NUREG/IA-0222 

 International 

 Agreement Report

 

Analysis of RELAP5/MOD3.3 

Prediction of 2-Inch Loss-of-Coolant 

Accident at Krško Nuclear Power Plant 

Prepared by: 

I. Parzer, B. Mavko 

Jožef Stefan Institute 

Jamova cesta 39 

SI-1000 Ljubljana, Slovenia 

A. Calvo, NRC Project Manager 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

March 2010 

 

Prepared as part of 

The Agreement on Research Participation and Technical Exchange 

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP) 

Published by 

U.S. Nuclear Regulatory Commission
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NUREG/IA-0222

Analysis of RELAP5/MOD3.3 Prediction of 

2-Inch Loss-of-Coolant Accident at Krško 

Nuclear Power Plant 

Manuscript Completed: December 2005 

Date Published: April 2010 

Prepared by: Iztok Parzer, Borut Mavko 

Jožef Stefan Institute 

Jamova cesta 39 

SI-1000 Ljubljana, Slovenia 

A. Calvo, NRC Project Manager 

Prepared as part of 

The Agreement on Research Participation and Technical Exchange 

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001

iii 

ABSTRACT 

The purpose of this analysis was to perform calculations of the loss-of-coolant accident (LOCA) 

for simulator verification and validation and to study the thermal-hydraulic response of the 

reactor coolant system. 

For the thermal-hydraulic analysis, the RELAP5/MOD3.3 code and input model provided by 

Krško Nuclear Power Plant was used. A small-break LOCA scenario was analyzed to estimate 

plant response to the opening of a break in cold leg No. 2 between the reactor coolant pump 

and the reactor pressure vessel. For the purpose of the analysis, the equivalent diameter of the 

cross-sectional area of the break was set to 5.08 centimeters (2 inches). 

In the presented study, the 2-inch LOCA scenario for the Krško Nuclear Power Plant was 

analyzed with regard to the differences between the Henry-Fauske and the Ransom-Trapp 

critical flow model. In addition, the study investigated the effect of the special offtake flow model 

at the break. Some variation cases were also run to capture the effect of flow bypasses in the 

reactor vessel on the loop seal clearing phenomena. 
iv 
v 

CONTENTS

Page

ABSTRACT.................................................................................................................................. iii

ACKNOWLEDGEMENT.............................................................................................................. vii

ABBREVIATIONS .......................................................................................................................viii

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

2. PLANT DESCRIPTION ...........................................................................................................3

3. THEORETICAL BACKGROUND ............................................................................................5

3.1 Ransom-Trapp Model........................................................................................................5

3.2 Henry-Fauske Model .........................................................................................................5

3.3 Phase Separation and Offtake Model ...............................................................................6

4. INPUT MODEL DESCRIPTION ..............................................................................................9

4.1 Hydrodynamic Component Description.............................................................................9

4.2 Regulation and Protection Logic .....................................................................................11

5. RESULTS..............................................................................................................................13

5.1 Base Analyses—Comparison of Critical Flow Models ....................................................13

5.2 Variation Analyses...........................................................................................................25

5.2.1 Vessel Bypass Configuration Influence...............................................................25

5.2.2 Offtake Model Influence ......................................................................................30

6. RELAP5/MOD3.3 RUN STATISTICS....................................................................................35

7. CONCLUSIONS....................................................................................................................39

8. REFERENCES......................................................................................................................41
vi 

Figures

Page

1. NPP Krško nodalization scheme...........................................................................................12

2. PRZ level...............................................................................................................................15

3. PRZ pressure........................................................................................................................15

4. Break flow .............................................................................................................................16

5. Primary mass ........................................................................................................................16

6. Cold leg No. 1 temperature...................................................................................................17

7. Cold leg No. 2 temperature...................................................................................................17

8. SG-1 pressure.......................................................................................................................18

9. SG-2 pressure.......................................................................................................................18

10. SG-1 level .............................................................................................................................19

11. SG-2 level .............................................................................................................................19

12. Accumulator No. 1 pressure..................................................................................................20

13. Accumulator No. 2 pressure..................................................................................................20

14. Accumulator No. 1 level ........................................................................................................21

15. Accumulator No. 2 level ........................................................................................................21

16. Core collapsed level..............................................................................................................22

17. Loop seal No. 1 reactor side collapsed level.........................................................................22

18. Loop seal No. 1 SG side collapsed level...............................................................................23

19. Loop seal No. 2 reactor side collapsed level.........................................................................23

20. Loop seal No. 2 SG side collapsed level...............................................................................24

21. Loop seal No. 1 pressures ....................................................................................................24

22. Primary pressure—vessel bypass variation ..........................................................................26

23. Break flow—vessel bypass variation.....................................................................................26

24. Primary mass—vessel bypass variation ...............................................................................27

25. Core collapsed level—vessel bypass variation.....................................................................27

26. Loop seal No. 1 reactor side collapsed level—vessel bypass variation................................28

27. Loop seal No. 1 SG side collapsed level—vessel bypass variation......................................28

28. Loop seal No. 2 reactor side collapsed level—vessel bypass variation................................29

29. Loop seal No. 2 SG side collapsed level—vessel bypass variation......................................29

30. Primary pressure—offtake model..........................................................................................30

31. Void fraction at the break—offtake model.............................................................................31

32. Break flow—offtake model ....................................................................................................31

33. Core collapsed level—offtake model.....................................................................................32

34. Loop seal No. 2 reactor side collapsed level—offtake model ...............................................32

35. Loop seal No. 2 SG side collapsed level—offtake model .....................................................33

36. Consumed CPU time for two base analyses cases (H-F and R-T).......................................35

37. Mass error for two base analyses cases (H-F and R-T) .......................................................36

38. Time step for two base analyses cases (H-F and R-T).........................................................36

39. Courant Δt for two base analyses cases (H-F and R-T) .......................................................37

Tables

Page

1. Run-Time Statistics ................................................................................................................35
vii 

