-----
- -
I - -
. - -
- I -
L-I TV i -
q Apc (
d-(37) 2 dt separating and then integrating we obtain, K~~~~~~~~~~~~
6 2 -- t (38)
PC Heat transfer to the pool of liquid can now be calculated by substituting eqn. (38) in (36).
The heat transfer for a period of 30 seconds was calculated using finite difference and simple analysis. The simple analysis gave a value within 10% of the result obtained by finite difference.
As Figs. 15 and 16 examplify, interface heat transfer is negligible..
2-Yet, the above calculation of heat transfer can be regarded as an upper limit, since a reduction of heat transfer due to accumulation of the condensate should be expected. This accumulation is caused by both the
/
free surface condensation and by the wall condensation which carries down and accumulate on the interface.
4.7 Comparison Between Different Modes of Heat Transfer In a pressurizer many other processes take place such as, constant dribble of spray; one or more banks of heaters heating the subcooled liquid; axial heat transfer from vapor to the liquid through the wall; radial heat transfer due to conduction to the liquid; heating the pool from vapor region.
Therefore, one must show that the effect of these processes are inconsequential, so that the overall model about to be discussed can be ju-stified..
Such a calculation was made for Experiment:
FT5 (see Appendix A.6).
The result of the quantative comparison between different kinds of heat transfer is shown in Table 4.1.
It is obvious that the interfacial heat transfer and axial conduction at the wall is negligible compared to e
heat transfer from the vapor to wall.
Another set of calculations were made using the dimensions of a Westinghouse pressurizer (see Appendix D for details on geometry). Table 4.2 shows the approximate time constant for each heat transfer process.
From these results, it can be seen that for insurge transients of the order of 20 minutes or less; only the conduction from vapor to wall should be considered in the model.
4.8 Overall Model In order to calculate the pressure response during an insurge, it is necessary to apply the 1st law to the steam volume. In this section, the conservation equations (derived in Appendix B) will be written using results of previous sections to account for the processes. As it is was explained in Chapter 3, experimental observations showed that the only non-equilibrium regions are the vapor and the subcooled liquid.
Therefore, the pressure response can be calculated by considering the vapor region as a thermodynamic system (see Fig.
18).
The first law applied to this region can be expressed as, JQ +
mihi =
+ p (39)
= mu + mu + p mu + pmu
(
mu + pu) + m ( + p)
=h + m (h u)
(40)
-, TABLE 4.1:
Order of Magnitude for Different Types of Heat Transfer Occuring During the Insurge Experiments Wall conduction time constant -
50 sec.
Q(t = 30 sec)
Type of heat transfer:
Conduction from vapor to wall Conduction from vapor to pool Wall axial conduction from vapor to cold liquid 230 BTU 3 BTU 3 BTU
. 1- --
--
-
4..
TABLE 4.2: Order of Magnitude for Time Constants of Different Types of Heat Transfer in the Case of a Westinghouse Pressurizer Time constant for:
Conduction from vapor to wall Axial conduction in the wall from vapor to sub-cooled liquid region Radial conduction from wall to subcooled liquid One bank of heaters Dribble from spray nozzle Conduction from vapor to liquid 1/2 hr.
25 hrs.
60 hrs.
1 hr.
4 hrs.
18000 hrs.
U-
.. 4 I
Ig l
l Il l
l l
l...........-.......
l l
MI l
l l
_I
. l CONFIGURATION OF THE SYSTEM FIG. 18
- -:
- -.: -., '
7,
- -- '..o., - -- -., -
Therefore, i
Qint - Qwall - rcond hcond = m (
Uv j) + kvhv (41)-
Conservation of mass yields; v= mcond (42)
From (41) and (42);
& int Qwall + v hcond Mv (v - uvp) + vhv (43)
Conservation of volume gives, v= - Ysg (44)
= m v +
uv (45)
Therefore, mv=sg v
mv 46
- V (46)
- also, hv= hv (p,T)
(4 UV= UV (p,T)
(48)
T = T(p)
(49)
From the above equations, t can be seen that equation (41) is a function of prerssure. In order to solve for pressure, an explicit, numerical scheme can be used.
Equation (41) can be written as (and neglecting int):
1+1 1
1+1 i
1+1 1
(Qwall - Qwall) - hcond (my
- m) - m [(hy - hv )
UV (p+
- pi)]-
(mVi+1 mv ) hv=
(50)
Using curved-fit properties for steam and water, and employing results of
§.4.4 and 4.5, equation (50) can be solved iteratively.
