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| issue date = 11/30/1981
| issue date = 11/30/1981
| title = Fog Inerting Analysis for PWR Ice Condenser Plants.
| title = Fog Inerting Analysis for PWR Ice Condenser Plants.
| author name = TSAI S S
| author name = Tsai S
| author affiliation = WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
| author affiliation = WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
| addressee name =  
| addressee name =  
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=Text=
=Text=
{{#Wiki_filter:.FOG INERTIHG ANALYSIS FOR PMR ICE CONDENSER PLANTS BY S.S.TSAI CORE AND CONTAINMEHT ANALYSIS NUCLEAR SAFETY DEPARTMENT WESTINGHOUSE ELECTRIC CORP.NOYEHBER 1981 8310140042 831010 PDR ADOCK 050003i5 P PDR 0430Q:1 ABSTRACT.The recent hydrogen burn test conducted at the Lawrence Livermore National Laboratory has raised the NRC and the ice condenser plant'owners concern about fog inerting probability and consequences in ice condenser plants.The present investigation is aimed at resolving this fog inerting issue.In this report, major fog formation and removal mechanisms that exist in the post-accident ice condenser containment are identified and quyntified.
{{#Wiki_filter:.                         FOG INERTIHG ANALYSIS FOR PMR ICE CONDENSER PLANTS BY S. S. TSAI CORE AND CONTAINMEHT ANALYSIS NUCLEAR SAFETY DEPARTMENT WESTINGHOUSE ELECTRIC CORP.
Methodologies have been developed for pre-dicting fog formatiop and removal rates and for predicting fog concen-trations in various compartments in an ice condenser containment.
NOYEHBER 1981 8310140042 831010 PDR ADOCK 050003i5 P             PDR 0430Q:1
This methodology development has resulted in two computer programs, FOG and FOGMASS.The FOG computer program employs the Hijikata-Mori boun-dary layer fog formation theory, and calculates the fog formation rates due to boundary layer and bulk stream condensation.
The computer pro-gram FOGMASS solves the mass conservation equations for fog droplets and calculates the fog concentrations in various compartments.
Both compu-ter programs have been used to predict fog concentrations in the'equoyah, McGuire, and D.C.Cook containments, using the CLASIX output data for a S>D accident sequence.In order to utilize the c'alculational results-from the study, a fog inerting criterion has been established.
This criterion uses the hydro-gen concentration, volume mean drop size, and fog concentration to define the fog inerting regime.For a given hydrogen concentration, the minimum fog inerting concentration was found to vary with the square of the volume mean drop size.This criterion has been verified by the Factory Mutual recent fog inerting test data.The application of the fog inerting criterion to the three ice condenser plants shows that fog inerting would not exist in the upper and lower compartments.
Fog inerting in the ice condenser upper plenum at hydro-gen concentratons at which glow plug igniters are designed to operate is very unlikely.0430Q: I TABLE OF CONTENTS Section Tftle~Pa e ABSTRACT TABL E OF CON TEN TS LIST OF TABLES LIST OF FIGURES 1V 1.0 2.0 3.0',BACKGROUND IN TROD UCT ION FOG GENERATING MECHANISMS IN AH ICE CONDENSER CONTAINMENT 3.1 Fog Generated by Break Flow 3.1.1 Amount of Fog Generated by Break Flow 3.1.2 Drop Sizes Generated by Break Flow 3.2 Hucleation of Fog Droplets in Containment Atmosphere


====3.2.1 Nucleation====
. The ABSTRACT recent hydrogen burn test conducted at the Lawrence Livermore National Laboratory has raised the NRC and the ice condenser plant
Theori es 3.2.1.1 Classical Theory of Homogeneous Nucleation 3.2.1.2 Heterogeneous Nucleation Theo ry 3.2.2 Fog Formati o n Condi ti on s 3.2.3 Conditions for Fog Formation Near a Cold Surface.3.2.4 Rate of Fog Formation 3.2.5 Fog Drop Sizes 3.3 Fine Mist Droplets From Containment Sprays 2-1 3-1 3-1 3-3 3-5 3-6 3-7 3-7 3-9 3-10 3-12 3-15 3-19 3-19 4.0 FOG REMOVAL MECHANISMS IH AH ICE CONDENSER CONTAIHME HT 4.1 Settling Due to Gravity 4.2 Agglomeration 4.3 Vapori zation 4.4 Removal by Spray Drops 4.5 Other Removal Mechanisms 4-1 0430Q: 1 TABLE OF CONTENTS (Continued)
    'owners concern about fog inerting probability and consequences in ice condenser plants. The present investigation is aimed at resolving this fog inerting issue. In this report, major fog formation and removal mechanisms that exist in the post-accident ice condenser containment are identified and quyntified. Methodologies have been developed for pre-dicting fog formatiop and removal rates and for predicting fog concen-trations in various compartments in an ice condenser containment.
Section Title~Pa e 5.0 FOG INERT IHG CRITERI A 5.1 Previous Mork 5.2 Present Theory 5.3 Verification of Theories by Experiments 5-1 5-2 5-6 6.0 ASSESSMENT OF FOG INERTING PROBABILITY IH ICE CONDENSER COHTAINMEHTS
This methodology development has resulted in two computer programs,    FOG and FOGMASS. The FOG  computer program employs the Hijikata-Mori boun-dary layer fog formation theory, and calculates the fog formation rates due to boundary layer and bulk stream condensation.     The computer pro-gram FOGMASS solves the mass conservation equations for fog droplets and calculates the fog concentrations in various compartments. Both compu-ter programs have been used to predict fog concentrations in the
  'equoyah, McGuire, and D. C. Cook containments, using the        CLASIX output data for a S>D accident sequence.
In order to    utilize  the c'alculational results-from the study, a fog inerting criterion    has been  established. This criterion  uses the hydro-gen concentration, volume mean drop size, and fog concentration to define the fog inerting regime. For a given hydrogen concentration, the minimum fog inerting concentration was found to vary with the square of the volume mean drop size. This criterion has been verified by the Factory Mutual recent fog inerting test data.
The    application of the fog inerting criterion to the three ice condenser plants shows that fog inerting would not exist in the upper and lower compartments. Fog inerting in the ice condenser upper plenum at hydro-gen concentratons at which glow plug igniters are designed to operate is very unlikely.
0430Q:   I


===6.1 Determination===
TABLE OF CONTENTS Section                          Tftle                      ~Pa e ABSTRACT TABLE OF CON TEN TS LIST    OF TABLES                                  1V LIST    OF FIGURES 1.0  ',BACKGROUND 2.0      IN TROD UCT ION                                  2-1 3.0    FOG GENERATING MECHANISMS                          3-1 IN AH ICE CONDENSER CONTAINMENT 3.1    Fog Generated    by Break Flow            3-1 3.1.1    Amount  of Fog Generated          3-3 by Break Flow 3.1.2 Drop Sizes Generated by Break Flow    3-5 3.2    Hucleation of Fog Droplets in Containment  3-6 Atmosphere 3.2.1    Nucleation Theori es              3-7 3.2.1.1 Classical Theory of      3-7 Homogeneous Nucleation 3.2.1.2 Heterogeneous Nucleation  3-9 Theo ry 3.2.2  Fog Formati o n Condi  ti on s    3-10 3.2.3    Conditions for Fog Formation Near  3-12 a  Cold Surface.
of Volume Fraction of Fog Droplets in Ice Condenser Containment Subcompartments
3.2.4 Rate of Fog Formation                3-15 3.2.5 Fog Drop Sizes                        3-19 3.3    Fine Mist Droplets From Containment Sprays  3-19 4.0    FOG REMOVAL MECHANISMS        IH  AH ICE CONDENSER CONTAIHMEHT 4.1    Settling    Due  to Gravity                4-1 4.2    Agglomeration 4.3    Vapori zation 4.4    Removal by Spray Drops 4.5    Other Removal Mechanisms 0430Q:  1


====6.1.1 Calculation====
TABLE OF CONTENTS    (Continued)
of mbreak 6.1.2 Calcul ation of 6.1.3 Calculation of m set 6.1.4 Ca 1 cul ation of m sP 6.2 Fog Inerting Probability in the Sequoyah Plant 6.3 Fog Inerting Probability in the McGuire Plant 6.4 Fog Inerting Probability in the D.C.Cook Plant 6.5 Effect of Fog on Global Combustion 6-1 6-1 6-5 6-6 6-6 6-7 6-7 6-23 6-37 6-50 7.0  
Section                        Title                            ~Pa e 5.0    FOG  INERT IHG CRITERI A                              5-1 5.1  Previous Mork 5.2  Present Theory                                  5-2 5.3  Verification of Theories      by Experiments    5-6 6.0    ASSESSMENT OF FOG INERTING PROBABILITY        IH ICE  6-1 CONDENSER COHTAINMEHTS 6.1    Determination of Volume Fraction of Fog          6-1 Droplets in Ice Condenser Containment Subcompartments 6.1.1   Calculation of mbreak                   6-5 6.1.2   Calcul ation of                         6-6 6.1.3   Calculation of m set                     6-6 6.1.4   Ca 1 cul ation of m                     6-7 sP 6.2 Fog Inerting Probability in the         Sequoyah   6-7 Plant 6.3   Fog   Inerting Probability in the     McGuire   6-23 Plant 6.4   Fog   Inerting Probability in the     D. C. Cook 6-37 Plant 6.5   Effect of   Fog on Global Combustion           6-50 7.0  


==SUMMARY==
==SUMMARY==
AND CONCLUSIONS 7-1 ACKNOWLEDGMENTS 7-3 REFERENCES R-1 APPENDIX A A-1 APPENDIX 8 B-1 0430Q:1 i fl LIST OF TABLES Tabl e No.Title~Pa e 6.1 FOG Input Data for Sequoyah Lower Compartment 6-18'.2 6.3 FOG Input Data for Sequoyah Ice Condenser Geometric Data for Sequoyah Containment 6-19 6-20 6.4 MARCH Prediction of Reactor Coolant Mass and Energy Release Rate for the S20 Sequence.6-21 6.5 Intercompartmental Fl ow Rates (ft/sec)3 Predicted by CLASIX for Sequoyah 6-22 6.6 FOG Input Data for McGuire Lower Compartment 6-33 6.7 FOG Input Data for HcGuire Ice Condenser 6-34 6.8 Geometric Data for McGuire Containment 6-35 6.9 Intercompartmental Flow Rates (ft/sec)Predicted by CLASIX for HcGuire 6-36 6.10 FOG Input Data for D.C.Cook Lower Compartment 6-46 6.11 FOG Input Data for D.C.Cook Ice Condenser 6-47 6.12 Geometric Data for D.C.Cook Containment 6-48 6.13 Intercompartmental Fl ow Rates (ft/sec)Predicted by CLASIX for D.C.Cook 6-49 iv 0430Q: 1 LIST OF FIGURES~Fi ure No.Titl e~Pa e 3.1 T-S Diagram for Reactor Coolant Discharged From Break 3-4 3.2~Vapor Pressure and Temperature Profile Hear a Cold Surface 3-14 3.3 Formation of Fog Hear a Cold Surface 3-16 3.4 Drop Size Distribution Predicted by Heiburger and Chien 3-20 3.5 Particle Size Distribution for 50 PSI Pressure Drop Across Hozzle No.1713 3-21 4.1 Terminal Velocity as a Function of Drop Radius in Steam-Air Atmospheres 4-5 4.2 Agglomeration Rates in Air Between Equal-Sized Drops 5.1 Minimum Ignition Energies and Quenching Distance 5-3 for Hydrogen-Oxygen Inert Gas Mixtures at Atmo-sphericc Pressure 5.2 The Ef feet of Droplet Spacing on Flame Quenching 5-4 5.3 Schematic Representation of Temperature Profile Through the Flame Front 5-7 The Parameter We.g as a Function of 1 (Y-Yf)/e~for Different Values of Kei 5-7 0430Q: 1 f)i' LIST OF FIGURES (Continued)
AND CONCLUSIONS                                 7-1 ACKNOWLEDGMENTS                                         7-3 REFERENCES                                             R-1 APPENDIX A                                             A-1 APPENDIX 8                                             B-1 0430Q:1
~Fi ure No.Title~Pa e 5.5 (K).t e.at the Flammability Limit as a Function of (Yu-Yf)/ei 5-8 5.6 5.7 Comparison Between Theories and Factory Mutual Fog Inerting Experiments on 4.76 Percent H2 r'I Comparison Between the Present Theory and Factory Mutual Fog Inerting Experiments on 7.2 Percent H2 5-10 5-11 5.8 Comparison Between the Present Theory and Factory Mutual Fog Inerting Experiments on 7.9 Percent H2 5-12 6.1 Sequoyah CLASIX Containment Model 6-8 6.2 Fog Formation in TVA Sequoyah Lower Compartment 6-10 6.3 Fog Formation in TVA Sequoyah Ice Condenser 6-11 6.4 6.5 Fog Concentration in Sequoyah Containment McGuire CLASIX Containment Model 6-14 6-24 6.6 Fog Formation in Duke McGuire Lower Compartment 6-25 6.7 Fog Formation in Duke McGuire Ice Condenser 6-26 6.8 Fog Concentr ation in McGuire Containment 6-29 6.9 D.C.Cook CLASIX Containment Model 6-38 0430Q:1 LIST OF FIGURES (Continued)
 
Title~Pa e Fog Formation in AEP Cook Lower Compartment 6-29 Fog Formation in AEP Cook Ice Condenser 6-40 6.12 Fog Concentration in D.C.Cook Containment 6-43 vii 0430(}:I  
i fl
 
LIST OF TABLES Tabl e No.                             Title                   ~Pa     e 6.1         FOG   Input Data for Sequoyah Lower Compartment 6-18'.2 FOG   Input Data for Sequoyah Ice Condenser         6-19 6.3        Geometric Data     for Sequoyah Containment         6-20 6.4         MARCH   Prediction of Reactor Coolant Mass   and   6-21 Energy Release Rate for the S20 Sequence.
Intercompartmental Fl ow Rates (ft /sec) 3           6-22 6.5 Predicted by CLASIX for Sequoyah 6.6         FOG   Input Data for McGuire Lower Compartment       6-33 6.7         FOG   Input Data for HcGuire Ice Condenser           6-34 6.8         Geometric Data for McGuire Containment               6-35 6.9         Intercompartmental     Flow Rates (ft /sec)         6-36 Predicted by     CLASIX   for HcGuire
: 6. 10       FOG   Input Data for D. C. Cook Lower Compartment 6-46 6.11       FOG   Input Data for D. C. Cook Ice Condenser     6-47 6.12         Geometric Data for D. C. Cook Containment             6-48 6.13         Intercompartmental Fl ow Rates     (ft /sec)         6-49 Predicted by CLASIX for D. C.       Cook iv 0430Q: 1
 
LIST   OF FIGURES
  ~Fi ure No.                               Titl e                       ~Pa e 3.1           T-S Diagram     for Reactor Coolant Discharged           3-4 From Break 3.2     ~
Vapor Pressure     and Temperature     Profile Hear     3-14 a Cold Surface 3.3           Formation of Fog Hear       a Cold Surface               3-16 3.4         Drop Size   Distribution Predicted       by Heiburger   3-20 and Chien 3.5         Particle Size Distribution for         50 PSI Pressure   3-21 Drop Across Hozzle No. 1713 4.1           Terminal Velocity as a Function         of Drop Radius 4-5 in Steam-Air Atmospheres 4.2         Agglomeration Rates       in Air Between Equal-Sized Drops sphericc 5.1         Minimum   Ignition Energies       and Quenching Distance 5-3 for Hydrogen-Oxygen Inert         Gas Mixtures at Atmo-Pressure 5.2         The   Ef feet of Droplet Spacing on Flame Quenching       5-4 5.3         Schematic Representation         of Temperature   Profile 5-7 Through the Flame Front The Parameter     We. g as a Function of               5-7 1
(Y- Yf)/ e for Different
                              ~
Values of Kei 0430Q: 1
 
f) i' LIST OF FIGURES   (Continued)
  ~Fi ure No.                             Title                       ~Pa e 5.5           (K) .t e. at the Flammability Limit as     a       5-8 Function of (Yu - Yf)/ei 5.6           Comparison Between Theories and Factory Mutual         5-10 Fog Inerting Experiments   on 4.76 Percent H2 r
                  'I 5.7            Comparison Between the Present Theory and             5-11 Factory Mutual Fog Inerting Experiments on 7.2 Percent H2 5.8           Comparison Between the Present Theory and             5-12 Factory Mutual Fog Inerting Experiments on 7.9 Percent H2 6.1           Sequoyah CLASIX Containment Model                     6-8 6.2           Fog Formation   in TVA Sequoyah   Lower Compartment 6-10 6.3           Fog Formation   in TVA Sequoyah   Ice Condenser     6-11 6.4           Fog Concentration     in Sequoyah Containment       6-14 6.5          McGuire CLASIX Containment Model                       6-24 6.6           Fog Formation   in Duke McGuire Lower Compartment   6-25 6.7           Fog Formation   in Duke McGuire   Ice Condenser     6-26 6.8           Fog Concentr ation in McGuire Containment             6-29 6.9           D. C. Cook CLASIX Containment Model                   6-38 0430Q:1
 
LIST OF FIGURES (Continued)
Title                 ~Pa e Fog Formation in AEP Cook Lower Compartment 6-29 Fog Formation in AEP Cook Ice Condenser     6-40 6.12   Fog Concentration in D.C. Cook Containment 6-43 vii 0430(}:I


==1.0 BACKGROUND==
==1.0 BACKGROUND==
The incident at Three Mile Island has demonstrated that a significant amount of hydrogen could be generated during core degradation.
This experience raised HRC concern about the safety of nuclear power plants, in terms of their capability to control hydrogen during severe acci-dents.Since ice condenser plants have a relatively small volume and low containment design pressure, the problem is magnified.
Therefore,the NRC has requested the ice condenser plant owners to study hydrogen control methods for use in their plants.In this regard, the Tennessee Valley Authority (TVA), Duke Power and American Electric Power (AEP)have proposed the use of glow plug igniters at various locations inside their ice condenser containments to ignite hydrogen at low concentration.
Recently, the NRC requested Lawrence Livermore National Laboratory (LLNL)to carry out experiments on these igniters to determine their effectiveness.
In these experiments, two tests with high steam concentration seemed to indicate that substantial fog formation could occur when saturated steam is'ischarged into a unheated vessel and under some conditions fog could effectively preclude hydrogen from combustion The LLHL tests raised some doubts about the effectiveness of glow plug igniters under fog formation conditions.
In a recent review of hydrogen related issues for ice condenser plants, the HRC has raised several questions concerning the probability and consequences of fog formation and steam supersaturation in ice condenser plants.In response to'the NRC questions, TVA, AEP, and Duke established experi-mental and theoretical analysis programs to study the fog inerting prob-lem.The experimental program was contracted to Factory Mutual.The experiments were designed to test glow plug igniter's performance under 4 different fogging conditions.
At the same time, the plant owners.requested Westinghouse to perform fog inerting analyses for the Sequoyah, McGuire, and D.C.Cook plants.This report presents the results of the Westinghouse studies.0430Q:1 a e 2.0 I NTRODUCT ION From the post-test analysis of the LLNL fpdrogen burn tests, it appears that substantial fog formation occurred inside the test vessel.Gen-erally, fog droplets are only few microns in diameter.These sizes of droplets have potential to prevent a fl'ammable gas mixture from combus-tion or quench a propagating flame.This is because these sizes of droplets vaporize very fast (on the order of miliseconds), absorbing an enormous amount of the heat released from combustion if a substantial quantity of these droplets is present in the atmosphere.
In comparison, large water droplets in the range of few hundred microns or larger (e.g.spray droplets)have no inerting effect on combustion and hence have insignificant effect on glow plug igniter's performance.
There-fore, the present analysis will be concentrated on the generation and removal of fog (mist), and its impact on the glow plug igniter system.There are a number of fog generation and removal mechanisms present in a post-accident ice condenser containment atmosphere.
The fog generation mechanisms include fog generated by the break flow (if it is two-phase), fog formation near the ice and structural heat sink surfaces (since the surface temperatures could be well below the dew point), and fog genera-tion due to homogeneous and heterogeneous nucleation in condensing bulk streams.The fog removal mechanisms include gravitational settling, agglomera-tion, vaporization and removal by spray droplets.In order to estimate the post-accident fog concentrations in ice condenser containments, these competing mechanisms must be studied, and evaluated.
To solve this problem, it requires a numerical integration of the mass conserva-.
tion equations for the mist droplets in the various containment subcom-partments.
By making some simplifying assumptions the transient fog concentration in the various subcompartments have been estimated.
0430Q I 2-1 The analysis presented here considers all the fog removal and generation mechanisms previously described.
In addition, it considers the fog entrainment in the intercompartmental flows (including fan flows)in the fog mass conservation equations.
In order to perform this analysis it was necessary to use CLASIX results for a S2D event as boundary condi-tions to the problem.In addition to calculation of fog concentrations in'various containment compartments, it was necessary to establish a fog'inerting criterion.
A fog inerting criterion has been proposed by Berman et al., which pre-dicts the minirpum fog concentration required to inert a given hydrogen concentration and given volume mean fog drop size.This criterion seems to overpredict the minimum fog inerting concentration, when compared with experimental data.A more realistic fog inerting theory is presented in the present study.The fog inerting methodology, analysis, and results are presented in the following sections of this report.Sections 3 and 4 present the, method-ology for calculating the fog formation and removal rates.Section 5 gives the fog inerting criteria, and Section 6 presents the results.0430Q: I 2-2 i'0 3.0 FOG GENERATING MECHANISMS IH AH ICE CONDENSER COHTAINMEHT The inerting capability of fog droplets depends on their sizes and con-centration in the containment atmosphere, as well as the hydrogen con-centration.
This section is intended to identify various fog generation mechanisms present in an ice condenser containment and to determine the drop sizes and the rates of fog generation from these mechanisms.
Three fog generation mechanisms are discussed in this section and the dominant fog generation mechanisms are identified.
3.1 FOG GENERATED BY BREAK FLOW The post-LOCA containment atmosphere is most likely to be a drop-laden atmosphere.
The large-scale simulated LOCA experiments conducted to date have directly or indirectly confirmed the presence of two-phase atmospheres.
For example, Marvikken and Battelle-Frankfurt (3)experiments were instrumented to measure fluid densities and water levels in various parts of the containment.
Therefore, fog generation by the break flow cannot be neglected.
The following discussion of this phenomenon pertains to small LOCAs.In the early stage of a small LOCA transient, a substantial.portion of the primary coolant discharged from the break will remain as liquid.Because of the superheat and high velocity, this liquid will be framen-ted by aerodynamic forces and homogeneous nucleation mechanism into'mall droplets.These droplets are expected to be entrained by the intercompartmental and fan flows and spread to other parts of the ice condenser containment.
During their travel throughout the containment, the fog droplets will be removed by gravitational settling, sprays, and vaporization.
The fog gene'ration period lasts until the water level in the reactor vessel falls to the break elevation and the break flow is no longer two-phase.'or the particular S<D sequence analyzed by0430Q: I 3-1 CLASIX, this period lasts for about 36 minutes and about 4.2 x (5)10 lbs of water has been discharged into the lower compartment during 5 thi s pe ri od of-time.After the water level in the reactor vessel falls below the break eleva-tion, the break flow rate is substantially reduced.The flow is essen-'ially steam and no fog droplets will be generated.
As a result, the lower compartment becomes superheated afterward.
Fog droplets may vaporize during their travel through this compartment and substantial removal of mist droplets are expected.Large suspended drops generated by the break flow will be removed very quickly.by gravitational settling and impingement.
For the drops larger than 20 u, the removal rate is high and complete removal only takes a few seconds.For the smallest drops (less than 1 u)the terminal veloc-ity is so small that they virtually remain suspended in the atmosphere indefinitely.
The only effective removal mechanisms for these sizes of drops are vaporization, and collision with larger spray drops.The weight fraction of these sizes of drops is estimated to be 1 per-cent generated by the break flow.The population of these small (3)drops can increase if nucleation of embryos occurs in a saturated atmo-sphere.0430Q:1 3-2 l 3.1.1 AMOUNT OF FOG GENERATED BY BREAK FLOW~~As discussed previously, the existence of a two-phase drop-laden regime has been observed experimentally.
In a.small LOCA, flashing of primary coolant at the break and subsequent vaporization of blowdown liquid represent a series of changes of thermodynamic states.Since the reac-tor coolant pressure is high, the break flow will be choked.The accel-eration of primary coolant to the break location is essentially an isen-tropic process, in which the pressure decreases to the point at which substantial homogeneous nucleation occurs.When the flow leaves the break, the liquid is framented by both the aerodynamic forces and the nucleation mechanism into small fog droplets.These fog droplets con-tinue to vaporize, because of the superheat in the droplets, until a thermodynamic equilibrium state is reached.Because of the high super-heat and large aerodynamic forces, it is expected that the fog droplets generated are very small.This vaporization process is essentially isenthalpic.
The existence of a two phase drop-laden regime can also be explained by use of a T-S diagram for steam as shown in Figure 3,1 (Figure 1 of Reference 6).It is shown in this figure that the blowdown liquid goes through a series of thermodynamic states, starting from the subcooled liquid state B.The liquid expands isentropically from the subcooled 0 state 8 to the state B>at the break, where a two-phase critical flow is developed.
At the same time, temperature changes from T to TI.After leaving the break, the droplets continue to vaporize because of excessive superheat until finally an equilibrium state B<is reached at which the droplets are in thermal equilibrium with their surroundings.
This vaporization process is essentially isenthalpic.
At this time, the droplet temperature drops to T>and the atmospheric temperature also rises to T>.For a small LOCA, the equilibrium tem-perature varies with time.According to the CLASIX analysis of the Sequoyah plant, the lower compartment gas temperature rises quickly from 100"F to approximately 200"F and then stay at this temperature for an extended period of time.Using these temperatures as final equilibrium 0430Q I 3-3
-Kg/cm2 100 10'r 450 400 350 300 0 250 200 150 100 50 600 400 300 g 200 100 i j I/t A2 0 0.0 0.2~0.4 0.6 0.8 X=1 FIGURE 3.1 T-S DIAGRAM FOR REACTOR COOLANT DISCHARGED FROM BREAK
.temperatures for water droplets, the weight fraction of water droplets in the break flow is approximately 50 percent, which is consistent with the MARCH calculations~7~
of the break flow rate and its energy release rate.The discussion given above is valid only when the initial state'of the break flow is subcooled or saturated liquid.After the water level inside the reactor vessel falls below the break elevation, the break flow will be steam.The moisture content of the steam will be very low, even though isentropic expansion may lead to homogeneous nucleation and subsequent condensation in the vapor stream.Depending on the super-saturation that can be achieved in this isentropic expansion, a conden-sation shock is possible when critical'supersaturation is reached.However, it is believed that the fog droplets generated by homogeneous nucleation in this supersonic jet is negligible as compared to other fog generating mechanisms.
Hence, it will be neglected in this present analysis.Therefore, the fog generation by the break flow is considered possible only when the water level in the reactor vessel is above the break elevation.
According to the MARCH~"~calculation at 2172 seconds into the acci-dent, the water level inside the reactor vessel falls below the break elevation for the S2D case analyzed in Reference 7.By this time approximately 421,000 lbs of water has been discharged from the break and 56 percent of this discharged fluid, i.e., 236,000 lbs, will be sus-pended in the atmosphere as condensate.
However, most of these droplets will later be removed by gravitational settling, sprays, and vaporiza-tion.3.1.2 DROP SIZES GENERATED BY BREAK FLOW The flashing jet experiment conducted by Brown and York~B~has indi-cated that the drop sizes produced by flashing.liquid are small.They derived a correlation for the linear mean drop size based on the test data.The correlation shows that the mean drop size is inversely pro-portional to the Weber number and it decreases linearly with increasing 0430Q:I 3-'5 superheat.
However, this correlation is applicable for liquid superheat less than 75'F and it can not be extrapolated to the large superheat of the reactor coolant.However, some conclusion concerning the drop sizes produced by blowdown of the reactor coolant can be drawn for this condi-tion., The break flow has much larger superheat and Weber number than those used in this experiment; therefore, the drop sizes produced by the break flow should be much smaller than-50'bserved in this experi-ment.Gido and Koestel have developed a method for estimating the.drop (9)size leaving the fragmentation/evaporation zone of a blowdown jet.This model is based on the assumption that drops with an'internal.
temperature difference of less than 5K will escape fragmentation.
This model has been verified by the low superheat, data of Brown and York.Application of this method to the LOCA condition shows that the maximum attainable drop size is 7p (this means that arly drop size larger than 7p will not escape framentation by homogeneous nucleation).
The corresponding mean drop size is about 4p, based on the observation of the largest drop size and mean drop size in the experiment reported in Reference 8.However, this volume mean drop size is not used in the present analysis.Instead, the present analysis uses 10 p mean drop size,.considering the drop agglomeration effect.3.2 NUCLEATION OF FOG DROPLETS IN CONTAINMENT ATMOSPHERE Nucleation of water embryos from the homogeneous vapor phase plays an important role in mist generation in ice condenser plants.Nucleation is a process by which tiny water embryos or condensation nuclei are formed from a pure vapor phase at a rapid rate.In incipient homogene-ous nucleation, the local gas temperature drops below the dew point corresponding to the local steam partial pressure and some degree of local supersaturation is needed.The degree of supersaturation needed to start nucleation depends on the number of condensation nuclei present in the containment.
These condensation nuclei could be very small water droplets or dust particles.
If sufficient number of condensation nuclei 0430Q:I 3-6 exist, supersaturation could be small.It is likely that the ice con-denser containment contains a subtantial number of dust particles such that little supersaturation is needed for nucleation.
This section is devoted to the discussion of fog formation by homogene-ous or heterogeneous nucleation.
The classical nucleation theories are used to explain the nucleation phenomenon.


====3.2.1 NUCLEATION====
The   incident at Three Mile Island has demonstrated that a significant amount of hydrogen could be generated during core degradation.      This experience raised HRC concern about the safety of nuclear power plants, in terms of their capability to control hydrogen during severe acci-dents. Since ice condenser plants have a relatively small volume and low containment design pressure, the problem is magnified. Therefore, the NRC has requested the ice condenser plant owners to study hydrogen control methods for use in their plants. In this regard, the Tennessee Valley Authority (TVA), Duke Power and American Electric Power (AEP) have proposed the use of glow plug igniters at various locations inside their ice condenser containments to ignite hydrogen at low concentration.
THEORIES The process of n0cleation of an embryo water drop is important in under-standing the mechanism of fog formation in ice condenser plants.Two types of nucleation process, namely, homogeneous and heterogeneous nucleations, and their theories will be discussed in Section 3.2.1.3.2.1.1 CLASSICAL THEORY OF HOMOGENEOUS NUCLEATION l)When an embryo droplet, usually assumed spherical, is formed from con-densation of water vapor molecules, its free energy changes.The change of free energy can be expressed as aG=4xr a" (4/3)xr nL KT Zn (p/p)where a is the surface free energy per unit area, or surface tension, r is the drop radius, P is the vapor pressure, P;s the saturation 0 Pressure at the droPlet temPerature, nL is number of molecules per ,unit volume, K is the Boltzman constant, and T is the drop temperature.
Recently, the NRC requested Lawrence Livermore National Laboratory (LLNL) to carry out experiments on these igniters to determine their effectiveness. In these experiments, two tests with high steam concentration seemed to indicate that substantial fog formation could occur when saturated steam is'ischarged into a unheated vessel and under some conditions fog could effectively preclude hydrogen from combustion The LLHL    tests raised  some doubts about the effectiveness of glow plug igniters under fog formation conditions. In a recent review of hydrogen related issues for ice condenser plants,       the HRC has raised several questions concerning the probability and consequences of fog formation and steam supersaturation in ice condenser plants.
The supersaturation S, is defined as P/P.Equation (3.1)represents a free energy barrier to the growth of the drops at a given suprsaturation.
In response to 'the   NRC  questions, TVA, AEP, and Duke established experi-mental and theoretical analysis programs to study the fog inerting prob-lem. The experimental program was contracted to Factory Mutual. The experiments were designed to test glow plug igniter's performance under 4
At maximum aG, the critical radius r" can be obtained from Equation 3.1 as r*20 0430/:1 3-7 r 1', i~I The drops of the critical size can be considered as condensation nuclei~~~~~~~~~~~~~~~since at this size the drops will grow with no change in free energy.This critical size represents an equilibrium size at which a supersatu-rated vapor at vapor pressure P is in equilibrium with this critical drop at a lower saturation pressure P.However, this equilibrium mode is unstable.For example, if a drop of the critical size origi-nally in equilibrium with the surrounding vapor suffers a sudden small increase in size due to condensation, then (if the drop temperature does not,change), Equation 3.2 shows that the equilibrium pressure, P, on its surface will decrease.Therefore, the actual vapor pressure will then be greater than the equilibrium value and further condensation will occur.This is why the drop of this critical size is called condensa-tion nucleus.The nucleation rate of critical-sized embryos can be obtained from the kinetics of a nonequilibrium distribution of embryos.The classical nucleation theory shows that there is a very sudden increase in the nucleation r ate when past a certain critical value of supersatura-tion.An extensive validation of the nucleation theory was conducted by Volmer and Flood in an experiment in which a number of vapors were expanded to visible condensation in a cylinder.The observed critical supersaturations agreed suprisingly well with theory in nearly all cases, including water vapor.Critical condensation nuclei sizes typically range from 10 to 100 atoms.These sizes are considerably smaller than the mean free path of the vapor molecules and therefore the rates of mass and heat transfer at'the drop surface cannot be predicted by bulk transport theories.In this case, the kinetic theory of gas should be used to predict the rates of mass and heat transfer at the drop surface.Starting from the kinetic theory of gas and the energy conservation equation, the rate of growth of a condensation nucleus was obtained by Hill et al.It was found that the growth rate is on the order of 10 ft/sec.Therefore, it takes only about I milisecond for the condensation nucleus to grow to a fog droplet size of I p.0430Q I 3-8 3.2.1.2 HETEROGENEOUS N UCL EAT ION THEORY Another mechanism of forming embryos is heterogeneous nucleation on foreign particles that could suspend in the containment atmosphere.
different fogging conditions. At the same time, the plant owners .
These particles may serve as nucleation sites for vapor and thus enhance the nucleation rate.The source of foreign particles in the containment following core degradation could come from fission product aerosols and dust particles.
requested Westinghouse to perform fog inerting analyses for the Sequoyah, McGuire, and D. C. Cook plants. This report presents the results of the Westinghouse studies.
The size distribution of these particles are important because the supersaturation required to form embryos depends on particle sizes.A typical size distribution of atmospheric aerosols is that of e Junge, taken from surveys made near Frankfurt A.H., German.The surveys found that the size range of dust particles is from 0.01 to I In the range from 0.01 to 0.5 p, there are between 100 and 10,000 particles per cubic centimeter.
0430Q:1
A majority of particles have sizes smaller than 1 micron.At the smallest size of 0.01 p, the critical supersaturation is about 1.02 and at the largest size the supersatura-tion is only 1.001.~~The other source of aerosol particulates is fission, products.During normal operation, the primary coolant contains very little fission pro-ducts.However, a large release of fission products, such as the gap release, could occur at about the same time the hydrogen releases.The amount of fission products released to the containment depends on acci-dent scenarios.
 
The distribution and transport of fission products in the containment can be predicted by the CORRAL code~~.The size di stribution of fission products.in the containment can be extrapolated from the CSE experiments~
a e
4~.These experiments indicated that soon after fission product release, the mean particle diameter was 15 p.A few hours later, the mean diameter decreased to about 5 p because of settling of large particles onto the floor.These sizes are substan-tially larger than those of dust particles and therefore, critical supersaturation is even smaller than values quoted above for the dust particles.
: 2. 0  I NTRODUCT ION From the post-test analysis of the  LLNL  fpdrogen burn tests,  it appears that substantial fog formation occurred inside the test vessel. Gen-erally, fog droplets are only few microns in diameter. These sizes of droplets have potential to prevent a fl'ammable gas mixture from combus-tion or quench a propagating flame. This is because these sizes of droplets vaporize very fast (on the order of miliseconds), absorbing an enormous amount of the heat released from combustion      if a substantial quantity of these droplets is present in the atmosphere. In comparison, large water droplets in the range of few hundred microns or larger (e.g.
0430Q:1 3-9 The atmospheric aerosols consist of particulates of various sizes, vari-ous chemical components, and various electrostatic charges.The aerosol particulates could be soluble or insoluble in water.All these proper-ties could affect the required supersaturation for nucleation.
spray droplets) have no inerting effect on combustion          and hence have insignificant effect on glow plug igniter's performance.       There-fore, the present analysis will be concentrated on the generation and removal of fog (mist), and its impact on the glow plug igniter system.
In the case of insoluble particulates, the contact angle, 6, between the"embryo and the particle surface is important.
There are  a number of fog generation  and removal mechanisms  present in a post-accident ice condenser containment atmosphere. The fog generation mechanisms include fog generated by the break flow      (if it  is two-phase),
If the particle is com-pletely wettable, 6="0, it forms a base on which a small amount of water can.form a drop of large radius of curvature and thus satisfy the Hemhol tz equation (Eq.3.2)at a much lower supersaturation than would be the case if same number of molecules form a drop with a particle core.Fletcher developed a relationship between the supersIatura-(I')tion and drop radius for several values of contact angle, assuming that the particle is spherical.
fog formation near the ice and structural heat sink surfaces (since the surface temperatures could be well below the dew point), and fog genera-tion due to homogeneous and heterogeneous nucleation in condensing bulk streams.
Competely wettable, a particle of 1 micron or so, when covered with a film of water, is theoretically at the crit-ical radius, and it needs only 1.001 critical supersaturation.
The fog removal mechanisms include gravitational      settling,  agglomera-tion, vaporization and removal by spray droplets.      In order to estimate the post-accident fog concentrations in ice condenser containments, these competing mechanisms must be studied, and evaluated. To solve this problem,  it requires a numerical integration of the mass conserva-.
The post-accident containment atmosphere is likely to contain a substan-~~~~~tial amount of aerosol particles.
tion equations for the mist droplets in the various containment subcom-partments. By making some simplifying assumptions the transient fog concentration in the various subcompartments have been estimated.
These particles will act as condensa-i)tion nuclei and therefore, little supersaturation is required to pre-cipitate condensation.
0430Q  I                            2-1
3.2.2 FOG FORlCTION CONDITIONS Fog formation in a mixture'f vapor and noncondensible gases has been of interest to meteorologists, and turbine and condenser designers.
 
Fog is formed by homogeneous or heterogeneous nucleation as a result of tem-perature drop below the dew point (sometimes with concommitant pressure drop).During the temperature drop, a local gas element will go through a series of thermodynamic states.Eventually, a state is reached at which incipient fog formation occurs.Some degree of vapor supersatura-t'ion is needed to precipitate fog formation.
The  analysis presented here considers  all  the fog removal and generation mechanisms previously described. In addition,  it considers the fog entrainment in the intercompartmental    flows (including fan flows) in the fog mass conservation equations. In order to perform this analysis it was necessary    to use CLASIX results for  a S2D  event as boundary condi-tions to the problem.
The vapor supersaturation at which rapid nucleation of vapor first appears is called critical supersaturation.
In addition to calculation    of fog concentrations in'various containment compartments, it was necessary to establish a fog'inerting criterion. A fog inerting criterion has been proposed by Berman et al., which pre-dicts the minirpum fog concentration required to inert a given hydrogen concentration and given volume mean fog drop size. This criterion seems to overpredict the minimum fog inerting concentration, when compared with experimental data. A more realistic fog inerting theory is presented in the present study.
The critical supersaturation, in general, is a 0430Q:1 3-10 e function of temperature, vapor properties, mixing time (if a mixing process is involved), and concentration and sizes of foreign particles.
The fog    inerting methodology, analysis, and results are presented in the following sections of this report. Sections 3 and 4 present the, method-ology for calculating the fog formation and removal rates. Section 5 gives the fog inerting criteria, and Section 6 presents the results.
The critical supersaturation data for water has been given in Reference 15.Fog formation in an ice condenser containment as a result of homogeneous or heterogeneous nucleation could occur: (i)inside the thermal boun-dary layer near a cold surface, (ii)in adiabatic or nearly adiabatic expansion of vapor jet, and (iii)in mixing of a hot vapor stream with another cooler gas.Surface cooling may create a region of local supersaturation within the thermal boundary layer, even though the bulk stream is still super-heated.If the local supersaturation reaches the critical supersatura-tion, incipient fog formation will commence.This condensation mecha-nism may exist in any compartments within the containment especially in the ice condenser where ice temperature is well below the dew point.When a high speed vapor-noncondensible gas mixture jet goes through an adiabatic or nearly adiabatic expansion, the gas mixt'ure temperature and pressure will drop rapidly such that condensation may occur somewhere in the expansion process.This is the case when a hydrogen-steam mixture jet exits from a break at a supersonic speed.The jet experiences a rapid expansion and if critical supersaturation is reached;condensation shock may occur somewhere within the expanding jet.This condensation mechanism can only occur in a compartment in which the hydrogen-steam mixture jet exists.Condensation in a fast expanding vapor-noncondensible gas jet is a localized phenomenon.
0430Q:  I                            2-2
Usually very little moisture is generated in the expansion process even if a condensation shock does exist.Therefore, the present study does not attempt to treat the condensation shock as a source of fog formation.
 