ACKNOWLEDGEMENT 

The RELAP5/MOD3.3 NPP Krško base input model and nodalization diagram are courtesy of 

Krško Nuclear Power Plant. 
viii 

ABBREVIATIONS 

AFW auxiliary feedwater 

CPU central processing unit 

ECCS emergency core cooling system 

H-F Henry-Fauske 

HPIS high-pressure injection system 

KFSS Krško full-scope simulator 

kg/s kilogram per second 

LOCA loss-of-coolant accident 

LPIS low-pressure injection system 

m meter 

MCR main control room 

MFW main feedwater 

mm millimeter 

MPa megapascal 

MWt megawatt thermal 

NPP nuclear power plant 

PRZ pressurizer 

PWR pressurized-water reactor 

RAM random access memory 

RCS reactor coolant system 

RCP reactor coolant pump 

RPV reactor pressure vessel 

R-T Ransom-Trapp 

s second 

SI safety injection 

SG steam generator 
1 

1. INTRODUCTION

Krško Nuclear Power Plant (NPP) obtained the Krško full-scope simulator (KFSS) as part of the 

modernization project in 1999. KFSS supports, in real time, training for the complete range of 

operation which can be performed from the main control room (MCR) and some selected plant 

areas (e.g., remote shutdown panels). 

Various activities have been undertaken for the purpose of simulator annual verification. Initially, 

these activities included simulator verification for the normal plant operation (normal power 

evolutions, plant heatup and cooldown), plant transients, and steady-state conditions at different 

power levels. The data recorded in the past and obtained from the MCR instrumentation and 

process information system were used. 

When conducting the simulator annual verification for selected design-basis accidents and 

certain transients, it is important to use the results of the best estimate analysis. This approach 

complies with American National Standards Institute/American Nuclear Society 

(ANSI/ANS)-3.5-1998, “Nuclear Power Plant Simulators for Use in Operator Training and 

Examination (Revision of ANSI/ANS-3.5-1993 and ANSI/ANS-3.5-1985)” (Ref. 1). 

The purpose of the present analysis was to perform loss-of-coolant accident (LOCA) 

calculations for verification and validation using the KFSS and to study the thermal-hydraulic 

response of the reactor coolant system (RCS) (Ref. 2). 

Several analyses during the past few years have proved that the original Ransom-Trapp break 

flow model has certain deficiencies and its predictions do not match experimental data. Thus, 

the older Henry-Fauske (H-F) break model has been again coded into RELAP5/MOD3. At first, 

the H-F model was an option, and the Ransom-Trapp (R-T) model was considered the main 

prediction tool. A longer testing period has established that the H-F model performs better for 

various test cases; it is now the main modeling tool in the code. The R-T model remains as a 

user option in the code. 

During the assessment program for the application of the RELAP5 code to Westinghouse’s 

proposed advanced passive design (i.e., the AP600), the following two shortcomings of the 

default R-T choking model were observed: 

(1) Two-Phase Critical Flow at Low Pressure: If the slip ratio is not forced to be nearly unity, 

the values calculated using the default choking model could be as much as an order of 

magnitude lower than the homogeneous equilibrium values. 

(2) Subcooled Break Flow: For thin orifice plates (used to model the break) and liquid 

conditions near the saturation point, the default choking model predicted values of the 

critical flow were 40–50 percent less than those observed experimentally. 

The most serious shortcoming occurred at low pressure (P ~ 2 bar) and low quality conditions. 

Another significant, but less serious, shortcoming of the default critical flow model was observed 

when the experimental break configuration was a thin orifice plate (t ~ 10 millimeters (mm)) and 

the flow was slightly subcooled. 
2 

In addition to the shortcomings discussed above, several users have reported problems, noting 

apparent discontinuities in the predicted critical flow values for the single-phase to two-phase 

transition and the appearance of a noncondensable gas in a two-phase mixture. Several users 

have also reported that the default critical flow model predicted values that were considerably 

“noisier” than those predicted by earlier versions of RELAP5 employing the H-F critical flow 

model. For these reasons, a modified form of the H-F critical flow model was reintroduced into 

the RELAP5 code. 

In the present study, the 2-inch LOCA scenario for the Krško NPP was analyzed with regard to 

the differences between the H-F and R-T critical flow models. The effect of the special offtake 

flow model at the break was also investigated. Some variation cases were run to capture the 

effect of flow bypasses in the reactor vessel on the loop seal clearing phenomena. 
3 

2. PLANT DESCRIPTION 

Krško NPP is a Westinghouse two-loop pressurized-water reactor (PWR) plant with a large dry 

containment. The plant has been in commercial operation since 1983. After modernization in 

2000, the plant’s fuel cycle was gradually prolonged from 12 (cycle 17) to 18 months (cycle 21). 

The power rating of the Krško NPP nuclear steam supply system is 2,000 megawatt thermal 

(MWt) (1,882 MWt before the plant modernization and power uprate), comprising 1,994 MWt 

(1,876 MWT before the plant modernization and power uprate) of core power output plus 6 MWt 

of reactor coolant pump (RCP) heat input. The nuclear steam supply system consists of a PWR, 

RCS, and associated auxiliary fluid systems. The RCS is arranged as two closed reactor 

coolant loops connected in parallel to the reactor vessel, each containing an RCP and a steam 

generator (SG). An electrically heated pressurizer is connected to one of the loops. 