4.9 Comparison Between Model Prediction and Data The model described in the previous section was compared against experiments ran at different insurge rates.
This was done by solving equation (50) and using insurged mass of water as input. For each of the runs, (descriptions given in Appendix A), the model approximated the experimental data quite well, Figs. 19,20,21. The small discrepancy seen is probably due to the parabolic temperature profile assumption; i.e.
having no thin "hot" region right at the inside wall early in the transient. Although the method of analysis was checked against data from low pressure experiments, this should not matter since the amount of condensation and the percentage pressure rises are smaller at higher pressures.
Therefore, this study should be applicable to high pressure processes.
A comparison of the limiting cases; i.e. adiabatic and equilibrium models, was made against experiment data, Fig. 22.
Not only these predictions showed a large difference in magnitude compared to each other (as was mentioned in 1.3), but they also failed to estimate the pressure response behavior satisfactorily.
sr:
1_--.
,i S
EXPERI MEN T 90 88 (I)
"I Ls_l 00(
5Z) w.
- rI (LU 86 84 82 80 78
'7 7-72 70
- FT5 I
U'
%0 20 30 10 60 TIME /SEC COMPARISON BETWEEN DATA AND MODEL: INSURGE rATE=O.78 in/sec 0
EXPERIMENT : F12 10 20 30 4-0 50 TIME /SEC COMI'ARISON Bt',F\\r%VEEN
)ATA AND MODEL: INSUIRGE RATE=0.6 in/sec i
90 88 86
, t--
X) a-
'T1 a;
N 0
hi a c:
-D U )
V)
LLi F-82 80 78 76 74 72 70 0
0 60
I.,
EXPERIMENT 10 20 s-ri 30 TIME /SEC COMlPARISON ETWIEN DATA AND MODEL: INSURGE RATE=0.44 in/see 86 81-II U) a-
'1 a;
No 82 80 78 76 74 LJJ Of U)
U)
LJ 0Cz-72 70 0'
0 50 60 I
EXPERIMENT 10 20 30 TIME 10 a'
t'3 (0
/SEC COMPARISON D13TWEEN LIMITING CASES: INSURGE RATE=O.78 in/sec I
250 200 C) a-150 G)
N N
V)
'(I)
LUJ 2-100 50 l
l l
l I_
/
ADIABATIC EQUILIBRIUM
__I I
I 0
- FT5' CHAPTER 5 Z
CONCLUSIONS
- 1) The limits of perfect mixing in the pressurizer and adiabatic compression of the steam bubble yield very different pressure responses. These pressure responses are so different in magnitude that they don't yield a reliable limit when calculating pressures during an insurge transient.
- 2) Wall heat transfer substantially reduces the peak pressure during an insurge transient.
- 3) Interface condensation is entirely negligible during an insurge transient of 5 minutes or less duration and for pool depths sufficient to submerge the inlet sprarger.
- 4) Wall axial conduction is quite negligible during an insurge transient of 5 minutes duration or less.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A
~~~~~~~~~~~
w
~:-K REFERENCES
- 1. Redfield, J.A.,
Pressurizer Performance During Loss-Of-Load Tests at Shipping Port", Nuclear Applications, V.4, March 1968.
- 2. Demuth, N.S., et al, "Effects of Condensation Modeling on Transient Behavior of Pressurized Water Reactors," Los Almos National Lab, LA-UR-82-2661.
- 3. Reeder, D.L., "Quick-Look Report on LOFT Nuclear Experiments," L6-1, L6-2, L6-3, EGG-LOFT-5270, Project No. P394, October 1980.
- 5. Retran II - A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems, Vol. 1, EPRI NP-408, 1977.
- 6. Nahavandi, A.N., et al., "A Comparison of Equilibrium and Non-equili-brium Thermodynamic Models in a Water-Reactor Pressurizer," ANS (1967, Winter Meeting).
- 7. Glasser, T.H., "Basic Equations for Predicting Performance of a Nuclear Power Plant Pressurizer," ASME -
S7-NESC-95.
- 8. Cunningham, J.P., et al., "PRESTO, A Pressurizer Transient Program for the IBM-704," YAEC-141.
- 9. Thomas, A.W. and Findlay, "PRE-A Pressurizer Transient Program for the Philco 2000 Computer, KAPL-M-E7-7.