0430Q:I 3-11 P
i' 0
The third mechanism, condensation due to mixing,may exist in a compart-ment where a hot hydrogen-steam mixture mixes with a relatively cold containment atmosphere.
 
During the mixing process, local critical supersaturation within the mixing gas could be reached and condensation would ensue.This mechanism could exist in the lower compartment in which relatively cold gas from the upper compartment is returned by the deck fans and mixed with the hot humid air.Thus, the mixing of cold and hot vapor streams will be treated in the present study.'owever, only bulk condensation is considered.
3.0    FOG GENERATING MECHANISMS IH  AH  ICE CONDENSER COHTAINMEHT The  inerting capability of fog droplets      depends on their sizes          and con-centration in the containment atmosphere, as well as the hydrogen con-centration. This section is intended to identify various fog generation mechanisms present in an ice condenser containment and to determine the drop sizes and the rates of fog generation from these mechanisms.                 Three fog generation mechanisms are discussed in this section and the dominant fog generation mechanisms      are  identified.
That is, it is not intended to'compute the temperature profile to predict the local condensation rate.Instead, the bulk gas is assumed at one uniform temperature, and bulk condensation will occur when mixing results in saturation conditions.
: 3. 1 FOG GENERATED BY BREAK FLOW The post-LOCA containment atmosphere      is most likely to  be a drop-laden atmosphere. The large-scale simulated LOCA experiments conducted to date have directly or indirectly confirmed the presence of two-phase atmospheres. For example, Marvikken (3) and Battelle - Frankfurt experiments were instrumented to measure fluid densities and water levels in various parts of the containment. Therefore, fog generation by the break flow cannot be neglected.          The following discussion of this phenomenon pertains to small LOCAs.
This is consistent with the CLASIX code assumption of uniform gas temperature.
In the early stage of a small LOCA transient, a substantial .portion of the primary coolant discharged from the break will remain as liquid.
Because of time restriction, it is almost impossible to treat all the condensation mechanisms.
Because of the superheat and high velocity, this liquid will be framen-ted by aerodynamic forces and homogeneous nucleation mechanism into'mall droplets. These droplets are expected to be entrained by the intercompartmental and fan flows and spread to other parts of the ice condenser containment. During their travel throughout the containment, the fog droplets will be removed by gravitational settling, sprays, and vaporization. The fog gene'ration period lasts until the water level in the reactor vessel falls to the break elevation and the break flow is no longer two-phase.'or the particular S<D sequence analyzed by 0430Q:  I                                3-1
However, major condensation mechanisms will be identified and treated in the present study.Before entering into the discussion of the methodology to calculate the fog formation rates from various fog formation mechanisms, a discussion of fog formation conditions is necessary.
 
Since the bulk condensation approach for the mixing process has been adopted, the fog formation conditions for the mixing process are simply that critical supersatura-tion is reached in the bulk stream.For practical purposes, the crit-ical supersaturation is assumed to be one since it is likely that plenty of condensation nuclei exist in the atmosphere before mixing condensa-tion takes place.3.2.3 CONDITIONS FOR FOG FORMATION NEAR A COLD SURFACE Fog starts to form at a fast rate near a cold surface when local vapor supersaturation reaches the critical supersaturation.
CLASIX, (5)    this period lasts for about 36 minutes and about 4.2 x 5
Near the cold surface, a thermal boundary layer is formed, within which local vapor pressure and saturation pressure vary.Typical vapor pressure and 0430Q: I 3-12 r
10    lbs of water has been discharged into the lower compartment during thi s  pe ri od of time.
temperature profiles, when the incipient homogenous nucleation first appears, are shown in Figure 3.2.It is seen in this figure that when the local vapor pressure reaches the critical vapor pressure there is a sudden appearance of fog in the boundary layer due to the fast nuclea-tion rate.Rosner and Epstein have derived fog formation condi-(ll)tions near a cold surface, assuming that the local vapor pressure curve is tangent to the critical vapor pressure curve at the fog incipient point.A more general fog-formation criterion was given by Hijikata and Mori 1 s hW~(dW)Wh ar wall (3.3)where hW=W-W w hT=T-T w and the weight fraction of condensing vapor, W, can be related to the partial pressure of the condensing vapor P as v W=1-(Pgp)(v/v)P v g (3.4)whe re P HN total pressure vapor molecular weight noncondensible gas molecular weight Equation (3.3)may be rewritten as n>2 (3.5)where M)(Qd)wal 1 0430Q: I 3-13  
After  the water level in the reactor vessel falls below the break eleva-tion,  the break flow rate is substantially reduced. The flow is essen-
'ially      steam and no fog droplets will be generated. As a result, the lower compartment becomes superheated afterward. Fog droplets may vaporize during their travel through this compartment and substantial removal of mist droplets are expected.
Large suspended        drops generated by the break flow will be removed very quickly. by  gravitational settling and impingement. For the drops larger than 20 u, the removal rate is high and complete removal only takes a few seconds.      For the smallest drops (less than 1 u) the terminal veloc-ity is so small that they virtually remain suspended in the atmosphere indefinitely. The only effective removal mechanisms for these sizes of drops are vaporization, and collision with larger spray drops. The weight fraction of these sizes of drops is estimated to be 1 per-cent (3) generated by the break flow. The population of these small drops can increase if nucleation of embryos occurs in a saturated atmo-sphere.
0430Q:1                                  3-2    l
 
3.1.1
    ~ ~  AMOUNT OF FOG GENERATED BY BREAK FLOW As discussed  previously, the existence of a two-phase drop-laden regime has been observed experimentally. In a .small LOCA, flashing of primary coolant at the break and subsequent vaporization of blowdown liquid represent a series of changes of thermodynamic states. Since the reac-tor coolant pressure is high, the break flow will be choked. The accel-eration of primary coolant to the break location is essentially an isen-tropic process, in which the pressure decreases to the point at which substantial homogeneous nucleation occurs. When the flow leaves the break, the liquid is framented by both the aerodynamic forces and the nucleation mechanism into small fog droplets. These fog droplets con-tinue to vaporize, because of the superheat in the droplets, until a thermodynamic equilibrium state is reached.      Because of the high super-heat and large aerodynamic forces, it is expected that the fog droplets generated are very small. This vaporization process is essentially isenthalpic.
The existence  of a two phase drop-laden regime can also be explained by use of a T-S diagram for steam as shown in Figure 3,1 (Figure 1 of Reference 6). It  is shown in this figure that the blowdown liquid goes through a series of thermodynamic states, starting from the subcooled liquid state B 0 . The liquid expands isentropically from the subcooled state 8 to the state B> at the break, where a two-phase critical flow is developed. At the same time, temperature changes from T to TI. After leaving the break, the droplets continue to vaporize because of excessive superheat until finally an equilibrium state B<
is reached at which the droplets are in thermal equilibrium with their surroundings. This vaporization process is essentially isenthalpic. At this time, the droplet temperature drops to T> and the atmospheric temperature also rises to T>. For a small LOCA, the equilibrium tem-perature varies with time. According to the CLASIX analysis of the Sequoyah plant, the lower compartment gas temperature rises quickly from 100"F to approximately 200"F and then stay at this temperature for an extended period of time. Using these temperatures as final equilibrium 0430Q    I                            3-3
 
Kg/cm2 100    10 r
600 450                              400 400 300 g 350 300 0                      200 250 200 150 100 100 i j  I A2 50                  /t 0
0.0          0.2           ~
0.4          0.6          0.8          X=1 FIGURE  3.1    T-S DIAGRAM    FOR REACTOR COOLANT DISCHARGED FROM BREAK
 
temperatures    for water droplets, the weight fraction of water droplets
. in the break    flow is approximately 50 percent, which is consistent with the MARCH calculations~7~ of the break flow rate release  rate.
and its  energy The  discussion given above is valid only when the initial state'of the break flow is subcooled or saturated liquid. After the water level inside the reactor vessel falls below the break elevation, the break flow will be steam. The moisture content of the steam will be very low, even though isentropic expansion may lead to homogeneous nucleation and subsequent condensation in the vapor stream. Depending on the super-saturation that can be achieved in this isentropic expansion, a conden-sation shock is possible when critical'supersaturation is reached.
However,     it  is believed that the fog droplets generated by homogeneous nucleation in this supersonic jet is negligible as compared to other fog generating mechanisms. Hence,       it  will be neglected in this present analysis. Therefore, the fog generation by the break flow is considered possible only when the water level in the reactor vessel is above the break elevation.
According to the MARCH~"~ calculation at 2172 seconds into the acci-dent, the water level inside the reactor vessel falls below the break elevation for the S2D case analyzed in Reference 7. By this time approximately 421,000 lbs of water has been discharged from the break and 56 percent of this discharged fluid, i.e., 236,000 lbs, will be sus-pended in the atmosphere as condensate.           However, most of these droplets will later    be removed by  gravitational settling, sprays,      and  vaporiza-tion.
3.1.2    DROP  SIZES GENERATED BY BREAK FLOW The    flashing jet experiment conducted by Brown and York~B~ has indi-cated that the drop sizes produced by flashing. liquid are small. They derived a correlation for the linear mean drop size based on the test data. The correlation shows that the mean drop size is inversely pro-portional to the Weber number and        it  decreases linearly with increasing 0430Q:I                                  3-'5
 
superheat. However, this correlation is applicable for liquid superheat less than 75'F and it can not be extrapolated to the large superheat of the reactor coolant. However, some conclusion concerning the drop sizes produced by blowdown of the reactor coolant can be drawn for this condi-tion., The break flow has much larger superheat and Weber number than those used in this experiment; therefore, the drop sizes produced by the break flow should be much smaller than -50'bserved in this experi-ment.
Gido and Koestel (9) have developed  a method  for estimating the. drop size leaving the fragmentation/evaporation zone of a blowdown jet. This model is based on the assumption that drops with an'internal. temperature difference of less than 5K will escape fragmentation. This model has been verified by the low superheat, data of Brown and York. Application of this method to the LOCA condition shows that the maximum attainable drop size is 7p (this means that arly drop size larger than 7p will not escape framentation by homogeneous nucleation). The corresponding mean drop size is about 4p, based on the observation of the largest drop size and mean drop size in the experiment reported in Reference 8. However, this volume mean drop size is not used in the present analysis.
Instead, the present analysis uses  10 p mean  drop size,. considering the drop agglomeration    effect.
3.2    NUCLEATION OF FOG DROPLETS IN CONTAINMENT ATMOSPHERE Nucleation of water embryos from the homogeneous vapor phase plays an important role in mist generation in ice condenser plants. Nucleation is a process by which tiny water embryos or condensation nuclei are formed from a pure vapor phase at a rapid rate. In incipient homogene-ous nucleation, the local gas temperature drops below the dew point corresponding to the local steam partial pressure and some degree of local supersaturation is needed. The degree of supersaturation needed to start nucleation depends on the number of condensation nuclei present in the containment. These condensation nuclei could be very small water droplets or dust particles. If sufficient number of condensation nuclei 0430Q:I                              3-6
 
exist, supersaturation could      be  small. It is likely that the ice con-denser containment contains      a  subtantial number of dust particles such that  little supersaturation    is needed for nucleation.
This section is devoted to the discussion of fog formation by homogene-ous or heterogeneous nucleation. The classical nucleation theories are used to explain the nucleation phenomenon.
3.2. 1  NUCLEATION THEORIES The process      of n0cleation of an embryo water drop is important in under-standing the mechanism of fog formation in ice condenser plants. Two types of nucleation process, namely, homogeneous and heterogeneous nucleations, and their theories will be discussed in Section 3.2.1.
3.2.1.1      CLASSICAL THEORY OF HOMOGENEOUS NUCLEATION When an    embryo  droplet, usually  assumed    spherical, is formed from con-l)  densation of water vapor molecules, of free energy can be expressed as its  free energy changes. The change aG =  4xr  a  " (4/3) xr  nL KT Zn    (p/p  )
where    a  is  the surface free energy per unit area, or surface tension, r is the drop radius, P is the vapor pressure, 0          P;s  the saturation Pressure at the droPlet temPerature, nL is number of molecules per
  ,unit volume, K is the Boltzman constant, and T is the drop temperature.
The supersaturation S, is defined as P/P .
Equation (3.1) represents a free energy barrier to the growth of the drops at a given suprsaturation.          At maximum aG, the critical radius    r" can be obtained from Equation 3.1 as r*          20 0430/:1                                    3-7
 
r 1',
i~I
 
of the critical size
                                                                                        ~
The drops
                            ~                          ~
can be considered      as condensation nuclei since at this size the drops will grow with no change in free energy.~
      ~            ~                    ~
This critical size represents an equilibrium size at which a supersatu-
        ~    ~ ~                                ~ ~  ~      ~          ~
rated vapor at vapor pressure P is in equilibrium with this critical drop at a lower saturation pressure P . However, this equilibrium mode is unstable.       For example,    if a drop of the critical size origi-nally in equilibrium with the surrounding vapor suffers a sudden small increase in size due to condensation, then            (if  the drop temperature does not,change), Equation 3.2 shows that the equilibrium pressure, P, on its surface will decrease.        Therefore, the actual vapor pressure will then be greater than the equilibrium value and further condensation will occur. This is why the drop of this critical size is called condensa-tion nucleus.
The    nucleation rate of critical-sized embryos can be obtained from the kinetics of a nonequilibrium distribution of embryos. The classical nucleation theory            shows that there is a very sudden increase in the nucleation r ate when past a certain critical value of supersatura-tion. An extensive validation of the nucleation theory was conducted by Volmer and Flood            in an experiment in which a number of vapors were expanded to visible condensation in a cylinder. The observed critical supersaturations agreed suprisingly well with theory in nearly all cases, including water vapor.
Critical condensation nuclei sizes typically              range from 10 to 100 atoms.      These sizes are considerably      smaller than the mean free path of the vapor molecules and therefore the rates of mass and heat transfer at
'the drop surface cannot be predicted by bulk transport theories. In this case, the kinetic theory of gas should be used to predict the rates of mass and heat transfer at the drop surface.
Starting from the kinetic theory of gas and the energy conservation equation, the rate of growth of a condensation nucleus was obtained by Hill et al.            It was found that the growth rate is on the order of 10        ft/sec. Therefore, it takes only about I milisecond for the condensation nucleus to grow to a fog droplet size of I p.
0430Q      I                                3-8
 
3.2. 1. 2 HETEROGENEOUS N UCL EAT ION THEORY Another mechanism of forming embryos      is heterogeneous nucleation on foreign particles that could suspend in the containment atmosphere.
These particles may serve as nucleation sites for vapor and thus enhance the nucleation rate. The source of foreign particles in the containment following core degradation could come from fission product aerosols and dust particles. The size distribution of these particles are important because the supersaturation required to form embryos depends on particle sizes.
A  typical size distribution of atmospheric aerosols is that of e
Junge, taken from surveys made near Frankfurt A.H., German. The surveys found that the size range of dust particles is from 0.01 to I In the range from 0.01 to 0.5 p, there are between 100 and 10,000 particles per cubic centimeter. A majority of particles have sizes smaller than 1 micron. At the smallest size of 0.01 p, the critical supersaturation is about 1.02 and at the largest size the supersatura-tion is only 1.001.
                  ~    ~
The other source    of aerosol particulates is fission, products. During normal operation, the primary coolant contains very little fission pro-ducts. However, a large release of fission products, such as the gap release, could occur at about the same time the hydrogen releases. The amount of fission products released to the containment depends on acci-dent scenarios. The distribution and transport of fission products in the containment can be predicted by the CORRAL code~ ~. The size di stribution of fission products .in the containment can be extrapolated from the CSE experiments~ 4~. These experiments indicated that soon after fission product release, the mean particle diameter was 15 p. A few hours later, the mean diameter decreased to about 5 p because of settling of large particles onto the floor. These sizes are substan-tially larger than those of dust particles and therefore, critical supersaturation is even smaller than values quoted above for the dust particles.
0430Q:1                                  3-9
 
The    atmospheric aerosols consist of particulates of various sizes, vari-ous chemical components, and various electrostatic charges.          The aerosol particulates could be soluble or insoluble in water. All these proper-ties could affect the required supersaturation for nucleation.
In the case of insoluble particulates, the contact angle, 6, between the "embryo and the particle surface is important. If the particle is com-pletely wettable, 6 ="0,        it  forms a base on which a small amount of water can. form a drop of large radius of curvature and thus satisfy the Hemhol tz equation (Eq. 3.2) at a much lower supersaturation than would be the case    if I')
same number of molecules form a drop with a particle core. Fletcher (          developed a relationship between the supersIatura-tion and drop radius for several values of contact angle, assuming that the particle is spherical.          Competely wettable, a particle of 1 micron or so, when covered with a film of water, is theoretically at the crit-ical radius,      and  it needs  only 1.001  critical supersaturation.
The    post-accident containment atmosphere is likely to contain a substan-tial amount of aerosol particles. These particles will act as condensa-
                                          ~
                                                ~
i    tion nuclei and therefore, little supersaturation is required to pre-
  )  cipitate condensation.
            ~                  ~
                                  ~
3.2.2      FOG FORlCTION CONDITIONS Fog      formation in a mixture'f vapor and noncondensible gases has been of interest to meteorologists, and turbine and condenser designers. Fog is formed by homogeneous or heterogeneous nucleation as a result of tem-perature drop below the dew point (sometimes with concommitant pressure drop). During the temperature drop, a local gas element will go through a series of thermodynamic states.            Eventually, a state is reached at which incipient fog formation occurs. Some degree of vapor supersatura-t'ion is needed to precipitate fog formation. The vapor supersaturation at which rapid nucleation of vapor first appears is called critical supersaturation.        The critical supersaturation,    in general, is a 0430Q:1                                        3-10
 
e function of temperature, vapor properties, mixing time (if a mixing process is involved), and concentration and sizes of foreign particles.
The critical supersaturation data for water has been given in Reference 15.
Fog  formation in  an  ice condenser containment as a result of homogeneous or heterogeneous nucleation could occur: (i) inside the thermal boun-dary layer near a cold surface, (ii) in adiabatic or nearly adiabatic expansion of vapor jet, and (iii) in mixing of a hot vapor stream with another cooler gas.
Surface cooling may create a region of local supersaturation within the thermal boundary layer, even though the bulk stream is still super-heated. If the local supersaturation reaches the critical supersatura-tion, incipient fog formation will commence. This condensation mecha-nism may exist in any compartments within the containment especially in the ice condenser where ice temperature is well below the dew point.
When a    high speed vapor - noncondensible gas mixture jet goes through an adiabatic or nearly adiabatic expansion, the gas mixt'ure temperature and pressure will drop rapidly such that condensation may occur somewhere in the expansion process. This is the case when a hydrogen-steam mixture jet exits from a break at a supersonic speed. The jet experiences a rapid expansion and      if critical supersaturation is reached; condensation shock may occur somewhere within the expanding jet. This condensation mechanism can only occur in a compartment in which the hydrogen-steam mixture jet exists.
Condensation      in a fast expanding vapor - noncondensible gas jet is a localized phenomenon. Usually very little moisture is generated in the expansion process even if a condensation shock does exist. Therefore, the present study does not attempt to treat the condensation shock as a source of fog formation.
0430Q:I                                    3-11
 
P The  third mechanism,  condensation due to mixing, may exist in a compart-ment where a hot hydrogen-steam mixture mixes with a relatively cold containment atmosphere. During the mixing process, local critical supersaturation within the mixing gas could be reached and condensation would ensue. This mechanism could exist in the lower compartment in which relatively cold gas from the upper compartment is returned by the deck fans and mixed    with the hot humid air.
Thus, the mixing    of cold and hot vapor streams will be treated in the present study. 'owever, only bulk condensation is considered. That is, it  is not intended to 'compute the temperature profile to predict the local condensation rate. Instead, the bulk gas is assumed at one uniform temperature, and bulk condensation will occur when mixing results in saturation conditions. This is consistent with the CLASIX code assumption of uniform gas temperature.
Because    of time restriction,  it is  almost impossible to treat all the condensation mechanisms.      However, major condensation mechanisms will be identified and treated in the present study.
Before entering into the discussion of the methodology to calculate the fog formation rates from various fog formation mechanisms, a discussion of fog formation conditions is necessary. Since the bulk condensation approach for the mixing process has been adopted, the fog formation conditions for the mixing process are simply that critical supersatura-tion is reached in the bulk stream. For practical purposes, the crit-ical supersaturation is assumed to be one since      it  is likely that plenty of condensation nuclei exist in the atmosphere before mixing condensa-tion takes place.
3.2.3      CONDITIONS FOR FOG FORMATION NEAR A COLD SURFACE Fog    starts to  form at a fast rate near a cold surface when local vapor supersaturation reaches the critical supersaturation.        Near the cold surface, a thermal boundary layer is formed, within which local vapor pressure and saturation pressure vary. Typical vapor pressure and 0430Q:  I                            3-12
 
r temperature      profiles, when the incipient        homogenous  nucleation first appears,      are shown in Figure 3.2. It is          seen in this figure that  when the local vapor pressure          reaches  the critical vapor pressure there is a sudden appearance of fog in the boundary layer due to the fast nuclea-tion rate. Rosner and Epstein (          ll)  have derived fog formation condi-tions near a cold surface, assuming that the local vapor pressure curve is tangent to the critical vapor pressure curve at the fog incipient point. A more general fog-formation criterion was given by Hijikata and Mori          1 s hW        (dW)
Wh
              ~
ar                                                              (3.3) wall where      hW=    W  -  W w
hT=T -        T w
and the weight        fraction of condensing vapor, W,        can be related to the partial pressure of the condensing vapor P v as
          =
(Pgp) (v/v      )
W 1-                                                                  (3.4)
P          v  g whe re      P                total pressure H                vapor molecular weight N                noncondensible gas molecular weight Equation (3.3)        may be  rewritten    as n>2                                                                  (3.5) where M) ( Qd) wal 1 0430Q:  I                                          3-13
 
21123 3 Pv, crit(T )
Pv, eq(T~)
Pv, oo I
II II II Pcrit (Tw) ll II II Pv, w 0                            OO SUPERSATURATED REGION THERMAL              SUPERHEATED BOUNDARY LAYER I
VAPOR SUPERSATURATED REGION O                                      Too 1
K          FOG D
CO D
z    Z O
O      O 0O Tw FIGURE 3.2 VAPOR PRESSURE  AND TEMPERATURE PROFILES NEAR A COLD SURFACE 3-14
 
The parameter    n  is  used  in the following section to calculate the fog formation rate.
          ~
                    ~  It  will be demonstrated that when n < 2, no fog forma-tion is possible.
3.2.4    RATE OF FOG FORMATION HEAR A COLO-SURFACE As has been discussed      in Section 3.2.3, fog will form near cold surfaces (e.g., in the ice condenser early in the transient. ) As discussed in Section 3.2.1, once water embryos are formed it takes only a few mili-seconds for them to grow to the micron size. After these micron size fog droplets are formed,        it needs very little supersaturation for fur-ther growth. Therefore, in the present analysis,        it  is assumed that vapor and droplets are in thermal equilibrium and local vapor pressure is equal to the local saturation pressure. This section is concerned with the transport of these micron-size fog droplets within the thermal boundary layer.
The boundary    layer fog formation rate can be determined using the Hijikata-Mori theory            of fog formation in the thermal boundary layer. It was assumed that a thin liquid film, having a thickness of e< on a cold surface, coexists with a gas-droplet flow in a two-phase boundary layer of thickness 6 outside the liquid film as shown in Figure 3.3.
It was  further    assumed    that the saturation condition exists within the two-phase boundary layer and the boundary layer approximation is appli-cable. Numerical solutions were obtained for the mass fraction of fog droplets, Y ot, at the gas-liquid film interface. The fog droplet flow rate at a distance X along the plate may be expressed in terms of Y as f'6 mf
              = L pJ      Yudy                                            (3.6) 0430(}:I                                    3-15
 
hfain Flow
                          ~0
      ~    ie Two Please Boundary layer Interface Liquid Film Cooling Surface FIGURE  3.3  FORtljATIOH OF FOG HEAR A COLD SURFACE
 
. where    Y                mass  fraction of fog droplets in the fog droplet density boundary layer Pv              vapor density Pg              noncondensible  gas  density Y
o      .        ~fly  =  ok~v+ ~g) y            =    coordinate perpendicular to the plate fog boundary layer thickness width of boundary layer Pv+    pg
              =
Y0 (1    - y/e)                                              (3.7) u=    U      (<(~)      -
                                      ~  (~)    )
          ~  (x)  =ax1<<                                                    (3.g) 4u =    e  (x) (1 - 6)                                            (3.10) where  a                  known  constant known const'ant free stream velocity 0430Q:1                                  3-17
 
I 0
 
Substituting Eqs. (3.7) through (3.10) into          Eq. (3.6),  we have the rate of fog formation
: 0. 25      0.025 mf  =pL6Y        U                                                  (3.11) oerivation of expressions for a, Y and g is given in Appendix Even though boundary layer fog formation may occur in any containment subcompartment, the fog formation rate is likely to be small except in the ice condenser.      For fog formation in the ice condenser, L is the total length of the periphery and x is the height of the ice bed.
During fog formation in the boundary layer, heat transfer to the cold surface will decrease the bulk fluid temperature.            If  the bulk fluid temperature drops below the dew point corresponding to the free stream vapor pressure, then bulk stream condensation could occur. In this case,  it  is assumed that the boundary layer thickness, s, will grow so thick that LeU~ becomes the gas volumetric flow rate Q through the con-densing compartment. This is a very conservative assumption in terms of the fog formation rate. Under this assumption Equation (3. 11) becomes
: 0. 25      0.025                              .(3.12) cond    o ~  "o    1:g        (1 -  g) where  m condd is  the  sum  of boundary  and  bulk stream fog formation rates.
0430Q 1                                  3-18
 
3.2.5  FOG DROP  SIZES As mentioned    earlier,  when homogeneous nucleation commences,  a large number  of condensation nuclei are formed and they grow to the micron size  within a few milliseconds. In heterogeneous nucleation, fog drop-lets  grow on aerosal particles, which are usually less than 1 p. In any case,  the final drop sizes are determined by the atmospheric conditions with  which the drops are in thermal equilibrium.
Neiburger and Chien(18) studied the growth of cloud drops by condensa-tion and calculated droplet size distribution based on a cloud cooling rate of 6 c/hr. The initial size distribution of condensation nuclei (sodium chloride) were chosen to correspond to available observations as shown in Figure 3.4 (designated as 0 second).      The calculated drop size distributions at 3000 and 6000 seconds are shown in Figure 3.4. It is seen that the sizes of fog droplets range from 0.01 p to 20 p. The volume mean drop size is 8 p at 3000 second.      The volume mean drop size for homogeneous nucleation is expected to be smaller than this value.
Fogs of volume mean drop sizes ranging from 9 to 14 p(30) have been observed to    exist in  a natural enviroment, e.g. valley. In the present stuQ, a volume mean      fog drop size of 10 p is chosen for fog deposition
-and inerting calculations.
3.3    FINE MIST DROPLETS    FROM CONTAINMENT SPRAYS The  containment sprays produce- fairly large drop sizes. A-typical con-tainment spray nozzle, e.g., Spraco 1713 nozzle, produces the size dis-tribution as shown in Figure 3.5, using a pressure difference of 50 psi across the nozzle( ).        It is seen that water droplets produced from containment range from 100 p to 2000 p. These large drops have          little effect on hydrogen combustion and flammability limits, as already demon-strated in the Fenwal tests( ) and more recent tests at Factory Mutual(21). To affect the combustion characteristics of a hydrogen mixture, the drop sizes have to be smaller than about 20 p, namely in the fog drop size ranges. Since containment sprays essentially do not produce drops in this size range, containment sprays will not be con-sidered as a means to produce fog droplets. Rather,          it will be con-sidered as a means to remove the fog droplets.
0430Q:I                                  3-19
 
~ ~ ~
~      ~
j
  ~    ~
          )
 
I <lO I20 lnO CD 80 ED 60 90 20 200    000    600    800      l000      l200    l900 l600    l800 2000 2200 PARTICLE  DI AllETER (Ml CROHS)
FIGURE 3.5    PARTICLE SIZE DISTRIBUTIOH FOR 50 PSI PRESSURE DROP ACROSS NOZZLE HO. 1713
 
1
.J "s    ~
0
 
4.0    FOG REMOYAL MECHANISMS IN AN ICE CONDENSER COHTAIHMEHT In Section 3, the mechanisms of generating fog droplets were discussed.
After these droplets are generated, they can be removed from the con-tainment atmosphere by. gravitational settling, vaporization, containment sprays, and impingement on structures. They can also coalesce with other drops during collision and form bigger drops. These bigger drops could easily settle out of the atmosphere under gravity. These fog droplet removal mechanisms will be discussed in this section.
4.1  SETTLING DUE      TO'RAVITY Drop removal rates due to      gravitational settling depend strongly on drop radius. The removal rate increases linearly with drop terminal veloc-ity, drop concentration, and settling area. The relationship may be expressed    as
                    "                                                      (4. I) r mset        t where  q  is the    mass of mist droplets per unit. volume, and A is the set-tling  area.
The  terminal velocity, Yt, is a strong function of drop radius and the relationship is shown in Figure 4.1. It is seen that the terminal velocity is approximately a linear function of drop radius in both lami-nar the turbulent regimes. For a 1000 p drop, its terminal velocity is above I m/s, while for a 10 p drop, which is the typical fog drop size, its terminal velocity is only about I cm/s. Therefore, there is very little removal by gravity for fog droplets.
0430Q:  I
 
4.2  AGGLOMERATION After the fog droplets are produced, the droplets will undergo changes in the number density and size distribution with time, when drops col-lide with each other and coalesce. The. agglomeration rate (No. of par-ticle per unit volume per unit time) has been found to be proportional to the square of the drop population density and the coagulation mecha-nisms dependent    rate constant  K For drops larger than
                    'I 1 g, the dominant mechanism is the difference in velocities between drops in adjacent streamlines. This is usually termed the velocity gradient coagulation. For drops smaller than 1 g, the velocity gradient effect becomes small, and drops are brought
'ogether by Brownian motion. This leads to greatly different agglomera-tion rates for different initial drop sizes. A typical agglomeration rate as a function of drop size in a moderately turbulent atmosphere is shown in Figure 4.2.      In Figure 4.2, the sharp rise of the agglomeration rate with drop diameter larger than 1 p implies that the larger drops agglomerate quickly to the maximum stable size supported by the atmo-spheric turbulerce. The agglomeration rates for drops less than 1 p are very small. Since most of the fog droplets are in. micron size ranges, the agglomeration rate is not large. It is assumed in the present analysis that the initial 4 u blowdown mean drop size will grow to 10 g (See Section 3.2.5). Agglomeration as a separate mechanism for fog growth has'been conservatively neglected.
4.3    VAPORIZATION Fog  droplets suspended in the containment atmosphere is considered to be in thermodynamic equilibrium with the surrounding gas. Mhen the sur-rounding atmosphere becomes superheated or when the droplets are entrained into a superheated subcompartment,      it can undergo vaporization or condensation.
4-2 0430Q:  1
 
In the present analysis,  it is assumed that water vapor  and mist drop-lets  are in thermal equilibrium at all times. Therefore, the amount of vaporization or condensation will be determined by the thermal equilib-rium state reached by the vapor and drops. In other words,    it is not intended to model heat transfer between the drops and the surrounding gas, and thus determine the vaporization rate. This is a good assump-tion for the small fog drop sizes.
4.4    REMOVAL BY SPRAY DROPS As mentioned above,  the containment spray droplets range from 100 u-2000 p, which are substantially larger than the fog droplets.      If fog droplets enter the spray zone, they will probably be removed by the spray droplets by colliding with them, since the spray drop mass is much larger than the fog drop mass. A simple analytical model is used in the present study which assumes that all the fog droplets residing in the spray zone will be swept by the sprays to the floor with the spray drop removal efficiency E. The spray removal rate may be expressed as m    =EQ    M/q    V                                        (4.2) where    E            spray drop removal efficiency Qsp volumetric flow rate of sprays volume fraction of spray droplets in the spray zone sp M            mass of fog in compartment volume V 4.5    OTHER REMOVAL MECHANISMS Another similar mechanism for fog removal is the formation of droplets in the ice condenser. These droplets which would be generated in the ice bed when the ice melts, would fall through the ice bed, and remove fog droplets from the flow through the ice condenser.      This large quan-tity of water would be effective in removing fog droplets. However, due to difficulty in modeling this removal mechanism,    it is conservatively neglected in the present analysis.
0430Q:I                              4-3
 
I In addition to the removal mechanisms mentioned above, fog can also be removed by impacting structural surfaces. Oue to the inertia of fog droplets, substantial fog removal by impacting structural surfaces could occur, when the drop-laden mixture flow passes through long, narrow, curved paths, such as ice basket flow paths, and fan ducts. Moreover, the centrifugal force exerting on the fog droplets, when they pass through the fans, could cause the fog droplets to impact the blade sur-faces or other parts of the fans. These removal mechanisms are believed to be significant; however, they are conservatively neglected in the present analysis. It is, therefore, believed that the present analysis is  very conservative.
4-4 0430Q:1
 
I
 
1 21273 1 TERMINAL DROP FALLING VELOCITIES IN 10    STEAM.AIR ATMOSPHERES            p~
1.0 CO Z
0.10                      TURBULENT AMINAR REGIME REGIME HATCHED REGION INDICATES:
50 <Re <55 0.01 0.001          001 DROP RADIUS (CM)
                                                  '1            1.0 FIGURE  4.1    TERHINAL VELOCITY AS A FUNCTION OF DROP RADIUS IN STEAH-AIR ATHOSPHERE 104
                                                                                ~
                                                                              ~
7 GRADIENT AGGLOMERATION u    103                  n    10  CM dv 100 S dy O
102 R                8ROWNI AN O                AGGLOMERATION I-                n  10  CM NET o    101 RATE 100 0.01          0.1              1.0 DROP DIAMETER (pM)
FIGURE  4.2    AGGLOHERATION RATES IN          AIR BETWEEN EQUAL-SIZED DROPS 4-'' 5
 
T
 
5.0  FOG INERT ING CRITERIA Recent hydrogen burn experiments conducted      at Lawrence Livermore Labora-tory indicated that substantial fog formation could occur when saturated steam is discharged into an unheated vessel.      It appeared that this fog prevented a glow plug igniter from successfully igniting the hydrogen mixture in the vessel. The ability of fog in inhibiting and quenching of hydrogen combustion can be explained as follows. The fog droplets suspended in the hydrogen-air-steam mixture act as a heat sink that could absorb a large amount of combustion heat, greatly reducing the pressure and temperature rises resulting from hydrogen combustion. If droplets are sufficiently small such that they could vaporize inside the thin ( Imm) flame front, the flame may be quenched or inhibited. For a flame speed of    2 m/s, the drop residence time is of the order of 0.5 x 10    seconds.        In such a short period of time, the droplets of initial    radius less than about 4 p will vaporize entirely in the flame front.
The quenching      of a propagating flame is also governed by the distance between droplets. As the droplets become closely packed, the total droplet surface area available for energy loss increases. A critical spacing between droplets exists such that a large fraction of th'e heat released is absorbed, thus preventing flame propagation. This critical spacing is known as the "quenching distance", which is usually deter-mined by propagating flames in tubes.
5.1    PREVIOUS WORK The  effectiveness of fog droplets in inhibiting or quenching a flame depends on its quenching distance, was determined by Berman et al.
as d  =  [4VIS3                                                  (5.1) where    V  is  the gas volume and S is the heat transfer surface area. For a  hydrogen-air mixture, the data on the quenching distance is shown in 04300:I                                5-1
 
Figure 5.1.~  ~    In the suspended  fog droplets, this volume-to-surface ratio (i.e.,
      ~  ~  V/S)    is equal to 1    d  (1  - n) where d    is the mean droplet diameter and n is the volume fraction of water. When four times this ratio approaches the quenching distance,          a critical droplet diameter can be obtained as qd c    2 (5.2)
Using this criterion for quenching a flame, for a given volume fraction of water and gas composition, d can be determined. The critical droplet diameter then can be determined from the above equation. The drop sizes less than the critical drop size is capable of quenching a f 1 arne.
A  plot of    Eq.    (5.2) for two hydrogen concentrations is shown  in Figure 5.2.
5.2    PRESENT THEORY The previous        theories do not model the heat transfer and combustion processes occurring between the burned gas and the suspended droplets.
A new theory has been developed, which models the heat loss and combus-tion.
0430Q:1                                    5-2
 
t ~" t 0
V
 
FEG. 5.1 MINIMUM IGNITION ENERGIES AND QUENCHING DISTANCE FOR KYDROGEN-OXYGEN INERT GAS MIXTURES AT ATMOSPHERIC PRESSURE 5-3
 
                              ~mS' REER~~
        ~~~~~~~MR~          ~ESESR~~
                              ~RSRES~~
        ~m ~~EEI~
&ALIIS
            ~ RRRE
                    ~~~
                              ~
                ~ERSRSRSRSR~ EEERR~~
BESSER~~~~~~~    SEERS~~~        ~
WMRE~
            ~ RRRR          EERRR RERRE
            ~ EEEE~ERRSR~EERRE~          ~~
~
~~RA
      ~~ ~~ ~  ~WE
~~ERIIESECEEEEEESSW
      ~SEERS EREEE~
SEERS~
                      ~ E~iFsSHSIWI RERRREMRS ESSES 0 ~ ~~l I
 
Consider    a  hydrogen/air/steam/mist droplets mixture in which a flame is gropagating. The flame may be divided into three zones: heating zone,
,reaction zone, and post-reaction zone as shown in Figure 5.3. The unburned gas at temperature T U move in the reacton zone with the laminar burning velocity S U . If the unburned gas density is p, then the constant mass flow rate m is equal to pS. The unburned gas is heated to ignition temperature T.1 and burned in the reaction zone to reach the flame temperature Tf. The fog droplets will act as a heat 'sink that reduces the flame temperature.              The problem has been formulated and solved by von Karman            (25) . In his formulation, three energy equations, which incorporate the heat loss terms, were written for the three zones described above. The solution to these equations yields the following relationship
                    -    (- T1      2      - Yf)
(-~
2 Ke.    =  1  exp          Ii ) (Y 1                                U
((    ~
                  ~((        ()
Ii                      1 +
1 K/Ii (5.3) where    e.
1 C
p (T.-T)/q i    U
                          ~Z /iw P m
Kei              (S/C w) ei P
the ratio of heat loss rate per unit volume to the heat release rate by chemical reaction per unit volume heat of combustion C                mean    specific heat 0430Q:1                                      5-5
 
V J
0
 
heat conductivity reaction rate    (mass  of fuel consumed  per  unit time per  unit  volume)
Yu                hydrogen mass    fraction in the heating      zone Yf                hydrogen mass    frac ti on in the reac  tion  zone
                            'u 'u A plot of,Eq. (5.3) is shown in Figure 5.4. It is seen that for a given Ke, there is a minimum value of (Yu - Yf)/e,-. Below this mini-mum value, there is no solution for the v e,. p.              Therefore, this value is considered as the flammability limit. At the flammability limit, the value of Ke. can be determined from Figure 5.4 or from Eq.
(5.3)  as
              )crit  ej      f  ((  u    Yf)/Gi)                                    (5.4)
'A  plot of (K)cr,.t e;      as a    function of (Yu- Yf)/ei is      shown  in Figure 5.5. Equation (5.4) may be expressed as 2                    (  Yu q
C p
p uSu  2 (Y  -Yf)    f(      e-(5. 5) 12  i (T,.    - Tu)
Detailed derivation procedure for Eq. (5.5), is given in Appendix B.
Using the data on S u from Reference (26) we can calculate the right hand side of Eq. (5.5) for a given composition and initial gas tempera-ture.
5.3    YERIFICATIOH    OF THEORIES BY EXPERIMENTS Experiments have been conducted at Factory Mutual to study the effects of water fog density, droplet diameter, and temperature on the lower 0430Q:  I
 