The reactor core is composed of 121 fuel assemblies. Square spacer grid assemblies and the 

upper and lower end fitting assemblies support the fuel rods in fuel assemblies. Each fuel 

assembly is composed of 16 x 16 rods; of these, only 235 places are used by fuel rods. Of the 

21 remaining places, 20 are evenly and symmetrically distributed across the cross-section of the 

assembly and are provided with thimble tubes which may be reserved for control rods and one 

control instrumentation tube for in-core thimble. 

The RCPs, one per coolant loop, are Westinghouse vertical, single-stage, centrifugal pumps of 

the shaft-seal type. 

The SGs, one per loop, are vertical U-tube, Siemens-Framatome type SG 72 W/D4-2 units, 

installed during the plant modernization in 2000. These new SGs replaced highly degraded 

Westinghouse D-4 SGs, each having preheating section. 

Engineered safety features are provided to prevent accident propagation, or to limit the 

consequences of postulated accidents, which might otherwise lead to damage of the system 

and release of fission products. The plant includes a number of engineered safety features, 

which include the following: 

• containment spray system 

• hydrogen control system 

• emergency core cooling system (ECCS) 

• component cooling water system 

• essential service water system 

• auxiliary feedwater system 

At present, activities are underway to replace the turbine and to gain additional power from new 

SGs. 

5 

3. THEORETICAL BACKGROUND

3.1 Ransom-Trapp Model

The two-phase choking model employed in RELAP5 is based on the model described by Trapp 

and Ransom (Ref. 3) for nonhomogeneous, nonequilibrium flow. These researchers developed 

analytic choking criteria using a characteristic analysis of a two-fluid model that included relative 

phasic acceleration terms and derivative-dependent mass transfer. During the original 

development and implementation of this model, both frozen flow and thermal equilibrium 

assumptions were employed to test the analytic criteria. Comparisons to existing data (Ref. 4) 

indicated that the thermal equilibrium assumption was the more appropriate and is thus 

assumed in the following development. 

The two-fluid model employed in the development of the RELAP5 two-phase choking criteria 

includes an overall mass conservation equation, two-phasic momentum equations, and the 

mixture energy equation written in terms of entropy. This equation set includes interface force 

terms due to relative acceleration; these terms have a significant effect on wave propagation. 

Energy dissipation terms associated with interface mass transfer and relative phase 

acceleration have been neglected in the mixture entropy equation. The characteristic velocities 

of the system of equations are the roots (λi, i < 4) of the characteristic polynomial: 

Aλ − B = 0 (1) 

The real part of any root λi gives the velocity of signal propagation along the corresponding path 

in the space/time plane. If the defined system of equations is considered for a particular region 

defined by 0 < x < L, the number of boundary conditions required at L equals the number of 

characteristic lines entering the solution region. At x = L, as long as any of the λi are less than 0, 

some information is needed at the boundary to get a solution. If all λi are greater than or equal 

to 0, no boundary conditions are needed at L and the solution of 0 < x < L is not affected by 

conditions outside the boundary at L. This situation defines the choking criteria: 

for j and for all i j λ j = 0 ≤ 4 λ j ≥ 0 ≠ (2) 

Reference 1 provides further detailed derivation of the choking criteria. 

3.2 Henry-Fauske Model

The steady-state, one-dimensional momentum equation for one-component, two-phase flow can 

be written as follows: 

− AdP = d mv uv + ml ul + dFw ( ) . .

 (3) 

For high-velocity flows in a converging nozzle, the wall shear forces are negligible compared to 

the momentum and pressure gradient terms, allowing the mass flux at the throat to be 

approximated by the following equation: 
6 

[ ]

t

v l

dP

d xu x u G

⎩

⎨

⎧

⎭

⎬ + − ⎫ = − (1 ) (4) 

At critical flow, the mass flow rate exhibits a maximum with respect to the throat pressure. 

Equations (3) and (4) can be combined to give the following expression for the critical flow rate 

for an isentropic homogeneous mixture with flashing: 

t s

v l

v l

c

P

x

v v

P

v

x

P

v

x

G

⎪⎭

⎪

⎬

⎫

⎩

⎨

⎧

∂

∂

+ − ∂

∂

+ − ∂

∂

− =

(1 ) ( )

2 1 (5) 

Embedded in this equation is the assumption that the two phases move with the same velocity; 

that is, that the slip ratio is unity. While at low pressure, this is certainly not the case. Henry and 

Fauske argued that the effects of thermal nonequilibrium were more important and that the 

effect of slip could be ignored. Equation (5) then serves as the choking criterion; however, to 

evaluate the critical mass flux, the quantities in this expression must be evaluated at the local 

conditions occurring at the throat. Thus, it is assumed that the phase velocities are equal. For 

normal nozzle configurations, there is little time for mass transfer to take place, and it is 

reasonable to assume that the amount of mass transferred during the expansion is negligible. 

Similarly, the amount of heat transferred between the phases during the expansion is also 

negligible, so that the liquid temperature is essentially constant. Since wall shear, heat transfer 

with the environment, and interfacial viscous terms were neglected, the system entropy during 

the expansion was assumed constant. 

The above assumptions eliminate the need to calculate the liquid-specific volume and the 

quality at the throat and also provide a relation for the vapor-specific volume in terms of the 

throat pressure and the upstream conditions. Evaluation of the throat pressure and the three 

differential terms remains. Putting all of the above assumptions into Equation (5), the final 

expression for the critical value of the mass flux is further determined in Reference 1. 

3.3 Phase Separation and Offtake Model

Phase separation usually results from gravitational forces, which cause the liquid phase to pool 

at the bottom of a vertical volume or on the bottom of a large horizontal pipe. This can occur if 

the flow rates of the phases in the volume are low enough so that gravitational forces overcome 

the frictional force between the phases that tends to keep the phases well mixed. The phase 

separation caused by gravitational forces is called flow stratification in RELAP5, and both the 

vertical and horizontal flow regime maps show stratification regions (Ref. 1). 