- 10.
Abraham, G., "Jet Diffusion in Stagnant Ambient Fluid," No. 29.
- 11.
Turner, J.S., "Jet with Negative or Reserving Buoyancy," Journal of Fluid Mechanics, 26, pp.779-792.
- 12.
Albertson, et al., "Diffusion of Submerged Jets," American Civil Engineers, 115, p.639-697.
- 13.
Reynolds, W.C., Report No. 58-A-248.
- 14.
Potter, Foss, "Fluid Mechanics," Wiley, 1975.
- 15.
Honan, T., Personal Communications.
- 16. RELAP5/MOD 1 Code Manual, Volume 1:
"System Models and Numerical Methods," NUREG/CR-1826, March 1982.
APPENDIX A Experimental Data Results of 5 different insurge experiments are shown in this Appendix.
Sections A.1 through A.3 include data taken with thermocouple at three different radial locations. Section A.3 is data for insurge to empty tank.
Sections A.4 and A.5 include data showing axial temperature distribution with only centerline temperature measurements. Section A.4 shows data for insurge to partially filled tank and Section A.5 shows data for insurge into empty tank.
A.1 Experiment:
BB4 Water level at t = 0 sec : L = 17 in.
Water level increase : L = 16 in.
Insurge time : t = 31 sec.
This experiment was ran using the first type of top flange (§2.1).
The presence of the plume was detected from Figs. A.1.6 through A.1.8.
From these plots, the plume speed was estimated.
As calculations showed, the plume travels with a speed slightly less than that of the insurged liquid level rise.
The pressure spikes, Fig. A.1.1, appear to be due to pickup in the leads. Though they confuse the data, they are not important.
- :_E S
Lr I=
CENTRE LINE 1/4" AWAY FROM WALL OUTSIDE WALL WATER LEVEL SATURATION TEMPERATURE LEGEND 0
0
-; -, - --
- ,L,
-j:
EXPER I MENT 30 40 TIME /SEC i
I.
82 80
'I U)
I.,'
I-..
I-4 78 76 74 Li U)
LU 0-1--
72 70 0
10 20
-li 60 50 I
EXPERIMENT
- BB4 150 200 TIME:
0 SEC 250 300 TEMPERATURE
/F
(
45 40 35
'I 30 i
t'3 25 wC-)
cI) 20 15 I
I I
I 0
0 0*
W I.
I I
I I,~~~~~o 10 5
0 100 I0l 350 I
EXPERIMENT :BB4 TIME:
3 SEC 0
25 20 15 K 10 5
I0_
100 I
%D 350 TEMPERATURE
/F 45 40 35
'I',
30 I-'-
I-a Z..
wL C-)
F-4 (I) 0 0
150 200 250 300 w
S 11 I
I I
I I,
I I
I
.4~
EXPERIMENT :BB4 150 200 250 TIME: 10 SEC 300 TEMPERATURE 45 40 C )
2:
FII I.
C)
GO H-
'I 35 30 25 20 15 10 5
L 0
[A 0:
I.
1
-J 0
100 350 I
I I
I I
I I
1
.I EXPERIMENT :BB4 150 200 TIME:
17 SEC 250 300 TEMPERATURE
/F 45
.1I, 40 35 C)Z_
30
'II H'
25 wC)
-4 C-,)
20 15 I
1-4 I
10 5
0 100 350
EXPERIMENT :BB4 TIME: 21 SEC 0
I 0
Q3A o
150 200 250 300 TEMPERATURE
/F
+5 40 35 C-)
2:-
30 25 "1
I-I-b 0%1 w
CD) c,-)
I-I 20 15 10 5
0-100
-J 350 I
I I
I I
I I
EXPERIMENT BB4 45 I.
40 TIME: 25 SEC 0
ol m
0 IAI 0
A 0
200 250 300 TEMPERATURE
/F 35 C-)
N 30 mT.