Tempore~,    7 m~~
zone (D xa0
                          ~ ~
lj t =m(r<-Vgw
                                    ~<a>
Deltonce, x xa(
FIGURE  5.3    SCHEMATIC REPRESENTATION OF TEMPERATURE PROFILE THROUGH THE FLAME FRONT A',a 0'(i                      0 20 0'ye                      030 0    .2. 4      6        l0  12 (Yv-YrVdt FIGURE  5.4    THE PARAMETER            A.      p AS A FUNCTION OF (Y    -  Y    )/0    FOR DIFFERENT VALUES OF KO 5-7
 
1 t 0.3 0.2 Ul I
CO 0.1 0.0 0
(YY))/0; FIGURE 5.5 (K)  8 AT THE FLA50BIL1'TY LINIT AS A FUNCTION OF ~Yu f
t                                                    ~i
 
4 flammability 1imi t of hydrogen-air-steam mixtures        . The results indicated that most of the fog nozzles tested at 20 C only changed the limit from 4.03 volume percent to 4.76 percent, corresponding to fog concentration in the range of 0.028-0.085 volume percent, and average drop size ranging from 45-90 microns. For the 50'C case, the lower flammability limit increases to 7.2 percent, corresponding to 0.01-0.04 volume percent of fog and 20-50 micron average drop sizes. The results demonstrated    that the fog inerting effect is  more pronounced at  small drop sizes.
Figures 5.6 through 5.8 show the comparison between the test data and the theoretical predictions. For this comparison, the present theory used the free stream temperature to calculate the thermodynamic proper-ties used in Equation (5.5). This yielded somewhat higher fog corcen-trations than those calculated by use of the mean 'of the flame and free stream temperatures. In Figures 5.6 and 5.7, the data suggests a linear relationship between the volume concentration and volume mean drop size on the log-log plot. It also suggests that the minimum fog inerting concentration varies approximately with the square of the volume mean drop size. In this regard, the present theory is consistent with the data while the Berman et al. theory is not.-
The present theory is in good agreement with the Factory Mutual data        at 4 76 percent H2', however,    it overpredict's the minimum fog inerting concentration at 7.2 percent H2.      The cause of this discrepancy  is still  unknown. The discrepancy may be caused by the uncertainty    of the data. The following discussion supports this claim. The          fog droplets are very small and they vaporize very fast in a flame. Therefore, the fog droplets behave as steam except for their larger heat absorption capability. When the fog droplets vaporize, they absorb the heat of vaporization which is much larger than the steam sensible heat. Typ-ically, the heat of vaporization of water is about 1000 Btu/lb and the average specific heat of steam in the temperature range of interest is about 0.48 Btu/lb. It is well known that a tydrogen flame cannot propa-gate in steam higher than about 64 percent in a steam-air mixture. At 7.9 H2, the adiabatic flame temperature is about 1240 F and therefore 5-9 0430Q:  I
 
oSpraco ZI63 LSpraco l 405-0604.
GSpraco  2020" l704 v'Spraco  l 806-l 605 l0~
CD              NON-FLAMMABLE .ZONE N
PRESENT THEORY CD FLAMMABLE ZONE BERMAN ET AL.
THEORY lo                      IO                  IOO  200 VOLUME MEAN DIAMETER, MICRONS FIGURE 5.6 COMPARISON BETWEEN THEORIES AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 4.76 PERCENT H~
5-10
 
I0' 0 Spraco 2I63-7604 8            v Spraco 2020-I 704 OSonicore    035H X
Non-Flammable Zone Flammable I
PRESENT THEORY                      .Zone O                                                                    50'C 72%  Hz In Air At IO IO                20                  40    50  60 70 8090.
VOLUME b]EAN DIAMETER, MICRONS.
FIGURE  5.7  COMPARISON BETWEEN THE PRESENT THEORY AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 7.2 PERCENT H2 5-11  '
 
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the increase of the steam sensible heat is about 540 Btu/lb. Conse-quently, for the same amount of fog droplets and steam, the fog droplets heat absorption capability is about 1.9 times higher. This means that the fog concentration which is equivalent to 22.1 percent steam in steam and air is capable of inerting 7.9 percent H2. lhis fog inerting concentration was calculated to be 1.61 x 10-4. To inert 7.2 percent H2, a minimum  fog concentration which corresponds to about 21.3 per-cent steam in steam and air is required. This gives a minimum fog incr ting concentration of 1.56 x 10    for 7.2 percent H2 .
estimates show that the present predictions are reasonable and conserva-tive. The present theory is conservative because      it neglects convective and radiative heat transfer and thus underpredicts the heat loss. The estimates are consistent with Factory Mutual data on 7.9 percent H2 but not on 7.2 percent H2.
It should  be noted  that in the tests three fog concentration measuring techniques were used. These three techniques gave substantially dif-ferent results. The discrepancy is at least one order of magnitude difference. The fog concentration data presented in Figures 5.6 through 5.8 were obtained from one of the techniques.      In view of the uncer-tainty of the data, care must be exercised in using them for inerting analysis purposes. They should be used in conjunction with the present fog inerting criterion in the assessment of fog inerting potential in      =
the ice condenser plants. Some uncertainty also exists in the present fog inerti ng theory . The uncertainty associated with the underpredic-tion of the heat loss and temperature dependence of the thermophysical properties is estimated to be +63 percent.
It should  also be pointed out that the Factory Mutual data and the pre-sent theory can only predict the minimum fog inerting concentration. To insure hydrogen burn in all directions in the ice condenser upper plenum,    further  work  in this area may be required.
0430Q:I                                5-13
 
P r
 
6.'0 ASSESSMENT OF FOG INERTING PROBABILITY IN ICE CONDENSER CONTAINMENTS As discussed    in the previous sections, there exists several mechanisms of generating and removing fog droplets from the ice condenser contain-ment. In addition, fog droplets are also transported from one subcom-partment to another by entrainment in the gas stream. The fog entrain-ment rate is difficult to assess without knowing the velocity field and drop size distribution. For simplifying purposes, it is presently assumed that, the mass fraction of mist droplets in the intercompart-mental and fan flows is the same as that within the subcompartment from which the flows are originated. 'his is a good assumption since the fog droplets are small. The amount of fog droplets in a subcompartment depends    on  all these  mechanisms.
The  total amount of fog droplets is important in- determining the volume fraction of suspended condensate in a subcompartment. This volume frac-tion, in turn, is used in the fog inerting criteria to determine whether a particular hydrogen mixture composition formed in a subcompartment at any time is flammable or not. In other words, by knowing the hydrogen concentration and the mean fog drop size, we can determine whether the calculated volume fraction of fog droplets is high enough to prevent the mixture from combustion.
6.1    DETERMINATION OF VOLUME FRACTION OF MIST DROPLETS IN ICE CONDENSER CONTAINMENTS Consider    a  subcompartment  in the ice condenser comtainment as shown in Figure 6.1. There exist several mechanisms by which mist drops can be generated or removed. Fog droplets can be generated by homogeneous or heterogeneous nucleation in the thermal boundary layer and/or in the bulk stream and they can increase in size by condensation or decrease in size by vaporization. The rate of generation of mist droplets by con-densation and their continued growth (or shrinkage due to vaporization) is represented by mcondd. The other mechanism of generating mist drop-lets considered in this analysis is the primary coolant discharge from the break and the rate of generating fog droplets from this mechanism is 0430Q:I                                  6-1
 
dj 1
 
represented    by moreakk.      Two  fog droplet removal mechanisms are consid-ed in this analysis:          one is gravitational settling and the other is
                              ~
moval by containment spray. The fog droplet removal rate by gravita-tional settling is represented by m sett and that by spray is represen-
                                                  ~
ted by m . In addition to the generating and removal mechanisms discussed above, the mist droplet concentration in a subcompartment is also affected by the intercompartmental and fan flows. In the intercom-partmental and fan flows, the mass fraction of fog droplets entrained is q and the gas mixture flow rate is m.                Therefore the rates of fog drop-lets mass into and out of a subcompartment are g qi mi and g n t m t, respectively.                It  should be noted that g n  ~  m.
and $ nout mout include the fog mass entrainment rates in all the intercompartmental and fan flows into and out of a subcompartment.
The mass conservation            equation for the fog droplets in    a  subcompartment may be expressed        as dM 1t        ~  in in          ~out out          break    cond    set    sp where    ( is'a summation over all the flow paths..In Eq. (6.1), if m
d is negative, then it becomes the rate of vaporization. Eq.
(6.1) can be integrated to give the total mass of condensate at time t c              ~"in in          ~"out out        break 0
cond  'set            sp
                ~" in 1        1
                                        ~" out i      i  +    i 1
in                  out      break 1        1          1 cond      set                i                                            (6.2) sp 0430Q:I                                          6-2
 
r The present    analysis will employ the CLASIX calculations of containment 4ransient during a small LOCA. In the CLASIX analysis, the entire ice condenser containment is usually divided into five or six subcompart-ments for analysis purposes.        Temperatures, total pressure, steam partial pressures, and intercompartmental flow rates are calculated during transients. This information is used in Eq. (6.2) to determine fog droplet mass.
When    applying Eq. (6. 1) to each individual subcompartment, we have the following fog mass, conservation equations in finite difference form:
U    er  Com  artment NUC  (t+    at) =
NUC(t) +  ()e.m (t)
UC,set        4C,s Lower  Com  artment NC  (t  + st)  =
NLC(t)  +
( )n.m(
                        ~"out out                                        (6.4)
LC,break LC,cond        LC,set      LC, f )      st 0430Q:1                                  6-3
 
P C
 
Ice Condenser      U    er Plenum MUP(t +    at)  =  MUP(t)  +'(7nin min(t) -      ~  "out mout(t)
                                        )              )
UP,cond(          UP,set(    )
Ice Condenser Lower Plenum s
MLP    t +  st)      MLP  t    (  gn(  m.  (t)                          (6.5)
                            ~soot  out(        LP      d( )    LP,set    )
Dead Ended Re      ion M()E  (t + at)    =
MUE(t) +    (pn;m;(t)                                (6.6) e
                            ~soot  out          "bE cond            set DE
                                                                            )
Fan/Accumul    ator  Rooms*
MEA    (t +  st) 'EA(t) + (Pn(n          m.  (t)                            (6.7) e
                          ~"out out            FA cond 4
WA    set        FA sp In the present analysis, the fog concentrations in the intercompart-mental and fan'flows are assumed to be the same as those in the compart-ment from which the flows are orginated.
* These rooms were analyzed only            for the  D. C. Cook  plant (See Figure 6.S).
      ~  ~
0430Q:1                                          6-4
 
i I'
 
In the equations given above, the intercompartmental and fan flow rates m.
in and moutt are provided by CLASIX calculational results. The procedures of calculating fog droplets generating and removal rates are based on the discussions in the previous sections and the details are given in the following sections.
6.1.1    CALCULATION OF HBREAK To date    little experimental  data is available to estimate the amount of fog droplets generated by the break flow. For a large LOCA, Almenas and Marchello      estimated that 13 percent of the total blowdown drop population (by weight) has drop radius range from 1 p to 20 p and only 1 tivee.
percent less than 1 p. This estimate is somewhat larger than the 4 p mean drop size sited in Section 3.1.2, which is believed to be conserva-Since we are only interested in fog drops smaller than 20 p, and only these drops can remain suspended in air until the time when the hydrogen is released, we assume that the estimate of Almenas and Marchello is applicable in small LOCAs and 14 percent of the suspended liquid are fog droplets which have a potential inerting effect.
The  fraction of reactor coolant discharged from the break remains as suspended liquid has been determined in Section 3. Knowing the break flow rates from a computer code such as MARCH, we can calculate the amount of liquid suspended in the atmosphere.      Then from the drop size distribution we can calculate the amount of fog droplets suspended in the atmosphere.
Oefining the blowdown rate as m , the liquid fraction of the break flow as gb, the fraction of fog droplets smaller than 20 p as fb, we have break    b    b ~b (6.8) 0430Q:1                                6-5
 
j
(
 
In the present analysis fb = 0.14 is used. fb becomes zero when the water level in the'eactor vessel falls below the break elevation.
6.1.2    CALCULATION OF MCOND As discussed    previously, m d is the rate of formation of mist drop-lets by nucleation, condensation, or vaporization. Nucleation of fog droplets can take place in the thermal boundary layer and in the bulk fluid. We conservatively assume that little supersaturation is needed for nucleation in the bulk stream and fog will form when the bulk stream steam partial pressure reaches the saturation steam pressure correspond-ing to the gas stream temperature.      Therefore, the bulk stream fog formation rates can be determined from the equilibrium thermodynamic states of the gas mixture.
The boundary    layer fog formation rate can be determined using the Hijikata-Mori theory          of fog formation in the thermal boundary layer as discussed in Section 3.2.4. The fog formation rate in the thermal boundary layer and the bulk stream is given by Eq. (3.12).
Boundary layer and bulk stream fog formation rates will be calculated for the ice condenser and lower compartment.
A computer program    called'FOG has been developed to calculate m computer program requires input of the volumetric gas flow rate, cond'his gas and wall temperatures, total pressure, and steam partial pressure.
This information can be obtained from the CLASIX output.
6.1.3      CALCULATION OF MSET The    rate of settling of the fog droplets depends on their terminal velocity, concentration and compartment cross sectional area. The droplet terminal velocity is a function of drop size. In the present study, Equation (4.1) will be used to calculate the fog gravitational settling rate.
6-6 0430Q:I
 
/~
~
 
6.1.4  CALCULATION OF MSp The mass  of a fog droplet  is much'maller than that of a spray droplet.
Therefore, when a spray droplet collides with a fog droplet, the fog droplet will coalesce with the spray drop and fall to the sump. In the present study, the fog removal rate by sprays is given by Equation (4.2).
It is  expected that the spray drop collection efficiency is very high, and therefore a 100 percent drop collection efficiency is assumed in the analysis. A sensitivity study is needed to be carried out to study the effect of E on the volume fraction of fog droplets.
A computer program  called  FOGMASS  has been developed  to solve Eqs. (6.3) through (6.7). This program uses a finite difference numerical scheme to carry out integration. This program takes input from FOG and CLASIX output data. Specific output data from CLASIX are time histories of gas temperature, wall temperature, total pressure, steam partial pressure, and intercompartmental. and fan flow rates.
6.2    FOG INERTING PROBABILITY  IN THE SEQUOYAH PLANT The computer codes,    FOG and FOGMASS, were used  to perform fog inerting analysis for the Sequoyah plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation. in the Sequoyah ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the Sequoyah containment    subcompartments.
T o compute  the fog formation rates in the ice condenser upper plenum and
'ower compartment, some output data from the Sequoyah CLASIX analy-sis (27) are needed. These data include time histories of gas tempera-ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 27. The subcompartmentaliza-ion model used in the Sequoyah CLASIX analysis is shown in Figure 6. 1.
In this study only the S2D accident scenario has been analyzed.
0430Q:I                                6-7
 
          'e J- '4
      ~
II


21123 3 Pv, crit(T)Pv, eq(T~)Pcrit (Tw)Pv, w I II II II ll II II 0 OO SUPERSATURATED REGION Pv, oo BOUNDARY LAYER THERMAL SUPERHEATED O K D CO z O 0 O 1 D Z O O I SUPERSATURATED REGION FOG VAPOR Too Tw FIGURE 3.2 VAPOR PRESSURE AND TEMPERATURE PROFILES NEAR A COLD SURFACE 3-14 The parameter n is used in the following section to calculate the fog~~formation rate.It will be demonstrated that when n<2, no fog forma-tion is possible.3.2.4 RATE OF FOG FORMATION HEAR A COLO-SURFACE As has been discussed in Section 3.2.3, fog will form near cold surfaces (e.g., in the ice condenser early in the transient.
FIGURE 6.1 SEQUOYAH CLASIX CONTAINMENT MODEL ICE CONDENSER                            UPPER UPPER PLENUhh                      COMPARTMENT ICE      BED ICE DEAD CONDENSER ENDED LOWER PLENUM                                                REGION COMPARTMENT AIR RETURN FAN/HYDROGEN SKIMMER SYSTEM FLOW PATH CONTAINS DQORS FLOW ALLOWED IN BOTH DIRECTIONS FLOW ALLOWED IN ONE DIRECTION SPRAY HEADER
)As discussed in Section 3.2.1, once water embryos are formed it takes only a few mili-seconds for them to grow to the micron size.After these micron size fog droplets are formed, it needs very little supersaturation for fur-ther growth.Therefore, in the present analysis, it is assumed that vapor and droplets are in thermal equilibrium and local vapor pressure is equal to the local saturation pressure.This section is concerned with the transport of these micron-size fog droplets within the thermal boundary layer.The boundary layer fog formation rate can be determined using the Hijikata-Mori theory of fog formation in the thermal boundary layer.It was assumed that a thin liquid film, having a thickness of e<on a cold surface, coexists with a gas-droplet flow in a two-phase boundary layer of thickness 6 outside the liquid film as shown in Figure 3.3.It was further assumed that the saturation condition exists within the two-phase boundary layer and the boundary layer approximation is appli-cable.Numerical solutions were obtained for the mass fraction of fog droplets, Y , at the gas-liquid film interface.
The fog droplet flow ot rate at a distance X along the plate may be expressed in terms of Y as f'6 mf=L pJ Yudy (3.6)0430(}:I 3-15 hfain Flow~0~ie Cooling Surface Two Please Boundary layer Interface Liquid Film FIGURE 3.3 FORtljATIOH OF FOG HEAR A COLD SURFACE
.where Y mass fraction of fog droplets in the boundary layer fog droplet density Pv vapor density Pg noncondensible gas density Y o.~fly=ok~v+~g)y=coordinate perpendicular to the plate fog boundary layer thickness width of boundary layer Pv+pg=Y0 (1-y/e)(3.7)u=U (<(~)-~(~))~(x)=ax1<<(3.g)4u=e (x)(1-6)(3.10)where a known constant known const'ant free stream velocity 0430Q:1 3-17 I 0 Substituting Eqs.(3.7)through (3.10)into Eq.(3.6), we have the rate of fog formation mf=pL6Y U 0.25 0.025 (3.11)oerivation of expressions for a, Y and g is given in Appendix Even though boundary layer fog formation may occur in any containment subcompartment, the fog formation rate is likely to be small except in the ice condenser.
For fog formation in the ice condenser, L is the total length of the periphery and x is the height of the ice bed.During fog formation in the boundary layer, heat transfer to the cold surface will decrease the bulk fluid temperature.
If the bulk fluid temperature drops below the dew point corresponding to the free stream vapor pressure, then bulk stream condensation could occur.In this case, it is assumed that the boundary layer thickness, s, will grow so thick that LeU~becomes the gas volumetric flow rate Q through the con-densing compartment.
This is a very conservative assumption in terms of the fog formation rate.Under this assumption Equation (3.11)becomes 0.25 0.025 cond o~"o 1:g (1-g).(3.12)where m d is the sum of boundary and bulk stream fog formation rates.cond 0430Q 1 3-18 3.2.5 FOG DROP SIZES As mentioned earlier, when homogeneous nucleation commences, a large number of condensation nuclei are formed and they grow to the micron size within a few milliseconds.
In heterogeneous nucleation, fog drop-lets grow on aerosal particles, which are usually less than 1 p.In any case, the final drop sizes are determined by the atmospheric conditions with which the drops are in thermal equilibrium.
Neiburger and Chien(18)studied the growth of cloud drops by condensa-tion and calculated droplet size distribution based on a cloud cooling rate of 6 c/hr.The initial size distribution of condensation nuclei (sodium chloride)were chosen to correspond to available observations as shown in Figure 3.4 (designated as 0 second).The calculated drop size distributions at 3000 and 6000 seconds are shown in Figure 3.4.It is seen that the sizes of fog droplets range from 0.01 p to 20 p.The volume mean drop size is 8 p at 3000 second.The volume mean drop size for homogeneous nucleation is expected to be smaller than this value.Fogs of volume mean drop sizes ranging from 9 to 14 p(30)have been observed to exist in a natural enviroment, e.g.valley.In the present stuQ, a volume mean fog drop size of 10 p is chosen for fog deposition-and inerting calculations.
3.3 FINE MIST DROPLETS FROM CONTAINMENT SPRAYS The containment sprays produce-fairly large drop sizes.A-typical con-tainment spray nozzle, e.g., Spraco 1713 nozzle, produces the size dis-tribution as shown in Figure 3.5, using a pressure difference of 50 psi across the nozzle().It is seen that water droplets produced from containment range from 100 p to 2000 p.These large drops have little effect on hydrogen combustion and flammability limits, as already demon-strated in the Fenwal tests()and more recent tests at Factory Mutual(21).
To affect the combustion characteristics of a hydrogen mixture, the drop sizes have to be smaller than about 20 p, namely in the fog drop size ranges.Since containment sprays essentially do not produce drops in this size range, containment sprays will not be con-sidered as a means to produce fog droplets.Rather, it will be con-sidered as a means to remove the fog droplets.0430Q:I 3-19
~~~~~j~~)
I<lO I20 lnO CD 80 ED 60 90 20 200 000 600 800 l000 l200 l900 l600 l800 2000 2200 PARTICLE D I AllETER (Ml CROHS)FIGURE 3.5 PARTICLE SIZE DISTRIBUTIOH FOR 50 PSI PRESSURE DROP ACROSS NOZZLE HO.1713
.J"s 1~0 4.0 FOG REMOYAL MECHANISMS IN AN ICE CONDENSER COHTAIHMEHT In Section 3, the mechanisms of generating fog droplets were discussed.
After these droplets are generated, they can be removed from the con-tainment atmosphere by.gravitational settling, vaporization, containment sprays, and impingement on structures.
They can also coalesce with other drops during collision and form bigger drops.These bigger drops could easily settle out of the atmosphere under gravity.These fog droplet removal mechanisms will be discussed in this section.4.1 SETTLING DUE TO'RAVITY Drop removal rates due to gravitational settling depend strongly on drop radius.The removal rate increases linearly with drop terminal veloc-ity, drop concentration, and settling area.The relationship may be expressed as mset t" r (4.I)where q is the mass of mist droplets per unit.volume, and A is the set-tling area.The terminal velocity, Yt, is a strong function of drop radius and the relationship is shown in Figure 4.1.It is seen that the terminal velocity is approximately a linear function of drop radius in both lami-nar the turbulent regimes.For a 1000 p drop, its terminal velocity is above I m/s, while for a 10 p drop, which is the typical fog drop size, its terminal velocity is only about I cm/s.Therefore, there is very little removal by gravity for fog droplets.0430Q: I


===4.2 AGGLOMERATION===
S' The FOG  input data for SequoyahS20 Case I are given in Tables 6.1 and 6.2, and the caIculational results are shown in Figures 6.2 and 6.3. In Figure 6.2, the fog formation rate in the lower compartment is shown.
After the fog droplets are produced, the droplets will undergo changes in the number density and size distribution with time, when drops col-lide with each other and coalesce.The.agglomeration rate (No.of par-ticle per unit volume per unit time)has been found to be proportional to the square of the drop population density and the coagulation mecha-nisms dependent rate constant K For drops larger than 1 g, the dominant mechanism is the difference in'I velocities between drops in adjacent streamlines.
For the first few hundred seconds the wall temperature is lower than the
This is usually termed the velocity gradient coagulation.
  'dew point corresponding to the steam partial pressure and therefore fog starts to form. After about 600 seconds, the fog formation rate becomes negligibly small since the wall temperature is only a few degrees below the dew point. There is no fog formation in th'e lower compartment after about,1800 seconds. The fog formation rate in the ice condenser is shown in Figure 6.3. It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment.      It increases with the ice condenser steam flow rate and reaches a peak of 14 lb/sec at about 1800,seconds. The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen rel ease.
For drops smaller than 1 g, the velocity gradient effect becomes small, and drops are brought'ogether by Brownian motion.This leads to greatly different agglomera-tion rates for different initial drop sizes.A typical agglomeration rate as a function of drop size in a moderately turbulent atmosphere is shown in Figure 4.2.In Figure 4.2, the sharp rise of the agglomeration rate with drop diameter larger than 1 p implies that the larger drops agglomerate quickly to the maximum stable size supported by the atmo-spheric turbulerce.
The   nine fog formation rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form and there is a built-in interpolation scheme in FOGtQSS to obtain values for the intermediate time steps.
The agglomeration rates for drops less than 1 p are very small.Since most of the fog droplets are in.micron size ranges, the agglomeration rate is not large.It is assumed in the present analysis that the initial 4 u blowdown mean drop size will grow to 10 g (See Section 3.2.5).Agglomeration as a separate mechanism for fog growth has'been conservatively neglected.
FOGNSS computes    the rate of fog generation by the break flow, th'e fog rate due to gravity, and the fog removal rate due to sprays, as'ettling well'as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as    follows.
The    rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the MARCH output (7)    'or  a small LOCA. The quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature. According to the MARCH predic-tion 0) the discharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds. Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged 0430(:I                              6-9


===4.3 VAPORIZATION===
I I I I I I I 00 I l I  III III I I
Fog droplets suspended in the containment atmosphere is considered to be in thermodynamic equilibrium with the surrounding gas.Mhen the sur-rounding atmosphere becomes superheated or when the droplets are entrained into a superheated subcompartment, it can undergo vaporization or condensation.
0430Q: 1 4-2 In the present analysis, it is assumed that water vapor and mist drop-lets are in thermal equilibrium at all times.Therefore, the amount of vaporization or condensation will be determined by the thermal equilib-rium state reached by the vapor and drops.In other words, it is not intended to model heat transfer between the drops and the surrounding gas, and thus determine the vaporization rate.This is a good assump-tion for the small fog drop sizes.4.4 REMOVAL BY SPRAY DROPS As mentioned above, the containment spray droplets range from 100 u-2000 p, which are substantially larger than the fog droplets.If fog droplets enter the spray zone, they will probably be removed by the spray droplets by colliding with them, since the spray drop mass is much larger than the fog drop mass.A simple analytical model is used in the present study which assumes that all the fog droplets residing in the spray zone will be swept by the sprays to the floor with the spray drop removal efficiency E.The spray removal rate may be expressed as m=EQ M/q V (4.2)where E Qsp sp M spray drop removal efficiency volumetric flow rate of sprays volume fraction of spray droplets in the spray zone mass of fog in compartment volume V 4.5 OTHER REMOVAL MECHANISMS Another similar mechanism for fog removal is the formation of droplets in the ice condenser.
These droplets which would be generated in the ice bed when the ice melts, would fall through the ice bed, and remove fog droplets from the flow through the ice condenser.
This large quan-tity of water would be effective in removing fog droplets.However, due to difficulty in modeling this removal mechanism, it is conservatively neglected in the present analysis.0430Q:I 4-3 I
In addition to the removal mechanisms mentioned above, fog can also be removed by impacting structural surfaces.Oue to the inertia of fog droplets, substantial fog removal by impacting structural surfaces could occur, when the drop-laden mixture flow passes through long, narrow, curved paths, such as ice basket flow paths, and fan ducts.Moreover, the centrifugal force exerting on the fog droplets, when they pass through the fans, could cause the fog droplets to impact the blade sur-faces or other parts of the fans.These removal mechanisms are believed to be significant; however, they are conservatively neglected in the present analysis.It is, therefore, believed that the present analysis is very conservative.
4-4 0430Q:1 I ,
1 21273 1 10 TERMINAL DROP FALLING VELOCITIES IN STEAM.AI R ATMOSPHERES p~1.0 CO Z 0.10 TURBULENT AMINAR REGIME REGIME HATCHED REGION INDICATES:
50<Re<55 0.01 1.0 0.001 001'1 DROP RADIUS (CM)FIGURE 4.1 TERHINAL VELOCITY AS A FUNCTION OF DROP RADIUS IN STEAH-AIR ATHOSPHERE 104~~7 u 103 O 102 R O I-o 101 GRADIENT AGGLOMERATION n 10 CM 100 S dv dy 8ROWNI AN AGGLOMERATION n 10 CM NET RATE 100 0.01 0.1 1.0 DROP DIAMETER (pM)FIGURE 4.2 AGGLOHERATION RATES IN AIR BETWEEN EQUAL-SIZED DROPS 4-''5 T ,
5.0 FOG INERT ING CRITERIA Recent hydrogen burn experiments conducted at Lawrence Livermore Labora-tory indicated that substantial fog formation could occur when saturated steam is discharged into an unheated vessel.It appeared that this fog prevented a glow plug igniter from successfully igniting the hydrogen mixture in the vessel.The ability of fog in inhibiting and quenching of hydrogen combustion can be explained as follows.The fog droplets suspended in the hydrogen-air-steam mixture act as a heat sink that could absorb a large amount of combustion heat, greatly reducing the pressure and temperature rises resulting from hydrogen combustion.
If droplets are sufficiently small such that they could vaporize inside the thin (Imm)flame front, the flame may be quenched or inhibited.
For a flame speed of 2 m/s, the drop residence time is of the order of 0.5 x 10 seconds.In such a short period of time, the droplets of initial radius less than about 4 p will vaporize entirely in the flame front.The quenching of a propagating flame is also governed by the distance between droplets.As the droplets become closely packed, the total droplet surface area available for energy loss increases.
A critical spacing between droplets exists such that a large fraction of th'e heat released is absorbed, thus preventing flame propagation.
This critical spacing is known as the"quenching distance", which is usually deter-mined by propagating flames in tubes.5.1 PREVIOUS WORK The effectiveness of fog droplets in inhibiting or quenching a flame depends on its quenching distance, was determined by Berman et al.as d=[4VIS3 (5.1)where V is the gas volume and S is the heat transfer surface area.For a hydrogen-air mixture, the data on the quenching distance is shown in 04300:I 5-1


Figure 5.1.In the suspended fog droplets, this volume-to-surface ratio~~~~(i.e., V/S)is equal to 1 d (1-n)where d is the mean droplet diameter and n is the volume fraction of water.When four times this ratio approaches the quenching distance, a critical droplet diameter can be obtained as qd c 2 (5.2)Using this criterion for quenching a flame, for a given volume fraction of water and gas composition, d can be determined.
K' g g          I I II I III I 1 I IIII I iI I  I I I' I I I   I I
The critical droplet diameter then can be determined from the above equation.The drop sizes less than the critical drop size is capable of quenching a f 1 arne.A plot of Eq.(5.2)for two hydrogen concentrations is shown in Figure 5.2.5.2 PRESENT THEORY The previous theories do not model the heat transfer and combustion processes occurring between the burned gas and the suspended droplets.A new theory has been developed, which models the heat loss and combus-tion.0430Q:1 5-2 t~" t 0 V FEG.5.1 MINIMUM IGNITION ENERGIES AND QUENCHING DISTANCE FOR KYDROGEN-OXYGEN INERT GAS MIXTURES AT ATMOSPHERIC PRESSURE 5-3
&ALIIS~mS'REER~~~~~~~~~MR~
~ESESR~~~RSRES~~~m~~EEI~~~RRRE~ERSRSRSRSR~
EEERR~~~WMRE~SEERS~~~BESSER~~~~~~~
~RRRR~~~EERRR RERRE~EEEE~ERRSR~EERRE~
~~~~RA~WE~E~iFsSHSIWI 0~~~l I~~ERIIESECEEEEEESSW RERRREMRS~~SEERS EREEE~~~~ESSES~~~SEERS~
Consider a hydrogen/air/steam/mist droplets mixture in which a flame is gropagating.
The flame may be divided into three zones: heating zone, ,reaction zone, and post-reaction zone as shown in Figure 5.3.The unburned gas at temperature T move in the reacton zone with the U laminar burning velocity S.If the unburned gas density is p, U then the constant mass flow rate m is equal to pS.The unburned gas is heated to ignition temperature T.and burned in the reaction 1 zone to reach the flame temperature Tf.The fog droplets will act as a heat'sink that reduces the flame temperature.
The problem has been formulated and solved by von Karman.In his formulation, three (25)energy equations, which incorporate the heat loss terms, were written for the three zones described above.The solution to these equations yields the following relationship 2 Ke.=1-exp (-T Ii)(Y-Yf)1 2 1 U 1 ((~~((()(-~Ii 1+K/Ii (5.3)where e.1 C (T.-T)/q p i U~Z/iw m P Kei (S/C w)ei P the ratio of heat loss rate per unit volume to the heat release rate by chemical reaction per unit volume heat of combustion C mean specific heat 0430Q:1 5-5 V J 0 heat conductivity reaction rate (mass of fuel consumed per unit time per unit volume)Yu hydrogen mass fraction in the heating zone Yf hydrogen mass f rac ti on in the reac ti on zone'u'u A plot of,Eq.(5.3)is shown in Figure 5.4.It is seen that for a given Ke, there is a minimum value of (Yu-Yf)/e,-.Below this mini-mum value, there is no solution for the v e,.p.Therefore, this value is considered as the flammability limit.At the flammability limit, the value of Ke.can be determined from Figure 5.4 or from Eq.(5.3)as)crit ej f ((u Yf)/Gi)(5.4)'A plot of (K)cr,.t e;as a function of (Yu-Yf)/ei is shown in Figure 5.5.Equation (5.4)may be expressed as 2 (Yu q p uSu (Y-Yf)f(e-C p 2 12 i (T,.-Tu)(5.5)Detailed derivation procedure for Eq.(5.5), is given in Appendix B.Using the data on S from Reference (26)we can calculate the right u hand side of Eq.(5.5)for a given composition and initial gas tempera-ture.5.3 YERIFICATIOH OF THEORIES BY EXPERIMENTS Experiments have been conducted at Factory Mutual to study the effects of water fog density, droplet diameter, and temperature on the lower 0430Q: I Tempore~, 7 m~~zone (D lj t=m(r<-Vgw
~~<a>xa0 xa(Deltonce, x~FIGURE 5.3 SCHEMATIC REPRESENTATION OF TEMPERATURE PROFILE THROUGH THE FLAME FRONT A',a 0'(i 0 20 0'ye 030 0.2.4 6 l0 12 (Yv-Yr Vdt FIGURE 5.4 THE PARAMETER A.p AS A FUNCTION OF (Y-Y)/0 FOR DIFFERENT VALUES OF KO 5-7 1 t 0.3 0.2 Ul I CO 0.1 0.0 0 (Y-Y))/0;FIGURE 5.5 (K)t 8 AT THE FLA50BIL1'TY LINIT AS A FUNCTION OF~Yu f~i 4
flammability 1imi t of hydrogen-air-steam mixtures.The results indicated that most of the fog nozzles tested at 20 C only changed the limit from 4.03 volume percent to 4.76 percent, corresponding to fog concentration in the range of 0.028-0.085 volume percent, and average drop size ranging from 45-90 microns.For the 50'C case, the lower flammability limit increases to 7.2 percent, corresponding to 0.01-0.04 volume percent of fog and 20-50 micron average drop sizes.The results demonstrated that the fog inerting effect is more pronounced at small drop sizes.Figures 5.6 through 5.8 show the comparison between the test data and the theoretical predictions.
For this comparison, the present theory used the free stream temperature to calculate the thermodynamic proper-ties used in Equation (5.5).This yielded somewhat higher fog corcen-trations than those calculated by use of the mean'of the flame and free stream temperatures.
In Figures 5.6 and 5.7, the data suggests a linear relationship between the volume concentration and volume mean drop size on the log-log plot.It also suggests that the minimum fog inerting concentration varies approximately with the square of the volume mean drop size.In this regard, the present theory is consistent with the data while the Berman et al.theory is not.-The present theory is in good agreement with the Factory Mutual data at 4 76 percent H2', however, it overpredict's the minimum fog inerting concentration at 7.2 percent H2.The cause of this discrepancy is still unknown.The discrepancy may be caused by the uncertainty of the data.The following discussion supports this claim.The fog droplets are very small and they vaporize very fast in a flame.Therefore, the fog droplets behave as steam except for their larger heat absorption capability.
When the fog droplets vaporize, they absorb the heat of vaporization which is much larger than the steam sensible heat.Typ-ically, the heat of vaporization of water is about 1000 Btu/lb and the average specific heat of steam in the temperature range of interest is about 0.48 Btu/lb.It is well known that a tydrogen flame cannot propa-gate in steam higher than about 64 percent in a steam-air mixture.At 7.9 H2, the adiabatic flame temperature is about 1240 F and therefore 0430Q: I 5-9


oSpraco ZI63 LSpraco l 405-0604.GSpraco 2020" l704 v'Spraco l 806-l 605 l0~CD N NON-FLAMMABLE.ZONE CD PRESENT THEORY BERMAN ET AL.THEORY FLAMMABLE ZONE lo IO IOO 200 VOLUME MEAN DIAMETER, MICRONS FIGURE 5.6 COMPARISON BETWEEN THEORIES AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 4.76 PERCENT H~5-10
4 8


I0'8 0 Spraco 2I63-7604 v Spraco 2020-I 704 OSonicore 035H X I O Non-Flammable Zone PRESENT THEORY Flammable.Zone 72%Hz In Air At 50'C IO IO 20 40 50 60 70 8090.VOLUME b]EAN DIAMETER, MICRONS.FIGURE 5.7 COMPARISON BETWEEN THE PRESENT THEORY AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 7.2 PERCENT H2'" 5-11' I
from the break  is essentially steam. Therefore, in the present stu@,
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it is  assumed  that no fog is generated by the break flow after 2172 seconds.
~aurpaaaaaaaapsnaaraaapsuulmaaaaaap
For fog removal by    gravitational settling, a volume mean drop size of 10 p was assumed. The terminal velocity of a 10 p drop is about I
~vaessasr MMVPP oeeso OR ss~reaMMMpeooeeaooso wswarsoproooas
  .cm/sec. Because of this low terminal velocity, gravitational settling is not an effective fog removal mechanism. The assumption of 10 p volume mean drop size is therefore conservative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.     It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative. Furthermore, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when    it passes through ducts and fans. All the assumptions mentioned above make the present analysis very conservative. The containment geometric data needed in computing the settling rate are given in Table 6.3.
~sass Mroooooas Rosr roooooooea oooos MMMpo spoaa ROOSE~Ss\~sr~or rr sos so aaa aaso I rrpseosessoasr rrpsoosoaaoesaa
f For fog removal by sprays, a spray flow rate of 9500 gpm was used for Sequoyah.     According to the Sequoyah CLASIX analysis~27~, the sprays are initiated at 142 seconds.      A volume fraction of sprays (volume of sprays divided by volume of the spray zone) of 3.3 x 10-4 was.used, which was obtained using a spray drop fall height of 107      ft, a spray zone volume of 485,500 ft3, and a volume mean drop size of 700 p. As previously discussed a spray removal of a 100 percent was used.
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In Figure 6.1, the directions of the intercompartmental fl'ows are shown. The intercompartmental flow rates for the six.flow paths and nine time steps were obtained from the OPS CLASIX analysis and are given in Table 6.5. The present analysis considers the intercompartmental flows'as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.
~111111al~tat 11111 tatta tat ta~ttaaam alAlaaaa llmlDlt mllmj NNNNtt~ttt
0430Q:I                                  6-12
~lll11 nuarm riinam llHlGlll glJ aaaaa fall QllI RS NNNN g NNNN NSSSNN amn aaaaa aIIII MIIIl~a~~NNNNtttttt
&Na RRRSIINNNN I t tatt~I Pea RE s sap alas Q%%%W ERlI111111 R1%%%11IIIIl lllll Il ERRII RIIll lllll HNOSIINIU lllll~~NPpla WSNNNNNN Iaaf III I ataa rrPPR pssw NNNOIFtatl NNNot atttt NNNNtttaaa NNNNtatlt I~Rss a ttaaa Ital IIII tati tata aaaf SN NNNNNN MNNNNNt SSNNNNH aauaan RQ RSIII1 ROIMLtl%III!1ll RSIIIIlI aaaaa oR lml lHH aaaawRItllaaaa llll IIII1llH l lOI IIIll Mll IIIIHHl II III I 1 I~l~l~y~~I)I 1~I~I~
the increase of the steam sensible heat is about 540 Btu/lb.Conse-quently, for the same amount of fog droplets and steam, the fog droplets heat absorption capability is about 1.9 times higher.This means that the fog concentration which is equivalent to 22.1 percent steam in steam and air is capable of inerting 7.9 percent H2.lhis fog inerting concentration was calculated to be 1.61 x 10-4.To inert 7.2 percent H2, a minimum fog concentration which corresponds to about 21.3 per-cent steam in steam and air is required.This gives a minimum fog incr ting concentration of 1.56 x 10 for 7.2 percent H2.estimates show that the present predictions are reasonable and conserva-tive.The present theory is conservative because it neglects convective and radiative heat transfer and thus underpredicts the heat loss.The estimates are consistent with Factory Mutual data on 7.9 percent H2 but not on 7.2 percent H2.It should be noted that in the tests three fog concentration measuring techniques were used.These three techniques gave substantially dif-ferent results.The discrepancy is at least one order of magnitude difference.
The fog concentration data presented in Figures 5.6 through 5.8 were obtained from one of the techniques.
In view of the uncer-tainty of the data, care must be exercised in using them for inerting analysis purposes.They should be used in conjunction with the present fog inerting criterion in the assessment of fog inerting potential in=the ice condenser plants.Some uncertainty also exists in the present fog inerti ng theory.The uncertainty associated with the underpredic-tion of the heat loss and temperature dependence of the thermophysical properties is estimated to be+63 percent.It should also be pointed out that the Factory Mutual data and the pre-sent theory can only predict the minimum fog inerting concentration.
To insure hydrogen burn in all directions in the ice condenser upper plenum, further work in this area may be required.0430Q:I 5-13 Pr 6.'0 ASSESSMENT OF FOG INERTING PROBABILITY IN ICE CONDENSER CONTAINMENTS As discussed in the previous sections, there exists several mechanisms of generating and removing fog droplets from the ice condenser contain-ment.In addition, fog droplets are also transported from one subcom-partment to another by entrainment in the gas stream.The fog entrain-ment rate is difficult to assess without knowing the velocity field and drop size distribution.
For simplifying purposes, it is presently assumed that, the mass fraction of mist droplets in the intercompart-mental and fan flows is the same as that within the subcompartment from which the flows are originated.
'his is a good assumption since the fog droplets are small.The amount of fog droplets in a subcompartment depends on all these mechanisms.
The total amount of fog droplets is important in-determining the volume fraction of suspended condensate in a subcompartment.
This volume frac-tion, in turn, is used in the fog inerting criteria to determine whether a particular hydrogen mixture composition formed in a subcompartment at any time is flammable or not.In other words, by knowing the hydrogen concentration and the mean fog drop size, we can determine whether the calculated volume fraction of fog droplets is high enough to prevent the mixture from combustion.