One consequence of stratification in a large horizontal pipe is that the properties of the fluid 

convected through a small flowpath in the pipe wall (i.e., a small break), called an offtake, 

depend on the location of the stratified liquid level in the large pipe relative to the location of the 

flowpath in the pipe wall. If the offtake is located in the bottom of the horizontal pipe, liquid will 

flow through the offtake until the liquid level starts to approach (but not reach) the bottom of the 

pipe, at which time some vapor will be pulled through the liquid layer and the fluid quality in the 

offtake will increase. If the phase separation phenomenon is ignored, vapor will be passed 

through the offtake regardless of the liquid level in the pipe. Likewise, if the offtake is located at 

the top of the pipe, vapor will be convected through the offtake until the liquid level rises high 
7 

enough so that liquid can be entrained from the stratified surface. The flow quality in the offtake 

will decrease as the liquid level rises. If the phase separation phenomenon is ignored, liquid will 

pass through the offtake for all stratified liquid levels regardless of their height relative to the 

offtake. Lastly, if the offtake is located in the side of the large horizontal pipe, the same 

phenomenon of gas pullthrough or liquid entrainment will occur, depending on the elevation of 

the stratified liquid level in the pipe relative to the location of the offtake in the wall of the pipe 

(Ref. 1). 

The results of the experiments showed that in most cases the depth or height (i.e., the distance 

between the stratified liquid level and the elevation of the offtake) for the onset of liquid 

entrainment or gas pullthrough could be defined by an equation of the following form (Ref. 1): 

[ ] ( ) 0.2

0.4

f g k

k

b

g

CW h

ρ ρ − ρ = (6) 

where subscript k refers to the continuous phase in the offtake, which is the phase flowing 

through the offtake before the onset of pullthrough or entrainment of the other phase. For an 

upward offtake, the gas phase is the continuous phase. For a downward offtake, the liquid 

phase is the continuous phase. For a side offtake, the gas phase is the continuous phase when 

the liquid level is below the offtake center, and the liquid phase is the continuous phase when 

the liquid level is above the offtake center. The variable Wk is the mass flow rate of the 

continuous phase in the offtake. 

For the specific case of a 2-inch LOCA at Krško NPP, a variation case was calculated for each 

analyzed break model (H-F and R-T), in which the break was situated at the side of the cold leg 

between the RCP and reactor vessel. Each time, the side offtake model was assumed. Based 

on the experimental studies, it may be concluded that the use of Equation (6) should give a 

reasonable representation of the test data if the following values are adopted for the correlation 

constant C (Ref. 1): 

• C = 0.75 for side offtake gas pullthrough 

• C = 0.69 for side offtake liquid entrainment 

The correlation for the flow quality through a side offtake has the following form (Ref. 1): 

( ) ( ) ( ) [ ]

0.5 1 1 1 0.5 1 R

o

CR X Xo R R X + − = + + (7) 

where 

b

g

f

o h

h X and R =

+

=

ρ

ρ 1

1.15 . (8) 

In Equation (7), C = 1.09 for gas pullthrough and C = 1.00 for liquid entrainment. 

9 

4. INPUT MODEL DESCRIPTION 

To perform this analysis, Krško NPP provided the base input model or “master input deck,” 

which is described in Krško NPP proprietary documents (Refs. 5 and 6). Figure 1 presents the 

scheme of the Krško NPP nodalization for the RELAP5/MOD3.3 code (Ref. 1). A full two-loop 

plant model was developed, including the new Siemens-Framatome type SG 72 W/D4-2 

replacement SGs. 

The model consists of 469 volumes, connected with 497 junctions. Plant structure is 

represented by 376 heat structures with 2,101 mesh points. The reactor protection and 

regulation systems and the safety systems’ operational logic and plant instrumentation is 

represented by 401 logical conditions (trips) and 575 control variables. 

4.1 Hydrodynamic Component Description

Components numbered from 101 to 165 represent the reactor vessel in the following manner: 

171, 173, and 175 lower downcomer 

101 and 103 lower head 

105 lower plenum 

107 core inlet 

111 reactor core 

115 core baffle bypass 

121 core outlet 

125, 131, and 141 upper plenum 

151 and 153 upper head 

165 upper downcomer 

113 and 145 guide tubes 

Components numbered 51, 53, and 55 represent the pressurizer surge line and volumes 61, 63, 

65, 67, and 69 represent the pressurizer vessel. Pressurizer spray lines (80, 81, and 84) are 

connected to the top of the pressurizer vessel and include the spray valves numbered 82 

and 83. Valves numbered 28 and 32 represent the two pressurizer power-operated relief valves 

and valves numbered 14 and 22 represent pressurizer safety valves. 

Primary piping is represented by the following components: 

201, 203, 205, 207, 209, and 211 hot leg No. 1 

251, 253, 255, 257, and 259 intermediate leg No. 1 with cold leg No. 1 loop seal 

265, 271, 273, 275, 277, and 279 cold leg No. 1 with the primary coolant pump No. 1 

301, 303, 305, 307, 309, and 311 hot leg No. 2 

351, 353, 355, 357, and 359 intermediate leg No. 2 with cold leg No. 2 loop seal 

365, 371, 373, 375, 377, and 379 cold leg No. 2 with the primary coolant pump No. 2 

Loops are symmetrical except for the pressurizer surge line and chemical and volume control 

system connections layout. 

Hydrodynamic components numbered from 701 to 882 represent the ECCS piping nodalization 
10 

and connections. The hydrodynamic components representing the high-pressure injection 

system (HPIS) pumps are time-dependent junctions 703 and 803, and time-dependent junctions 

750 and 850 represent the low-pressure injection system (LPIS) pumps. Accumulators are 

numbered 701 and 801, and their lineup provides cold-leg injection only. The ECCS connects to 

both cold legs (junctions 719-01 and 819-01). Direct vessel ECCS injection through 

junctions 746 and 748 opens simultaneously upon generation of a safety injection (SI) signal. 