0Q I-
-4 25 LL C) 2:
20 15 10 5
0-100 150 I4 350 I
I I
I I
I I
EXPERIMENT
- BB4 150 TIME: 27 SEC 200 250 300 TEMPERATURE
/F 45 35 30 xr C-)
F'I oi 25 wC-)
2-LI) 20 15 10 I
I I
I 0
- In O
A 0
I
~I II 5
i 0
100 350 r
Ii
.r.I
EXPERIMENT :BB4 TIME: 30 SEC 0
CA 0
0 150 200 250 300 TEMPERATURE
/F 45 40 35 C-)
30 III OQ
'0 25 w
C) c/)
20 15 10 5
0_
100
-I Lj 350
w -
I I
I I
I I
I I
I I
I I
I
EXPERIMENT
- BB4 TIME: 35 SEC 0
0h VI 0
150 200 250 300 TEMPERATURE
/F 45 40 35 CD I,;p 1-30 I
1-N 0
25 L,J IC-)
U)
II 20 15 10 5
' 0 100 Ioa' 350 I
I I
I I
I I
t
EXPERIMENT
- BB4 TIME: 50 SEC
.cI z
H-CD C)
CI)
- I 10 5
'.I (A L 14
-3 350 TEMPERATURE
/F J.'
t
'iA-t 45 40 35 30 25 20 15 II I
I 0
(A (A
0 0
I I
Y) 100 150 200 250 300 i
A.2 Experiment:
TR8 Water level at t = 0 sec : L = 17 in.
Water level increase : L = 19 in.
Insurge Time : t = 78 sec.
This was a slow transient and the radially located thermocouples were used.
The presence of the plume can be seen from Figs. A.2.9 through A.2.10.
After the insurge was stopped; heat transfer from wall to the liquid was done by natural convection mechanism, Fig. A.2.11.
N
EXPERIMENT : trU 20 30 40 50 60
-TIME /SEC 82 I-,r U)
N-80 78 76 74 I.-4 IA]
cr_
(1-
.2.
72 70 Ii
%0 0
10 70 c0
I,.,
EXPERIMEN -
1rB 0.50 0.45 co 0350 L 0.35
-J E 0.25
~0.20 CD) 0.10 0.05 0.00 0
10 20 30 40 50 60 70 80 TIME /SEC
-f-
s EXPERIMENT :IrB TTME:
1 SC 0
0 150 200 250 300 TEMPERATURE
/F 45 40 CD) 1-35 30 25 w
LU C-)
F-1 C.)
20 15 10 5
L xi 100 Ix CD 350 I
I I
I I~~~~~~~~~~~
I I
I
EXPER I MEN1
- I r M
'1 40 35 200 250 TENPERATU1E
/F C)
'-I 64
-4 7q
- o
.r.
Li.J C)
I--
U)
_f C
30 25 20 15 10 5
0 rA
-r I-
.~~~~~~~~~~~~~~~~~~t
' i100 300 350
- i I
1TlME:
rj t--C I00 r13 1
EXPlIRMlNT : tr[
150 200 250 lME: 10 SIC 300 TEMPERATURE
/F 15 10 FI 35 30 25 hti 00 t~3 Ul J
C.)
-4 20 15 10
'.1 5
I, co 0
100 350 I
EXPERIMENT :tr8 TIME: 20 SEC 0
F-F3 0
Fi 1m I.
150 200 250 300 TEMPERAI-URE
/F 45 40 35 C)
N--
30 I
0' 25 I U) 2:
-.)
20 15 10 5-0-
100 02 350 I
I I
I I
I
EXPERIMENT
- r8 TIME: 30 SEC 0
I?N o
0 0
150 200 250 300 TEMPERAI-URE
/F 45 40 I
C-)
N 30
'11 I-i 25 LU CD 7-~
(1)
-C
,'l 20 15 10 5
xi 100 tn 350 I
I I
I I
I I
L
EXPERIMENT :rT 150 200 250 300 coa 350 TEMPERAT-URE
/1-45 40 35
-)
N OQi
>D co Li C-)
(I) cm 30 25 20 15 10 5
II 0
100 I
I
TIME: 40 SEC
EXPERIMENT :1r8 200 250 TIME: 50 SEC 300 TEMPERATURE
/F 45 4-0 35 30 25
$--I OQ LiJ C)z
.)
20 i5 10 5
0 100 CO
-41 350 I
LXPILR t MlIN 1- : t r O 1 ] Ml. : (;0 ',1:(
10 35 I:
C..
30 25 LLI U)
F -
(I) 20 15 10 5
0 100 UX~~~~~~~~~~~~~~~~~~~.
0 C) n A
0 150 200 250 300 TEMPERATURE 5*11 I-s.
OQ I;o 0
co to 350
EXPER IMlEN 1 :1 r TIMI-: '10 Sc 0
V!