===6.1 DETERMINATION===
r It is  seen  in Figure 6.1 that  two  trains of the air return fan  and hydrogen skinner system take suction from the dead ended region and from the upper compartment and discharge into the lower compartment. The fans are initiated at 712 seconds. The fan head-flow curve reported in Reference 27 was used to compute the fan flow rates.         Fan flow rates of 1645  ft /sec 3
OF VOLUME FRACTION OF MIST DROPLETS IN ICE CONDENSER CONTAINMENTS Consider a subcompartment in the ice condenser comtainment as shown in Figure 6.1.There exist several mechanisms by which mist drops can be generated or removed.Fog droplets can be generated by homogeneous or heterogeneous nucleation in the thermal boundary layer and/or in the bulk stream and they can increase in size by condensation or decrease in size by vaporization.
and 10  ft /sec 3
The rate of generation of mist droplets by con-densation and their continued growth (or shrinkage due to vaporization) is represented by m d.The other mechanism of generating mist drop-cond lets considered in this analysis is the primary coolant discharge from the break and the rate of generating fog droplets from this mechanism is 0430Q:I 6-1 dj1 represented by m k.Two fog droplet removal mechanisms are consid-oreak~~ed in this analysis: one is gravitational settling and the other is moval by containment spray.The fog droplet removal rate by gravita-tional settling is represented by m t and that by spray is represen-set ted by m.In addition to the generating and removal mechanisms discussed above, the mist droplet concentration in a subcompartment is also affected by the intercompartmental and fan flows.In the intercom-partmental and fan flows, the mass fraction of fog droplets entrained is q and the gas mixture flow rate is m.Therefore the rates of fog drop-lets mass into and out of a subcompartment are g qimiand g n t m t, respectively.
were used  for the air return fan and the hydrogen skimmer      system, respectively. These flow rates were calculated using average ap's between the upper compartment and the lower compart-ment, and between the dead ended region and the lower compartment.         It was also assumed. that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
It should be noted that g n~m.and$nout mout include the fog mass entrainment rates in all the intercompartmental and fan flows into and out of a subcompartment.
The  results of the FOGMASS calculation are shown in Figure 6.4. It is seen  that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing. At about 700 seconds, the lower compartment
The mass conservation equation for the fog droplets in a subcompartment may be expressed as dM 1t~in in~out out break cond set sp where (is'a summation over all the flow paths..In Eq.(6.1), if m d is negative, then it becomes the rate of vaporization.
    .fog concentration reaches its peak of 2.2 x 10 . Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases.           However,-
Eq.(6.1)can be integrated to give the total mass of condensate at time t c~"in in~"out out break 0 cond&#x17d;set sp 1 1 i i+i~" in in~" out out break 1 1 1 1 cond set sp i (6.2)0430Q:I 6-2 r
the upper plenum fog concentration keeps rising until about 900 seconds, due to an increasing fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 5.4 x 10          at about 900 seconds.       The lower plenum fog concentration is almost the same as the lower compartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum. -Therefore, these two volumes behave as a single volume fn terms of fog concentration.
The present analysis will employ the CLASIX calculations of containment 4ransient during a small LOCA.In the CLASIX analysis, the entire ice condenser containment is usually divided into five or six subcompart-ments for analysis purposes.Temperatures, total pressure, steam partial pressures, and intercompartmental flow rates are calculated during transients.
At    2172 seconds,     the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations.         The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment. The effect of .sprays on .the upper compartment fog concen-tration is clearly seen in Figure 6.4. At 142 seconds, the sprays are 0430Q:I                                    6-13
This information is used in Eq.(6.2)to determine fog droplet mass.When applying Eq.(6.1)to each individual subcompartment, we have the following fog mass, conservation equations in finite difference form: U er Com artment NUC (t+at)=NUC(t)+()e.m(t)UC,set 4C,s Lower Com artment NC (t+st)=NLC(t)+()n.m(~"out out LC,break (6.4)LC,cond LC,set LC, f)st0430Q:1 6-3 P C Ice Condenser U er Plenum MUP(t+at)=MUP(t)+'(7nin min(t)-~"out mout(t)UP,cond()UP,set())Ice Condenser Lower Plenum s MLP t+st)MLP t (gn(m.(t)(6.5)~soot out(LP d()LP,set)Dead Ended Re ion M()E (t+at)=MUE(t)+(pn;m;(t)
(6.6)e~soot out"bE cond DE set)Fan/Accumul ator Rooms*MEA (t+st)&#x17d;EA(t)+(Pn(n m.(t)e~"out out FA cond (6.7)4 WA set FA sp In the present analysis, the fog concentrations in the intercompart-mental and fan'flows are assumed to be the same as those in the compart-ment from which the flows are orginated.
*These rooms were analyzed only for the D.C.Cook plant (See Figure~~6.S).0430Q:1 6-4 iI' In the equations given above, the intercompartmental and fan flow rates m.and m t are provided by CLASIX calculational results.The in out procedures of calculating fog droplets generating and removal rates are based on the discussions in the previous sections and the details are given in the following sections.6.1.1 CALCULATION OF HBREAK To date little experimental data is available to estimate the amount of fog droplets generated by the break flow.For a large LOCA, Almenas and Marchello estimated that 13 percent of the total blowdown drop population (by weight)has drop radius range from 1 p to 20 p and only 1 percent less than 1 p.This estimate is somewhat larger than the 4 p mean drop size sited in Section 3.1.2, which is believed to be conserva-tivee.Since we are only interested in fog drops smaller than 20 p, and only these drops can remain suspended in air until the time when the hydrogen is released, we assume that the estimate of Almenas and Marchello is applicable in small LOCAs and 14 percent of the suspended liquid are fog droplets which have a potential inerting effect.The fraction of reactor coolant discharged from the break remains as suspended liquid has been determined in Section 3.Knowing the break flow rates from a computer code such as MARCH, we can calculate the amount of liquid suspended in the atmosphere.
Then from the drop size distribution we can calculate the amount of fog droplets suspended in the atmosphere.
Oefining the blowdown rate as m , the liquid fraction of the break flow as gb, the fraction of fog droplets smaller than 20 p as fb, we have break b b~b (6.8)0430Q:1 6-5 j (
In the present analysis fb=0.14 is used.fb becomes zero when the water level in the'eactor vessel falls below the break elevation.


====6.1.2 CALCULATION====
t I
OF MCOND As discussed previously, m d is the rate of formation of mist drop-lets by nucleation, condensation, or vaporization.
r I          I I    0  g I      I I< I                                      >>
Nucleation of fog droplets can take place in the thermal boundary layer and in the bulk fluid.We conservatively assume that little supersaturation is needed for nucleation in the bulk stream and fog will form when the bulk stream steam partial pressure reaches the saturation steam pressure correspond-ing to the gas stream temperature.
ll I I I        I I
Therefore, the bulk stream fog formation rates can be determined from the equilibrium thermodynamic states of the gas mixture.The boundary layer fog formation rate can be determined using the Hijikata-Mori theory of fog formation in the thermal boundary layer as discussed in Section 3.2.4.The fog formation rate in the thermal boundary layer and the bulk stream is given by Eq.(3.12).Boundary layer and bulk stream fog formation rates will be calculated for the ice condenser and lower compartment.
I
A computer program called'FOG has been developed to calculate m cond'his computer program requires input of the volumetric gas flow rate, gas and wall temperatures, total pressure, and steam partial pressure.This information can be obtained from the CLASIX output.6.1.3 CALCULATION OF MSET The rate of settling of the fog droplets depends on their terminal velocity, concentration and compartment cross sectional area.The droplet terminal velocity is a function of drop size.In the present study, Equation (4.1)will be used to calculate the fog gravitational settling rate.0430Q:I 6-6
                        ~
~/~  
                        ~
                          ~ ~
I  ~ ~      ~ ~
I ~
I  a II I III III III III II II II I
II I    I II II    I>>
fl    I>>
II    I>>
II    I>>
II II    I I
II    I ll II II l
I  MTH II      >>
II    I ~
II I~


====6.1.4 CALCULATION====
t~
OF MSp The mass of a fog droplet is much'maller than that of a spray droplet.Therefore, when a spray droplet collides with a fog droplet, the fog droplet will coalesce with the spray drop and fall to the sump.In the present study, the fog removal rate by sprays is given by Equation (4.2).It is expected that the spray drop collection efficiency is very high, and therefore a 100 percent drop collection efficiency is assumed in the analysis.A sensitivity study is needed to be carried out to study the effect of E on the volume fraction of fog droplets.A computer program called FOGMASS has been developed to solve Eqs.(6.3)through (6.7).This program uses a finite difference numerical scheme to carry out integration.
-      turned  on and  the upper compartment fog concentration drops sharply until about 600 seconds. At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompartmen-tal flow into the compartment increases sharply at that time. A peak concentration of 7 x 10 -6 in the upper compartment is reached at about 1200 seconds.
This program takes input from FOG and CLASIX output data.Specific output data from CLASIX are time histories of gas temperature, wall temperature, total pressure, steam partial pressure, and intercompartmental.
Hydrogen  starts to release into the containment at about 3804 seconds, according to the MARCH calculation (27) . It reaches 4 volume percent at about 4300,',4400,  and 4670 seconds    in the lower compartment, upper plenum, and upper compartment,    respectively.
and fan flow rates.6.2 FOG INERTING PROBABILITY IN THE SEQUOYAH PLANT The computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the Sequoyah plant.FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation.
At  4300 seconds,  the calculated lower compartment fog concentration is
in the Sequoyah ice condenser and lower plenum.Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the Sequoyah containment subcompartments.
                -7 9.7 x 10 , which is about an order of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H2. At 4670 seconds, the upper compartment fog concentration is 1.35 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*. At the times of reaching 8.5 percent H2, the fog concentrations in the lower and upper compart-ments are even lower than the figures given above. Therefore,          it  is concluded that the fog concentrations'n the lower and upper compart-ments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion. .
T o compute the fog formation rates in the ice condenser upper plenum and'ower compartment, some output data from the Sequoyah CLASIX analy-(27)sis are needed.These data include time histories of gas tempera-ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates.In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 27.The subcompartmentaliza-ion model used in the Sequoyah CLASIX analysis is shown in Figure 6.1.In this study only the S2D accident scenario has been analyzed.0430Q:I 6-7 J-'4'e~II FIGURE 6.1 SEQUOYAH CLASIX CONTAINMENT MODEL ICE CONDENSER UPPER PLENUhh UPPER COMPARTMENT ICE BED ICE CONDENSER LOWER PLENUM COMPARTMENT DEAD ENDED REGION AIR RETURN FAN/HYDROGEN SKIMMER SYSTEM FLOW PATH CONTAINS DQORS FLOW ALLOWED IN BOTH DIRECTIONS FLOW ALLOWED IN ONE DIRECTION SPRAY HEADER S'
  .However, at 4400 seconds, the calculated fog concentration in the upper plenum is 6.1 x 10
The FOG input data for SequoyahS20 Case I are given in Tables 6.1 and 6.2, and the caIculational results are shown in Figures 6.2 and 6.3.In Figure 6.2, the fog formation rate in the lower compartment is shown.For the first few hundred seconds the wall temperature is lower than the'dew point corresponding to the steam partial pressure and therefore fog starts to form.After about 600 seconds, the fog formation rate becomes negligibly small since the wall temperature is only a few degrees below the dew point.There is no fog formation in th'e lower compartment after about,1800 seconds.The fog formation rate in the ice condenser is shown in Figure 6.3.It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment.
                          -5 which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10          or higher for 10 p volume mean drop size. At 4600 seconds, the upper plenum hydrogen concentration reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10        or higher is required to inert 7.2 percent H . In comparison, the present theory on fog inerting pre-dicts 1.02 x 10 for 7.2 percent H2.
It increases with the ice condenser steam flow rate and reaches a peak of 14 lb/sec at about 1800,seconds.
The fog  inerting criterion  used  is described in Section 5.2.
The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen rel ease.The nine fog formation rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form and there is a built-in interpolation scheme in FOGtQSS to obtain values for the intermediate time steps.FOGNSS computes the rate of fog generation by the break flow, th'e fog'ettling rate due to gravity, and the fog removal rate due to sprays, as well'as the rates of fog entrainment by intercompartmental and fan flows.The input data needed to calculate each of these rates are dis-cussed as follows.The rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the MARCH output'or a small LOCA.The (7)quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature.
0430Q:1                                   6-15
According to the MARCH predic-tion the discharge of liquid by the break flow into the lower com-0)partment lasts for only 2172 seconds.Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged 0430(:I 6-9
 
Therefore,  it appears  that  it is  possible to inert    7  percent  H2  but unlikely. However, at 8 percent H2 in the upper plenum, which occurs at about 4650 seconds, the fog concentration is 5.5 x 10 5, which is too low to inert 8 percent H2. An extrapolation of the Factory Mutual 8 percent H2 data to 10 p volume mean drop size and the present pre-diction give 1.9 x 10-4 and l.2 x 10-4 for the minimum required fog inerting concentration, respectively . Therefore both the theory and the extrapolation of test data show that fog inerting will not occur in the upper plenum.
The glow plug    igniters  which have been    installed in the   Sequoyah con-tainment were designed to burn hydrogen lower than 8.0 percent. As discussed previously, no fog inerting effects will be expected in the Sequoyah lower and upper compartments.        Therefore, the glow plug igni-tet s are expected to function as designed in these two compartments.           It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent.
However,  it  seems very unlikely that the same igniters would fail to ignite 8.0 percent H2 as designed, considering the fact that consider-Pg  able conservatism has been exercised in the present analysis.
Sensitivity studies of the spray      removal  efficiency  and the fraction of blowdown  droplets smaller than 20 p for the Sequoyah plant have been performed. A case of 10 percent spray removal efficiency was run using FOGMASS. The calculational results showed that the fog concentrations in the lower compartment, lower plenum,        and upper. compartment    at 4600 seconds were increased      approximately by a factor of 10. However, these concentrations are still too low to inert 8 percent hydrogen- In com-parison, the fog concentration in the upper plenum is increased by only 20 percent because the concentration at this time is primarily deter-mined by the fog formation rate in the ice condenser.             This increase is too small to change the conclusion given previously on the inerting probability in the upper plenum. Another case in which all the blowdown droplets were assumed to be smaller than 20 p was run using FOGMASS.
The calculational results showed that at 4600 seconds the fog concentra-tions in the lower compartment and lower plenum were increased by 15 0430Q  I                               6-16


I I I I I I I 00 I l I III III I I K'
g g I I II I I I I I 1 I IIII I i I I I I I'I I I I I 4 8 from the break is essentially steam.Therefore, in the present stu@, it is assumed that no fog is generated by the break flow after 2172 seconds.For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed.The terminal velocity of a 10 p drop is about I.cm/sec.Because of this low terminal velocity, gravitational settling is not an effective fog removal mechanism.
The assumption of 10 p volume mean drop size is therefore conservative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.
It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative.
Furthermore, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans.All the assumptions mentioned above make the present analysis very conservative.
The containment geometric data needed in computing the settling rate are given in Table 6.3.f For fog removal by sprays, a spray flow rate of 9500 gpm was used for Sequoyah.According to the Sequoyah CLASIX analysis~27~, the sprays are initiated at 142 seconds.A volume fraction of sprays (volume of sprays divided by volume of the spray zone)of 3.3 x 10-4 was.used, which was obtained using a spray drop fall height of 107 ft, a spray zone volume of 485,500 ft3, and a volume mean drop size of 700 p.As previously discussed a spray removal of a 100 percent was used.In Figure 6.1, the directions of the intercompartmental fl'ows are shown.The intercompartmental flow rates for the six.flow paths and nine time steps were obtained from the OPS CLASIX analysis and are given in Table 6.5.The present analysis considers the intercompartmental flows'as the mechanisms of transporting fog from one compartment to another.It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.
0430Q:I 6-12 r
It is seen in Figure 6.1 that two trains of the air return fan and hydrogen skinner system take suction from the dead ended region and from the upper compartment and discharge into the lower compartment.
The fans are initiated at 712 seconds.The fan head-flow curve reported in Reference 27 was used to compute the fan flow rates.Fan flow rates of 1645 ft/sec and 10 ft/sec were used for the air return fan and the 3 3 hydrogen skimmer system, respectively.
These flow rates were calculated using average ap's between the upper compartment and the lower compart-ment, and between the dead ended region and the lower compartment.
It was also assumed.that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
The results of the FOGMASS calculation are shown in Figure 6.4.It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing.
At about 700 seconds, the lower compartment.fog concentration reaches its peak of 2.2 x 10.Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases.
However,-the upper plenum fog concentration keeps rising until about 900 seconds, due to an increasing fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum.The upper plenum fog concentration reaches its peak of 5.4 x 10 at about 900 seconds.The lower plenum fog concentration is almost the same as the lower compartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum.-Therefore, these two volumes behave as a single volume fn terms of fog concentration.
At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after.The effect is more pronounced for the lower compartment and lower plenum fog concentrations.
The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment.
The effect of.sprays on.the upper compartment fog concen-tration is clearly seen in Figure 6.4.At 142 seconds, the sprays are0430Q:I 6-13 t
I r I I<I ll I I I II I III III III III II II II I II I II II fl II II II II II ll II II II II II I I>>I>>I>>I>>I I I l I>>I~I I I MTH I>>0 g I I~~~~I~I>>I~~I a I~~~
t~
-turned on and the upper compartment fog concentration drops sharply until about 600 seconds.At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompartmen-tal flow into the compartment increases sharply at that time.A peak-6 concentration of 7 x 10 in the upper compartment is reached at about 1200 seconds.Hydrogen starts to release into the containment at about 3804 seconds, according to the MARCH calculation
.It reaches 4 volume percent (27)at about 4300,',4400, and 4670 seconds in the lower compartment, upper plenum, and upper compartment, respectively.
At 4300 seconds, the calculated lower compartment fog concentration is 9.7 x 10 , which is about an order of magnitude smaller than the-7 minimum fog concentrations required for inerting 4 percent H2.At 4670 seconds, the upper compartment fog concentration is 1.35 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*.At the times of reaching 8.5 percent H2, the fog concentrations in the lower and upper compart-ments are even lower than the figures given above.Therefore, it is concluded that the fog concentrations'n the lower and upper compart-ments are too low to have any inerting effect.The use of the present theory on fog inerting also leads to the same conclusion.
..However, at 4400 seconds, the calculated fog concentration in the upper-5 plenum is 6.1 x 10 which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction.
The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10 or higher for 10 p volume mean drop size.At 4600 seconds, the upper plenum hydrogen concentration reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H.In comparison, the present theory on fog inerting pre-dicts 1.02 x 10 for 7.2 percent H2.The fog inerting criterion used is described in Section 5.2.0430Q:1 6-15 Therefore, it appears that it is possible to inert 7 percent H2 but unlikely.However, at 8 percent H2 in the upper plenum, which occurs at about 4650 seconds, the fog concentration is 5.5 x 10 5, which is too low to inert 8 percent H2.An extrapolation of the Factory Mutual 8 percent H2 data to 10 p volume mean drop size and the present pre-diction give 1.9 x 10-4 and l.2 x 10-4 for the minimum required fog inerting concentration, respectively
.Therefore both the theory and the extrapolation of test data show that fog inerting will not occur in the upper plenum.Pg The glow plug igniters which have been installed in the Sequoyah con-tainment were designed to burn hydrogen lower than 8.0 percent.As discussed previously, no fog inerting effects will be expected in the Sequoyah lower and upper compartments.
Therefore, the glow plug igni-tet s are expected to function as designed in these two compartments.
It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent.However, it seems very unlikely that the same igniters would fail to ignite 8.0 percent H2 as designed, considering the fact that consider-able conservatism has been exercised in the present analysis.Sensitivity studies of the spray removal efficiency and the fraction of blowdown droplets smaller than 20 p for the Sequoyah plant have been performed.
A case of 10 percent spray removal efficiency was run using FOGMASS.The calculational results showed that the fog concentrations in the lower compartment, lower plenum, and upper.compartment at 4600 seconds were increased approximately by a factor of 10.However, these concentrations are still too low to inert 8 percent hydrogen-In com-parison, the fog concentration in the upper plenum is increased by only 20 percent because the concentration at this time is primarily deter-mined by the fog formation rate in the ice condenser.
This increase is too small to change the conclusion given previously on the inerting probability in the upper plenum.Another case in which all the blowdown droplets were assumed to be smaller than 20 p was run using FOGMASS.The calculational results showed that at 4600 seconds the fog concentra-tions in the lower compartment and lower plenum were increased by 15 0430Q I 6-16
(\
(\
percent while the increases in the upper plenum and upper compartment were negligibly small.The insensitivity of the fog concentrations to the parameter of the fraction of blowdown droplets smaller than 20 u is due to the effectiveness of the spray removal.At 4600 seconds, almost all the blowdown droplets are removed by the sprays.The sensitivity studies showed that the fog concentration in the upper plenum at the time of significant hydrogen release is not sensitive to the spray removal efficiency and the fraction of blowdown droplets smaller than 20 g.0430(:1 6-17 L'j I TABLE 6.1 FOG IHPUT QATA FOR SfgUOYAH LOWER COMPARTMENT Time (sec)Lower Compartment Gas flow Rate (ft/sec)Temp.('F)Temp ('F)Gas Wall Steam Total Partial Pressure Pressure~(sia)~(s(a)60 610 1210 1810 2410 3010 3510 4010 4510 1404.5 646.7 3157.2 3115.5 2913.7 2871.?, 2739.3 2755.9 2848.8 150 215 188 188 180 179 178 175 197 118 16.7 202 21.6 176 20.4 176 20.5 173 20.1 169'9.9 169 19.9 164.19.4 173 19.8 15.3 8.9 8.8 7.5 7.2 6.9 5.5 4.8 0430Q:1 6-18 TABLE 6.2 FOG INPUT DATA FOR SEQUOYAH ICE CONDENSER Ice Condenser Gas Flow Rate Time (sec)(ft/sec)Gas Temp.('F)Ice Temps ('F)Steam Total Partial Pressure Pressure~(sia)~(sia)60 610 1210 1810 2410 3010 3510 4010 4510 1082 96.4'2654 2799 2679 2629 2502 2594 2628 120 132 186 188 182 179 178 171 187 32 32 32 32 32 32 32 32 32 16.6 21.8 20.4 20.5 20.0 19.9 19.9 19.4 19.8 2.5 2.3 8.1 8.8 7.6 7.2 7.0 5.7 4.7 0430Q 1 6-19 (P
percent while the increases in the upper plenum and upper compartment were negligibly small. The insensitivity of the fog concentrations to the parameter of the fraction of blowdown droplets smaller than 20 u is due to the effectiveness of the spray removal. At 4600 seconds, almost all the blowdown droplets are removed by the sprays. The sensitivity studies showed that the fog concentration in the upper plenum at the time of significant hydrogen release is not sensitive to the spray removal efficiency and the fraction of blowdown droplets smaller than 20 g.
TABLE 6.3 GEOMETRIC DATA FOR SEgUOYAH CONTAIHMEHT Volume (ft)3 Floor Area (ft)Lower Compartment 289,000 5,410 Ice Condenser Lower Plenum 24,200 3,100 Ice Condenser Upper Plenum 47,000 3,200 Upper Compartment 651,000 10,390 Dead Ended Region 94,000 3,350 0430(:1 6-20
6-17 0430(:1
: k.
-TABLE 6.4 MARCH PREDICTION OF REACTOR COOLANT MASS AND ENERGY RELEASE RATE FOR THE S2D SEQUENCE Time (seconds)H20 Mass Re1ease Rate (Ibm/sec)H20 Energy Re1ease Rate (Btu/sec)0.0 2172 2478 3180 3804 4428 4752 5700 6012 6960 7062 7206 197.2 190.5 44.85 53.53 34.82 21.40 48.42 19.42 14.07-5.253 4.718 4.060 1.167 x 10 1.097 x 10 5.230 x 10 6.547 x 10 4.262 x 102.842 x 10 5.558 x 10 2.182 x 10 1.583 x 10 5.989 x 10 3 5.388'x 10 3 4.693 x 10 0430Q:1 6-21 I g TABLE 6.5 IHTERCOMPARTHENTAL fLOM RATES (ft/sec)PREDICTED BY CLASIX FOR SEQUOYAH Time (sec)Flow From Flow From Flow From flow From flow From LC to LP LP to UP UP to UC UC to LC DE to LC 6.001E1 6.100E2 1.210E3 1.810E3 2.410E3 3.010E3 3.510E3 4.010E3 4.510E3 1.175E3 3.580E2 2.864E3 2.828E3'.695E3 2.654E3 2.528E3 2.613E3 2.694E3 1.082E3 9.641E1 2.654E3 2.799E3 2.679E3 2.629E3 2.502E3 2.594E3 2.628E3 7.029E2-3.931E1 1.272E3 1.323E3 1.375E3 1.407E3 1.352E3 1.537E3 1.627E3-1.095E2-1.106E2-,3.348E1-4.426E1-9.905E1-1.304E2-2.113E1-2.676E2-1.838E2-1.094E2-1.793E2-1.088E2-1.502E2-6.855E1-1.634E2-6.326E1-1.643E2-4.699E1 0430Q:I 6-22 4 6.3 FOG IHERTIHG PROBABILITY IH THE McGUIRE PLAHT I The computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the McGuire plant.FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the McGuire ice condenser and lower plenum.Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the McGuire containment subcompartments.
To compute the fog formation rates in the ice condenser upper plenum and lower compartment,'some output data from the McGuire CLASIX analy-sis are needed.These data include time histories of gas tempera-(28)ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates.In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 28.The subcompartmentaliza-tion model used in the McGuire CLASIX analysis is shown in Figure 6.5.In this study only the S20 accident scenario has been analyzed by CLASIX for McGuire.4~The FOG input data for McGuire S2D Case I are given in Tables 6.6 and 6.7, and the calculational results are shown in Figures 6.6 and 6.7.In Figure 6.6, the fog formation rate in the lower compartment is shown.For the first few hundred seconds the wall temperature is lower than the dew point corresponding to the steam partial pressure and therefore fog starts to form.The fog formation rate is low because the wall tempera-'ure is only a few degrees below the dew point.Fog formation in the lower compartment becomes zero after about 600 seconds.The fog forma-tion rate in the ice condenser is shown in Figure 6.7.It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment.
The fog formation rate increases with the ice condenser steam flow rate and reaches the first peak at about 1510 sec-onds.Then the rate decreases because of the decrease in the steam flow rate.The fog formation and the steam flow rates start to increase again at about 2510 seconds.The fog formation rate reaches the second 0430Q:I 6-23


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~~  
 
TABLE 6.1    FOG  IHPUT QATA FOR SfgUOYAH LOWER COMPARTMENT Steam Lower Compartment      Gas      Wall    Total      Partial Gas  flow Rate        Temp. Temp    Pressure  Pressure Time (sec)    (ft  /sec)            ('F)    ('F)    ~(sia)    ~(s(a) 60                1404.5            150      118    16. 7 610                646.7            215      202    21. 6      15.3 1210                3157.2            188      176    20.4        8.9 1810                3115.5            188      176    20.5        8.8 2410                2913.7            180      173    20.1        7.5 3010                2871.?,          179      169  '9.9          7.2 3510                2739.3            178      169    19.9        6.9 4010                2755.9          175      164 . 19.4        5.5 4510                2848.8          197      173    19.8        4.8 0430Q:1                              6-18
 
TABLE  6.2  FOG INPUT DATA FOR SEQUOYAH ICE CONDENSER Steam Ice Condenser          Gas      Ice    Total      Partial Gas  Flow Rate        Temp. Temps  Pressure  Pressure Time (sec)    (ft /sec)              ('F)    ('F)  ~(sia)      ~(sia) 60                1082            120      32      16. 6      2.5 610                  96.4          132      32      21.8      2.3 1210              '2654              186      32      20.4      8.1 1810                2799              188      32      20.5      8.8 2410                2679              182      32      20.0      7.6 3010                2629              179      32      19.9      7.2 3510                2502              178      32      19.9      7.0 4010                2594              171      32    19.4        5.7 4510                2628              187      32    19.8        4.7 6-19 0430Q  1
 
(P TABLE 6.3 GEOMETRIC DATA FOR SEgUOYAH CONTAIHMEHT Volume  (ft3 )    Floor Area  (ft )
Lower Compartment                  289,000              5,410 Ice Condenser Lower Plenum                          24,200              3,100 Ice Condenser Upper Plenum                          47,000              3,200 Upper Compartment                    651,000              10,390 Dead Ended Region                      94,000              3,350 0430(:1                            6-20
 
k.
-              TABLE 6.4  MARCH PREDICTION OF REACTOR COOLANT MASS AND ENERGY RELEASE RATE FOR THE S2D SEQUENCE Time          H20 Mass Re1ease  Rate    H20 Energy Re1ease  Rate
( seconds)            (Ibm/sec)                    (Btu/sec) 0.0                197.2                        1.167 x 10 2172              190.5                        1.097 x 10 2478                44.85                      5.230 x 10 3180                53.53                      6.547 x 10 3804                34.82                      4.262 x 10 4428                21.40                      2.842 x 10 4752                48.42                      5.558 x 10 5700                19.42                      2.182 x 10 6012                14.07-                      1.583 x 10 6960                  5.253                      5.989 x 10 3 3
7062                  4.718                      5.388'x  10 7206                  4.060                      4.693 x 10 6-21 0430Q:1
 
I g TABLE      6.5 IHTERCOMPARTHENTAL fLOM RATES  (ft /sec)
PREDICTED BY CLASIX FOR SEQUOYAH Time    Flow From          Flow From    Flow From  flow From    flow From (sec)    LC    to    LP    LP  to UP    UP  to UC  UC to LC      DE to LC 6.001E1  1. 175E3            1.082E3      7.029E2  -9. 905E1    -1.304E2
: 6. 100E2 3.580E2            9. 641E1    -3. 931E1  -2.113E1      -2.676E2 1.210E3  2.864E3            2. 654E3      1. 272E3  -1. 838E2    -1.094E2 1.810E3                      2. 799E3      1.323E3  -1.793E2      -1.088E2 2.828E3'.695E3 2.410E3                      2. 679E3      1.375E3  -1. 502E2    -6. 855E1 3.010E3  2.654E3            2.629E3      1.407E3  -1.634E2      -6.326E1 3.510E3  2.528E3            2.502E3      1.352E3  -1. 643E2    -4. 699E1 4.010E3  2. 613E3            2.594E3      1.537E3  -1.095E2      -,3.348E1
: 4. 510E3 2. 694E3            2.628E3      1.627E3  -1. 106E2    -4.426E1 6-22 0430Q:I
 
4 6.3  FOG  IHERTIHG PROBABILITY IH THE McGUIRE PLAHT I
The computer codes,    FOG and FOGMASS, were used to perform fog inerting analysis for the McGuire plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the McGuire ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the McGuire containment subcompartments.
To compute the fog    formation rates in the ice condenser upper plenum and lower compartment, 'some output data from the McGuire CLASIX analy-sis (28) are needed. These data include time histories of gas tempera-ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 28. The subcompartmentaliza-tion model used in the McGuire CLASIX analysis is shown in Figure 6.5.
In this study only the S20 accident scenario has been analyzed by CLASIX    for McGuire.
4 ~
The    FOG  input data for McGuire S2D Case I are given in Tables 6.6 and 6.7, and the calculational results are shown in Figures 6.6 and 6.7. In Figure 6.6, the fog formation rate in the lower compartment is shown.
For the first few hundred seconds the wall temperature is lower than the dew point corresponding to the steam partial pressure and therefore fog starts to form. The fog formation rate is low because the wall tempera-
'ure is only a few degrees below the dew point. Fog formation in the lower compartment becomes zero after about 600 seconds. The fog forma-tion rate in the ice condenser is shown in Figure 6.7.        It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment. The fog formation rate increases with the ice condenser steam flow rate and reaches the first peak at about 1510 sec-onds. Then the rate decreases because of the decrease in the steam flow rate. The fog formation and the steam flow rates start to increase again at about 2510 seconds. The fog formation rate reaches the second 0430Q:I                                  6-23
 
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peak of I0.2 1b/sec at about 3260 seconds.The eight fog formation'rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form.FOGNSS computes the rate of fog generation by the break flow, the fog settling rate due to gravity, and the fog removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows.The input data needed to calculate each of these rates are dis-cussed as follows.0)'The rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the NRCH output for a small LOCA.The P)quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature.
peak   of I0.2 1b/sec at about 3260 seconds. The eight fog formation
According to the NRCH predic-tion the discharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds.Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam.Therefore, in the present study, it is assumed that no fog is generated by the break flow after 2172 seconds.For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed.The assumption of 10 p volume mean drop size is con-servative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.
      'rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form.
It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative.
FOGNSS computes       the rate of fog generation by the break flow, the fog settling rate due to gravity, and the fog removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as     follows.
Furthermore, no con-sideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans.All the assumptions mentioned above make the present analysis very conservative.
The   rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the NRCH output P) for a small LOCA. The quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature. According to the NRCH predic-tion       the discharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds. Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam. Therefore, in the present study,
The containment geometric data needed in computing the settling rate are given in Table 6.8.0430Q I 6-27 C 4 For fog removal by sprays, a spray flow rate of 6800 gpm was used for RcGuire.According to the HcGuire CLASIX analysis , the sprays are initiated at 124 seconds.A volume fraction of sprays (volume of sprays divided by volume of the spray zone)of 3.3 x 10 was used.As pre-viously discussed a spray removal efficiency of a 100 percent efficiency was used.In Figure 6.5, the directions of the intercompartmental flows are shown.The intercompartmental flow rates for the six flow paths and eight time steps were obtained from the OPS CLASIX analysis and are given in Table 6.9.The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another.It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.
: 0)  it   is assumed that no fog is generated by the break flow after 2172 seconds.
Figure 6.5 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions.
For fog removal by gravitational       settling,   a volume mean drop size of 10 p was assumed.       The assumption of 10 p volume mean drop size is con-servative, considering the fact that         for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.       It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative.           Furthermore, no con-sideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when           it passes through ducts and fans. All the assumptions mentioned above make the present analysis very conservative.           The containment geometric data needed in computing the settling rate are given in Table 6.8.
The fans are initiated at 694 sec-onds.The fan head-flow curve reported in Reference 28 was used to 3 compute the fan flow rates.Fan flow rates of 1000 ft/sec and 100 ft/sec were used for the air return fan and the hydrogen skimmer 3 system, respectively.
6-27 0430Q      I
These flow rates were calculated using average ap's between the upper compartment and the lower compartment, and between the dead ended region and the upper compartment.
 
It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
C 4 For fog removal by sprays, a spray flow rate of 6800 gpm was used for RcGuire. According to the HcGuire CLASIX analysis         , the sprays are initiated at 124 seconds. A volume fraction of sprays (volume of sprays divided by volume of the spray zone) of 3.3 x 10 was used. As pre-viously discussed a spray removal efficiency of a 100 percent efficiency was used.
The results of the FOGMASS calculation are shown in Figure 6.8.It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing.
In Figure 6.5, the directions of the intercompartmental flows are shown. The intercompartmental flow rates for the six flow paths and eight time steps were obtained from the OPS CLASIX analysis and are given in Table 6.9. The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.
At about 600 seconds, the lower compartment fog concentration reaches its peak of 1.6 x 10.Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases.
Figure 6.5 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions. The fans are initiated at 694 sec-onds. The fan head-flow curve reported in Reference 28 was used to compute the fan flow rates. Fan flow rates of 1000 ft /sec and 100 3
However, the upper plenum fog concentration keeps rising until about 800 seconds, 0430Q:I 6-28  
ft 3
~~0 I~I~~I'I I~~~0 WCa~~~~.~0~0~4~0~~~  
      /sec were used for the air return fan and the hydrogen skimmer system, respectively. These flow rates were calculated using average ap's between the upper compartment and the lower compartment, and between the dead ended region and the upper compartment.       It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
The     results of the FOGMASS calculation are shown in Figure 6.8. It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing. At about 600 seconds, the lower compartment fog concentration reaches its peak of 1.6 x 10 . Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases.         However, the upper plenum fog concentration keeps rising until about 800 seconds, 0430Q:I                               6-28
 
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due to an increasing fog.formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum.The upper plenum fog concentration reaches its peak of 6.4 x 10 at about 800 seconds.The lower plenum fog concentration is almost the same as the lower copartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum.Therefore, these two volumes behave as a single volume in terms of fog concentration.
due to an increasing fog.formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 6.4 x 10       at about 800 seconds. The lower plenum fog concentration is almost the same as the lower copartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum. Therefore, these two volumes behave as a single volume in terms of fog concentration.
At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and,'herefore, the fog concentrations drop sharply there-after.The effect is more pronounced for the lower compartment and lower plenum fog concentrations.
At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and,'herefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations.       The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment. The effect of sprays on the upper compartment fog concen-tration is clearly seen in Figure 6.8. At 124 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 600 seconds. At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompart-mental flow into the compartment increases sharply at that time. A peak concentration of 7.5 x 10 in the upper compartment is reached at about 1500 seconds.
The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment.
Hydrogen   starts to release into the containment at about 3804 seconds, according to the MARCH calculation         . It reaches 4 volume percent at about 4300, 4400, and 4850 seconds in the lower compartment, upper pl enum, and upper compartment, respectively.
The effect of sprays on the upper compartment fog concen-tration is clearly seen in Figure 6.8.At 124 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 600 seconds.At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompart-mental flow into the compartment increases sharply at that time.A peak concentration of 7.5 x 10 in the upper compartment is reached at about 1500 seconds.Hydrogen starts to release into the containment at about 3804 seconds, according to the MARCH calculation
At 4300 seconds, the calculated lower compartment fog concentration is 8 4 x   10,   which is about an order of magnitude smaller than the minimum   fog concentrations required for inerting 4 percent H2. At 4850 seconds,     the upper compartment fog concentration is 1.47 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*.= At the times of
.It reaches 4 volume percent at about 4300, 4400, and 4850 seconds in the lower compartment, upper pl enum, and upper compartment, respectively.
* The fog inerting criterion used is described in Section 5.2.
At 4300 seconds, the calculated lower compartment fog concentration is 8 4 x 10, which is about an order of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H2.At 4850 seconds, the upper compartment fog concentration is 1.47 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*.=At the times of*The fog inerting criterion used is described in Section 5.2.0430Q: 1 6-30 reaching 8.5 percent H2, the fog concentrations in the lower and upper compartments are even lower than the figures given above.Therefore, it is concluded that the fog concentrations in the lower and upper compart-ments are too low to have any inerting effect.The use of the present theory on fog inerting also leads to the same conclusion.
0430Q:   1                             6-30
However, at 4400 seconds, the calculated fog concentration in the upper plenum is 9.8 x 10 which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction.
 