The primary side of the SG is represented by inlet and outlet plenum, among which a single 

pipe represents the U-tube bundle, as follows: 

215, 217, and 219 SG 1 inlet plenum (hot side) and tubesheet inlet 

223, 225, 227, 233, 235, and 237 SG 1 U-tubes 

241, 243, and 245 SG 1 tubesheet outlet and outlet plenum (cold side) 

315, 317, and 319 SG 2 inlet plenum (hot side) and tube sheet inlet 

323, 325, 327, 333, 335, and 337 SG 2 U-tubes 

341, 343, and 345 SG 2 tubesheet outlet and outlet plenum (cold side) 

The following hydrodynamic components represent the parts of the SG secondary side: 

415, 417, and 419 SG 1 riser 

421 and 427 SG 1 separator and separator pool 

411 and 413 SG 1 downcomer 

423, 425, and 429 SG 1 steam dome 

515, 517, and 519 SG 2 riser 

521 and 527 SG 2 separator and separator pool 

511 and 513 SG 2 downcomer 

523, 525, and 529 SG 2 steam dome 

The main steamlines are represented by volumes 451, 453, 455, 457, 459, and 461 (SG 1) and 

551, 553, 555, 557, 559, and 561 (SG 1), divided by main steam isolation valves (458 and 558). 

SG relief (482 and 582) and safety valves (484, 486, 488, 492, and 494 and 584, 586, 588, 592, 

and 594) are situated upstream of the isolation valves. Turbine valve (604) and steam dump 

(611) flow is regulated by corresponding logic. 

The main feedwater (MFW) piping is represented by volumes 471, 473, 475, 407, and 409 

(SG 1) and 471, 573, 575, 507, and 509 (SG 2), branching from the MFW header (500). 

Auxiliary feedwater (AFW) is injected above the SG riser (via volumes 437, 443, 445, and 447), 

and its piping is represented by volumes 671, 673 (motor-driven AFW 1), 675 and 677 (AFW 2), 

and 681, 683, 685, 687, 695, and 697 (turbine-driven AFW). 
11 

4.2 Regulation and Protection Logic

To accurately represent the Krško NPP behavior, the model includes a considerable number of 

control variables and general tables. These represent the protection, monitoring, and simplified 

control systems used only during steady-state initialization, as well as the following main plant 

control systems: 

• rod control system 

• pressurizer pressure control system 

• pressurizer level control system 

• SG level control system 

• steam dump 

The rod control system has been modeled for point kinetics. The present model can be used for 

transient analysis with either of the following two options: 

(1) with constant or predefined core power transient as a function of time (including decay 

power calculation) 

(2) with rod control system in auto or manual mode 

The following plant protection systems are defined using trip logic: 

• reactor trip 

• SI signal 

• turbine trip 

• steamline isolation 

• MFW isolation 

• AFW start 
12 

151

171

121

111 0605

04030201

115

01

020304

05

06

07

08

175

107

105

103

101

69

656361

201 203 205 207

51

209

53

01 02 03 04 05 06 07

11

10

09

08

55

257

01 02 03 04

259

265 271 273 275 277 279

313

379 377 375 373 371 365

359

357

353

355

01 02 03 04

551

553555

557

559

561

301 303 305 307 309 311

211

253

255

351

906

905

11

10

09

08

0706

05

04

03

02

01

67

901

902

165

131

171

173

0201

719

718

717

715

713 711

801

811 813

815

817

819

818

02 01

02

01

992

991

993

701

Base deck ID:

branchpipetime dependent volume

pumpaccumulatorjunction orientation

crossflow junctiontime dependent junctionvalve

601

603

605

05

04

03

02

01

604

598

271 371

01 02

04

03

05

02

03 04 05

0706 80 81

0201

03 04

84

82 83

90

91

96

95

88

93

86

92

912 911

913 914

171

727725723

722

721

720

705 805

820

745

743

746 748

749747

872

882

871 881 861

760 860

857

853

851

757753751

731

732

740

741

831

832

727

582

584

586

588

592

594

951 953

01

08

01

02

02

01

01

0101

01

02

01

01 02

01

01 02

01

141

03

02

01

131125

02

02

01

02

01

01 02

03

01 02

01 01 01 01 01 01 01

01

01

02 01

01

02 01

02

01 01 01 01

01

703

01 01

01

01

01

01

01

01 02

01 01

750

01

01

01

803

01 01

01

01

01

850

01

01

01

02

01

02

01 01

375 377

01 01

01

01

01

01

01 01 01 01 01 01

01

01

01

01

02

0101

02 01

02

01 01 01 01

xxx junction described at branch xxx

915

804 704

612

611

916

03

145

04

03

02

01

131

05

ACC 1 ACC 2

RCP 2 RCP 1

SG 2

RPV

PRZ

charging

letdown

451

453

455

457

459

461

217

215 245

243

219 241

933

223

225

07

06

05

04

03

02

01

227

237

08

429

427

423

415

010203040506

411

213

251

0201

413

484

486

488492494

951 953

482

498

03 04 05

01

01

01

01

02

02

01

01

01

0101

01

02

03

01

01

01

02

01

01 01

01

01

01

01

601

SG 1

05

04

030201

417

421

425

419

02 934

443

447

445

01

01

02

01

01

01

315 345

317 343

319 341

935

323

325

07

06

0504

03

02

01

327

337

08

529

527

523

515

511

513

01

01

01

02

02

01

01

01

01

01

01

02

03

01

01

01

02

01

517

521

525

519

02 936

543 545

547

01

01

02

01

01

01

113

01

01

nekCClrv

458 558

01

02

03 04

013

014

01

02

03 04

021

022 028

027

032

01

02 03 04

025 011

01

07 06 05 04

03

02

01

407 409

930

931

01

07 06 05 04

0302

01

507

233

235

01

0102030405060708

333

335

01

010203040506

07

08

121110

09

0807

121110

09

080706

05

04030201

121110090807060504030201

091011

121314

06

153

01

02

01

07

08

09

10

09

08

0706

01

0203040506

07

08

09

10

0908

07

06

05

04030201

509

475

0706

0504030201

406

474

473

0504030201

472

471500

930

931

575

0706

0504030201

506

574

573

04

03

0201

572

571500

939

938

01

02 03

671

672 01 02 03 673 435

941

940

01

02

681

683

01

02

685

686

695

02 01 03

696

687 02

01

697

02

01

943

942

01

02 03

675

676

677

01 02 03 04

535

01 02 03 04 05 06

07 08

10

09 437

11

01

02 03 04 05

08

07

06

537

01

02

03

01

01

01 01

01

02

945

944

947

946

949

948

978

976

974 972

443

543

437 537

MD AFWpump 01

TD AFWpumpMD AFWpump 02

HPIS

LPIS

MFWheader

MFWheader

674

688

678

698

01

607

606

Figure 1 Krško NPP nodalization scheme 
13 

5. RESULTS 

5.1 Base Analyses—Comparison of Critical Flow Models

This set of analyses evaluated the differences between the default H-F and the R-T critical flow 

models. 

After the break occurred, the primary system started draining and the pressurizer pressure 

dropped very quickly to the saturation pressure of the hot legs. The pressurizer emptied 

(Figure 2) in 34 seconds using the H-F model and in 30 seconds using the R-T model after the 

break opening and stayed empty. Primary pressure (Figure 3) is one of the most important 

parameters during a small-break LOCA event, since it dictates the tripping sequence and many 

setpoints used in the analysis. The reactor was tripped when the filtered primary pressure 

(LEAD-LAG) dropped below 12.994 megapascals (MPa). 

An SI signal was produced when the primary pressure dropped to 12.27 MPa. Soon after that, 

the HPIS pumps started to deliver cold borated water into the primary system, reaching the 

break location. At the point where the highly subcooled liquid entered the break, the R-T model 

calculated a significantly higher break flow (Figure 4) than did the default H-F model. As a 

consequence, the primary inventory (Figure 5) was depleted much faster in the R-T case than in 

the default H-F case. This led to further important differences in the transient predictions. 

The power produced in the core was transferred out of the primary system; therefore, both 

hot-leg temperatures decreased. At the beginning of the transient, the temperatures of the cold 

legs (Figures 6 and 7) decreased because of a pressure drop of the primary system to the 

saturation temperature. Later, the cold-leg temperatures followed the loop seal behavior. When 

the loop seal was cleared, the cold-leg temperature suddenly dropped; when the loop seal 

refilled, the temperature increased. 

Initially after the reactor trip, the MFW was isolated and the turbine valves were closed. Closure 

of the turbine valves caused a shrink effect. The heat generated in the core started to heat the 

SGs. The heat input caused the pressure in the SGs (Figures 8 and 9) to increase. Later, the 

AFW pumps started to inject the cold water into the SGs, which then started to cool. When the 

SG narrow range levels (Figures 10 and 11) reached 72 percent, the AFW pumps were stopped 

and the SG pressures stabilized 1,000 seconds later. 

The closure of the turbine valves caused the SG narrow range levels (Figures 10 and 11) to 

shrink. Both levels increased when the AFW pumps started to inject into the SGs. 

When the primary pressure reached 4.96 MPa, the accumulators started to inject. As the 

accumulators discharged, the accumulator pressure (Figures 12 and 13) decreased. The 

accumulators (Figures 14 and 15) were not emptied by the end of calculation time in the H-F 

case. This phenomenon happened much earlier in the R-T case. 

The core partly uncovered (Figure 16) because of the loop seal formation (Figures 17, 18, 19, 

and 20). When the loop seal was first cleared, the liquid in the downcomer refilled the core. 

Later, the core stayed partially uncovered and the core level oscillated slightly because the cold 

water injected from the accumulator into the cold leg and downcomer evaporated in the core. 
14 

The generated steam increased the pressure, which reduced the accumulator flow. 

Rather unphysical oscillations in primary pressure were observed during multiple loop seal 

clearings. One possible explanation is that primary pressure spikes were in the range of 2 MPa, 

while the pressure difference needed to clear a loop seal of approximate 3 meters in height 

should not exceed 0.025 MPa. Observing the pressure difference on both sides of the loop seal 

(Figure 21) provides more detailed insight into the phenomena. It can be deduced that the HPIS 

injection flow caused the main pressure rise. Since the upper parts of the system had emptied 

by the time of the first loop seal clearing, pressure spikes could propagate through the reactor 

vessel upper head bypass, empty hot legs, and SG tubes to the SG side of the loop seal. Thus, 

the additional pressure rise resulting from vapor generation in the core, which was the origin of 

the driving force for the loop seal clearing, was only superposed to the main pressure spike. 