0 L&
0 150 200 250 300 TEMPERATURE
/F 40 35 30 C),
I7-,
25 "1
I')j LtJ C)
I.-
U)
'--4 20 15 10 r
.I 0
100 co
'0 3 5J0 p
I I
I I
I I
I I
A.3 Experiment:
FF1 Water level at t = 0 sec : L = 0 in.
Water level increase : L = 18 in.
Insurge time : t = 35 sec.
This experiment was ran using the radially located thermocouple arrangement. The transient was initiated by insurging cold water to the tank filled with saturated steam.
As Fig. A.3.1 showes; the pressure dropped for the first 10 sec, due to the large heat-transfer at the interface associated with breaking of jet throuah it. After t = 18 sec; the liquid region acted as a piston and compressed steam, resulting into a pressure rise.
-I-
EXPERI MENT 68 I.
66 I
Cl 19 cr m
()
L,_
H Q2:
.4
- F-62 60 58 56 20 30 TIME /SEC FFI IC 0
10 10 50 60
-X 7 I
EXPERIMENT 1.0 0.9 C-)
LJ C/)
co N-w
- 1 CD L~
3 U-LI)
I 0.8 0.7 0.6 0.5 0.3 0.2 I
60 TIME
/SEC
- Fl-1
'0 10 20 30 10 50
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I I
I I
0;0O I
I I
I, I
EXPER1MEN1
- F'F 1 TIME:
0 SEC 0
0 0
150 200 250 300 l]EMPERATURE
/F
..1 45 40 35 30 I
C-
'-4 11
-u r
Z4 w
25 Ld C-)
ct)
F--I M l>'
20 15 10 5 -
0-100 w
350
-e. 'r.
I I
I I
EXPERIMENTI :F 1 TIME:
10 SEC 0
w 0
- 0 150 250 300 TEMPERATURE
/F
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t-Il Z4 25 LLU I--
Cl
'20 15 t0 5
100 4-350
.r._"-*_<,;etwt_40-I I
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EXPERIMENT FF1 TlME: 20 SEC 0
0 Q3
- 0 150 200 250 300 TEMPERATURE
/F 45 10 35 30
,c-)
25 I
00
- 31 LiJ C-,
C) 20 15 10 0
100 Ln I
350 I
I I
I I
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I
EXPERIMEN :FFl 150 200 250 TIME: 28 SEC 300 TEMPERATURE
/F 45 40 IC-
~z
'-4 N
'll p-i.
OQ L1j Z13 30 25 20 15 LiJ F-4 (1) 10 5
0 I
100 350
EXPERIMENT
- FF1 IME: 35 SEC 0
0 0
150 200 250 300 TEMPERATURE
/F 45 40 35 30 r
CD)
'N.
25
'0
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I-1-'l 20 15 10 5 -
0 100 I
350 I
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EXPERIMENT :FFl 200 TIME:
7 Sl.C 0
0 0
es 0
150 300 TEMPERATURE
/F 45 0
35
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l 20
- 15 10 I
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350 I
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EXPERIM[N1-
- Ff 1 150 TIME: 59 SEC 200 250 300 TEMPERATURE
/F
'4' 1-5 4-0 35 30 C-)
'-I 25 "I
F Z.
DI
.LtC)
(n B-20 15 10 5
0 I%O
%a 100 350
-100-A.4 Experiment:
ST4 Water level at t =
sec : L 17 in.
Water level increase : aL = 18 in.
Insurge time : t = 41 sec.
This experiment was done using the axially located thermocouples. As it is shown in Figs. A.4.4 through A.4.11; there are two distinct liquid region:
the main liquid region, which retains its initial temperature; and the subcooled liquid region which consists of few layers of stratified liquid.
Liquid temperature distribution in Fig. A.4.8 was traced for a better visualization.
The subcooled liquid region proved to be stable after the insurge was stopped, Figs. A.4.9 through A.4.t1.
J 1-1----I --.
EXPER I MENT IL,J,
'-Ii 1-
- D:
(I)
(I)
Ldcc I--.
I 20 30 TIME /SEC I
86 84 Sf4' 82 80 78
'76 74 72 70 I0
'I 0
10 40 50 60
),.1..
I I
EXPER I MENT Sid 1.0 0.9 C) 0.8 0.7 w <c 0.5
~~1.'11.