The data shows that in order to inert 4.76 percent H2 the fog concentration niust be 8.4 x 10 or higher for 10 p volume mean drop size.At 4500 seconds, the upper plenum hydrogen concentration
reaching 8.5 percent H2, the fog concentrations in the lower and upper compartments are even lower than the figures given above. Therefore,                 it is concluded that the fog concentrations in the lower and upper compart-ments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion.
-5 reaches about 7 percent and the fog concentration is 9.3 x 10 Again, an extrapolation of the Factory Mutual data to)0 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H2.In comparison, the present theory on fog inerting pr e-dicts 1.02 x 10 for 7.2 percent H2.Therefore, it appears that it is possible to inert 7 percent H2, but unlikely.However, at 8 per-cent H2 in the upper plenum, which occurs at about 4600 seconds, the fog concentration is 9.1 x 10, which is too low to inert 8 percent An extrapolation of the Factory Mutual 8 percent H2 data to 10 4 u volume mean drop size and the present prediction give 1.9 x 10 and 1.2 x 10 for the minimum required fog incr ting concentration, respectively.
However,   at 4400 seconds, the calculated fog concentration in the upper plenum is 9.8 x 10       which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration niust be 8.4 x 10       or higher for 10 p volume mean drop size. At 4500 seconds, the upper plenum hydrogen concentration
Therefore, both the theory and the extrapolation of the'est data indicate that fog inertihg will not occur.The glow plug igniters which have been installed in the McGuire contain-ment were designed to burn hydrogen lower than 8.5 percent.As discus-sed previously, no fog inerting effects will be expected in the McGuire lower and upper compartments.
                                                                      -5 reaches about 7 percent and the fog concentration is 9.3 x 10 Again, an extrapolation of the Factory Mutual data to )0 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H2. In comparison, the present theory on fog inerting pr e-dicts 1.02 x 10 for 7.2 percent H2. Therefore,           it appears that it is possible to inert 7 percent H2, but unlikely. However, at 8 per-cent H2 in the upper plenum, which occurs at about 4600 seconds, the fog concentration is 9.1 x 10, which is too low to inert 8 percent An extrapolation of the Factory Mutual 8 percent H2 data to 10 u   volume mean drop size and the present prediction give 1.9 x 10 4 and 1.2 x 10     for the minimum required fog incr ting concentration, respectively. Therefore, both the theory and the extrapolation of           the'est data indicate that fog inertihg will not occur.
Therefore, the glow plug ignite s are expected to function as desi'gned in these two compartments.
The glow plug igniters which have been installed in the McGuire           contain-ment were designed to burn hydrogen lower than 8.5 percent. As           discus-sed   previously, no fog inerting effects will be expected   in the McGuire lower and upper compartments. Therefore, the         glow plug ignite   s are expected to function as desi'gned in these two     compartments. It may           be possibly that fog present in the ice condenser         upper plenum may prevent the glow plug ignite s from igniting hydrogen       below 7 percent. However, it   seems very unlikely that the same igniters     would fail to ignite 8.5 "The fog     inerting'criterion used is described Section 5.2.
It may be possibly that fog present in the ice condenser upper plenum may prevent the glow plug ignite s from igniting hydrogen below 7 percent.However, it seems very unlikely that the same igniters would fail to ignite 8.5"The fog inerting'criterion used is described Section 5.2.0430Q:1 6-31 percent H2 as designed, considering the fact that considerable conser-vatism has been exercised in the present analysis.0430Q:1 6-32 TABLE 6.6 FOG INPUT DATA FOR McGUIRE LOWER COMPARTMENT Lower Compartment Gas Gas Flow Rate Temp.Time (sec)(ft/sec)('F)Wall Total Temp.Pressure Steam Partial Pressure~(si a)60 510 1510 2010 2510 3260 3760 4510 1624.6 1248.1 2387.8 2393.8 1940.7 2055.-5 1801.7 1919.3 160 149 16.5 225 215 22.2 205 198 21.9 205 198 22 195 193'21.5 200 195 21.6 200 , 194 21 250 222 21.2 18.3 12.6 12.4 10.4 10.8 9.3 7.3 0430/:1 6-33 TABLE 6.7 FOG IHPUT DATA FOR HcGUIRE ICE COHDEHSER Ice Condenser Gas Flow Rate Time (sec)(ft/sec)Steam Gas Ice Total Parti al Temp.Temp.Pressure Pressure 60 510 1510 2010 2510 3260 3760 4510 820.5 107.1 1926 1637 1145 1630 1514 1464 90 130 190 193 188 195 193 192 32 32 32 32 32 32 32 32 16.5 22.2"21.9 22 21.4 21.6 21.1 22.1 2.3 9.3 8.6 10.3 8.1 7.1 0430Q:1 6-34 TABLE 6.8 GEOMETRIC DATA FOR McGUIRE CONTAINMENT
0430Q:1                                 6-31
'I Volume (ft)Floor Area (ft)Lower Compartment 237,400 5,410 Ice Condenser Lower Plenum 24,200 3,100 Ice Condenser Upper Plenum 47,000 3,200 Upper Compartment 670,000 10,390 Dead Ended Region 130, 900 3,350 0430Q:1~6-35 l
 
TABLE 6.9 IHTERCOMPARTMEHTAL FLOW RATES (ft/sec)3 PREDICTED BY CLASIX FOR McGUIRE Time (sec)Flow From flow From Flow From Flow From Flow from LC to LP LP to UP UP to UC UC to LC DE to LC 6.001E1 5.100E2 1.510E3 2.010E3 2.510E3 3.260E3 3.760E3 4.510E3 1.351E3 8.716E2 2.008E3 2.010E3 1.722E3 1.713E3 1.546E3 1.634E3 8.205E2 1.071E2 1.926E3 1.637E3 1.145E3 1.630E3 1.514E3 1.464E3-1.198E2-1.538E2-2.863E1-3.479E2-1.900E2-1.898E2-2.266E2,-1.572E2 5.783E2 ,-2.269E1 8.635E2 6.869E2 4.807E2 6.666E2 7.231E2-1.410E2-2.087E2-7.767E1-1.338E2-1.289E2-1.268E2 7.640E2-1.328E2-1.515E2 0430Q:1 6-36 6.4 FOG INERTING PROBABILITY IN THE D.C.COOK PLANT f'he computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the D.C.Cook plant.FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the D.C.Cook ice condenser and lower plenum.Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the D.C.Cook containment subcompartments.
percent H2 as designed, considering the fact that considerable conser-vatism has been exercised in the present analysis.
To compute the, fog formation rates in the ice condenser upper plenum and lower compartment, some'output data from the Cook CLASIX analysis (29)are needed.These data include time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each contain-ment subcompartment, as well as the intercompartmental and fan flow rates.In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 29.The subcompartmentalization model used in the Cook CLASIX analysis is shown in Figure 6.9.In this study only the S20 accident scenario has been analyzed.The FOG input data for Cook S2D Case.1 are given in Tables 6.10 and 6.11, and the calculational results ar e shown in Figures 6.10 and 6.11.'n Figure 6.10, the fog formation rate in the lower compartment is shown.It is seen that the fog formation rate is negligibly small.It should be noted that the calculation of the lower compartment fog concentration in the 0.C.Cook plant starts at 600 seconds instead of 60 seconds used for the other two plants.The fog formation rate in the lower compartme starts to increase at about 4200 seconds because of the increase in the steam partial pressure.It reaches 0.017 lb/sec at about 4590 seconds.Fog formation in the lower compartment will stop after 4700 seconds because of the hydrogen burn thereafter.
6-32 0430Q:1
The fog formation rate in the ice condenser is shown in Figure 6.11.It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment.
 