This pressure was only about 0.03 MPa, as can be estimated from Figure 21. 
15 

-10

0

10

20

30

40

50

60

0 10 20 30 40 50

Time [s]

Level [%]

H-F

R-T

Figure 2 PRZ level 

0

2

4

6

8

10

12

14

16

18

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

R-T

Figure 3 PRZ pressure 
16 

0

50

100

150

200

250

0 2000 4000 6000 8000 10000

Time [s]

Mass flow [kg/s]

H-F

R-T

Figure 4 Break flow 

0

20

40

60

80

100

120

140

0 2000 4000 6000 8000 10000

x 1000

Time [s]

Mass [kg]

H-F

R-T

Figure 5 Primary mass 
17 

300

350

400

450

500

550

600

0 2000 4000 6000 8000 10000

Time [s]

Temperature [K]

H-F

R-T

Figure 6 Cold leg No. 1 temperature 

300

350

400

450

500

550

600

0 2000 4000 6000 8000 10000

Time [s]

Temperature [K]

H-F

R-T

Figure 7 Cold leg No. 2 temperature 
18 

0

1

2

3

4

5

6

7

8

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

R-T

Figure 8 SG 1 pressure 

0

1

2

3

4

5

6

7

8

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

R-T

Figure 9 SG 2 pressure 
19 

0

10

20

30

40

50

60

70

80

0 2000 4000 6000 8000 10000

Time [s]

Level [%]

H-F

R-T

Figure 10 SG 1 level 

0

10

20

30

40

50

60

70

80

0 2000 4000 6000 8000 10000

Time [s]

Level [%]

H-F

R-T

Figure 11 SG 2 level 
20 

0

1

2

3

4

5

6

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

R-T

Figure 12 Accumulator No. 1 pressure 

0

1

2

3

4

5

6

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

R-T

Figure 13 Accumulator No. 2 pressure 
21 

0

10

20

30

40

50

60

70

0 2000 4000 6000 8000 10000

Time [s]

Level [%]

H-F

R-T

Figure 14 Accumulator No. 1 level 

0

10

20

30

40

50

60

70

0 2000 4000 6000 8000 10000

Time [s]

Level [%]

H-F

R-T

Figure 15 Accumulator No. 2 level 
22 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

R-T

Figure 16 Core collapsed level 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

R-T

Figure 17 Loop seal No. 1 reactor side collapsed level 
23 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

R-T

Figure 18 Loop seal No. 1 SG side collapsed level 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

R-T

Figure 19 Loop seal No. 2 reactor side collapsed level 
24 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

R-T

Figure 20 Loop seal No. 2 SG side collapsed level 

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

7600 7800 8000 8200 8400 8600 8800

Time [s]

Pressure [MPa]

H-F - SG side

H-F - reactor side

Figure 21 Loop seal No. 1 pressures 
25 

5.2 Variation Analyses

Two variation analyses were performed to investigate the vessel bypass configuration and the 

influence of the offtake model at the break. 

5.2.1 Vessel Bypass Configuration Influence 

For this analysis, the bypass flow from the reactor vessel downcomer to the upper plenum of the 

reactor vessel was closed. This assumption is acceptable because temperature changes in the 

reactor vessel structures can cause some structures to expand more than others, enabling the 

circular opening between the core barrel and downcomer (where the hot leg loosely enters the 

core barrel) to reclose (junction 171-02 between downcomer inlet volume 171-01 and upper 

plenum 125.01). 

The other bypass flow was modified at junction 151-01 between upper head volume 151-01 and 

upper downcomer volume 165-03. For this junction, an additional friction coefficient, FJUNF 

(and FJUNR), of 10 was introduced. 

However, as can be observed from the next set of figures, this change did not significantly 

influence the transient’s course. The case with reduced vessel bypasses is marked “H-F 

byp.red.” on the figures. 

The primary pressure (Figure 22) was oscillatory and decreased slightly faster in the H-F 

byp.red. case than in the default H-F case, which caused HPIS and accumulator injection earlier 

in the transient. In the first part of the transient, break flow was similar on average to the default 

H-F case, but somewhat smoother. In the later phase of the transient, more oscillatory break 

flow can be observed in the H-F byp.red. case, which is slightly higher on average than in the 

H-F case (Figure 23). As a result, primary mass depletion was no deeper; however, more 

oscillatory behavior can be observed in the H-F byp.red. case (Figure 24). 

Some differences can be seen in the core collapsed level, which, because of the slightly larger 

break flow, stayed at a slightly lower level than in the H-F case, although it was more oscillatory 

(Figure 25). The loop seal levels (Figures 26, 27, 28, and 29) also reflect these oscillations. 
26 

0

2

4

6

8

10

12

14

16

18

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

H-F byp.red.

Figure 22 Primary pressure—vessel bypass variation 

0

50

100

150

200

250

0 2000 4000 6000 8000 10000

Time [s]

Mass flow [kg/s]

H-F

H-F byp.red.

Figure 23 Break flow—vessel bypass variation 
27 

0

20

40

60

80

100

120

140

0 2000 4000 6000 8000 10000

x 1000

Time [s]

Mass [kg]

H-F

H-F byp.red.

Figure 24 Primary mass—vessel bypass variation 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F byp.red.

Figure 25 Core collapsed level—vessel bypass variation 
28 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F byp.red.

Figure 26 Loop seal No. 1 reactor side collapsed level—vessel bypass variation 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F byp.red.

Figure 27 Loop seal No. 1 SG side collapsed level—vessel bypass variation 
29 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F byp.red.

Figure 28 Loop seal No. 2 reactor side collapsed level—vessel bypass variation 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F byp.red.

Figure 29 Loop seal No. 2 SG side collapsed level—vessel bypass variation 
30 

5.2.2 Offtake Model Influence 

The next set of figures includes the offtake model, marked as “H-F offtake,” at the break and 

shows a similar, although smaller, effect to the previous variation in reactor vessel bypass 

configuration. Specifically, the enlarged insurge of vapor through the liquid phase into the break 

enabled a slightly faster primary pressure decrease (Figure 30) in the later phase of the 

transient. 