I C)
L..0.2 Le 0.2 0.1 0.0 I
0 10 20 30
'0 50 60 TIME
/SEC
EXPERIMENT
- ST4 TIME:
I SEC A
OA C
A CA A
a A
A I,
100 150 200 250 300 TEMPERATURE
/F I
45 40 35 C-)
'--4 N.1 I
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50 I0 350 S L k -=
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EXPERIMENT STI TIME:
5 SEC A
oQA OA A
c.
A A
A 100 150 200 250 0
300 TEMPERATURE
/F 45 40
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1.
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t I
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50
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200 250 300 TEMPERATURE
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- STI 100 150 200 250 TIME: 20 SEC 300 TEMIPERATURE
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EXPERIMENT :ST4 TIME: 25 SEC A
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0 250 300 1TEMPERATURE
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100 150 200 250 300 TEMPERATURE
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EXPERIMlNT :ST4 I ME: 65 SEC I
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EXPERIMLNT'
- STI 1IME: '15 SEC A
CA
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30-25-20-15 10 5
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/F 40 35 A
A 0
A 0
A 0
A 100 150 200 250 300 l
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-112-A.5 Experiment:
EM9 Water level at t = 0 sec : L = 0 in.
Water level increase : L = 18 in.
Insurge time : t = 31 sec.
This transient was initiated by insurging cold water into the tank filled with saturated vapor.
The axially located thermocouples were used for determining temperature distribution inside the tank.
It should be noted that the sudden drop in pressure at time, t = 14 sec. (Fig. A.5.1), is due to the presence of the window, see Fig. 2. It is postulated that due to an area increase, a new surface is formed hence an increase in the interfacial heat transfer and a drop in pressure.
This experiment also showed that the behavior and temperature distribution of the subcooled liquid region in the case of insurge to partially filled tank, e.g. experiment: ST4, is quite similar to that of empty tank transients (see Figs. A.5.5 through A.5.14).
EXPERIMENT 30
- EM9 TIME /SEC C,
74 73 U) gti1 U'
'-I 72 71 70 69 68
- D U)
LU
- E:
F--
-a
)-A 67 66 0
10 20 40 50 60
EXPERIMENT 1.4 C-)
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co Lcr-
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10 20 30
- EM9 40 TIME
/SEC
==Go.1
==
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1 SEC 200 250 300 TEMPERATURE
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- ---~~~~~~~~~~
b I.
100 150 200 250 300 TEMPERATURE
.t 45 40 35 C-)
2:
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13 SEC 300 TEMPERATURE
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17 SEC 300 TEMPERATURE
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A at A
6 A
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100 150 200 250 300 TEMPERATURE
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A 0
100 150 200 250 300 TEMPERATURE
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0 100 150 200 250 300 TEMPERATURE
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- EM9 TIME: 50 SEC I
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A (A
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A A
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100 150 200 250 300 350 TEMPERATURE
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50
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- EM9 100 150 200 250 TIME: 59 SEC 300 TEMPERATURE
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CD 25
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t-(I)l 20 15 10 5
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- '~'
1 N
NRK-1d2-
-127-A.6 Miscellaneous Experiments The following description of experiments, belong to the experiments that were referred to during the main text, but were not described in the previous sections.
Experiment : KK1 Water level at t = 0 sec : L = 17 in.
Water level increase : AL = 18 in.
Insurge time : t = 41 sec.
Experiment : FT5 Water level at t = 0 : L = 17 in.
Water level increase : AL = 18 in.
Insurge time :It = 23 sec.,
Experiment : FT2 Water level at t = 0 : L = 17 in.
Water level increase : AL = 18 in.
Insurge time : t = 30 sec.
i
-128-APPENDIX B Conservation Equations for Deformable Control Volume Energy Equation for a deformable control volume can be written as t14];
dp
& +
dy
_If epdV + f p(e + -) Vr dA dt c.v.
c.s.
P
+
PVb-(B.1) c.s.
- where, e = specific energy s +
inertia + Wshear Vr = velocity of fluid relative to control surface boundary Vb = velocity of control surface boundary For any region in the pressurizer, kinetic and potential energy can be neglected.
Furthermore, O
(B.2)
So, Q=-t (mu) + X u + pu) + p (B.3) dt Conservation of mass can be written as;
--n.-
I.
~~o - -
-129-d -
pdV + f.
p Vr
= O dt cve c.s.