It increases with the ice condenser steam flow rate and reaches a peak of about 15.6 lb/sec at about 1200 seconds.The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen release.0430Q 1 6-37
TABLE 6.6   FOG INPUT DATA FOR McGUIRE LOWER COMPARTMENT Steam Lower Compartment   Gas     Wall    Total      Partial Gas Flow Rate       Temp. Temp. Pressure  Pressure Time (sec)     (ft /sec)             ('F)                       ~(si a) 60               1624.6         160      149      16. 5 510                1248.1         225      215    22.2      18. 3 1510              2387.8           205      198    21.9      12. 6 2010                2393.8           205      198    22        12.4 2510                1940.7           195      193    '21.5      10.4 3260                2055.-5         200      195    21.6      10.8 3760                1801.7           200    , 194    21          9.3 4510                1919.3           250      222    21.2       7.3 6-33 0430/:1
~~~~~~~0 o~0~~0~l~0~~~~~~~c~+j~~~~~~'J~'~~~  
 
TABLE 6.7  FOG IHPUT DATA FOR HcGUIRE ICE COHDEHSER Steam Ice Condenser        Gas      Ice    Total      Parti al Gas Flow Rate        Temp. Temp. Pressure  Pressure Time (sec)  (ft /sec) 60            820. 5            90      32      16.5 510            107. 1          130      32      22.2        2.3 1510            1926            190      32      "21.9        9.3 2010            1637            193      32      22 2510            1145            188      32      21.4        8.6 3260            1630            195      32      21. 6     10.3 3760            1514            193      32      21. 1      8.1 4510              1464            192      32      22.1        7.1 6-34 0430Q:1
 
TABLE 6.8 GEOMETRIC DATA FOR McGUIRE CONTAINMENT
                                                              'I Volume    (ft )    Floor Area  (ft )
Lower Compartment                    237,400            5,410 Ice Condenser Lower Plenum                          24,200            3,100 Ice Condenser Upper Plenum                          47,000            3,200 Upper Compartment                    670,000            10,390 Dead Ended Region                    130, 900            3,350
                                  ~ 6-35 0430Q:1
 
l TABLE 6.9  IHTERCOMPARTMEHTAL FLOW RATES    (ft3 /sec)
PREDICTED BY CLASIX FOR McGUIRE Time    Flow From    flow From      Flow From  Flow From      Flow from (sec)   LC  to LP    LP to UP      UP  to  UC UC  to LC      DE  to LC 6.001E1  1. 351E3      8.205E2        5.783E2  -1. 198E2      -1. 538E2
: 5. 100E2 8.716E2      1.071E2      , -2. 269E1  -2.863E1      -3.479E2
: 1. 510E3 2.008E3      1. 926E3        8.635E2  -1. 900E2      -1.898E2 2.010E3  2.010E3      1. 637E3        6.869E2  -2.266E2,      -1.572E2
: 2. 510E3 1.722E3      1. 145E3        4.807E2  -1. 410E2      -7. 767E1 3.260E3  1.713E3       1. 630E3        6.666E2  -2.087E2      -1.338E2 3.760E3  1.546E3      1. 514E3        7. 231E2  -1.289E2      -1.268E2
: 4. 510E3 1.634E3      1. 464E3        7. 640E2  -1. 328E2      -1. 515E2 6-36 0430Q:1
 
6.4    FOG  INERTING PROBABILITY IN THE D. C. COOK PLANT f'he computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the D. C. Cook plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the D. C. Cook ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the D. C. Cook containment subcompartments.
To compute    the, fog formation rates in the ice condenser upper plenum and lower compartment, some'output data from the Cook CLASIX analysis (29) are needed. These data include time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each contain-ment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 29. The subcompartmentalization model used in the Cook CLASIX analysis is shown in Figure 6.9. In this study only the S20 accident scenario has been analyzed.
The  FOG  input data for Cook S2D Case .1 are given in Tables 6.10 and 6.11, and the calculational results ar e shown in Figures 6.10 and    6.11.'n Figure 6.10, the fog formation rate in the lower compartment is shown. It is seen that the fog formation rate is negligibly small. It should be noted that the calculation of the lower compartment fog concentration in the 0 . C. Cook plant starts at 600 seconds instead of 60 seconds used for the other two plants.      The fog formation rate in the lower compartme starts to increase at about 4200 seconds because of the increase in the steam partial pressure.       It reaches 0.017 lb/sec at about 4590 seconds. Fog formation in the lower compartment will stop after 4700 seconds because of the hydrogen burn thereafter. The fog formation rate in the ice condenser is shown in Figure 6.11. It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment. It increases with the ice condenser steam flow rate and reaches a peak of about 15.6 lb/sec at about 1200 seconds.      The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen release.
0430Q    1                              6-37
 
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                                ~  ~ ~ 0 o ~
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                                ~  l ~ 0
                              ~  ~ ~
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I  I I II I I  I I I  I I I  I I I  I II e I
 
I I I' I I II I  II II I Il I I III I I
 
The eight fog formation rates in the lower compartment        and  in the ice
. condenser are input to FOGMASS in a tabular form.
.:  FOGMASS  computes the     rate of fog generation  by the break  flow, the fog settling rate due to gravity, and the fog-removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as follows.
The  rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the MARCH output P) for a small LOCA. The
                        'I quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature.        According to the MARCH predic-tion P)  the di,scharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds.        Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam. Therefore, in the present study, it  is assumed that no fog is generated by the break flow after 2172 seconds.
For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed.      The assumption of 10 p volume mean drop size is con--
servative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.      It  should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis even more conservative.            Further-more, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when    it passes through ducts and fans. All the assumptions men-tioned above make the present analysis very conservative. The contain-ment geometric data needed in computing the settling rate are given in Table 6.12.
0430Q:I                                      6-41
 
C For fog removal by sprays, spray flow rates of 4000, 1800, and 528 gpm were used for the upper compartment, lower compartment, and fan/accumulator rooms, respectively. According to the Cook CLASIX analysis~   ~, the sprays are initiated at 141 seconds. A volume fraction of sprays '(volume of sprays divided by volume of the spray zone) of 3.3 x 10-4 was used. As previously discussed a spray removal efficiency of  a 100 percent efficiency  was used.
In Figure 6.9, the directions of the intercompartmental flows are shown. The intercompartmental flow rates for the six flow paths and eight time steps 'were obtained from the OPS CLASIX analysis and are given in Table 6. 13. The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those:in the compartments from which the flows are originated.
Figure 6.9 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions. The fans are initiated at 711 sec-onds. The fan head-flow curve reported in Reference 29 was used to compute the fan flow rates. Fan flow rates of 1388, 61.76, and 4.13 ft3/sec were used for the flows from the upper compartment, lower compartment, and dead ended region to the fan/accumulator rooms, respectively. These flow rates were calculated using the hp's between the the fan/accumulator rooms and three other compartments.      It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
The  results of the FOGMASS calculation are shown in Figure 6.12. It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, and the ice condenser lower plenum are high. At about 140 seconds, the lower compartment fog concentration reaches its peak of 1 x 10-4. After the sprays are initiated at 141 seconds, the fog concentrations in the lower compartment, upper compartment, and fan/accumulator rooms drop sharply. However, the upper plenum fog concentration keeps rising until about 1200 seconds,'ue to an increasing 0430Q:1                                6-42
 
I                  I I I  I  ~
I    ~ ~    ~  T ~
T ~ ~
I  ~
I          ~  ~ I
 
'l fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 2.4 x 10        at about 1200 seconds.
After about 1200 seconds, the lower plenum fog concentration is almost the same as the lower copartment fog concentration since the intercompartmental flows quickly make the fog concentrations in these two compartments    uniform. Therefore, these two volumes behave    as a single volume in terms of fog concentration.
At  2172 seconds,  the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations.      The highest fog concentration exists in the ice condenser upper plenum. The effect of sprays on the upper compartment fog concentration is clearly seen in Figure 6.12. At 141 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 300 seconds. At about 300 seconds, the upper compartment fog concentration starts to increase again because the intercompartmental flow into the compartment increases
                                                              -6 sharply at that time. A peak concentration of 9.5 x 10          in the upper compartment is reached at about 1400 seconds.
Hydrogen    starts to release into the containment at about 3804 seconds, according to the HARCH calculation          . It reaches 4 volume percent at about 4350, 4370, and 4700 seconds in the lower compartment, upper plenum, and upper compartment, respectively.
At 4350 seconds, the calculated lower compartment fog concentration is 10 , which is about two orders of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H . At 4700
                                                                    -6 seconds, the upper compartment fog concentration is 2.4 x 10 , which is about a factor of two smaller than the minimum fog concentration required for inerting 4 percent H *. At the times of reaching 8.5
* The fog  inerting criterion used  is described in Section 5.2.
0430Q:1                                6-44


I I I II I I I I I I I I I I I I II e I I
percent   H , the fog concentrations in the lower and upper compartments are even lower than the figures given above. Therefore,         it is concluded that the fog concentrations in the lower and upper compartments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion.
I I'I I II I II I I I Il I I I I I I I The eight fog formation rates in the lower compartment and in the ice.condenser are input to FOGMASS in a tabular form..: FOGMASS computes the rate of fog generation by the break flow, the fog settling rate due to gravity, and the fog-removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows.The input data needed to calculate each of these rates are dis-cussed as follows.The rate of reactor coolant release to the containment and the coolant'I P)enthalpy were obtained from the MARCH output for a small LOCA.The quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature.
However, at 4370 seconds,       the calculated fog concentration in the upper plenum is 6.5 x 10       which's higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10         or higher for 10 p volume mean drop size. At 4530 seconds, the upper plenum hydrogen concentration
According to the MARCH predic-tion the di,scharge of liquid by the break flow into the lower com-P)partment lasts for only 2172 seconds.Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam.Therefore, in the present study, it is assumed that no fog is generated by the break flow after 2172 seconds.For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed.The assumption of 10 p volume mean drop size is con--servative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially.
                                                                      -5 reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10         or higher is required to inert 7.2 percent H2. In comparison the present theory of fog inerting predicts 1.02 x 10       for 7.2 percent H2. Therefore,   it appears that   it is possible to inert 7 percent H2, but unlikely. However, at 8 percent H2 in the upper plenum, which occurs at about 4600 sec'onds, the fog
It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis even more conservative.
                              -5 concentration is 5.1 x       10,   which is too low to inert 8 percent H2. An extrapolation of the Factory Mutual 8 percent H data to 10 4
Further-more, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans.All the assumptions men-tioned above make the present analysis very conservative.
u volume mean drop size and the present prediction give 1.9 x 10             and 1.2 x   10     for the minimum required fog inerting concentration, respectively.
The contain-ment geometric data needed in computing the settling rate are given in Table 6.12.0430Q:I 6-41 C
The glow plug igniters which have been installed in the Cook containment were designed to burn hydrogen lower than 8 percent.         As discussed pre-viously,   no   fog inerting effects will be expected in the Cook lower and upper compartments.       Therefore, the glow plug igniters are expected to function as designed in these two compartments.         It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent. However,           it seems very unlikely that the same igniters would fail to ignite 8 percent H2 as designed, considering the fact that considerable conservatism has been exercised in the present analysis.
For fog removal by sprays, spray flow rates of 4000, 1800, and 528 gpm were used for the upper compartment, lower compartment, and fan/accumulator rooms, respectively.
0430Q   1                                 6-45
According to the Cook CLASIX analysis~~, the sprays are initiated at 141 seconds.A volume fraction of sprays'(volume of sprays divided by volume of the spray zone)of 3.3 x 10-4 was used.As previously discussed a spray removal efficiency of a 100 percent efficiency was used.In Figure 6.9, the directions of the intercompartmental flows are shown.The intercompartmental flow rates for the six flow paths and eight time steps'were obtained from the OPS CLASIX analysis and are given in Table 6.13.The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another.It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those:in the compartments from which the flows are originated.
Figure 6.9 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions.
The fans are initiated at 711 sec-onds.The fan head-flow curve reported in Reference 29 was used to compute the fan flow rates.Fan flow rates of 1388, 61.76, and 4.13 ft3/sec were used for the flows from the upper compartment, lower compartment, and dead ended region to the fan/accumulator rooms, respectively.
These flow rates were calculated using the hp's between the the fan/accumulator rooms and three other compartments.
It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.
The results of the FOGMASS calculation are shown in Figure 6.12.It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, and the ice condenser lower plenum are high.At about 140 seconds, the lower compartment fog concentration reaches its peak of 1 x 10-4.After the sprays are initiated at 141 seconds, the fog concentrations in the lower compartment, upper compartment, and fan/accumulator rooms drop sharply.However, the upper plenum fog concentration keeps rising until about 1200 seconds,'ue to an increasing 0430Q:1 6-42 I I I~T~~I~~I~I I I~T~~~I
'l fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum.The upper plenum fog concentration reaches its peak of 2.4 x 10 at about 1200 seconds.After about 1200 seconds, the lower plenum fog concentration is almost the same as the lower copartment fog concentration since the intercompartmental flows quickly make the fog concentrations in these two compartments uniform.Therefore, these two volumes behave as a single volume in terms of fog concentration.
At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after.The effect is more pronounced for the lower compartment and lower plenum fog concentrations.
The highest fog concentration exists in the ice condenser upper plenum.The effect of sprays on the upper compartment fog concentration is clearly seen in Figure 6.12.At 141 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 300 seconds.At about 300 seconds, the upper compartment fog concentration starts to increase again because the intercompartmental flow into the compartment increases-6 sharply at that time.A peak concentration of 9.5 x 10 in the upper compartment is reached at about 1400 seconds.Hydrogen starts to release into the containment at about 3804 seconds, according to the HARCH calculation
.It reaches 4 volume percent at about 4350, 4370, and 4700 seconds in the lower compartment, upper plenum, and upper compartment, respectively.
At 4350 seconds, the calculated lower compartment fog concentration is 10 , which is about two orders of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H.At 4700-6 seconds, the upper compartment fog concentration is 2.4 x 10 , which is about a factor of two smaller than the minimum fog concentration required for inerting 4 percent H*.At the times of reaching 8.5*The fog inerting criterion used is described in Section 5.2.0430Q:1 6-44 percent H , the fog concentrations in the lower and upper compartments are even lower than the figures given above.Therefore, it is concluded that the fog concentrations in the lower and upper compartments are too low to have any inerting effect.The use of the present theory on fog inerting also leads to the same conclusion.
However, at 4370 seconds, the calculated fog concentration in the upper plenum is 6.5 x 10 which's higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction.
The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10 or higher for 10 p volume mean drop size.At 4530 seconds, the upper plenum hydrogen concentration
-5 reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H2.In comparison the present theory of fog inerting predicts 1.02 x 10 for 7.2 percent H2.Therefore, it appears that it is possible to inert 7 percent H2, but unlikely.However, at 8 percent H2 in the upper plenum, which occurs at about 4600 sec'onds, the fog-5 concentration is 5.1 x 10, which is too low to inert 8 percent H2.An extrapolation of the Factory Mutual 8 percent H data to 10 4 u volume mean drop size and the present prediction give 1.9 x 10 and 1.2 x 10 for the minimum required fog inerting concentration, respectively.
The glow plug igniters which have been installed in the Cook containment were designed to burn hydrogen lower than 8 percent.As discussed pre-viously, no fog inerting effects will be expected in the Cook lower and upper compartments.
Therefore, the glow plug igniters are expected to function as designed in these two compartments.
It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent.However, it seems very unlikely that the same igniters would fail to ignite 8 percent H2 as designed, considering the fact that considerable conservatism has been exercised in the present analysis.0430Q 1 6-45 TABLE 6.10 FOG INPUT DATA FOR D.C.COOK LOWER COMPARTMENT Time (sec)Lower Compartment Gas Wal 1 Total Gas Flow Rate Temp..Temp.Pressure (ft/sec)('F)('F)~(sia)Steam Partial Pressure.~(si a)600 1200 1800 2400 3000 3600 4200 4590 799.4 2798.2 , 2805.8 2513.6 2448.5 2359.7 2272.3 2482.7 222 190 190 180 178 175 165 168 215.2 183.5 180.3 177.2 170.4 169.3 21.8 20.2 20 19.6 19.3 19.2 161.9 18.8 161 19,5 17.4 9.4 9.1 7.6 7.2 6.4 5.3 5.8 0430Q:1 6-46


TABLE 6.11 FOG INPUT DATA FOR D.C.COOK ICE CONDENSER Ice Condenser Gas Flow Rate Time (sec)(f t/sec)3 Gas Temp.('F)Ice Temp~('F)Total Pressure~(si a)Steam Partial Pressure~(si a)600 1200 1800 2400 3000 3600 4200 4590 76 2548 2572 2359 2256 2199 2126 2312 147 190 188 184 187 175 166 163 32 32 32 32 32 32 32 32 21.8 20.1 19.9 19.7 19.3 19.2 18.8 19'.8 3.4 9.3 9.0 7.9 7.1 6.6 5.3 4.3 0430Q:I 6-47 TABLE 6.12 GEOMETRIC DATA FOR D.C.COOK CONTAINMENT Volume (ft)Floor Area (ft)Lower Compartment 249,681 5,410 Ice Condenser Lower Plenum 24,700 3,100 Ice Condenser Upper Plenum 47,010 3,200 Upper Compartment 681,283 10,390 Dead Ended Region Fan/Accumulator Rooms 61,105 54,828 853 2,500 0430Q:I 6-48 TABLE 6.13 INTERCOMPARTMENTAL FLOW RATES (ft/sec)PREDICTED BY CLASIX FOR D.C.COOK Time (sec)Flow From Flow From Flow From Flow From Flow From Flow From LC to LP LP to UP UP to UC UC to LC DE to LC F/A to LC 600 1200 1800 2400 3000 3600 4200 4590 6.387E2 2.577E3 2.600E,3 2.356E3;2.273E3 2.202E3 2.136E3 2.346E3 7.600E1 2.548E3 ,2.572E3 2.359E3 2.256E3 2.199E3 2.126E3 2.312E3-4.410E1 1.106E3 1.155E3 1.145E3 1.178E3 1.190E3 l.258E3 1.400E3-3.746E1'1.740E2-1.232E2-4.720E1-1.620E 2-4.381E 1-1.325E2-2.512E1-1.463E2-2.923E1-1.334E2-2.333E1-1.183E2-1.802E1-1.130E2-2.371E1-1.229E2 1.509E3 1.529E3 1.595E3 1.553E3 1.603E3 1.642E3 1.650E3 0430Q:I 6-49
TABLE 6.10  FOG INPUT DATA FOR D. C. COOK LOWER COMPARTMENT Steam Lower Compartment    Gas     Wal 1  Total      Partial Gas  Flow Rate       Temp.. Temp. Pressure  Pressure .
Time (sec)   (ft /sec)             ('F)     ('F)   ~(sia)     ~(si a) 600               799.4          222      215.2  21. 8     17.4 1200              2798.2          190      183.5  20.2       9.4 1800            , 2805.8           190      180.3   20          9.1 2400              2513.6           180      177.2  19. 6       7.6 3000               2448.5          178      170.4  19.3       7.2 3600              2359.7           175      169.3  19. 2       6.4 4200              2272.3          165      161.9  18.8        5.3 4590              2482.7          168      161    19,5        5.8 0430Q:1                            6-46


6.5 EFFECT OF FOG ON GLOBAL COMBUSTION In order to assess the effect of fog on the deflagration limit of hydro-gen, which is defined as the minimum hydrogen concentration at which the flame propagates in, all directions, a flame temperature criterion which considers fog droplets as a heat sink was used.This criterion assumes that the critical flame temperature of 710 C is still applicable to a hydrogen mixture which contains fog droplets.For a given fog concen-tration, the heat required to heat a unit mass of the mixture to 710 c can be calculated.'hen the hydrogen concentration needed to supply this amount of heat, assuming 100 percent combustion, can be deter-mined.Using this method, the calculated fog concentrations of 5.5 x 10 and 5.1 x 10 for the Sequoyah plant at 4650 seconds and for the D.C.Cook Plant at 4600 seconds, respectively, were found to be capable of raising the deflagration limit to 10.6 vol.percent H2.In-5 comparison, the calculated fog concentration of 9.1 x 10 for the McGuire plant at 4600 seconds was found to be capable of raising the deflagration limit to 12 vol.percent H2.This study shows that in order to achieve global combustion in the upper plenum, hydrogen concen-tration higher than 8.5 percent may be required.The effect of increas-ing hydrogen concentration required to obtain global combustion in.the upper plenum should be investigated.
TABLE  6. 11    FOG INPUT DATA FOR D. C. COOK ICE CONDENSER Steam Ice Condenser          Gas      Ice    Total      Partial Gas Flow Rate          Temp. Temp  ~ Pressure  Pressure Time ( sec)    ( ft 3
F 0430Q:1 6-50 7.0  
                        /sec)            ('F)      ('F)  ~(si a)    ~(si a) 600                    76            147      32    21. 8        3.4 1200                  2548            190      32      20. 1      9.3 1800                  2572            188      32      19.9        9.0 2400                  2359            184      32      19.7        7.9 3000                  2256            187      32      19.3        7.1 3600                  2199            175      32      19.2        6.6 4200                  2126            166      32      18.8        5.3 4590                  2312              163      32      19'.8      4.3 0430Q:I                                  6-47
 
TABLE 6.12 GEOMETRIC DATA FOR D. C. COOK CONTAINMENT Volume  (ft )      Floor Area  (ft )
Lower Compartment                  249,681              5,410 Ice Condenser Lower Plenum                        24,700              3,100 Ice Condenser Upper Plenum                        47,010              3,200 Upper Compartment                  681,283            10,390 Dead Ended Region                    61,105                853 Fan/Accumulator  Rooms              54,828              2,500 0430Q:I                              6-48
 
TABLE  6.13    INTERCOMPARTMENTAL FLOW RATES  (ft /sec)
PREDICTED BY CLASIX FOR D. C. COOK Time  Flow From      Flow From    Flow From    Flow From  Flow From Flow From (sec)  LC  to  LP    LP  to  UP  UP  to UC    UC  to LC  DE  to LC  F/A to  LC 600  6.387E2        7. 600E1    -4.410E1    -3.746E1    -1. 232E2  -1. 229E2 1200  2. 577E3      2. 548E3      1. 106E3  '1.740E2      -4.720E1    1. 509E3 1800  2. 600E,3    ,2.572E3      1.155E3    -1. 620E 2  -4. 381E 1  1. 529E3 2400  2.356E3    ;  2.359E3      1.145E3    -1.325E2    -2.512E1    1. 595E3 3000  2.273E3        2.256E3      1. 178E3    -1. 463E2  -2. 923E1  1.553E3 3600  2.202E3        2.199E3      1. 190E3    -1.334E2    -2.333E1    1.603E3 4200  2.136E3        2.126E3      l. 258E3    -1. 183E2  -1. 802E1  1.642E3 4590  2.346E3        2.312E3      1.400E3    -1. 130E2  -2. 371E1  1.650E3 0430Q:I                              6-49
 
6.5  EFFECT OF FOG ON GLOBAL COMBUSTION In order to assess the effect of fog   on the deflagration   limit of hydro-gen, which   is defined as the minimum hydrogen concentration at which the flame propagates in, all directions, a flame temperature criterion which considers fog droplets as a heat sink was used. This criterion assumes that the critical flame temperature of 710 C is still applicable to a hydrogen mixture which contains fog droplets. For a given fog concen-tration, the heat required to heat a unit mass of the mixture to 710 c can be   calculated.'hen     the hydrogen concentration needed to supply this amount of heat, assuming 100 percent combustion, can be deter-mined. Using this method, the calculated fog concentrations of 5.5 x 10     and 5.1 x 10   for the Sequoyah plant at 4650 seconds and for the D. C. Cook Plant at 4600 seconds, respectively, were found to be capable of raising the deflagration limit to 10.6 vol. percent H2. In
                                                                -5 comparison, the calculated fog concentration of 9.1 x 10         for the McGuire plant at 4600 seconds was found to be capable of raising the deflagration limit to 12 vol. percent H2. This study shows that in order to achieve global combustion in the upper plenum, hydrogen concen-tration higher than 8.5 percent may be required. The effect of increas-ing hydrogen concentration required to obtain global combustion in .the upper plenum should be investigated.
F 0430Q:1                               6-50
 
7.0  


==SUMMARY==
==SUMMARY==
AND CONCLUSIONS The present study has developed a systematic methodology to study the potential fog inerting problem for the PWR ice condenser plants.In the present investigation, major fog formation and removal mechanisms are identified and quantified.
AND CONCLUSIONS The present study has developed a systematic methodology to study the potential fog inerting problem for the PWR ice condenser plants. In the present investigation, major fog formation and removal mechanisms are identified and quantified. Theoretical models are developed to predict the fog formation rate due to boundary layer and bulk stream condensa-tion, the fog removal rates due to gravitational settling and contain-ment sprays. The mass conservation equations for the fog droplets in each of the containment subcompertments are solved simultaneously in order to obtain time histories of fog concentration. These equations incorporate fog formation due to condensation, fog generation due to break flow, fog removal due to gravitational settling and sprays, trans-port of fog by the intercompartmental flows and fan flows. Computer programs FOG and FOGMASS have been developed to compute fog formation rates and fog concentrations in each of the containment subcompart-ments. These two computer programs have been used to analyze a S<D accident sequence for the Sequoyah, McGuire, and D.C. Cook plants. The analyses employed output data from the Sequoyah CLASIX analyses.       Speci-fically, time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates were used in the present analysis.
Theoretical models are developed to predict the fog formation rate due to boundary layer and bulk stream condensa-tion, the fog removal rates due to gravitational settling and contain-ment sprays.The mass conservation equations for the fog droplets in each of the containment subcompertments are solved simultaneously in order to obtain time histories of fog concentration.
A fog inerting   criterion has been developed to predict the minimum fog concentration required to inert a given hydrogen concentration and volume mean fog drop size. The present fog inerting criterion has been shown to be in agreement with the Factory Mutual data.       The criterion shows that the minimum fog inerting concentration varies with the square of the volume mean fog drop size.
These equations incorporate fog formation due to condensation, fog generation due to break flow, fog removal due to gravitational settling and sprays, trans-port of fog by the intercompartmental flows and fan flows.Computer programs FOG and FOGMASS have been developed to compute fog formation rates and fog concentrations in each of the containment subcompart-ments.These two computer programs have been used to analyze a S<D accident sequence for the Sequoyah, McGuire, and D.C.Cook plants.The analyses employed output data from the Sequoyah CLASIX analyses.Speci-fically, time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates were used in the present analysis.A fog inerting criterion has been developed to predict the minimum fog concentration required to inert a given hydrogen concentration and volume mean fog drop size.The present fog inerting criterion has been shown to be in agreement with the Factory Mutual data.The criterion shows that the minimum fog inerting concentration varies with the square of the volume mean fog drop size.The present study shows that the fog concentrations in the upper and lower compartments of the three plants analyzed are too low to have any inerting effect on hydrogen mixtures.Therefore, the proposed glow plug igniters are expected to function as designed in these two compart-ments.It may be possible that fog present in the ice condenser upper 0430Q: I 7-1  
The present   study shows that the fog concentrations in the upper and lower compartments of the three plants analyzed are too low to have any inerting effect on hydrogen mixtures. Therefore, the proposed glow plug igniters are expected to function as designed in these two compart-ments. It may be possible that fog present in the ice condenser upper 7-1 0430Q:  I
 
plenum may prevent the glow plug    igniters from igniting hydrogen below  7 percent. ~ However, it seems
                      ~
very unlikely that the same igniters  would fail to ignite  8.5 percent
                  ~
H2 as designed.
It should  be recognized  that the existing theories and data can only predict the minimum fog concentration for inerting. Further work may      be required to verify the fog inerting theory associated with flame propagation in all directions.
7-2 0430Q:I
 
A CKNOWL EDGME NTS The  author wishes to express his sincere gratitude to Mr. N.J. Liparulo, Dr s. Y. Srinivas, B. Lewis, and B. Karlovitz for assistance,  sugges-tions, and helpful discussions, particularly in the area of the fog inerting criteria and the flame temperature criteria for fog, to Messrs. D. F. Paddleford, R. Bryan, F. G. Hudson, and K. Shiu for valuab1e.comnents, to Mr. K. C. Perry, Mr. S. J. Reiser, and Ms.,R. M. Mariner for providing data on the three ice condenser plants, and to Mr. T. J.,Miele for providing pr ogramming assistance.
He  also would like to thank TYA, Duke Power, and  AEP for providing the financial support.
0430Q:1                              7-3
 
REFERENCES
: 1. B. Lowry,  "Preliminary Results: A Study of Hydrogen Igniters,"
ENNBO-45;  Lawrence Livermore National Laboratory, November 17, 1980.
: 2.  "Additional guestions on Hydrogen Control System for Ice Condenser Plants," NRC memo from L. Rubenstein to R. Tedesco, dated June 26, 1981.
: 3.  "The Marvikken  Full Scale Containment Experiments,"  MXB-301 AB Atomenergi, March, 1977.    *
: 4. T. F. Kanzleiter, "LOCA Experiments With a PWR Multi-Compartment Model Containment," Trans. 1977 LWR Safety Conf., Idaho Falls, Idaho, 1977.
: 5. G.'M. Fuls, "The CLASIX Computer Program    for the  Hydrogen Release and Degradation", OPS-07A35, Offshore Power Systems, 1981.
: 6. K. K. Almenas, "The Physical    State of Post-Loss-of-Coolant Accident Containment Atmospheres," Vol. 44, Nuclear Technology, pp. 411.-427, August, 1979.
: 7.  "Summary  of Analysis of Ice Condenser Containment Response to Hydro-gen  Transients," Offshore Power Systems report No. RP-28A52, Septem-ber, 1980.
: 8. R. Brown and  J. L. York, "Sprays Formed by Flashing Liquid Jets,"
Vol. 8, No. 2, AICh.E Journal, p. 149, May, 1962.
(
: 9. R. G. Gido, and A. Koestel, "LOCA-Generated Drop Size Prediction - A Thermal Framentation Model," Trans. Am. Nucl. Soc., 30, p. 371. 1978.
: 10. P. G. Hill, H. Witting,  and E. P. Demetri, "Condensation  of Metal Vapors During Rapid    Expansion," Journal of Heat Transfer, p. 303, November, 1963.
R-1 0430/:1
: 11. M. Volmer and H. Flood, Z. Physik Chemic, A170, p. 273, 1934.
: 12. C. E. Junge, Advan. Geophys.,    H. Landsberg and  J. Van Mieghem, ed.,
4.1, Academic Press,  New York, 1958.
: 13. R. J. Burian, and P. Cybulskis, "CORRAL    II User  Manual," Battelle Columbus Laboratories, January, 1977.
: 14. R. K. Hilliard and L. F. Coleman, "Natural Transport Effects on Fission Product Behavior in the Containment Systems Experiment,"
BNWL-7457, Battelle-Northwest, Richland, Washington, 1970.
: 15. N. H. Fletcher, J. Chem. Phys., 29, p. 572; 31, p. 1136, 1958.
: 16. D. E. Rosner and M. Epstein, "Fog Formation Conditions Near Cold Surfaces," Vol. 28, No. 1, J. of Colloid and Interface Sci., Septem-ber, 1968.
: 17. K. Hijikata,  and Y. Mori, "Forced Convective Heat Transfer of a    Gas With Condensing Vapor Around a Flat Plate," Vol. 2, No. 1, Heat Transfer - Jap. Res., pp. 81-101, January, 1973.
: 18. M. Neiburger and C. W. Chien, "Computation      of the Growth of Cloud Drops by Condensation Using an Electronic Digital Computer,"
Geophys. Monograph No. 5, pp. 191-209, 1960.
: 19. R. M. Kemper,    "Iodine  Removal by Spray  in the  Salem  Station Contain-ment," WCAP-7952, Westinghouse    Electric Corp., August,    1972.
: 20. N. J. Liparulo, J. E. Olhoeft and D. F. Paddleford, "Glow Plug Ignitor Tests in H2 Mixtures," WCAP-5909, Westinghouse Electric Corp., March 6, 1981.
: 21. R. G. Zalosh and S. N. Bajpai, "Water Fog Inerting of Hy'drogen -    Air Mixtures," EPRI Project Preliminary Rp. 1932-1, September, 1981.
0430Q:I
 
22.~ J. M. Marchello, "Control of Air Pollution Source," Marcel Dekker,
        ~
Inc., Hew York, 1976.
          ~            ~
                            ~
: 23. Letter from    B. Lewis and B. Karlovitz to L. E. Hochreiter, dated  may 5, 1980.
: 24. M. Berman,    et al., "Analysis of Hydrogen Mitigation for Degraded Core Accidents in the Sequoyah Nuclear Power Plant," Sandia draft report, December 1, 1980.
: 25. T. von Karman', Unpublished notes, 1956.
: 26. S. S. Tsai, "Flame Temperature      Criteria Tests,"  HS-CCA-81-039, West-inghouse  internal  memo,  dated June 17, 1981.
: 27. Attachment    to Offshore  Power System  letter PST-HE-109, dated May 22, 1981.
: 28. Attachment    to Offshore  Power System  letter PST-NE-106, dated May 14, 1981.
: 29. Attachment to Offshore Power System        letter  PST-HE-218, dated August 6, 1981.
: 30. M. L. Corrin,      J. R. Connel, and A. J. Gero,  "An Assessment  of Warm Fog  - Nucleation, Control,  and Recommended  Research," NASACR-2477, November, 1974.
0430Q:1                                R-3
 
APPENDIX A I
C 0 MP U TAT 0N    0F Y o
AND g  IN  E Q UATI 0 N {3 1 2 )
The  Hijikata-Mori fog formation theory                    used the boundary layer approximation for the continuity, momentum, and energy equations. The fog concentration and velocity profiles in the boundary layer are assumed in Eqs. (3.7) and (3.S).                Substituting Eqs. (3.7) through (3.10) into the conservation equations, we have 3      3          7 Y
o
                                      +vcaI =0                                        (A-1)
V
        -(    +      )~ -m'rr <'m " 'm< V-'-'
3        7          1 (A-2) 9      9        311,'-'
mm ".                    -  3 z " ') xI                      (A-3)
A(n)+B(n) g+                  C(n)+~E    7 Y
              =g)p--
                'F)Pr        V o
                                  -  V o
(1+E)      Y 0
(A-4) where A    (n)-              3  (n+ 5) n+        n+
B(n)    =            3  (n+ 6) n+            n+        n+
C(n)    =            3  (n+    7) bW 2 hW h
E    =Hr  Pg 0430Q:1                                            A-1
 
0 6 v vl 00 weight fraction of vapor at free stream W
0 weight fraction of vapor at wall aW        W'-W S        Schmidt number kinetic vi scosity component  of the free stream velocity perpendicular to the wall heat of vaporization fg C          specific heat of non-condensible gas pg hT        T  -  T o
TOO      gas temperature  at free stream T
0 gas  temperature at wall Equations (A-I) through (A-4) are four algebraic equations for four unknowns, Y , g, R, and v'      These equations have been solved by the computer program FOG. In FOG, the values of Y , g, and R are computed and used in Eq. (3.12) to compute the fog formation rate.
A-2 0430Q:1


plenum may prevent the glow plug igniters from igniting hydrogen below 7~~~percent.However, it seems very unlikely that the same igniters would fail to ignite 8.5 percent H2 as designed.It should be recognized that the existing theories and data can only predict the minimum fog concentration for inerting.Further work may be required to verify the fog inerting theory associated with flame propagation in all directions.
I APPENDIX B
0430Q:I 7-2 A CKNOWL EDGME NTS The author wishes to express his sincere gratitude to Mr.N.J.Liparulo, Dr s.Y.Srinivas, B.Lewis, and B.Karlovitz for assistance, sugges-tions, and helpful discussions, particularly in the area of the fog inerting criteria and the flame temperature criteria for fog, to Messrs.D.F.Paddleford, R.Bryan, F.G.Hudson, and K.Shiu for valuab1e.comnents, to Mr.K.C.Perry, Mr.S.J.Reiser, and Ms.,R.M.Mariner for providing data on the three ice condenser plants, and to Mr.T.J.,Miele for providing pr ogramming assistance.
.                                   DERIVATION OF EQUATION    (5.5)
He also would like to thank TYA, Duke Power, and AEP for providing the financial support.0430Q:1 7-3
This appendix gives detailed procedures to derive Eq. (5.5), starting from Eq. (5.4) crit ei              u
                                        - Yf)/ei)                                  (5.4)
E wher e  the    ratio of heat loss rate per unit        volume  to the heat release rate    by  chemic'al reaction per unit volume,         (K)    t, is defined as Kcr    t=S/Cw    P and the ratio of sensible heat to heat of combustion, e;,             is defined  as
: e. =C 1
p (T.-T)/q 1      u To  arrive at Eq. (5.5),         it  is necesary to assume that all the heat loss is attributed to convection heat transfer to fog droplets of only one drop size. Under this assumption, the rate of heat loss per unit volume per degree, S, may be expressed as S=nxdh where      n    =    number  of  drops per  unit volume d    =    volume mean drop size h    =    heat'transfer coefficient It is    further    assumed    that the relative velocity between the droplets and the mixture flow is so small that heat transfer coefficient, h, can be approximated by the conduction            limit. Under  this assumption, Eq.
(B-3) reduces to d
04 30Q: I                                    B-I


REFERENCES 1.B.Lowry,"Preliminary Results: A Study of Hydrogen Igniters," ENNBO-45;Lawrence Livermore National Laboratory, November 17, 1980.2."Additional guestions on Hydrogen Control System for Ice Condenser Plants," NRC memo from L.Rubenstein to R.Tedesco, dated June 26, 1981.3."The Marvikken Full Scale Containment Experiments," MXB-301 AB Atomenergi, March, 1977.*4.T.F.Kanzleiter,"LOCA Experiments With a PWR Multi-Compartment Model Containment," Trans.1977 LWR Safety Conf., Idaho Falls, Idaho, 1977.5.G.'M.Fuls,"The CLASIX Computer Program for the Hydrogen Release and Degradation", OPS-07A35, Offshore Power Systems, 1981.6.K.K.Almenas,"The Physical State of Post-Loss-of-Coolant Accident Containment Atmospheres," Vol.44, Nuclear Technology, pp.411.-427, August, 1979.7."Summary of Analysis of Ice Condenser Containment Response to Hydro-gen Transients," Offshore Power Systems report No.RP-28A52, Septem-ber, 1980.8.R.Brown and J.L.York,"Sprays Formed by Flashing Liquid Jets," Vol.8, No.2, AICh.E Journal, p.149, May, 1962.(9.R.G.Gido, and A.Koestel,"LOCA-Generated Drop Size Prediction
~,
-A Thermal Framentation Model," Trans.Am.Nucl.Soc., 30, p.371.1978.10.P.G.Hill, H.Witting, and E.P.Demetri,"Condensation of Metal Vapors During Rapid Expansion," Journal of Heat Transfer, p.303, November, 1963.0430/:1 R-1 11.M.Volmer and H.Flood, Z.Physik Chemic, A170, p.273, 1934.12.C.E.Junge, Advan.Geophys., H.Landsberg and J.Van Mieghem, ed., 4.1, Academic Press, New York, 1958.13.R.J.Burian, and P.Cybulskis,"CORRAL II User Manual," Battelle Columbus Laboratories, January, 1977.14.R.K.Hilliard and L.F.Coleman,"Natural Transport Effects on Fission Product Behavior in the Containment Systems Experiment," BNWL-7457, Battelle-Northwest, Richland, Washington, 1970.15.N.H.Fletcher, J.Chem.Phys., 29, p.572;31, p.1136, 1958.16.D.E.Rosner and M.Epstein,"Fog Formation Conditions Near Cold Surfaces," Vol.28, No.1, J.of Colloid and Interface Sci., Septem-ber, 1968.17.K.Hijikata, and Y.Mori,"Forced Convective Heat Transfer of a Gas With Condensing Vapor Around a Flat Plate," Vol.2, No.1, Heat Transfer-Jap.Res., pp.81-101, January, 1973.18.M.Neiburger and C.W.Chien,"Computation of the Growth of Cloud Drops by Condensation Using an Electronic Digital Computer," Geophys.Monograph No.5, pp.191-209, 1960.19.R.M.Kemper,"Iodine Removal by Spray in the Salem Station Contain-ment," WCAP-7952, Westinghouse Electric Corp., August, 1972.20.N.J.Liparulo, J.E.Olhoeft and D.F.Paddleford,"Glow Plug Ignitor Tests in H2 Mixtures," WCAP-5909, Westinghouse Electric Corp., March 6, 1981.21.R.G.Zalosh and S.N.Bajpai,"Water Fog Inerting of Hy'drogen-Air Mixtures," EPRI Project Preliminary Rp.1932-1, September, 1981.0430Q:I
  ~4 k


22.J.M.Marchello,"Control of Air Pollution Source," Marcel Dekker,~~~~~Inc., Hew York, 1976.23.Letter from B.Lewis and B.Karlovitz to L.E.Hochreiter, dated may 5, 1980.24.M.Berman, et al.,"Analysis of Hydrogen Mitigation for Degraded Core Accidents in the Sequoyah Nuclear Power Plant," Sandia draft report, December 1, 1980.25.T.von Karman', Unpublished notes, 1956.26.S.S.Tsai,"Flame Temperature Criteria Tests," HS-CCA-81-039, West-inghouse internal memo, dated June 17, 1981.27.Attachment to Offshore Power System letter PST-HE-109, dated May 22, 1981.28.Attachment to Offshore Power System letter PST-NE-106, dated May 14, 1981.29.Attachment to Offshore Power System letter PST-HE-218, dated August 6, 1981.30.M.L.Corrin, J.R.Connel, and A.J.Gero,"An Assessment of Warm Fog-Nucleation, Control, and Recommended Research," NASACR-2477, November, 1974.0430Q:1 R-3
ATTACHMENT 5 TO AEP:NRC:0500K FOG INERTING CRITERIA FOR HYDROGEN/AIR MIXTURES DONALD C. COOK NUCLEAR PLANT UNIT NOS. l AND 2


APPENDIX A C 0 MP U TAT I 0N 0 F Y o AN D g I N E Q UAT I 0 N{3 1 2)The Hijikata-Mori fog approximation for the fog concentration and assumed in Eqs.(3.7)into the conservation formation theory used the boundary layer continuity, momentum, and energy equations.
CO}}
The velocity profiles in the boundary layer are and (3.S).Substituting Eqs.(3.7)through (3.10)equations, we have 3 3 V-(+)~9 9 7 Y+v=0 I o ca-m'rr<'m"'m<V-'-'3 7 1 mm".'-'-z"')x 311, 3 I (A-1)(A-2)(A-3)A(n)+B(n)g+C(n)+~E Y 7'F)Pr o o=g)p--V-V (1+E)Y 0 (A-4)where A (n)-B(n)=C(n)=3 (n+5)n+n+3 (n+6)n+n+n+3 (n+7)bW 2 hW h E=Hr Pg 0430Q:1 A-1 0
6 v vl 00 W 0 aW S fg C pg hT T OO T 0 weight fraction of vapor at free stream weight fraction of vapor at wall W'-W Schmidt number kinetic vi scosity component of the free stream velocity perpendicular to the wall heat of vaporization specific heat of non-condensible gas T-T o gas temperature at free stream gas temperature at wall Equations (A-I)through (A-4)are four algebraic equations for four unknowns, Y , g, R, and v'These equations have been solved by the computer program FOG.In FOG, the values of Y , g, and R are computed and used in Eq.(3.12)to compute the fog formation rate.0430Q:1 A-2 I
.APPENDIX B DERIVATION OF EQUATION (5.5)This appendix gives detailed procedures to derive Eq.(5.5), starting from Eq.(5.4)crit ei u-Yf)/ei)(5.4)E wher e the ratio of heat loss rate per unit volume to the heat release rate by chemic'al reaction per unit volume, (K)t, is defined as Kcr t=S/Cw P and the ratio of sensible heat to heat of combustion, e;, is defined as e.=C (T.-T)/q 1 p 1 u To arrive at Eq.(5.5), it is necesary to assume that all the heat loss is attributed to convection heat transfer to fog droplets of only one drop size.Under this assumption, the rate of heat loss per unit volume per degree, S, may be expressed as S=nxdh where n=number of drops per unit volume d=volume mean drop size h=heat'transfer coefficient It is further assumed that the relative velocity between the droplets and the mixture flow is so small that heat transfer coefficient, h, can be approximated by the conduction limit.Under this assumption, Eq.(B-3)reduces to d 04 30Q: I B-I
~,~4 k ATTACHMENT 5 TO AEP:NRC:0500K FOG INERTING CRITERIA FOR HYDROGEN/AIR MIXTURES DONALD C.COOK NUCLEAR PLANT UNIT NOS.l AND 2 CO}}

Latest revision as of 02:40, 4 February 2020

Fog Inerting Analysis for PWR Ice Condenser Plants.
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. FOG INERTIHG ANALYSIS FOR PMR ICE CONDENSER PLANTS BY S. S. TSAI CORE AND CONTAINMEHT ANALYSIS NUCLEAR SAFETY DEPARTMENT WESTINGHOUSE ELECTRIC CORP.

NOYEHBER 1981 8310140042 831010 PDR ADOCK 050003i5 P PDR 0430Q:1

. The ABSTRACT recent hydrogen burn test conducted at the Lawrence Livermore National Laboratory has raised the NRC and the ice condenser plant

'owners concern about fog inerting probability and consequences in ice condenser plants. The present investigation is aimed at resolving this fog inerting issue. In this report, major fog formation and removal mechanisms that exist in the post-accident ice condenser containment are identified and quyntified. Methodologies have been developed for pre-dicting fog formatiop and removal rates and for predicting fog concen-trations in various compartments in an ice condenser containment.

This methodology development has resulted in two computer programs, FOG and FOGMASS. The FOG computer program employs the Hijikata-Mori boun-dary layer fog formation theory, and calculates the fog formation rates due to boundary layer and bulk stream condensation. The computer pro-gram FOGMASS solves the mass conservation equations for fog droplets and calculates the fog concentrations in various compartments. Both compu-ter programs have been used to predict fog concentrations in the

'equoyah, McGuire, and D. C. Cook containments, using the CLASIX output data for a S>D accident sequence.

In order to utilize the c'alculational results-from the study, a fog inerting criterion has been established. This criterion uses the hydro-gen concentration, volume mean drop size, and fog concentration to define the fog inerting regime. For a given hydrogen concentration, the minimum fog inerting concentration was found to vary with the square of the volume mean drop size. This criterion has been verified by the Factory Mutual recent fog inerting test data.

The application of the fog inerting criterion to the three ice condenser plants shows that fog inerting would not exist in the upper and lower compartments. Fog inerting in the ice condenser upper plenum at hydro-gen concentratons at which glow plug igniters are designed to operate is very unlikely.

0430Q: I

TABLE OF CONTENTS Section Tftle ~Pa e ABSTRACT TABLE OF CON TEN TS LIST OF TABLES 1V LIST OF FIGURES 1.0 ',BACKGROUND 2.0 IN TROD UCT ION 2-1 3.0 FOG GENERATING MECHANISMS 3-1 IN AH ICE CONDENSER CONTAINMENT 3.1 Fog Generated by Break Flow 3-1 3.1.1 Amount of Fog Generated 3-3 by Break Flow 3.1.2 Drop Sizes Generated by Break Flow 3-5 3.2 Hucleation of Fog Droplets in Containment 3-6 Atmosphere 3.2.1 Nucleation Theori es 3-7 3.2.1.1 Classical Theory of 3-7 Homogeneous Nucleation 3.2.1.2 Heterogeneous Nucleation 3-9 Theo ry 3.2.2 Fog Formati o n Condi ti on s 3-10 3.2.3 Conditions for Fog Formation Near 3-12 a Cold Surface.

3.2.4 Rate of Fog Formation 3-15 3.2.5 Fog Drop Sizes 3-19 3.3 Fine Mist Droplets From Containment Sprays 3-19 4.0 FOG REMOVAL MECHANISMS IH AH ICE CONDENSER CONTAIHMEHT 4.1 Settling Due to Gravity 4-1 4.2 Agglomeration 4.3 Vapori zation 4.4 Removal by Spray Drops 4.5 Other Removal Mechanisms 0430Q: 1

TABLE OF CONTENTS (Continued)

Section Title ~Pa e 5.0 FOG INERT IHG CRITERI A 5-1 5.1 Previous Mork 5.2 Present Theory 5-2 5.3 Verification of Theories by Experiments 5-6 6.0 ASSESSMENT OF FOG INERTING PROBABILITY IH ICE 6-1 CONDENSER COHTAINMEHTS 6.1 Determination of Volume Fraction of Fog 6-1 Droplets in Ice Condenser Containment Subcompartments 6.1.1 Calculation of mbreak 6-5 6.1.2 Calcul ation of 6-6 6.1.3 Calculation of m set 6-6 6.1.4 Ca 1 cul ation of m 6-7 sP 6.2 Fog Inerting Probability in the Sequoyah 6-7 Plant 6.3 Fog Inerting Probability in the McGuire 6-23 Plant 6.4 Fog Inerting Probability in the D. C. Cook 6-37 Plant 6.5 Effect of Fog on Global Combustion 6-50 7.0

SUMMARY

AND CONCLUSIONS 7-1 ACKNOWLEDGMENTS 7-3 REFERENCES R-1 APPENDIX A A-1 APPENDIX 8 B-1 0430Q:1

i fl

LIST OF TABLES Tabl e No. Title ~Pa e 6.1 FOG Input Data for Sequoyah Lower Compartment 6-18'.2 FOG Input Data for Sequoyah Ice Condenser 6-19 6.3 Geometric Data for Sequoyah Containment 6-20 6.4 MARCH Prediction of Reactor Coolant Mass and 6-21 Energy Release Rate for the S20 Sequence.

Intercompartmental Fl ow Rates (ft /sec) 3 6-22 6.5 Predicted by CLASIX for Sequoyah 6.6 FOG Input Data for McGuire Lower Compartment 6-33 6.7 FOG Input Data for HcGuire Ice Condenser 6-34 6.8 Geometric Data for McGuire Containment 6-35 6.9 Intercompartmental Flow Rates (ft /sec) 6-36 Predicted by CLASIX for HcGuire

6. 10 FOG Input Data for D. C. Cook Lower Compartment 6-46 6.11 FOG Input Data for D. C. Cook Ice Condenser 6-47 6.12 Geometric Data for D. C. Cook Containment 6-48 6.13 Intercompartmental Fl ow Rates (ft /sec) 6-49 Predicted by CLASIX for D. C. Cook iv 0430Q: 1

LIST OF FIGURES

~Fi ure No. Titl e ~Pa e 3.1 T-S Diagram for Reactor Coolant Discharged 3-4 From Break 3.2 ~

Vapor Pressure and Temperature Profile Hear 3-14 a Cold Surface 3.3 Formation of Fog Hear a Cold Surface 3-16 3.4 Drop Size Distribution Predicted by Heiburger 3-20 and Chien 3.5 Particle Size Distribution for 50 PSI Pressure 3-21 Drop Across Hozzle No. 1713 4.1 Terminal Velocity as a Function of Drop Radius 4-5 in Steam-Air Atmospheres 4.2 Agglomeration Rates in Air Between Equal-Sized Drops sphericc 5.1 Minimum Ignition Energies and Quenching Distance 5-3 for Hydrogen-Oxygen Inert Gas Mixtures at Atmo-Pressure 5.2 The Ef feet of Droplet Spacing on Flame Quenching 5-4 5.3 Schematic Representation of Temperature Profile 5-7 Through the Flame Front The Parameter We. g as a Function of 5-7 1

(Y- Yf)/ e for Different

~

Values of Kei 0430Q: 1

f) i' LIST OF FIGURES (Continued)

~Fi ure No. Title ~Pa e 5.5 (K) .t e. at the Flammability Limit as a 5-8 Function of (Yu - Yf)/ei 5.6 Comparison Between Theories and Factory Mutual 5-10 Fog Inerting Experiments on 4.76 Percent H2 r

'I 5.7 Comparison Between the Present Theory and 5-11 Factory Mutual Fog Inerting Experiments on 7.2 Percent H2 5.8 Comparison Between the Present Theory and 5-12 Factory Mutual Fog Inerting Experiments on 7.9 Percent H2 6.1 Sequoyah CLASIX Containment Model 6-8 6.2 Fog Formation in TVA Sequoyah Lower Compartment 6-10 6.3 Fog Formation in TVA Sequoyah Ice Condenser 6-11 6.4 Fog Concentration in Sequoyah Containment 6-14 6.5 McGuire CLASIX Containment Model 6-24 6.6 Fog Formation in Duke McGuire Lower Compartment 6-25 6.7 Fog Formation in Duke McGuire Ice Condenser 6-26 6.8 Fog Concentr ation in McGuire Containment 6-29 6.9 D. C. Cook CLASIX Containment Model 6-38 0430Q:1

LIST OF FIGURES (Continued)

Title ~Pa e Fog Formation in AEP Cook Lower Compartment 6-29 Fog Formation in AEP Cook Ice Condenser 6-40 6.12 Fog Concentration in D.C. Cook Containment 6-43 vii 0430(}:I

1.0 BACKGROUND

The incident at Three Mile Island has demonstrated that a significant amount of hydrogen could be generated during core degradation. This experience raised HRC concern about the safety of nuclear power plants, in terms of their capability to control hydrogen during severe acci-dents. Since ice condenser plants have a relatively small volume and low containment design pressure, the problem is magnified. Therefore, the NRC has requested the ice condenser plant owners to study hydrogen control methods for use in their plants. In this regard, the Tennessee Valley Authority (TVA), Duke Power and American Electric Power (AEP) have proposed the use of glow plug igniters at various locations inside their ice condenser containments to ignite hydrogen at low concentration.

Recently, the NRC requested Lawrence Livermore National Laboratory (LLNL) to carry out experiments on these igniters to determine their effectiveness. In these experiments, two tests with high steam concentration seemed to indicate that substantial fog formation could occur when saturated steam is'ischarged into a unheated vessel and under some conditions fog could effectively preclude hydrogen from combustion The LLHL tests raised some doubts about the effectiveness of glow plug igniters under fog formation conditions. In a recent review of hydrogen related issues for ice condenser plants, the HRC has raised several questions concerning the probability and consequences of fog formation and steam supersaturation in ice condenser plants.

In response to 'the NRC questions, TVA, AEP, and Duke established experi-mental and theoretical analysis programs to study the fog inerting prob-lem. The experimental program was contracted to Factory Mutual. The experiments were designed to test glow plug igniter's performance under 4

different fogging conditions. At the same time, the plant owners .

requested Westinghouse to perform fog inerting analyses for the Sequoyah, McGuire, and D. C. Cook plants. This report presents the results of the Westinghouse studies.

0430Q:1

a e

2. 0 I NTRODUCT ION From the post-test analysis of the LLNL fpdrogen burn tests, it appears that substantial fog formation occurred inside the test vessel. Gen-erally, fog droplets are only few microns in diameter. These sizes of droplets have potential to prevent a fl'ammable gas mixture from combus-tion or quench a propagating flame. This is because these sizes of droplets vaporize very fast (on the order of miliseconds), absorbing an enormous amount of the heat released from combustion if a substantial quantity of these droplets is present in the atmosphere. In comparison, large water droplets in the range of few hundred microns or larger (e.g.

spray droplets) have no inerting effect on combustion and hence have insignificant effect on glow plug igniter's performance. There-fore, the present analysis will be concentrated on the generation and removal of fog (mist), and its impact on the glow plug igniter system.

There are a number of fog generation and removal mechanisms present in a post-accident ice condenser containment atmosphere. The fog generation mechanisms include fog generated by the break flow (if it is two-phase),

fog formation near the ice and structural heat sink surfaces (since the surface temperatures could be well below the dew point), and fog genera-tion due to homogeneous and heterogeneous nucleation in condensing bulk streams.

The fog removal mechanisms include gravitational settling, agglomera-tion, vaporization and removal by spray droplets. In order to estimate the post-accident fog concentrations in ice condenser containments, these competing mechanisms must be studied, and evaluated. To solve this problem, it requires a numerical integration of the mass conserva-.

tion equations for the mist droplets in the various containment subcom-partments. By making some simplifying assumptions the transient fog concentration in the various subcompartments have been estimated.

0430Q I 2-1

The analysis presented here considers all the fog removal and generation mechanisms previously described. In addition, it considers the fog entrainment in the intercompartmental flows (including fan flows) in the fog mass conservation equations. In order to perform this analysis it was necessary to use CLASIX results for a S2D event as boundary condi-tions to the problem.

In addition to calculation of fog concentrations in'various containment compartments, it was necessary to establish a fog'inerting criterion. A fog inerting criterion has been proposed by Berman et al., which pre-dicts the minirpum fog concentration required to inert a given hydrogen concentration and given volume mean fog drop size. This criterion seems to overpredict the minimum fog inerting concentration, when compared with experimental data. A more realistic fog inerting theory is presented in the present study.

The fog inerting methodology, analysis, and results are presented in the following sections of this report. Sections 3 and 4 present the, method-ology for calculating the fog formation and removal rates. Section 5 gives the fog inerting criteria, and Section 6 presents the results.

0430Q: I 2-2

i' 0

3.0 FOG GENERATING MECHANISMS IH AH ICE CONDENSER COHTAINMEHT The inerting capability of fog droplets depends on their sizes and con-centration in the containment atmosphere, as well as the hydrogen con-centration. This section is intended to identify various fog generation mechanisms present in an ice condenser containment and to determine the drop sizes and the rates of fog generation from these mechanisms. Three fog generation mechanisms are discussed in this section and the dominant fog generation mechanisms are identified.

3. 1 FOG GENERATED BY BREAK FLOW The post-LOCA containment atmosphere is most likely to be a drop-laden atmosphere. The large-scale simulated LOCA experiments conducted to date have directly or indirectly confirmed the presence of two-phase atmospheres. For example, Marvikken (3) and Battelle - Frankfurt experiments were instrumented to measure fluid densities and water levels in various parts of the containment. Therefore, fog generation by the break flow cannot be neglected. The following discussion of this phenomenon pertains to small LOCAs.

In the early stage of a small LOCA transient, a substantial .portion of the primary coolant discharged from the break will remain as liquid.

Because of the superheat and high velocity, this liquid will be framen-ted by aerodynamic forces and homogeneous nucleation mechanism into'mall droplets. These droplets are expected to be entrained by the intercompartmental and fan flows and spread to other parts of the ice condenser containment. During their travel throughout the containment, the fog droplets will be removed by gravitational settling, sprays, and vaporization. The fog gene'ration period lasts until the water level in the reactor vessel falls to the break elevation and the break flow is no longer two-phase.'or the particular S<D sequence analyzed by 0430Q: I 3-1

CLASIX, (5) this period lasts for about 36 minutes and about 4.2 x 5

10 lbs of water has been discharged into the lower compartment during thi s pe ri od of time.

After the water level in the reactor vessel falls below the break eleva-tion, the break flow rate is substantially reduced. The flow is essen-

'ially steam and no fog droplets will be generated. As a result, the lower compartment becomes superheated afterward. Fog droplets may vaporize during their travel through this compartment and substantial removal of mist droplets are expected.

Large suspended drops generated by the break flow will be removed very quickly. by gravitational settling and impingement. For the drops larger than 20 u, the removal rate is high and complete removal only takes a few seconds. For the smallest drops (less than 1 u) the terminal veloc-ity is so small that they virtually remain suspended in the atmosphere indefinitely. The only effective removal mechanisms for these sizes of drops are vaporization, and collision with larger spray drops. The weight fraction of these sizes of drops is estimated to be 1 per-cent (3) generated by the break flow. The population of these small drops can increase if nucleation of embryos occurs in a saturated atmo-sphere.

0430Q:1 3-2 l

3.1.1

~ ~ AMOUNT OF FOG GENERATED BY BREAK FLOW As discussed previously, the existence of a two-phase drop-laden regime has been observed experimentally. In a .small LOCA, flashing of primary coolant at the break and subsequent vaporization of blowdown liquid represent a series of changes of thermodynamic states. Since the reac-tor coolant pressure is high, the break flow will be choked. The accel-eration of primary coolant to the break location is essentially an isen-tropic process, in which the pressure decreases to the point at which substantial homogeneous nucleation occurs. When the flow leaves the break, the liquid is framented by both the aerodynamic forces and the nucleation mechanism into small fog droplets. These fog droplets con-tinue to vaporize, because of the superheat in the droplets, until a thermodynamic equilibrium state is reached. Because of the high super-heat and large aerodynamic forces, it is expected that the fog droplets generated are very small. This vaporization process is essentially isenthalpic.

The existence of a two phase drop-laden regime can also be explained by use of a T-S diagram for steam as shown in Figure 3,1 (Figure 1 of Reference 6). It is shown in this figure that the blowdown liquid goes through a series of thermodynamic states, starting from the subcooled liquid state B 0 . The liquid expands isentropically from the subcooled state 8 to the state B> at the break, where a two-phase critical flow is developed. At the same time, temperature changes from T to TI. After leaving the break, the droplets continue to vaporize because of excessive superheat until finally an equilibrium state B<

is reached at which the droplets are in thermal equilibrium with their surroundings. This vaporization process is essentially isenthalpic. At this time, the droplet temperature drops to T> and the atmospheric temperature also rises to T>. For a small LOCA, the equilibrium tem-perature varies with time. According to the CLASIX analysis of the Sequoyah plant, the lower compartment gas temperature rises quickly from 100"F to approximately 200"F and then stay at this temperature for an extended period of time. Using these temperatures as final equilibrium 0430Q I 3-3

Kg/cm2 100 10 r

600 450 400 400 300 g 350 300 0 200 250 200 150 100 100 i j I A2 50 /t 0

0.0 0.2 ~

0.4 0.6 0.8 X=1 FIGURE 3.1 T-S DIAGRAM FOR REACTOR COOLANT DISCHARGED FROM BREAK

temperatures for water droplets, the weight fraction of water droplets

. in the break flow is approximately 50 percent, which is consistent with the MARCH calculations~7~ of the break flow rate release rate.

and its energy The discussion given above is valid only when the initial state'of the break flow is subcooled or saturated liquid. After the water level inside the reactor vessel falls below the break elevation, the break flow will be steam. The moisture content of the steam will be very low, even though isentropic expansion may lead to homogeneous nucleation and subsequent condensation in the vapor stream. Depending on the super-saturation that can be achieved in this isentropic expansion, a conden-sation shock is possible when critical'supersaturation is reached.

However, it is believed that the fog droplets generated by homogeneous nucleation in this supersonic jet is negligible as compared to other fog generating mechanisms. Hence, it will be neglected in this present analysis. Therefore, the fog generation by the break flow is considered possible only when the water level in the reactor vessel is above the break elevation.

According to the MARCH~"~ calculation at 2172 seconds into the acci-dent, the water level inside the reactor vessel falls below the break elevation for the S2D case analyzed in Reference 7. By this time approximately 421,000 lbs of water has been discharged from the break and 56 percent of this discharged fluid, i.e., 236,000 lbs, will be sus-pended in the atmosphere as condensate. However, most of these droplets will later be removed by gravitational settling, sprays, and vaporiza-tion.

3.1.2 DROP SIZES GENERATED BY BREAK FLOW The flashing jet experiment conducted by Brown and York~B~ has indi-cated that the drop sizes produced by flashing. liquid are small. They derived a correlation for the linear mean drop size based on the test data. The correlation shows that the mean drop size is inversely pro-portional to the Weber number and it decreases linearly with increasing 0430Q:I 3-'5

superheat. However, this correlation is applicable for liquid superheat less than 75'F and it can not be extrapolated to the large superheat of the reactor coolant. However, some conclusion concerning the drop sizes produced by blowdown of the reactor coolant can be drawn for this condi-tion., The break flow has much larger superheat and Weber number than those used in this experiment; therefore, the drop sizes produced by the break flow should be much smaller than -50'bserved in this experi-ment.

Gido and Koestel (9) have developed a method for estimating the. drop size leaving the fragmentation/evaporation zone of a blowdown jet. This model is based on the assumption that drops with an'internal. temperature difference of less than 5K will escape fragmentation. This model has been verified by the low superheat, data of Brown and York. Application of this method to the LOCA condition shows that the maximum attainable drop size is 7p (this means that arly drop size larger than 7p will not escape framentation by homogeneous nucleation). The corresponding mean drop size is about 4p, based on the observation of the largest drop size and mean drop size in the experiment reported in Reference 8. However, this volume mean drop size is not used in the present analysis.

Instead, the present analysis uses 10 p mean drop size,. considering the drop agglomeration effect.

3.2 NUCLEATION OF FOG DROPLETS IN CONTAINMENT ATMOSPHERE Nucleation of water embryos from the homogeneous vapor phase plays an important role in mist generation in ice condenser plants. Nucleation is a process by which tiny water embryos or condensation nuclei are formed from a pure vapor phase at a rapid rate. In incipient homogene-ous nucleation, the local gas temperature drops below the dew point corresponding to the local steam partial pressure and some degree of local supersaturation is needed. The degree of supersaturation needed to start nucleation depends on the number of condensation nuclei present in the containment. These condensation nuclei could be very small water droplets or dust particles. If sufficient number of condensation nuclei 0430Q:I 3-6

exist, supersaturation could be small. It is likely that the ice con-denser containment contains a subtantial number of dust particles such that little supersaturation is needed for nucleation.

This section is devoted to the discussion of fog formation by homogene-ous or heterogeneous nucleation. The classical nucleation theories are used to explain the nucleation phenomenon.

3.2. 1 NUCLEATION THEORIES The process of n0cleation of an embryo water drop is important in under-standing the mechanism of fog formation in ice condenser plants. Two types of nucleation process, namely, homogeneous and heterogeneous nucleations, and their theories will be discussed in Section 3.2.1.

3.2.1.1 CLASSICAL THEORY OF HOMOGENEOUS NUCLEATION When an embryo droplet, usually assumed spherical, is formed from con-l) densation of water vapor molecules, of free energy can be expressed as its free energy changes. The change aG = 4xr a " (4/3) xr nL KT Zn (p/p )

where a is the surface free energy per unit area, or surface tension, r is the drop radius, P is the vapor pressure, 0 P;s the saturation Pressure at the droPlet temPerature, nL is number of molecules per

,unit volume, K is the Boltzman constant, and T is the drop temperature.

The supersaturation S, is defined as P/P .

Equation (3.1) represents a free energy barrier to the growth of the drops at a given suprsaturation. At maximum aG, the critical radius r" can be obtained from Equation 3.1 as r* 20 0430/:1 3-7

r 1',

i~I

of the critical size

~

The drops

~ ~

can be considered as condensation nuclei since at this size the drops will grow with no change in free energy.~

~ ~ ~

This critical size represents an equilibrium size at which a supersatu-

~ ~ ~ ~ ~ ~ ~ ~

rated vapor at vapor pressure P is in equilibrium with this critical drop at a lower saturation pressure P . However, this equilibrium mode is unstable. For example, if a drop of the critical size origi-nally in equilibrium with the surrounding vapor suffers a sudden small increase in size due to condensation, then (if the drop temperature does not,change), Equation 3.2 shows that the equilibrium pressure, P, on its surface will decrease. Therefore, the actual vapor pressure will then be greater than the equilibrium value and further condensation will occur. This is why the drop of this critical size is called condensa-tion nucleus.

The nucleation rate of critical-sized embryos can be obtained from the kinetics of a nonequilibrium distribution of embryos. The classical nucleation theory shows that there is a very sudden increase in the nucleation r ate when past a certain critical value of supersatura-tion. An extensive validation of the nucleation theory was conducted by Volmer and Flood in an experiment in which a number of vapors were expanded to visible condensation in a cylinder. The observed critical supersaturations agreed suprisingly well with theory in nearly all cases, including water vapor.

Critical condensation nuclei sizes typically range from 10 to 100 atoms. These sizes are considerably smaller than the mean free path of the vapor molecules and therefore the rates of mass and heat transfer at

'the drop surface cannot be predicted by bulk transport theories. In this case, the kinetic theory of gas should be used to predict the rates of mass and heat transfer at the drop surface.

Starting from the kinetic theory of gas and the energy conservation equation, the rate of growth of a condensation nucleus was obtained by Hill et al. It was found that the growth rate is on the order of 10 ft/sec. Therefore, it takes only about I milisecond for the condensation nucleus to grow to a fog droplet size of I p.

0430Q I 3-8

3.2. 1. 2 HETEROGENEOUS N UCL EAT ION THEORY Another mechanism of forming embryos is heterogeneous nucleation on foreign particles that could suspend in the containment atmosphere.

These particles may serve as nucleation sites for vapor and thus enhance the nucleation rate. The source of foreign particles in the containment following core degradation could come from fission product aerosols and dust particles. The size distribution of these particles are important because the supersaturation required to form embryos depends on particle sizes.

A typical size distribution of atmospheric aerosols is that of e

Junge, taken from surveys made near Frankfurt A.H., German. The surveys found that the size range of dust particles is from 0.01 to I In the range from 0.01 to 0.5 p, there are between 100 and 10,000 particles per cubic centimeter. A majority of particles have sizes smaller than 1 micron. At the smallest size of 0.01 p, the critical supersaturation is about 1.02 and at the largest size the supersatura-tion is only 1.001.

~ ~

The other source of aerosol particulates is fission, products. During normal operation, the primary coolant contains very little fission pro-ducts. However, a large release of fission products, such as the gap release, could occur at about the same time the hydrogen releases. The amount of fission products released to the containment depends on acci-dent scenarios. The distribution and transport of fission products in the containment can be predicted by the CORRAL code~ ~. The size di stribution of fission products .in the containment can be extrapolated from the CSE experiments~ 4~. These experiments indicated that soon after fission product release, the mean particle diameter was 15 p. A few hours later, the mean diameter decreased to about 5 p because of settling of large particles onto the floor. These sizes are substan-tially larger than those of dust particles and therefore, critical supersaturation is even smaller than values quoted above for the dust particles.

0430Q:1 3-9

The atmospheric aerosols consist of particulates of various sizes, vari-ous chemical components, and various electrostatic charges. The aerosol particulates could be soluble or insoluble in water. All these proper-ties could affect the required supersaturation for nucleation.

In the case of insoluble particulates, the contact angle, 6, between the "embryo and the particle surface is important. If the particle is com-pletely wettable, 6 ="0, it forms a base on which a small amount of water can. form a drop of large radius of curvature and thus satisfy the Hemhol tz equation (Eq. 3.2) at a much lower supersaturation than would be the case if I')

same number of molecules form a drop with a particle core. Fletcher ( developed a relationship between the supersIatura-tion and drop radius for several values of contact angle, assuming that the particle is spherical. Competely wettable, a particle of 1 micron or so, when covered with a film of water, is theoretically at the crit-ical radius, and it needs only 1.001 critical supersaturation.

The post-accident containment atmosphere is likely to contain a substan-tial amount of aerosol particles. These particles will act as condensa-

~

~

i tion nuclei and therefore, little supersaturation is required to pre-

) cipitate condensation.

~ ~

~

3.2.2 FOG FORlCTION CONDITIONS Fog formation in a mixture'f vapor and noncondensible gases has been of interest to meteorologists, and turbine and condenser designers. Fog is formed by homogeneous or heterogeneous nucleation as a result of tem-perature drop below the dew point (sometimes with concommitant pressure drop). During the temperature drop, a local gas element will go through a series of thermodynamic states. Eventually, a state is reached at which incipient fog formation occurs. Some degree of vapor supersatura-t'ion is needed to precipitate fog formation. The vapor supersaturation at which rapid nucleation of vapor first appears is called critical supersaturation. The critical supersaturation, in general, is a 0430Q:1 3-10

e function of temperature, vapor properties, mixing time (if a mixing process is involved), and concentration and sizes of foreign particles.

The critical supersaturation data for water has been given in Reference 15.

Fog formation in an ice condenser containment as a result of homogeneous or heterogeneous nucleation could occur: (i) inside the thermal boun-dary layer near a cold surface, (ii) in adiabatic or nearly adiabatic expansion of vapor jet, and (iii) in mixing of a hot vapor stream with another cooler gas.

Surface cooling may create a region of local supersaturation within the thermal boundary layer, even though the bulk stream is still super-heated. If the local supersaturation reaches the critical supersatura-tion, incipient fog formation will commence. This condensation mecha-nism may exist in any compartments within the containment especially in the ice condenser where ice temperature is well below the dew point.

When a high speed vapor - noncondensible gas mixture jet goes through an adiabatic or nearly adiabatic expansion, the gas mixt'ure temperature and pressure will drop rapidly such that condensation may occur somewhere in the expansion process. This is the case when a hydrogen-steam mixture jet exits from a break at a supersonic speed. The jet experiences a rapid expansion and if critical supersaturation is reached; condensation shock may occur somewhere within the expanding jet. This condensation mechanism can only occur in a compartment in which the hydrogen-steam mixture jet exists.

Condensation in a fast expanding vapor - noncondensible gas jet is a localized phenomenon. Usually very little moisture is generated in the expansion process even if a condensation shock does exist. Therefore, the present study does not attempt to treat the condensation shock as a source of fog formation.

0430Q:I 3-11

P The third mechanism, condensation due to mixing, may exist in a compart-ment where a hot hydrogen-steam mixture mixes with a relatively cold containment atmosphere. During the mixing process, local critical supersaturation within the mixing gas could be reached and condensation would ensue. This mechanism could exist in the lower compartment in which relatively cold gas from the upper compartment is returned by the deck fans and mixed with the hot humid air.

Thus, the mixing of cold and hot vapor streams will be treated in the present study. 'owever, only bulk condensation is considered. That is, it is not intended to 'compute the temperature profile to predict the local condensation rate. Instead, the bulk gas is assumed at one uniform temperature, and bulk condensation will occur when mixing results in saturation conditions. This is consistent with the CLASIX code assumption of uniform gas temperature.

Because of time restriction, it is almost impossible to treat all the condensation mechanisms. However, major condensation mechanisms will be identified and treated in the present study.

Before entering into the discussion of the methodology to calculate the fog formation rates from various fog formation mechanisms, a discussion of fog formation conditions is necessary. Since the bulk condensation approach for the mixing process has been adopted, the fog formation conditions for the mixing process are simply that critical supersatura-tion is reached in the bulk stream. For practical purposes, the crit-ical supersaturation is assumed to be one since it is likely that plenty of condensation nuclei exist in the atmosphere before mixing condensa-tion takes place.

3.2.3 CONDITIONS FOR FOG FORMATION NEAR A COLD SURFACE Fog starts to form at a fast rate near a cold surface when local vapor supersaturation reaches the critical supersaturation. Near the cold surface, a thermal boundary layer is formed, within which local vapor pressure and saturation pressure vary. Typical vapor pressure and 0430Q: I 3-12

r temperature profiles, when the incipient homogenous nucleation first appears, are shown in Figure 3.2. It is seen in this figure that when the local vapor pressure reaches the critical vapor pressure there is a sudden appearance of fog in the boundary layer due to the fast nuclea-tion rate. Rosner and Epstein ( ll) have derived fog formation condi-tions near a cold surface, assuming that the local vapor pressure curve is tangent to the critical vapor pressure curve at the fog incipient point. A more general fog-formation criterion was given by Hijikata and Mori 1 s hW (dW)

Wh

~

ar (3.3) wall where hW= W - W w

hT=T - T w

and the weight fraction of condensing vapor, W, can be related to the partial pressure of the condensing vapor P v as

=

(Pgp) (v/v )

W 1- (3.4)

P v g whe re P total pressure H vapor molecular weight N noncondensible gas molecular weight Equation (3.3) may be rewritten as n>2 (3.5) where M) ( Qd) wal 1 0430Q: I 3-13

21123 3 Pv, crit(T )

Pv, eq(T~)

Pv, oo I

II II II Pcrit (Tw) ll II II Pv, w 0 OO SUPERSATURATED REGION THERMAL SUPERHEATED BOUNDARY LAYER I

VAPOR SUPERSATURATED REGION O Too 1

K FOG D

CO D

z Z O

O O 0O Tw FIGURE 3.2 VAPOR PRESSURE AND TEMPERATURE PROFILES NEAR A COLD SURFACE 3-14

The parameter n is used in the following section to calculate the fog formation rate.

~

~ It will be demonstrated that when n < 2, no fog forma-tion is possible.

3.2.4 RATE OF FOG FORMATION HEAR A COLO-SURFACE As has been discussed in Section 3.2.3, fog will form near cold surfaces (e.g., in the ice condenser early in the transient. ) As discussed in Section 3.2.1, once water embryos are formed it takes only a few mili-seconds for them to grow to the micron size. After these micron size fog droplets are formed, it needs very little supersaturation for fur-ther growth. Therefore, in the present analysis, it is assumed that vapor and droplets are in thermal equilibrium and local vapor pressure is equal to the local saturation pressure. This section is concerned with the transport of these micron-size fog droplets within the thermal boundary layer.

The boundary layer fog formation rate can be determined using the Hijikata-Mori theory of fog formation in the thermal boundary layer. It was assumed that a thin liquid film, having a thickness of e< on a cold surface, coexists with a gas-droplet flow in a two-phase boundary layer of thickness 6 outside the liquid film as shown in Figure 3.3.

It was further assumed that the saturation condition exists within the two-phase boundary layer and the boundary layer approximation is appli-cable. Numerical solutions were obtained for the mass fraction of fog droplets, Y ot, at the gas-liquid film interface. The fog droplet flow rate at a distance X along the plate may be expressed in terms of Y as f'6 mf

= L pJ Yudy (3.6) 0430(}:I 3-15

hfain Flow

~0

~ ie Two Please Boundary layer Interface Liquid Film Cooling Surface FIGURE 3.3 FORtljATIOH OF FOG HEAR A COLD SURFACE

. where Y mass fraction of fog droplets in the fog droplet density boundary layer Pv vapor density Pg noncondensible gas density Y

o . ~fly = ok~v+ ~g) y = coordinate perpendicular to the plate fog boundary layer thickness width of boundary layer Pv+ pg

=

Y0 (1 - y/e) (3.7) u= U (<(~) -

~ (~) )

~ (x) =ax1<< (3.g) 4u = e (x) (1 - 6) (3.10) where a known constant known const'ant free stream velocity 0430Q:1 3-17

I 0

Substituting Eqs. (3.7) through (3.10) into Eq. (3.6), we have the rate of fog formation

0. 25 0.025 mf =pL6Y U (3.11) oerivation of expressions for a, Y and g is given in Appendix Even though boundary layer fog formation may occur in any containment subcompartment, the fog formation rate is likely to be small except in the ice condenser. For fog formation in the ice condenser, L is the total length of the periphery and x is the height of the ice bed.

During fog formation in the boundary layer, heat transfer to the cold surface will decrease the bulk fluid temperature. If the bulk fluid temperature drops below the dew point corresponding to the free stream vapor pressure, then bulk stream condensation could occur. In this case, it is assumed that the boundary layer thickness, s, will grow so thick that LeU~ becomes the gas volumetric flow rate Q through the con-densing compartment. This is a very conservative assumption in terms of the fog formation rate. Under this assumption Equation (3. 11) becomes

0. 25 0.025 .(3.12) cond o ~ "o 1:g (1 - g) where m condd is the sum of boundary and bulk stream fog formation rates.

0430Q 1 3-18

3.2.5 FOG DROP SIZES As mentioned earlier, when homogeneous nucleation commences, a large number of condensation nuclei are formed and they grow to the micron size within a few milliseconds. In heterogeneous nucleation, fog drop-lets grow on aerosal particles, which are usually less than 1 p. In any case, the final drop sizes are determined by the atmospheric conditions with which the drops are in thermal equilibrium.

Neiburger and Chien(18) studied the growth of cloud drops by condensa-tion and calculated droplet size distribution based on a cloud cooling rate of 6 c/hr. The initial size distribution of condensation nuclei (sodium chloride) were chosen to correspond to available observations as shown in Figure 3.4 (designated as 0 second). The calculated drop size distributions at 3000 and 6000 seconds are shown in Figure 3.4. It is seen that the sizes of fog droplets range from 0.01 p to 20 p. The volume mean drop size is 8 p at 3000 second. The volume mean drop size for homogeneous nucleation is expected to be smaller than this value.

Fogs of volume mean drop sizes ranging from 9 to 14 p(30) have been observed to exist in a natural enviroment, e.g. valley. In the present stuQ, a volume mean fog drop size of 10 p is chosen for fog deposition

-and inerting calculations.

3.3 FINE MIST DROPLETS FROM CONTAINMENT SPRAYS The containment sprays produce- fairly large drop sizes. A-typical con-tainment spray nozzle, e.g., Spraco 1713 nozzle, produces the size dis-tribution as shown in Figure 3.5, using a pressure difference of 50 psi across the nozzle( ). It is seen that water droplets produced from containment range from 100 p to 2000 p. These large drops have little effect on hydrogen combustion and flammability limits, as already demon-strated in the Fenwal tests( ) and more recent tests at Factory Mutual(21). To affect the combustion characteristics of a hydrogen mixture, the drop sizes have to be smaller than about 20 p, namely in the fog drop size ranges. Since containment sprays essentially do not produce drops in this size range, containment sprays will not be con-sidered as a means to produce fog droplets. Rather, it will be con-sidered as a means to remove the fog droplets.

0430Q:I 3-19

~ ~ ~

~ ~

j

~ ~

)

I <lO I20 lnO CD 80 ED 60 90 20 200 000 600 800 l000 l200 l900 l600 l800 2000 2200 PARTICLE DI AllETER (Ml CROHS)

FIGURE 3.5 PARTICLE SIZE DISTRIBUTIOH FOR 50 PSI PRESSURE DROP ACROSS NOZZLE HO. 1713

1

.J "s ~

0

4.0 FOG REMOYAL MECHANISMS IN AN ICE CONDENSER COHTAIHMEHT In Section 3, the mechanisms of generating fog droplets were discussed.

After these droplets are generated, they can be removed from the con-tainment atmosphere by. gravitational settling, vaporization, containment sprays, and impingement on structures. They can also coalesce with other drops during collision and form bigger drops. These bigger drops could easily settle out of the atmosphere under gravity. These fog droplet removal mechanisms will be discussed in this section.

4.1 SETTLING DUE TO'RAVITY Drop removal rates due to gravitational settling depend strongly on drop radius. The removal rate increases linearly with drop terminal veloc-ity, drop concentration, and settling area. The relationship may be expressed as

" (4. I) r mset t where q is the mass of mist droplets per unit. volume, and A is the set-tling area.

The terminal velocity, Yt, is a strong function of drop radius and the relationship is shown in Figure 4.1. It is seen that the terminal velocity is approximately a linear function of drop radius in both lami-nar the turbulent regimes. For a 1000 p drop, its terminal velocity is above I m/s, while for a 10 p drop, which is the typical fog drop size, its terminal velocity is only about I cm/s. Therefore, there is very little removal by gravity for fog droplets.

0430Q: I

4.2 AGGLOMERATION After the fog droplets are produced, the droplets will undergo changes in the number density and size distribution with time, when drops col-lide with each other and coalesce. The. agglomeration rate (No. of par-ticle per unit volume per unit time) has been found to be proportional to the square of the drop population density and the coagulation mecha-nisms dependent rate constant K For drops larger than

'I 1 g, the dominant mechanism is the difference in velocities between drops in adjacent streamlines. This is usually termed the velocity gradient coagulation. For drops smaller than 1 g, the velocity gradient effect becomes small, and drops are brought

'ogether by Brownian motion. This leads to greatly different agglomera-tion rates for different initial drop sizes. A typical agglomeration rate as a function of drop size in a moderately turbulent atmosphere is shown in Figure 4.2. In Figure 4.2, the sharp rise of the agglomeration rate with drop diameter larger than 1 p implies that the larger drops agglomerate quickly to the maximum stable size supported by the atmo-spheric turbulerce. The agglomeration rates for drops less than 1 p are very small. Since most of the fog droplets are in. micron size ranges, the agglomeration rate is not large. It is assumed in the present analysis that the initial 4 u blowdown mean drop size will grow to 10 g (See Section 3.2.5). Agglomeration as a separate mechanism for fog growth has'been conservatively neglected.

4.3 VAPORIZATION Fog droplets suspended in the containment atmosphere is considered to be in thermodynamic equilibrium with the surrounding gas. Mhen the sur-rounding atmosphere becomes superheated or when the droplets are entrained into a superheated subcompartment, it can undergo vaporization or condensation.

4-2 0430Q: 1

In the present analysis, it is assumed that water vapor and mist drop-lets are in thermal equilibrium at all times. Therefore, the amount of vaporization or condensation will be determined by the thermal equilib-rium state reached by the vapor and drops. In other words, it is not intended to model heat transfer between the drops and the surrounding gas, and thus determine the vaporization rate. This is a good assump-tion for the small fog drop sizes.

4.4 REMOVAL BY SPRAY DROPS As mentioned above, the containment spray droplets range from 100 u-2000 p, which are substantially larger than the fog droplets. If fog droplets enter the spray zone, they will probably be removed by the spray droplets by colliding with them, since the spray drop mass is much larger than the fog drop mass. A simple analytical model is used in the present study which assumes that all the fog droplets residing in the spray zone will be swept by the sprays to the floor with the spray drop removal efficiency E. The spray removal rate may be expressed as m =EQ M/q V (4.2) where E spray drop removal efficiency Qsp volumetric flow rate of sprays volume fraction of spray droplets in the spray zone sp M mass of fog in compartment volume V 4.5 OTHER REMOVAL MECHANISMS Another similar mechanism for fog removal is the formation of droplets in the ice condenser. These droplets which would be generated in the ice bed when the ice melts, would fall through the ice bed, and remove fog droplets from the flow through the ice condenser. This large quan-tity of water would be effective in removing fog droplets. However, due to difficulty in modeling this removal mechanism, it is conservatively neglected in the present analysis.

0430Q:I 4-3

I In addition to the removal mechanisms mentioned above, fog can also be removed by impacting structural surfaces. Oue to the inertia of fog droplets, substantial fog removal by impacting structural surfaces could occur, when the drop-laden mixture flow passes through long, narrow, curved paths, such as ice basket flow paths, and fan ducts. Moreover, the centrifugal force exerting on the fog droplets, when they pass through the fans, could cause the fog droplets to impact the blade sur-faces or other parts of the fans. These removal mechanisms are believed to be significant; however, they are conservatively neglected in the present analysis. It is, therefore, believed that the present analysis is very conservative.

4-4 0430Q:1

I

1 21273 1 TERMINAL DROP FALLING VELOCITIES IN 10 STEAM.AIR ATMOSPHERES p~

1.0 CO Z

0.10 TURBULENT AMINAR REGIME REGIME HATCHED REGION INDICATES:

50 <Re <55 0.01 0.001 001 DROP RADIUS (CM)

'1 1.0 FIGURE 4.1 TERHINAL VELOCITY AS A FUNCTION OF DROP RADIUS IN STEAH-AIR ATHOSPHERE 104

~

~

7 GRADIENT AGGLOMERATION u 103 n 10 CM dv 100 S dy O

102 R 8ROWNI AN O AGGLOMERATION I- n 10 CM NET o 101 RATE 100 0.01 0.1 1.0 DROP DIAMETER (pM)

FIGURE 4.2 AGGLOHERATION RATES IN AIR BETWEEN EQUAL-SIZED DROPS 4- 5

T

5.0 FOG INERT ING CRITERIA Recent hydrogen burn experiments conducted at Lawrence Livermore Labora-tory indicated that substantial fog formation could occur when saturated steam is discharged into an unheated vessel. It appeared that this fog prevented a glow plug igniter from successfully igniting the hydrogen mixture in the vessel. The ability of fog in inhibiting and quenching of hydrogen combustion can be explained as follows. The fog droplets suspended in the hydrogen-air-steam mixture act as a heat sink that could absorb a large amount of combustion heat, greatly reducing the pressure and temperature rises resulting from hydrogen combustion. If droplets are sufficiently small such that they could vaporize inside the thin ( Imm) flame front, the flame may be quenched or inhibited. For a flame speed of 2 m/s, the drop residence time is of the order of 0.5 x 10 seconds. In such a short period of time, the droplets of initial radius less than about 4 p will vaporize entirely in the flame front.

The quenching of a propagating flame is also governed by the distance between droplets. As the droplets become closely packed, the total droplet surface area available for energy loss increases. A critical spacing between droplets exists such that a large fraction of th'e heat released is absorbed, thus preventing flame propagation. This critical spacing is known as the "quenching distance", which is usually deter-mined by propagating flames in tubes.

5.1 PREVIOUS WORK The effectiveness of fog droplets in inhibiting or quenching a flame depends on its quenching distance, was determined by Berman et al.

as d = [4VIS3 (5.1) where V is the gas volume and S is the heat transfer surface area. For a hydrogen-air mixture, the data on the quenching distance is shown in 04300:I 5-1

Figure 5.1.~ ~ In the suspended fog droplets, this volume-to-surface ratio (i.e.,

~ ~ V/S) is equal to 1 d (1 - n) where d is the mean droplet diameter and n is the volume fraction of water. When four times this ratio approaches the quenching distance, a critical droplet diameter can be obtained as qd c 2 (5.2)

Using this criterion for quenching a flame, for a given volume fraction of water and gas composition, d can be determined. The critical droplet diameter then can be determined from the above equation. The drop sizes less than the critical drop size is capable of quenching a f 1 arne.

A plot of Eq. (5.2) for two hydrogen concentrations is shown in Figure 5.2.

5.2 PRESENT THEORY The previous theories do not model the heat transfer and combustion processes occurring between the burned gas and the suspended droplets.

A new theory has been developed, which models the heat loss and combus-tion.

0430Q:1 5-2

t ~" t 0

V

FEG. 5.1 MINIMUM IGNITION ENERGIES AND QUENCHING DISTANCE FOR KYDROGEN-OXYGEN INERT GAS MIXTURES AT ATMOSPHERIC PRESSURE 5-3

~mS' REER~~