Hence, for any given region m = -
i (B.4)
(B.5)
~~~~~~~~~~~~-
I'l-.LI a
~~~--
L
-130-APPENDIX C Orifice Plate and Its Calibration An orifice plate, made of 1/8" stainless steel plate, was used to measure the mass flow rate. The inlet opening was 0.218" in diameter and was tapered at 400 angle.
The orifice was calibrated off the test loop with water. The data were plotted (see Fig. Cl) on a LOG-LOG graph of mass flow rate versus the pressure drop across the orifice. This data was approximated by log10(;) = -0.889672 + (0.482954) loglo(Ap)
(C.1)
- where, m = mass flow rate of water through the orifice Ap = pressure drop across the orifice, psi 4'
I I
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I I
I I
I I I**
FLOW U
I~~~~~~~~~~~~~~~~
II I
I I
III I
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l i i 10 PRESSURE DROP FIG.
C I 02
/PS I I.,
10 C-)
U) 10 w
F-:
CD LL U)
C/o
-I
'110 I~
10 7
- 1.
14-
.4 :
WA
po- : - &
"31m ull :
i
-132-APPENDIX D DETAILS OF A WESTINGHOUSE PRESSURIZER In this Appendix, the geometric and some operational routines for a Westinghouse pressurizer will be discussed 15).
Figures D.1 and D.2 shows the details of such a pressurizer.
As it is shown in these diagrams, the pressurizer is equipped with immersion heaters coming in from the bottom.
There are five banks of heaters. Banks A,, D and E are backup heaters and are either fully onn or fully off.
Back C is the control bank. The output of the heaters are given in Table D-1. A graph of total heater output versus system pressure for pressurizer levels between 11.5% and 52%
is given in Fig. D-3.
Under normal operating conditions, i.e. system pressure at or below 2012 psia, there is a dribbling flow from the spray nozzle at an approximate rate of 1.5 gpm.
-133-TABLE D-1:
Output of the Heaters Bank Heat Output (KW)
A 303.5 B
260 C
173 D
303.5 E
260 I
0
. m e -.-w -
ItL U.,., -
rinai
'6I.i.Il
I. S44-
,vnj p.t
p
i.e z
t1tL I
me W -
S. I T h+.m.f...*
U..-.
-w
e-
GENERAL ARRANGEMENT FOR WESTINGHOUSE PRESSURIZER I-A W
z-I FIG. DI -
FOR Th.E W#4TKtt SEE SECT W AM END VtW
.w r-Zi............
4i
~~~~~~~~~~~b rl
!--I L Ufl 14 _-
0
\\
_-S t,*-
<3~~~~~~l5.
4-<
S. a"ss.z "l"'X-"'
a~~
~~~
w a
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~
l..
- s..tt a.,,. -"
s..
1 54....4
-@ts j.rn
_2 U
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ss..c.* -
.@sdG.awsS a ca.
- Cat _-*=
555 Sat w
tt 4ne fl W v n.-
- t -
1,7 ip..
-I [Xi1 J ;f m la es.*c S
If E
X.--
- 4, L. J 1 J / u 2 L :..\\..
TO a uMLVe
,e Stt Ct a,,
ft*
!A.LLr
a..
we us.i,..
- w. -
,...j..4s...a..ee antS
- -. *
a.. -
L
- .a..
ens -
t.
5*
St -
- 5**
t.a hh 4 Sm U n*
.5 a*.as Sat S - -
'
R_.
I I. m.
I*
"S let Se on-WICS tr
- _SC
.a*
I-MI f-aft
- =:--
tW..
SIM t Th.
tee
.= -
5
-~ aS ta set so A.-.
l"~~~~~~~~~~~~~~~~
~~~~
S CS
-tnttee' FIG. D2 -
OUTLINE OF WESTINGHOUSE PRESSURIZER a
Iw VI I -I
- I
..I 1
._w _"
1 I
i
-. 1--II-K.
-,i
!T t
I II AU Nei I-It A8zz I
nM
-136-1400 '-
1200 1000.4.
4.
4.
4 i
l Bank A,B,D Bank C (control)
Bank E 1965 PP.ESSUPIZER. PRESSURE 2010 2020 (PSIA)
TOTAL HEATER OUTPUT FIG. D3 I.-
Fs 800 0
w z
600 w
Wa 400 200 t
.I i.
I I
.1
-