~~~~~~~MR~ ~ESESR~~

~RSRES~~

~m ~~EEI~

&ALIIS

~ RRRE

~~~

~

~ERSRSRSRSR~ EEERR~~

BESSER~~~~~~~ SEERS~~~ ~

WMRE~

~ RRRR EERRR RERRE

~ EEEE~ERRSR~EERRE~ ~~

~

~~RA

~~ ~~ ~ ~WE

~~ERIIESECEEEEEESSW

~SEERS EREEE~

SEERS~

~ E~iFsSHSIWI RERRREMRS ESSES 0 ~ ~~l I

Consider a hydrogen/air/steam/mist droplets mixture in which a flame is gropagating. The flame may be divided into three zones: heating zone,

,reaction zone, and post-reaction zone as shown in Figure 5.3. The unburned gas at temperature T U move in the reacton zone with the laminar burning velocity S U . If the unburned gas density is p, then the constant mass flow rate m is equal to pS. The unburned gas is heated to ignition temperature T.1 and burned in the reaction zone to reach the flame temperature Tf. The fog droplets will act as a heat 'sink that reduces the flame temperature. The problem has been formulated and solved by von Karman (25) . In his formulation, three energy equations, which incorporate the heat loss terms, were written for the three zones described above. The solution to these equations yields the following relationship

- (- T1 2 - Yf)

(-~

2 Ke. = 1 exp Ii ) (Y 1 U

(( ~

~(( ()

Ii 1 +

1 K/Ii (5.3) where e.

1 C

p (T.-T)/q i U

~Z /iw P m

Kei (S/C w) ei P

the ratio of heat loss rate per unit volume to the heat release rate by chemical reaction per unit volume heat of combustion C mean specific heat 0430Q:1 5-5

V J

0

heat conductivity reaction rate (mass of fuel consumed per unit time per unit volume)

Yu hydrogen mass fraction in the heating zone Yf hydrogen mass frac ti on in the reac tion zone

'u 'u A plot of,Eq. (5.3) is shown in Figure 5.4. It is seen that for a given Ke, there is a minimum value of (Yu - Yf)/e,-. Below this mini-mum value, there is no solution for the v e,. p. Therefore, this value is considered as the flammability limit. At the flammability limit, the value of Ke. can be determined from Figure 5.4 or from Eq.

(5.3) as

)crit ej f (( u Yf)/Gi) (5.4)

'A plot of (K)cr,.t e; as a function of (Yu- Yf)/ei is shown in Figure 5.5. Equation (5.4) may be expressed as 2 ( Yu q

C p

p uSu 2 (Y -Yf) f( e-(5. 5) 12 i (T,. - Tu)

Detailed derivation procedure for Eq. (5.5), is given in Appendix B.

Using the data on S u from Reference (26) we can calculate the right hand side of Eq. (5.5) for a given composition and initial gas tempera-ture.

5.3 YERIFICATIOH OF THEORIES BY EXPERIMENTS Experiments have been conducted at Factory Mutual to study the effects of water fog density, droplet diameter, and temperature on the lower 0430Q: I

Tempore~, 7 m~~

zone (D xa0

~ ~

lj t =m(r<-Vgw

~<a>

Deltonce, x xa(

FIGURE 5.3 SCHEMATIC REPRESENTATION OF TEMPERATURE PROFILE THROUGH THE FLAME FRONT A',a 0'(i 0 20 0'ye 030 0 .2. 4 6 l0 12 (Yv-YrVdt FIGURE 5.4 THE PARAMETER A. p AS A FUNCTION OF (Y - Y )/0 FOR DIFFERENT VALUES OF KO 5-7

1 t 0.3 0.2 Ul I

CO 0.1 0.0 0

(YY))/0; FIGURE 5.5 (K) 8 AT THE FLA50BIL1'TY LINIT AS A FUNCTION OF ~Yu f

t ~i

4 flammability 1imi t of hydrogen-air-steam mixtures . The results indicated that most of the fog nozzles tested at 20 C only changed the limit from 4.03 volume percent to 4.76 percent, corresponding to fog concentration in the range of 0.028-0.085 volume percent, and average drop size ranging from 45-90 microns. For the 50'C case, the lower flammability limit increases to 7.2 percent, corresponding to 0.01-0.04 volume percent of fog and 20-50 micron average drop sizes. The results demonstrated that the fog inerting effect is more pronounced at small drop sizes.

Figures 5.6 through 5.8 show the comparison between the test data and the theoretical predictions. For this comparison, the present theory used the free stream temperature to calculate the thermodynamic proper-ties used in Equation (5.5). This yielded somewhat higher fog corcen-trations than those calculated by use of the mean 'of the flame and free stream temperatures. In Figures 5.6 and 5.7, the data suggests a linear relationship between the volume concentration and volume mean drop size on the log-log plot. It also suggests that the minimum fog inerting concentration varies approximately with the square of the volume mean drop size. In this regard, the present theory is consistent with the data while the Berman et al. theory is not.-

The present theory is in good agreement with the Factory Mutual data at 4 76 percent H2', however, it overpredict's the minimum fog inerting concentration at 7.2 percent H2. The cause of this discrepancy is still unknown. The discrepancy may be caused by the uncertainty of the data. The following discussion supports this claim. The fog droplets are very small and they vaporize very fast in a flame. Therefore, the fog droplets behave as steam except for their larger heat absorption capability. When the fog droplets vaporize, they absorb the heat of vaporization which is much larger than the steam sensible heat. Typ-ically, the heat of vaporization of water is about 1000 Btu/lb and the average specific heat of steam in the temperature range of interest is about 0.48 Btu/lb. It is well known that a tydrogen flame cannot propa-gate in steam higher than about 64 percent in a steam-air mixture. At 7.9 H2, the adiabatic flame temperature is about 1240 F and therefore 5-9 0430Q: I

oSpraco ZI63 LSpraco l 405-0604.

GSpraco 2020" l704 v'Spraco l 806-l 605 l0~

CD NON-FLAMMABLE .ZONE N

PRESENT THEORY CD FLAMMABLE ZONE BERMAN ET AL.

THEORY lo IO IOO 200 VOLUME MEAN DIAMETER, MICRONS FIGURE 5.6 COMPARISON BETWEEN THEORIES AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 4.76 PERCENT H~

5-10

I0' 0 Spraco 2I63-7604 8 v Spraco 2020-I 704 OSonicore 035H X

Non-Flammable Zone Flammable I

PRESENT THEORY .Zone O 50'C 72% Hz In Air At IO IO 20 40 50 60 70 8090.

VOLUME b]EAN DIAMETER, MICRONS.

FIGURE 5.7 COMPARISON BETWEEN THE PRESENT THEORY AND FACTORY MUTUAL FOG INERTING EXPERIMENTS ON 7.2 PERCENT H2 5-11 '

I MKRCs CIKFRN~EMsaNIVMIsstasa RCFiaalspoaaaCIR ggrll aaaaasn RWMSRIl JIRINNNmg WNNNNW NSW&NN

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~

as Esssg

~ aa IIII ann

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sar El vaassrvs Ras RW asarp~asssao I I ~

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the increase of the steam sensible heat is about 540 Btu/lb. Conse-quently, for the same amount of fog droplets and steam, the fog droplets heat absorption capability is about 1.9 times higher. This means that the fog concentration which is equivalent to 22.1 percent steam in steam and air is capable of inerting 7.9 percent H2. lhis fog inerting concentration was calculated to be 1.61 x 10-4. To inert 7.2 percent H2, a minimum fog concentration which corresponds to about 21.3 per-cent steam in steam and air is required. This gives a minimum fog incr ting concentration of 1.56 x 10 for 7.2 percent H2 .

estimates show that the present predictions are reasonable and conserva-tive. The present theory is conservative because it neglects convective and radiative heat transfer and thus underpredicts the heat loss. The estimates are consistent with Factory Mutual data on 7.9 percent H2 but not on 7.2 percent H2.

It should be noted that in the tests three fog concentration measuring techniques were used. These three techniques gave substantially dif-ferent results. The discrepancy is at least one order of magnitude difference. The fog concentration data presented in Figures 5.6 through 5.8 were obtained from one of the techniques. In view of the uncer-tainty of the data, care must be exercised in using them for inerting analysis purposes. They should be used in conjunction with the present fog inerting criterion in the assessment of fog inerting potential in =

the ice condenser plants. Some uncertainty also exists in the present fog inerti ng theory . The uncertainty associated with the underpredic-tion of the heat loss and temperature dependence of the thermophysical properties is estimated to be +63 percent.

It should also be pointed out that the Factory Mutual data and the pre-sent theory can only predict the minimum fog inerting concentration. To insure hydrogen burn in all directions in the ice condenser upper plenum, further work in this area may be required.

0430Q:I 5-13

P r

6.'0 ASSESSMENT OF FOG INERTING PROBABILITY IN ICE CONDENSER CONTAINMENTS As discussed in the previous sections, there exists several mechanisms of generating and removing fog droplets from the ice condenser contain-ment. In addition, fog droplets are also transported from one subcom-partment to another by entrainment in the gas stream. The fog entrain-ment rate is difficult to assess without knowing the velocity field and drop size distribution. For simplifying purposes, it is presently assumed that, the mass fraction of mist droplets in the intercompart-mental and fan flows is the same as that within the subcompartment from which the flows are originated. 'his is a good assumption since the fog droplets are small. The amount of fog droplets in a subcompartment depends on all these mechanisms.

The total amount of fog droplets is important in- determining the volume fraction of suspended condensate in a subcompartment. This volume frac-tion, in turn, is used in the fog inerting criteria to determine whether a particular hydrogen mixture composition formed in a subcompartment at any time is flammable or not. In other words, by knowing the hydrogen concentration and the mean fog drop size, we can determine whether the calculated volume fraction of fog droplets is high enough to prevent the mixture from combustion.

6.1 DETERMINATION OF VOLUME FRACTION OF MIST DROPLETS IN ICE CONDENSER CONTAINMENTS Consider a subcompartment in the ice condenser comtainment as shown in Figure 6.1. There exist several mechanisms by which mist drops can be generated or removed. Fog droplets can be generated by homogeneous or heterogeneous nucleation in the thermal boundary layer and/or in the bulk stream and they can increase in size by condensation or decrease in size by vaporization. The rate of generation of mist droplets by con-densation and their continued growth (or shrinkage due to vaporization) is represented by mcondd. The other mechanism of generating mist drop-lets considered in this analysis is the primary coolant discharge from the break and the rate of generating fog droplets from this mechanism is 0430Q:I 6-1

dj 1

represented by moreakk. Two fog droplet removal mechanisms are consid-ed in this analysis: one is gravitational settling and the other is

~

moval by containment spray. The fog droplet removal rate by gravita-tional settling is represented by m sett and that by spray is represen-

~

ted by m . In addition to the generating and removal mechanisms discussed above, the mist droplet concentration in a subcompartment is also affected by the intercompartmental and fan flows. In the intercom-partmental and fan flows, the mass fraction of fog droplets entrained is q and the gas mixture flow rate is m. Therefore the rates of fog drop-lets mass into and out of a subcompartment are g qi mi and g n t m t, respectively. It should be noted that g n ~ m.

and $ nout mout include the fog mass entrainment rates in all the intercompartmental and fan flows into and out of a subcompartment.

The mass conservation equation for the fog droplets in a subcompartment may be expressed as dM 1t ~ in in ~out out break cond set sp where ( is'a summation over all the flow paths..In Eq. (6.1), if m

d is negative, then it becomes the rate of vaporization. Eq.

(6.1) can be integrated to give the total mass of condensate at time t c ~"in in ~"out out break 0

cond 'set sp

~" in 1 1

~" out i i + i 1

in out break 1 1 1 cond set i (6.2) sp 0430Q:I 6-2

r The present analysis will employ the CLASIX calculations of containment 4ransient during a small LOCA. In the CLASIX analysis, the entire ice condenser containment is usually divided into five or six subcompart-ments for analysis purposes. Temperatures, total pressure, steam partial pressures, and intercompartmental flow rates are calculated during transients. This information is used in Eq. (6.2) to determine fog droplet mass.

When applying Eq. (6. 1) to each individual subcompartment, we have the following fog mass, conservation equations in finite difference form:

U er Com artment NUC (t+ at) =

NUC(t) + ()e.m (t)

UC,set 4C,s Lower Com artment NC (t + st) =

NLC(t) +

( )n.m(

~"out out (6.4)

LC,break LC,cond LC,set LC, f ) st 0430Q:1 6-3

P C

Ice Condenser U er Plenum MUP(t + at) = MUP(t) +'(7nin min(t) - ~ "out mout(t)

) )

UP,cond( UP,set( )

Ice Condenser Lower Plenum s

MLP t + st) MLP t ( gn( m. (t) (6.5)

~soot out( LP d( ) LP,set )

Dead Ended Re ion M()E (t + at) =

MUE(t) + (pn;m;(t) (6.6) e

~soot out "bE cond set DE

)

Fan/Accumul ator Rooms*

MEA (t + st) 'EA(t) + (Pn(n m. (t) (6.7) e

~"out out FA cond 4

WA set FA sp In the present analysis, the fog concentrations in the intercompart-mental and fan'flows are assumed to be the same as those in the compart-ment from which the flows are orginated.

  • These rooms were analyzed only for the D. C. Cook plant (See Figure 6.S).

~ ~

0430Q:1 6-4

i I'

In the equations given above, the intercompartmental and fan flow rates m.

in and moutt are provided by CLASIX calculational results. The procedures of calculating fog droplets generating and removal rates are based on the discussions in the previous sections and the details are given in the following sections.

6.1.1 CALCULATION OF HBREAK To date little experimental data is available to estimate the amount of fog droplets generated by the break flow. For a large LOCA, Almenas and Marchello estimated that 13 percent of the total blowdown drop population (by weight) has drop radius range from 1 p to 20 p and only 1 tivee.

percent less than 1 p. This estimate is somewhat larger than the 4 p mean drop size sited in Section 3.1.2, which is believed to be conserva-Since we are only interested in fog drops smaller than 20 p, and only these drops can remain suspended in air until the time when the hydrogen is released, we assume that the estimate of Almenas and Marchello is applicable in small LOCAs and 14 percent of the suspended liquid are fog droplets which have a potential inerting effect.

The fraction of reactor coolant discharged from the break remains as suspended liquid has been determined in Section 3. Knowing the break flow rates from a computer code such as MARCH, we can calculate the amount of liquid suspended in the atmosphere. Then from the drop size distribution we can calculate the amount of fog droplets suspended in the atmosphere.

Oefining the blowdown rate as m , the liquid fraction of the break flow as gb, the fraction of fog droplets smaller than 20 p as fb, we have break b b ~b (6.8) 0430Q:1 6-5

j

(

In the present analysis fb = 0.14 is used. fb becomes zero when the water level in the'eactor vessel falls below the break elevation.

6.1.2 CALCULATION OF MCOND As discussed previously, m d is the rate of formation of mist drop-lets by nucleation, condensation, or vaporization. Nucleation of fog droplets can take place in the thermal boundary layer and in the bulk fluid. We conservatively assume that little supersaturation is needed for nucleation in the bulk stream and fog will form when the bulk stream steam partial pressure reaches the saturation steam pressure correspond-ing to the gas stream temperature. Therefore, the bulk stream fog formation rates can be determined from the equilibrium thermodynamic states of the gas mixture.

The boundary layer fog formation rate can be determined using the Hijikata-Mori theory of fog formation in the thermal boundary layer as discussed in Section 3.2.4. The fog formation rate in the thermal boundary layer and the bulk stream is given by Eq. (3.12).

Boundary layer and bulk stream fog formation rates will be calculated for the ice condenser and lower compartment.

A computer program called'FOG has been developed to calculate m computer program requires input of the volumetric gas flow rate, cond'his gas and wall temperatures, total pressure, and steam partial pressure.

This information can be obtained from the CLASIX output.

6.1.3 CALCULATION OF MSET The rate of settling of the fog droplets depends on their terminal velocity, concentration and compartment cross sectional area. The droplet terminal velocity is a function of drop size. In the present study, Equation (4.1) will be used to calculate the fog gravitational settling rate.

6-6 0430Q:I

/~

~

6.1.4 CALCULATION OF MSp The mass of a fog droplet is much'maller than that of a spray droplet.

Therefore, when a spray droplet collides with a fog droplet, the fog droplet will coalesce with the spray drop and fall to the sump. In the present study, the fog removal rate by sprays is given by Equation (4.2).

It is expected that the spray drop collection efficiency is very high, and therefore a 100 percent drop collection efficiency is assumed in the analysis. A sensitivity study is needed to be carried out to study the effect of E on the volume fraction of fog droplets.

A computer program called FOGMASS has been developed to solve Eqs. (6.3) through (6.7). This program uses a finite difference numerical scheme to carry out integration. This program takes input from FOG and CLASIX output data. Specific output data from CLASIX are time histories of gas temperature, wall temperature, total pressure, steam partial pressure, and intercompartmental. and fan flow rates.

6.2 FOG INERTING PROBABILITY IN THE SEQUOYAH PLANT The computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the Sequoyah plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation. in the Sequoyah ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the Sequoyah containment subcompartments.

T o compute the fog formation rates in the ice condenser upper plenum and

'ower compartment, some output data from the Sequoyah CLASIX analy-sis (27) are needed. These data include time histories of gas tempera-ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 27. The subcompartmentaliza-ion model used in the Sequoyah CLASIX analysis is shown in Figure 6. 1.

In this study only the S2D accident scenario has been analyzed.

0430Q:I 6-7

'e J- '4

~

II

FIGURE 6.1 SEQUOYAH CLASIX CONTAINMENT MODEL ICE CONDENSER UPPER UPPER PLENUhh COMPARTMENT ICE BED ICE DEAD CONDENSER ENDED LOWER PLENUM REGION COMPARTMENT AIR RETURN FAN/HYDROGEN SKIMMER SYSTEM FLOW PATH CONTAINS DQORS FLOW ALLOWED IN BOTH DIRECTIONS FLOW ALLOWED IN ONE DIRECTION SPRAY HEADER

S' The FOG input data for SequoyahS20 Case I are given in Tables 6.1 and 6.2, and the caIculational results are shown in Figures 6.2 and 6.3. In Figure 6.2, the fog formation rate in the lower compartment is shown.

For the first few hundred seconds the wall temperature is lower than the

'dew point corresponding to the steam partial pressure and therefore fog starts to form. After about 600 seconds, the fog formation rate becomes negligibly small since the wall temperature is only a few degrees below the dew point. There is no fog formation in th'e lower compartment after about,1800 seconds. The fog formation rate in the ice condenser is shown in Figure 6.3. It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment. It increases with the ice condenser steam flow rate and reaches a peak of 14 lb/sec at about 1800,seconds. The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen rel ease.

The nine fog formation rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form and there is a built-in interpolation scheme in FOGtQSS to obtain values for the intermediate time steps.

FOGNSS computes the rate of fog generation by the break flow, th'e fog rate due to gravity, and the fog removal rate due to sprays, as'ettling well'as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as follows.

The rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the MARCH output (7) 'or a small LOCA. The quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature. According to the MARCH predic-tion 0) the discharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds. Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged 0430(:I 6-9

I I I I I I I 00 I l I III III I I

K' g g I I II I III I 1 I IIII I iI I I I I' I I I I I

4 8

from the break is essentially steam. Therefore, in the present stu@,

it is assumed that no fog is generated by the break flow after 2172 seconds.

For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed. The terminal velocity of a 10 p drop is about I

.cm/sec. Because of this low terminal velocity, gravitational settling is not an effective fog removal mechanism. The assumption of 10 p volume mean drop size is therefore conservative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially. It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative. Furthermore, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans. All the assumptions mentioned above make the present analysis very conservative. The containment geometric data needed in computing the settling rate are given in Table 6.3.

f For fog removal by sprays, a spray flow rate of 9500 gpm was used for Sequoyah. According to the Sequoyah CLASIX analysis~27~, the sprays are initiated at 142 seconds. A volume fraction of sprays (volume of sprays divided by volume of the spray zone) of 3.3 x 10-4 was.used, which was obtained using a spray drop fall height of 107 ft, a spray zone volume of 485,500 ft3, and a volume mean drop size of 700 p. As previously discussed a spray removal of a 100 percent was used.

In Figure 6.1, the directions of the intercompartmental fl'ows are shown. The intercompartmental flow rates for the six.flow paths and nine time steps were obtained from the OPS CLASIX analysis and are given in Table 6.5. The present analysis considers the intercompartmental flows'as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.

0430Q:I 6-12

r It is seen in Figure 6.1 that two trains of the air return fan and hydrogen skinner system take suction from the dead ended region and from the upper compartment and discharge into the lower compartment. The fans are initiated at 712 seconds. The fan head-flow curve reported in Reference 27 was used to compute the fan flow rates. Fan flow rates of 1645 ft /sec 3

and 10 ft /sec 3

were used for the air return fan and the hydrogen skimmer system, respectively. These flow rates were calculated using average ap's between the upper compartment and the lower compart-ment, and between the dead ended region and the lower compartment. It was also assumed. that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.

The results of the FOGMASS calculation are shown in Figure 6.4. It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing. At about 700 seconds, the lower compartment

.fog concentration reaches its peak of 2.2 x 10 . Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases. However,-

the upper plenum fog concentration keeps rising until about 900 seconds, due to an increasing fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 5.4 x 10 at about 900 seconds. The lower plenum fog concentration is almost the same as the lower compartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum. -Therefore, these two volumes behave as a single volume fn terms of fog concentration.

At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations. The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment. The effect of .sprays on .the upper compartment fog concen-tration is clearly seen in Figure 6.4. At 142 seconds, the sprays are 0430Q:I 6-13

t I

r I I I 0 g I I I< I >>

ll I I I I I

I

~

~

~ ~

I ~ ~ ~ ~

I ~

I a II I III III III III II II II I

II I I II II I>>

fl I>>

II I>>

II I>>

II II I I

II I ll II II l

I MTH II >>

II I ~

II I~

t~

- turned on and the upper compartment fog concentration drops sharply until about 600 seconds. At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompartmen-tal flow into the compartment increases sharply at that time. A peak concentration of 7 x 10 -6 in the upper compartment is reached at about 1200 seconds.

Hydrogen starts to release into the containment at about 3804 seconds, according to the MARCH calculation (27) . It reaches 4 volume percent at about 4300,',4400, and 4670 seconds in the lower compartment, upper plenum, and upper compartment, respectively.

At 4300 seconds, the calculated lower compartment fog concentration is

-7 9.7 x 10 , which is about an order of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H2. At 4670 seconds, the upper compartment fog concentration is 1.35 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*. At the times of reaching 8.5 percent H2, the fog concentrations in the lower and upper compart-ments are even lower than the figures given above. Therefore, it is concluded that the fog concentrations'n the lower and upper compart-ments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion. .

.However, at 4400 seconds, the calculated fog concentration in the upper plenum is 6.1 x 10

-5 which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10 or higher for 10 p volume mean drop size. At 4600 seconds, the upper plenum hydrogen concentration reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H . In comparison, the present theory on fog inerting pre-dicts 1.02 x 10 for 7.2 percent H2.

The fog inerting criterion used is described in Section 5.2.

0430Q:1 6-15

Therefore, it appears that it is possible to inert 7 percent H2 but unlikely. However, at 8 percent H2 in the upper plenum, which occurs at about 4650 seconds, the fog concentration is 5.5 x 10 5, which is too low to inert 8 percent H2. An extrapolation of the Factory Mutual 8 percent H2 data to 10 p volume mean drop size and the present pre-diction give 1.9 x 10-4 and l.2 x 10-4 for the minimum required fog inerting concentration, respectively . Therefore both the theory and the extrapolation of test data show that fog inerting will not occur in the upper plenum.

The glow plug igniters which have been installed in the Sequoyah con-tainment were designed to burn hydrogen lower than 8.0 percent. As discussed previously, no fog inerting effects will be expected in the Sequoyah lower and upper compartments. Therefore, the glow plug igni-tet s are expected to function as designed in these two compartments. It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent.

However, it seems very unlikely that the same igniters would fail to ignite 8.0 percent H2 as designed, considering the fact that consider-Pg able conservatism has been exercised in the present analysis.

Sensitivity studies of the spray removal efficiency and the fraction of blowdown droplets smaller than 20 p for the Sequoyah plant have been performed. A case of 10 percent spray removal efficiency was run using FOGMASS. The calculational results showed that the fog concentrations in the lower compartment, lower plenum, and upper. compartment at 4600 seconds were increased approximately by a factor of 10. However, these concentrations are still too low to inert 8 percent hydrogen- In com-parison, the fog concentration in the upper plenum is increased by only 20 percent because the concentration at this time is primarily deter-mined by the fog formation rate in the ice condenser. This increase is too small to change the conclusion given previously on the inerting probability in the upper plenum. Another case in which all the blowdown droplets were assumed to be smaller than 20 p was run using FOGMASS.

The calculational results showed that at 4600 seconds the fog concentra-tions in the lower compartment and lower plenum were increased by 15 0430Q I 6-16

(\

percent while the increases in the upper plenum and upper compartment were negligibly small. The insensitivity of the fog concentrations to the parameter of the fraction of blowdown droplets smaller than 20 u is due to the effectiveness of the spray removal. At 4600 seconds, almost all the blowdown droplets are removed by the sprays. The sensitivity studies showed that the fog concentration in the upper plenum at the time of significant hydrogen release is not sensitive to the spray removal efficiency and the fraction of blowdown droplets smaller than 20 g.

6-17 0430(:1

L 'j I

TABLE 6.1 FOG IHPUT QATA FOR SfgUOYAH LOWER COMPARTMENT Steam Lower Compartment Gas Wall Total Partial Gas flow Rate Temp. Temp Pressure Pressure Time (sec) (ft /sec) ('F) ('F) ~(sia) ~(s(a) 60 1404.5 150 118 16. 7 610 646.7 215 202 21. 6 15.3 1210 3157.2 188 176 20.4 8.9 1810 3115.5 188 176 20.5 8.8 2410 2913.7 180 173 20.1 7.5 3010 2871.?, 179 169 '9.9 7.2 3510 2739.3 178 169 19.9 6.9 4010 2755.9 175 164 . 19.4 5.5 4510 2848.8 197 173 19.8 4.8 0430Q:1 6-18

TABLE 6.2 FOG INPUT DATA FOR SEQUOYAH ICE CONDENSER Steam Ice Condenser Gas Ice Total Partial Gas Flow Rate Temp. Temps Pressure Pressure Time (sec) (ft /sec) ('F) ('F) ~(sia) ~(sia) 60 1082 120 32 16. 6 2.5 610 96.4 132 32 21.8 2.3 1210 '2654 186 32 20.4 8.1 1810 2799 188 32 20.5 8.8 2410 2679 182 32 20.0 7.6 3010 2629 179 32 19.9 7.2 3510 2502 178 32 19.9 7.0 4010 2594 171 32 19.4 5.7 4510 2628 187 32 19.8 4.7 6-19 0430Q 1

(P TABLE 6.3 GEOMETRIC DATA FOR SEgUOYAH CONTAIHMEHT Volume (ft3 ) Floor Area (ft )

Lower Compartment 289,000 5,410 Ice Condenser Lower Plenum 24,200 3,100 Ice Condenser Upper Plenum 47,000 3,200 Upper Compartment 651,000 10,390 Dead Ended Region 94,000 3,350 0430(:1 6-20

k.

- TABLE 6.4 MARCH PREDICTION OF REACTOR COOLANT MASS AND ENERGY RELEASE RATE FOR THE S2D SEQUENCE Time H20 Mass Re1ease Rate H20 Energy Re1ease Rate

( seconds) (Ibm/sec) (Btu/sec) 0.0 197.2 1.167 x 10 2172 190.5 1.097 x 10 2478 44.85 5.230 x 10 3180 53.53 6.547 x 10 3804 34.82 4.262 x 10 4428 21.40 2.842 x 10 4752 48.42 5.558 x 10 5700 19.42 2.182 x 10 6012 14.07- 1.583 x 10 6960 5.253 5.989 x 10 3 3

7062 4.718 5.388'x 10 7206 4.060 4.693 x 10 6-21 0430Q:1

I g TABLE 6.5 IHTERCOMPARTHENTAL fLOM RATES (ft /sec)

PREDICTED BY CLASIX FOR SEQUOYAH Time Flow From Flow From Flow From flow From flow From (sec) LC to LP LP to UP UP to UC UC to LC DE to LC 6.001E1 1. 175E3 1.082E3 7.029E2 -9. 905E1 -1.304E2

6. 100E2 3.580E2 9. 641E1 -3. 931E1 -2.113E1 -2.676E2 1.210E3 2.864E3 2. 654E3 1. 272E3 -1. 838E2 -1.094E2 1.810E3 2. 799E3 1.323E3 -1.793E2 -1.088E2 2.828E3'.695E3 2.410E3 2. 679E3 1.375E3 -1. 502E2 -6. 855E1 3.010E3 2.654E3 2.629E3 1.407E3 -1.634E2 -6.326E1 3.510E3 2.528E3 2.502E3 1.352E3 -1. 643E2 -4. 699E1 4.010E3 2. 613E3 2.594E3 1.537E3 -1.095E2 -,3.348E1
4. 510E3 2. 694E3 2.628E3 1.627E3 -1. 106E2 -4.426E1 6-22 0430Q:I

4 6.3 FOG IHERTIHG PROBABILITY IH THE McGUIRE PLAHT I

The computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the McGuire plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the McGuire ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the McGuire containment subcompartments.

To compute the fog formation rates in the ice condenser upper plenum and lower compartment, 'some output data from the McGuire CLASIX analy-sis (28) are needed. These data include time histories of gas tempera-ture, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 28. The subcompartmentaliza-tion model used in the McGuire CLASIX analysis is shown in Figure 6.5.

In this study only the S20 accident scenario has been analyzed by CLASIX for McGuire.

4 ~

The FOG input data for McGuire S2D Case I are given in Tables 6.6 and 6.7, and the calculational results are shown in Figures 6.6 and 6.7. In Figure 6.6, the fog formation rate in the lower compartment is shown.

For the first few hundred seconds the wall temperature is lower than the dew point corresponding to the steam partial pressure and therefore fog starts to form. The fog formation rate is low because the wall tempera-

'ure is only a few degrees below the dew point. Fog formation in the lower compartment becomes zero after about 600 seconds. The fog forma-tion rate in the ice condenser is shown in Figure 6.7. It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment. The fog formation rate increases with the ice condenser steam flow rate and reaches the first peak at about 1510 sec-onds. Then the rate decreases because of the decrease in the steam flow rate. The fog formation and the steam flow rates start to increase again at about 2510 seconds. The fog formation rate reaches the second 0430Q:I 6-23

II

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peak of I0.2 1b/sec at about 3260 seconds. The eight fog formation

'rates in the lower compartment and in the ice condenser are input to FOGNSS in a tabular form.

FOGNSS computes the rate of fog generation by the break flow, the fog settling rate due to gravity, and the fog removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as follows.

The rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the NRCH output P) for a small LOCA. The quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature. According to the NRCH predic-tion the discharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds. Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam. Therefore, in the present study,

0) it is assumed that no fog is generated by the break flow after 2172 seconds.

For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed. The assumption of 10 p volume mean drop size is con-servative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially. It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis conservative. Furthermore, no con-sideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans. All the assumptions mentioned above make the present analysis very conservative. The containment geometric data needed in computing the settling rate are given in Table 6.8.

6-27 0430Q I

C 4 For fog removal by sprays, a spray flow rate of 6800 gpm was used for RcGuire. According to the HcGuire CLASIX analysis , the sprays are initiated at 124 seconds. A volume fraction of sprays (volume of sprays divided by volume of the spray zone) of 3.3 x 10 was used. As pre-viously discussed a spray removal efficiency of a 100 percent efficiency was used.

In Figure 6.5, the directions of the intercompartmental flows are shown. The intercompartmental flow rates for the six flow paths and eight time steps were obtained from the OPS CLASIX analysis and are given in Table 6.9. The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those in the compartments from which the flows are originated.

Figure 6.5 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions. The fans are initiated at 694 sec-onds. The fan head-flow curve reported in Reference 28 was used to compute the fan flow rates. Fan flow rates of 1000 ft /sec and 100 3

ft 3

/sec were used for the air return fan and the hydrogen skimmer system, respectively. These flow rates were calculated using average ap's between the upper compartment and the lower compartment, and between the dead ended region and the upper compartment. It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.

The results of the FOGMASS calculation are shown in Figure 6.8. It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, ice condenser lower and upper plenums are about the same and increasing. At about 600 seconds, the lower compartment fog concentration reaches its peak of 1.6 x 10 . Afterward, the intercompartmental flows transport more fog droplets out of the lower compartment than are generated by the break flow and condensation and, therefore, the lower compartment fog concentration decreases. However, the upper plenum fog concentration keeps rising until about 800 seconds, 0430Q:I 6-28

~

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~ ~~ ~.

~ 0~0~4~0~

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due to an increasing fog.formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 6.4 x 10 at about 800 seconds. The lower plenum fog concentration is almost the same as the lower copartment fog concentration because of little difference in the intercompartmental flow rates into and out of the ice condenser lower plenum. Therefore, these two volumes behave as a single volume in terms of fog concentration.

At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and,'herefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations. The highest fog concentration exists in the ice condenser upper plenum while the lowest exists in the upper compartment. The effect of sprays on the upper compartment fog concen-tration is clearly seen in Figure 6.8. At 124 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 600 seconds. At about 600 seconds, the upper compartment fog concentration starts to increase again because the intercompart-mental flow into the compartment increases sharply at that time. A peak concentration of 7.5 x 10 in the upper compartment is reached at about 1500 seconds.

Hydrogen starts to release into the containment at about 3804 seconds, according to the MARCH calculation . It reaches 4 volume percent at about 4300, 4400, and 4850 seconds in the lower compartment, upper pl enum, and upper compartment, respectively.

At 4300 seconds, the calculated lower compartment fog concentration is 8 4 x 10, which is about an order of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H2. At 4850 seconds, the upper compartment fog concentration is 1.47 x 10 which is about a factor of five smaller than the minimum fog concen-tration required for inerting 4 percent H2*.= At the times of

  • The fog inerting criterion used is described in Section 5.2.

0430Q: 1 6-30

reaching 8.5 percent H2, the fog concentrations in the lower and upper compartments are even lower than the figures given above. Therefore, it is concluded that the fog concentrations in the lower and upper compart-ments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion.

However, at 4400 seconds, the calculated fog concentration in the upper plenum is 9.8 x 10 which is higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration niust be 8.4 x 10 or higher for 10 p volume mean drop size. At 4500 seconds, the upper plenum hydrogen concentration

-5 reaches about 7 percent and the fog concentration is 9.3 x 10 Again, an extrapolation of the Factory Mutual data to )0 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H2. In comparison, the present theory on fog inerting pr e-dicts 1.02 x 10 for 7.2 percent H2. Therefore, it appears that it is possible to inert 7 percent H2, but unlikely. However, at 8 per-cent H2 in the upper plenum, which occurs at about 4600 seconds, the fog concentration is 9.1 x 10, which is too low to inert 8 percent An extrapolation of the Factory Mutual 8 percent H2 data to 10 u volume mean drop size and the present prediction give 1.9 x 10 4 and 1.2 x 10 for the minimum required fog incr ting concentration, respectively. Therefore, both the theory and the extrapolation of the'est data indicate that fog inertihg will not occur.

The glow plug igniters which have been installed in the McGuire contain-ment were designed to burn hydrogen lower than 8.5 percent. As discus-sed previously, no fog inerting effects will be expected in the McGuire lower and upper compartments. Therefore, the glow plug ignite s are expected to function as desi'gned in these two compartments. It may be possibly that fog present in the ice condenser upper plenum may prevent the glow plug ignite s from igniting hydrogen below 7 percent. However, it seems very unlikely that the same igniters would fail to ignite 8.5 "The fog inerting'criterion used is described Section 5.2.

0430Q:1 6-31

percent H2 as designed, considering the fact that considerable conser-vatism has been exercised in the present analysis.

6-32 0430Q:1

TABLE 6.6 FOG INPUT DATA FOR McGUIRE LOWER COMPARTMENT Steam Lower Compartment Gas Wall Total Partial Gas Flow Rate Temp. Temp. Pressure Pressure Time (sec) (ft /sec) ('F) ~(si a) 60 1624.6 160 149 16. 5 510 1248.1 225 215 22.2 18. 3 1510 2387.8 205 198 21.9 12. 6 2010 2393.8 205 198 22 12.4 2510 1940.7 195 193 '21.5 10.4 3260 2055.-5 200 195 21.6 10.8 3760 1801.7 200 , 194 21 9.3 4510 1919.3 250 222 21.2 7.3 6-33 0430/:1

TABLE 6.7 FOG IHPUT DATA FOR HcGUIRE ICE COHDEHSER Steam Ice Condenser Gas Ice Total Parti al Gas Flow Rate Temp. Temp. Pressure Pressure Time (sec) (ft /sec) 60 820. 5 90 32 16.5 510 107. 1 130 32 22.2 2.3 1510 1926 190 32 "21.9 9.3 2010 1637 193 32 22 2510 1145 188 32 21.4 8.6 3260 1630 195 32 21. 6 10.3 3760 1514 193 32 21. 1 8.1 4510 1464 192 32 22.1 7.1 6-34 0430Q:1

TABLE 6.8 GEOMETRIC DATA FOR McGUIRE CONTAINMENT

'I Volume (ft ) Floor Area (ft )

Lower Compartment 237,400 5,410 Ice Condenser Lower Plenum 24,200 3,100 Ice Condenser Upper Plenum 47,000 3,200 Upper Compartment 670,000 10,390 Dead Ended Region 130, 900 3,350

~ 6-35 0430Q:1

l TABLE 6.9 IHTERCOMPARTMEHTAL FLOW RATES (ft3 /sec)

PREDICTED BY CLASIX FOR McGUIRE Time Flow From flow From Flow From Flow From Flow from (sec) LC to LP LP to UP UP to UC UC to LC DE to LC 6.001E1 1. 351E3 8.205E2 5.783E2 -1. 198E2 -1. 538E2

5. 100E2 8.716E2 1.071E2 , -2. 269E1 -2.863E1 -3.479E2
1. 510E3 2.008E3 1. 926E3 8.635E2 -1. 900E2 -1.898E2 2.010E3 2.010E3 1. 637E3 6.869E2 -2.266E2, -1.572E2
2. 510E3 1.722E3 1. 145E3 4.807E2 -1. 410E2 -7. 767E1 3.260E3 1.713E3 1. 630E3 6.666E2 -2.087E2 -1.338E2 3.760E3 1.546E3 1. 514E3 7. 231E2 -1.289E2 -1.268E2
4. 510E3 1.634E3 1. 464E3 7. 640E2 -1. 328E2 -1. 515E2 6-36 0430Q:1

6.4 FOG INERTING PROBABILITY IN THE D. C. COOK PLANT f'he computer codes, FOG and FOGMASS, were used to perform fog inerting analysis for the D. C. Cook plant. FOG was used to calculate the rates of fog formation due to boundary layer and bulk stream condensation in the D. C. Cook ice condenser and lower plenum. Then these fog formation rates were used in FOGMASS to compute the fog concentrations in each of the D. C. Cook containment subcompartments.

To compute the, fog formation rates in the ice condenser upper plenum and lower compartment, some'output data from the Cook CLASIX analysis (29) are needed. These data include time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each contain-ment subcompartment, as well as the intercompartmental and fan flow rates. In order to utilize the CLASIX output data, the ice condenser containment is subcompartmentalized in the FOGMASS program in exactly the same manner as in Reference 29. The subcompartmentalization model used in the Cook CLASIX analysis is shown in Figure 6.9. In this study only the S20 accident scenario has been analyzed.

The FOG input data for Cook S2D Case .1 are given in Tables 6.10 and 6.11, and the calculational results ar e shown in Figures 6.10 and 6.11.'n Figure 6.10, the fog formation rate in the lower compartment is shown. It is seen that the fog formation rate is negligibly small. It should be noted that the calculation of the lower compartment fog concentration in the 0 . C. Cook plant starts at 600 seconds instead of 60 seconds used for the other two plants. The fog formation rate in the lower compartme starts to increase at about 4200 seconds because of the increase in the steam partial pressure. It reaches 0.017 lb/sec at about 4590 seconds. Fog formation in the lower compartment will stop after 4700 seconds because of the hydrogen burn thereafter. The fog formation rate in the ice condenser is shown in Figure 6.11. It is seen that the fog formation rate in the ice condenser is much larger than that in the lower compartment. It increases with the ice condenser steam flow rate and reaches a peak of about 15.6 lb/sec at about 1200 seconds. The fog formation rate in the ice condenser then begins to decrease and is low at the time of significant hydrogen release.

0430Q 1 6-37

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The eight fog formation rates in the lower compartment and in the ice

. condenser are input to FOGMASS in a tabular form.

.: FOGMASS computes the rate of fog generation by the break flow, the fog settling rate due to gravity, and the fog-removal rate due to sprays, as well as the rates of fog entrainment by intercompartmental and fan flows. The input data needed to calculate each of these rates are dis-cussed as follows.

The rate of reactor coolant release to the containment and the coolant enthalpy were obtained from the MARCH output P) for a small LOCA. The

'I quality of the break flow was calculated using the enthalpy and the lower compartment gas temperature. According to the MARCH predic-tion P) the di,scharge of liquid by the break flow into the lower com-partment lasts for only 2172 seconds. Afterward, the water level in the reactor vessel drops below the break elevation and the fluid discharged from the break is essentially steam. Therefore, in the present study, it is assumed that no fog is generated by the break flow after 2172 seconds.

For fog removal by gravitational settling, a volume mean drop size of 10 p was assumed. The assumption of 10 p volume mean drop size is con--

servative, considering the fact that for a few thousand seconds the drop agglomeration mechanism would be able to increase volume mean drop size substantially. It should also be noted that a smaller volume mean drop size means that the minimum fog inerting concentration would be reduced and thus makes the present analysis even more conservative. Further-more, no consideration was given to the deposition of fog on the walls and vertical surfaces of the structure, or for fog removal in the fan flows when it passes through ducts and fans. All the assumptions men-tioned above make the present analysis very conservative. The contain-ment geometric data needed in computing the settling rate are given in Table 6.12.

0430Q:I 6-41

C For fog removal by sprays, spray flow rates of 4000, 1800, and 528 gpm were used for the upper compartment, lower compartment, and fan/accumulator rooms, respectively. According to the Cook CLASIX analysis~ ~, the sprays are initiated at 141 seconds. A volume fraction of sprays '(volume of sprays divided by volume of the spray zone) of 3.3 x 10-4 was used. As previously discussed a spray removal efficiency of a 100 percent efficiency was used.

In Figure 6.9, the directions of the intercompartmental flows are shown. The intercompartmental flow rates for the six flow paths and eight time steps 'were obtained from the OPS CLASIX analysis and are given in Table 6. 13. The present analysis considers the intercompart-mental flows as the mechanisms of transporting fog from one compartment to another. It was assumed in the present analysis that the fog concen-trations in the intercompartment flows are the same as those:in the compartments from which the flows are originated.

Figure 6.9 shows two trains of the air return fan and hydrogen skimmer system and the fan flow directions. The fans are initiated at 711 sec-onds. The fan head-flow curve reported in Reference 29 was used to compute the fan flow rates. Fan flow rates of 1388, 61.76, and 4.13 ft3/sec were used for the flows from the upper compartment, lower compartment, and dead ended region to the fan/accumulator rooms, respectively. These flow rates were calculated using the hp's between the the fan/accumulator rooms and three other compartments. It was also assumed that the fog concentrations in the fan flows are the same as those in the compartments from which the flows are originated.

The results of the FOGMASS calculation are shown in Figure 6.12. It is seen that for the first few hundred seconds the fog concentrations in the lower compartment, and the ice condenser lower plenum are high. At about 140 seconds, the lower compartment fog concentration reaches its peak of 1 x 10-4. After the sprays are initiated at 141 seconds, the fog concentrations in the lower compartment, upper compartment, and fan/accumulator rooms drop sharply. However, the upper plenum fog concentration keeps rising until about 1200 seconds,'ue to an increasing 0430Q:1 6-42

I I I I I ~

I ~ ~ ~ T ~

T ~ ~

I ~

I ~ ~ I

'l fog formation in the ice condenser and more fog entrained in the intercompartmental flow into the upper plenum. The upper plenum fog concentration reaches its peak of 2.4 x 10 at about 1200 seconds.

After about 1200 seconds, the lower plenum fog concentration is almost the same as the lower copartment fog concentration since the intercompartmental flows quickly make the fog concentrations in these two compartments uniform. Therefore, these two volumes behave as a single volume in terms of fog concentration.

At 2172 seconds, the break flow in the lower compartment stops genera-ting fog and, therefore, the fog concentrations drop sharply there-after. The effect is more pronounced for the lower compartment and lower plenum fog concentrations. The highest fog concentration exists in the ice condenser upper plenum. The effect of sprays on the upper compartment fog concentration is clearly seen in Figure 6.12. At 141 seconds, the sprays are turned on and the upper compartment fog concentration drops sharply until about 300 seconds. At about 300 seconds, the upper compartment fog concentration starts to increase again because the intercompartmental flow into the compartment increases

-6 sharply at that time. A peak concentration of 9.5 x 10 in the upper compartment is reached at about 1400 seconds.

Hydrogen starts to release into the containment at about 3804 seconds, according to the HARCH calculation . It reaches 4 volume percent at about 4350, 4370, and 4700 seconds in the lower compartment, upper plenum, and upper compartment, respectively.

At 4350 seconds, the calculated lower compartment fog concentration is 10 , which is about two orders of magnitude smaller than the minimum fog concentrations required for inerting 4 percent H . At 4700

-6 seconds, the upper compartment fog concentration is 2.4 x 10 , which is about a factor of two smaller than the minimum fog concentration required for inerting 4 percent H *. At the times of reaching 8.5

  • The fog inerting criterion used is described in Section 5.2.

0430Q:1 6-44

percent H , the fog concentrations in the lower and upper compartments are even lower than the figures given above. Therefore, it is concluded that the fog concentrations in the lower and upper compartments are too low to have any inerting effect. The use of the present theory on fog inerting also leads to the same conclusion.

However, at 4370 seconds, the calculated fog concentration in the upper plenum is 6.5 x 10 which's higher than the Factory Mutual fog inerting data extrapolated to 10 p drops and the present theoretical prediction. The data shows that in order to inert 4.76 percent H2 the fog concentration must be 8.4 x 10 or higher for 10 p volume mean drop size. At 4530 seconds, the upper plenum hydrogen concentration

-5 reaches about 7 percent and the fog concentration is 5.5 x 10 Again, an extrapolation of the Factory Mutual data to 10 p shows that fog concentration of 2.1 x 10 or higher is required to inert 7.2 percent H2. In comparison the present theory of fog inerting predicts 1.02 x 10 for 7.2 percent H2. Therefore, it appears that it is possible to inert 7 percent H2, but unlikely. However, at 8 percent H2 in the upper plenum, which occurs at about 4600 sec'onds, the fog

-5 concentration is 5.1 x 10, which is too low to inert 8 percent H2. An extrapolation of the Factory Mutual 8 percent H data to 10 4

u volume mean drop size and the present prediction give 1.9 x 10 and 1.2 x 10 for the minimum required fog inerting concentration, respectively.

The glow plug igniters which have been installed in the Cook containment were designed to burn hydrogen lower than 8 percent. As discussed pre-viously, no fog inerting effects will be expected in the Cook lower and upper compartments. Therefore, the glow plug igniters are expected to function as designed in these two compartments. It may be possible that fog present in the ice condenser upper plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent. However, it seems very unlikely that the same igniters would fail to ignite 8 percent H2 as designed, considering the fact that considerable conservatism has been exercised in the present analysis.

0430Q 1 6-45

TABLE 6.10 FOG INPUT DATA FOR D. C. COOK LOWER COMPARTMENT Steam Lower Compartment Gas Wal 1 Total Partial Gas Flow Rate Temp.. Temp. Pressure Pressure .

Time (sec) (ft /sec) ('F) ('F) ~(sia) ~(si a) 600 799.4 222 215.2 21. 8 17.4 1200 2798.2 190 183.5 20.2 9.4 1800 , 2805.8 190 180.3 20 9.1 2400 2513.6 180 177.2 19. 6 7.6 3000 2448.5 178 170.4 19.3 7.2 3600 2359.7 175 169.3 19. 2 6.4 4200 2272.3 165 161.9 18.8 5.3 4590 2482.7 168 161 19,5 5.8 0430Q:1 6-46

TABLE 6. 11 FOG INPUT DATA FOR D. C. COOK ICE CONDENSER Steam Ice Condenser Gas Ice Total Partial Gas Flow Rate Temp. Temp ~ Pressure Pressure Time ( sec) ( ft 3

/sec) ('F) ('F) ~(si a) ~(si a) 600 76 147 32 21. 8 3.4 1200 2548 190 32 20. 1 9.3 1800 2572 188 32 19.9 9.0 2400 2359 184 32 19.7 7.9 3000 2256 187 32 19.3 7.1 3600 2199 175 32 19.2 6.6 4200 2126 166 32 18.8 5.3 4590 2312 163 32 19'.8 4.3 0430Q:I 6-47

TABLE 6.12 GEOMETRIC DATA FOR D. C. COOK CONTAINMENT Volume (ft ) Floor Area (ft )

Lower Compartment 249,681 5,410 Ice Condenser Lower Plenum 24,700 3,100 Ice Condenser Upper Plenum 47,010 3,200 Upper Compartment 681,283 10,390 Dead Ended Region 61,105 853 Fan/Accumulator Rooms 54,828 2,500 0430Q:I 6-48

TABLE 6.13 INTERCOMPARTMENTAL FLOW RATES (ft /sec)

PREDICTED BY CLASIX FOR D. C. COOK Time Flow From Flow From Flow From Flow From Flow From Flow From (sec) LC to LP LP to UP UP to UC UC to LC DE to LC F/A to LC 600 6.387E2 7. 600E1 -4.410E1 -3.746E1 -1. 232E2 -1. 229E2 1200 2. 577E3 2. 548E3 1. 106E3 '1.740E2 -4.720E1 1. 509E3 1800 2. 600E,3 ,2.572E3 1.155E3 -1. 620E 2 -4. 381E 1 1. 529E3 2400 2.356E3  ; 2.359E3 1.145E3 -1.325E2 -2.512E1 1. 595E3 3000 2.273E3 2.256E3 1. 178E3 -1. 463E2 -2. 923E1 1.553E3 3600 2.202E3 2.199E3 1. 190E3 -1.334E2 -2.333E1 1.603E3 4200 2.136E3 2.126E3 l. 258E3 -1. 183E2 -1. 802E1 1.642E3 4590 2.346E3 2.312E3 1.400E3 -1. 130E2 -2. 371E1 1.650E3 0430Q:I 6-49

6.5 EFFECT OF FOG ON GLOBAL COMBUSTION In order to assess the effect of fog on the deflagration limit of hydro-gen, which is defined as the minimum hydrogen concentration at which the flame propagates in, all directions, a flame temperature criterion which considers fog droplets as a heat sink was used. This criterion assumes that the critical flame temperature of 710 C is still applicable to a hydrogen mixture which contains fog droplets. For a given fog concen-tration, the heat required to heat a unit mass of the mixture to 710 c can be calculated.'hen the hydrogen concentration needed to supply this amount of heat, assuming 100 percent combustion, can be deter-mined. Using this method, the calculated fog concentrations of 5.5 x 10 and 5.1 x 10 for the Sequoyah plant at 4650 seconds and for the D. C. Cook Plant at 4600 seconds, respectively, were found to be capable of raising the deflagration limit to 10.6 vol. percent H2. In

-5 comparison, the calculated fog concentration of 9.1 x 10 for the McGuire plant at 4600 seconds was found to be capable of raising the deflagration limit to 12 vol. percent H2. This study shows that in order to achieve global combustion in the upper plenum, hydrogen concen-tration higher than 8.5 percent may be required. The effect of increas-ing hydrogen concentration required to obtain global combustion in .the upper plenum should be investigated.

F 0430Q:1 6-50

7.0

SUMMARY

AND CONCLUSIONS The present study has developed a systematic methodology to study the potential fog inerting problem for the PWR ice condenser plants. In the present investigation, major fog formation and removal mechanisms are identified and quantified. Theoretical models are developed to predict the fog formation rate due to boundary layer and bulk stream condensa-tion, the fog removal rates due to gravitational settling and contain-ment sprays. The mass conservation equations for the fog droplets in each of the containment subcompertments are solved simultaneously in order to obtain time histories of fog concentration. These equations incorporate fog formation due to condensation, fog generation due to break flow, fog removal due to gravitational settling and sprays, trans-port of fog by the intercompartmental flows and fan flows. Computer programs FOG and FOGMASS have been developed to compute fog formation rates and fog concentrations in each of the containment subcompart-ments. These two computer programs have been used to analyze a S<D accident sequence for the Sequoyah, McGuire, and D.C. Cook plants. The analyses employed output data from the Sequoyah CLASIX analyses. Speci-fically, time histories of gas temperature, wall temperature, total pressure, and steam partial pressure in each containment subcompartment, as well as the intercompartmental and fan flow rates were used in the present analysis.

A fog inerting criterion has been developed to predict the minimum fog concentration required to inert a given hydrogen concentration and volume mean fog drop size. The present fog inerting criterion has been shown to be in agreement with the Factory Mutual data. The criterion shows that the minimum fog inerting concentration varies with the square of the volume mean fog drop size.

The present study shows that the fog concentrations in the upper and lower compartments of the three plants analyzed are too low to have any inerting effect on hydrogen mixtures. Therefore, the proposed glow plug igniters are expected to function as designed in these two compart-ments. It may be possible that fog present in the ice condenser upper 7-1 0430Q: I

plenum may prevent the glow plug igniters from igniting hydrogen below 7 percent. ~ However, it seems

~

very unlikely that the same igniters would fail to ignite 8.5 percent

~

H2 as designed.

It should be recognized that the existing theories and data can only predict the minimum fog concentration for inerting. Further work may be required to verify the fog inerting theory associated with flame propagation in all directions.

7-2 0430Q:I

A CKNOWL EDGME NTS The author wishes to express his sincere gratitude to Mr. N.J. Liparulo, Dr s. Y. Srinivas, B. Lewis, and B. Karlovitz for assistance, sugges-tions, and helpful discussions, particularly in the area of the fog inerting criteria and the flame temperature criteria for fog, to Messrs. D. F. Paddleford, R. Bryan, F. G. Hudson, and K. Shiu for valuab1e.comnents, to Mr. K. C. Perry, Mr. S. J. Reiser, and Ms.,R. M. Mariner for providing data on the three ice condenser plants, and to Mr. T. J.,Miele for providing pr ogramming assistance.

He also would like to thank TYA, Duke Power, and AEP for providing the financial support.

0430Q:1 7-3

REFERENCES

1. B. Lowry, "Preliminary Results: A Study of Hydrogen Igniters,"

ENNBO-45; Lawrence Livermore National Laboratory, November 17, 1980.

2. "Additional guestions on Hydrogen Control System for Ice Condenser Plants," NRC memo from L. Rubenstein to R. Tedesco, dated June 26, 1981.
3. "The Marvikken Full Scale Containment Experiments," MXB-301 AB Atomenergi, March, 1977. *
4. T. F. Kanzleiter, "LOCA Experiments With a PWR Multi-Compartment Model Containment," Trans. 1977 LWR Safety Conf., Idaho Falls, Idaho, 1977.
5. G.'M. Fuls, "The CLASIX Computer Program for the Hydrogen Release and Degradation", OPS-07A35, Offshore Power Systems, 1981.
6. K. K. Almenas, "The Physical State of Post-Loss-of-Coolant Accident Containment Atmospheres," Vol. 44, Nuclear Technology, pp. 411.-427, August, 1979.
7. "Summary of Analysis of Ice Condenser Containment Response to Hydro-gen Transients," Offshore Power Systems report No. RP-28A52, Septem-ber, 1980.
8. R. Brown and J. L. York, "Sprays Formed by Flashing Liquid Jets,"

Vol. 8, No. 2, AICh.E Journal, p. 149, May, 1962.

(

9. R. G. Gido, and A. Koestel, "LOCA-Generated Drop Size Prediction - A Thermal Framentation Model," Trans. Am. Nucl. Soc., 30, p. 371. 1978.
10. P. G. Hill, H. Witting, and E. P. Demetri, "Condensation of Metal Vapors During Rapid Expansion," Journal of Heat Transfer, p. 303, November, 1963.

R-1 0430/:1

11. M. Volmer and H. Flood, Z. Physik Chemic, A170, p. 273, 1934.
12. C. E. Junge, Advan. Geophys., H. Landsberg and J. Van Mieghem, ed.,

4.1, Academic Press, New York, 1958.

13. R. J. Burian, and P. Cybulskis, "CORRAL II User Manual," Battelle Columbus Laboratories, January, 1977.
14. R. K. Hilliard and L. F. Coleman, "Natural Transport Effects on Fission Product Behavior in the Containment Systems Experiment,"

BNWL-7457, Battelle-Northwest, Richland, Washington, 1970.

15. N. H. Fletcher, J. Chem. Phys., 29, p. 572; 31, p. 1136, 1958.
16. D. E. Rosner and M. Epstein, "Fog Formation Conditions Near Cold Surfaces," Vol. 28, No. 1, J. of Colloid and Interface Sci., Septem-ber, 1968.
17. K. Hijikata, and Y. Mori, "Forced Convective Heat Transfer of a Gas With Condensing Vapor Around a Flat Plate," Vol. 2, No. 1, Heat Transfer - Jap. Res., pp.81-101, January, 1973.
18. M. Neiburger and C. W. Chien, "Computation of the Growth of Cloud Drops by Condensation Using an Electronic Digital Computer,"

Geophys. Monograph No. 5, pp. 191-209, 1960.

19. R. M. Kemper, "Iodine Removal by Spray in the Salem Station Contain-ment," WCAP-7952, Westinghouse Electric Corp., August, 1972.
20. N. J. Liparulo, J. E. Olhoeft and D. F. Paddleford, "Glow Plug Ignitor Tests in H2 Mixtures," WCAP-5909, Westinghouse Electric Corp., March 6, 1981.
21. R. G. Zalosh and S. N. Bajpai, "Water Fog Inerting of Hy'drogen - Air Mixtures," EPRI Project Preliminary Rp. 1932-1, September, 1981.

0430Q:I

22.~ J. M. Marchello, "Control of Air Pollution Source," Marcel Dekker,

~

Inc., Hew York, 1976.

~ ~

~

23. Letter from B. Lewis and B. Karlovitz to L. E. Hochreiter, dated may 5, 1980.
24. M. Berman, et al., "Analysis of Hydrogen Mitigation for Degraded Core Accidents in the Sequoyah Nuclear Power Plant," Sandia draft report, December 1, 1980.
25. T. von Karman', Unpublished notes, 1956.
26. S. S. Tsai, "Flame Temperature Criteria Tests," HS-CCA-81-039, West-inghouse internal memo, dated June 17, 1981.
27. Attachment to Offshore Power System letter PST-HE-109, dated May 22, 1981.
28. Attachment to Offshore Power System letter PST-NE-106, dated May 14, 1981.
29. Attachment to Offshore Power System letter PST-HE-218, dated August 6, 1981.
30. M. L. Corrin, J. R. Connel, and A. J. Gero, "An Assessment of Warm Fog - Nucleation, Control, and Recommended Research," NASACR-2477, November, 1974.

0430Q:1 R-3

APPENDIX A I

C 0 MP U TAT 0N 0F Y o

AND g IN E Q UATI 0 N {3 1 2 )

The Hijikata-Mori fog formation theory used the boundary layer approximation for the continuity, momentum, and energy equations. The fog concentration and velocity profiles in the boundary layer are assumed in Eqs. (3.7) and (3.S). Substituting Eqs. (3.7) through (3.10) into the conservation equations, we have 3 3 7 Y

o

+vcaI =0 (A-1)

V

-( + )~ -m'rr <'m " 'm< V-'-'

3 7 1 (A-2) 9 9 311,'-'

mm ". - 3 z " ') xI (A-3)

A(n)+B(n) g+ C(n)+~E 7 Y

=g)p--

'F)Pr V o

- V o

(1+E) Y 0

(A-4) where A (n)- 3 (n+ 5) n+ n+

B(n) = 3 (n+ 6) n+ n+ n+

C(n) = 3 (n+ 7) bW 2 hW h

E =Hr Pg 0430Q:1 A-1

0 6 v vl 00 weight fraction of vapor at free stream W

0 weight fraction of vapor at wall aW W'-W S Schmidt number kinetic vi scosity component of the free stream velocity perpendicular to the wall heat of vaporization fg C specific heat of non-condensible gas pg hT T - T o

TOO gas temperature at free stream T

0 gas temperature at wall Equations (A-I) through (A-4) are four algebraic equations for four unknowns, Y , g, R, and v' These equations have been solved by the computer program FOG. In FOG, the values of Y , g, and R are computed and used in Eq. (3.12) to compute the fog formation rate.

A-2 0430Q:1

I APPENDIX B

. DERIVATION OF EQUATION (5.5)

This appendix gives detailed procedures to derive Eq. (5.5), starting from Eq. (5.4) crit ei u

- Yf)/ei) (5.4)

E wher e the ratio of heat loss rate per unit volume to the heat release rate by chemic'al reaction per unit volume, (K) t, is defined as Kcr t=S/Cw P and the ratio of sensible heat to heat of combustion, e;, is defined as

e. =C 1

p (T.-T)/q 1 u To arrive at Eq. (5.5), it is necesary to assume that all the heat loss is attributed to convection heat transfer to fog droplets of only one drop size. Under this assumption, the rate of heat loss per unit volume per degree, S, may be expressed as S=nxdh where n = number of drops per unit volume d = volume mean drop size h = heat'transfer coefficient It is further assumed that the relative velocity between the droplets and the mixture flow is so small that heat transfer coefficient, h, can be approximated by the conduction limit. Under this assumption, Eq.

(B-3) reduces to d

04 30Q: I B-I

~,

~4 k

ATTACHMENT 5 TO AEP:NRC:0500K FOG INERTING CRITERIA FOR HYDROGEN/AIR MIXTURES DONALD C. COOK NUCLEAR PLANT UNIT NOS. l AND 2

CO

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