The offtake model reflected a slightly lower void fraction in the vicinity of the break (Figure 31), 

since it was transported faster through the break (Figure 32). This had a smaller influence on 

the loop seal clearing process (Figure 33) and an even smaller influence on the core collapsed 

level development (Figures 34 and 35). 

However, many calculation problems appeared in the vicinity of the break during the 

accumulator discharge period. These problems may have been the consequence of cold water 

flowing into the cold leg, which caused additional problems in calculating water properties in 

volume 375-01. The time step was reduced by a factor of 10, which produced significantly larger 

consumption of CPU time. In addition, the code aborted on several occasions; thus, after 

several restarts with the reduced time step, the calculation was finally interrupted before 

5,000 seconds of transient time. 

0

2

4

6

8

10

12

14

16

18

0 2000 4000 6000 8000 10000

Time [s]

Pressure [MPa]

H-F

H-F offtake

Figure 30 Primary pressure—offtake model 
31 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2000 4000 6000 8000 10000

Time [s]

Void [ ]

H-F

H-F offtake

Figure 31 Void fraction at the break—offtake model

0

50

100

150

200

250

0 2000 4000 6000 8000 10000

Time [s]

Mass flow [kg/s]

H-F

H-F offtake

Figure 32 Break flow—offtake model 
32 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F offtake

Figure 33 Core collapsed level—offtake model 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F offtake

Figure 34 Loop seal No. 2 reactor side collapsed level—offtake model 
33 

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2000 4000 6000 8000 10000

Time [s]

Level [m]

H-F

H-F offtake

Figure 35 Loop seal No. 2 SG side collapsed level—offtake model 

35 

6. RELAP5/MOD3.3 RUN STATISTICS 

MOD3.3 calculations were performed on a SUN FIRE V880 server with four UltraSPARC III 

750-megahertz processors and 16 gigabytes of main RAM, running under the SOLARIS 9 

operating system. 

Table 1 shows run-time statistics for the two analyzed base cases, H-F and R-T. 

Table 1 Run-Time Statistics 

Analyzed case Computer CPU

time (s) 

Total number of

time steps (NT)

Total number of 

volumes (N) 

Grind time

CPU/(NT*N)

both cases — 1000 s of steady state 3516.21 26303 469 2.85E-04 

Henry-Fauske (H-F) — default 38525.94 292310 469 2.81E-04 

Ransom-Trapp (R-T) 49307.04 373392 469 2.82E-04 

Figure 36 illustrates the CPU time consumed for the two base analyses cases (H-F and R-T). 

Figures 37 to 39, respectively, show the mass error, time step, and Courant Δt for the two base 

analyses cases (H-F and R-T). 

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000

x 103

Time [s]

Time [s]

H-F

R-T

Figure 36 CPU time consumed for two base analyses cases (H-F and R-T) 
36 

0

100

200

300

400

500

600

0 2000 4000 6000 8000 10000

Time [s]

Mass [kg]

H-F

R-T

Figure 37 Mass error for two base analyses cases (H-F and R-T) 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 2000 4000 6000 8000 10000

Time [s]

Time [s]

H-F

R-T

Figure 38 Time step for two base analyses cases (H-F and R-T) 
37 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 2000 4000 6000 8000 10000

Time [s]

Time [s]

H-F

R-T

Figure 39 Courant Δt for two base analyses cases (H-F and R-T) 

39 

7. CONCLUSIONS

The 2-inch LOCA transient was analyzed for Krško NPP using the KFSS for verification. The 

results indicated standard LOCA behavior with fast initial primary pressure decrease and loop 

seal clearing phenomena. 

The ECCS mitigated the consequences of the LOCA accident initiated by the break in cold leg 

No. 2 between the RCP and reactor vessel. 

In the later phase of the transient, somewhat oscillatory behavior of the various parameters was 

observed, which caused multiple loop seal clearing cycles. This was found to be the 

consequence of the periodic flooding of both loop seals by the cold borated water from the 

HPIS, accumulators, and LPIS. 

The mechanism of loop seal clearing phenomena was investigated for this specific case. It was 

shown that large pressure spikes originate in ECCS behavior and do not represent 

nonphysical results. 

Using some variation cases, the influence of the vessel bypass configuration and the offtake 

model at the break location was also studied. The results showed that these two model 

variations do not significantly affect the transient course. 

The ECCS model should be improved, since the HPIS and LPIS pumps are modeled as 

time-dependent junctions, although their flow depends on filtered primary pressure to smooth 

the time-dependent junction response. 

41 

8. REFERENCES

1. American National Standards Institute/American Nuclear Society, “Nuclear Power Plant 

Simulators for Use in Operator Training and Examination (Revision of 

ANSI/ANS-3.5-1993 and ANSI/ANS-3.5-1985),” ANSI/ANS-3.5-1998. 

2. I. Parzer, I. Kljenak, and A. Prošek, “RELAP5/MOD3.3 and CONTAIN 2.0 Transient 

Analysis of Loss-of-Coolant Accident (LOCA) for Krško Full Scope Simulator (KFSS),” 

IJS-DP-9046, Rev. 1, NEK-ESD-TR-07/05, Ljubljana, March 2005 (Proprietary). 

3. U.S. Nuclear Regulatory Commission, “RELAP5/MOD3.3 Code Manual,” Vol. 1, “Code 

Structure, System Models, and Solution Methods”; Vol. 2, “Users’ Guide and Input 

Requirements”; Vol. 3, “Developmental Assessment Problems”; Vol. 4, “Models and 

Correlations”; Vol. 5, “Users’ Guidelines”; Vol. 6, “RELAP5/MOD3 Code Manual—

Validation of Numerical Techniques in RELAP5/MOD3.0”; Vol. 7, “Summaries and 

Reviews of Independent Code Assessment Reports”; and Vol. 8, “Programmers 

Manual,” NUREG/CR 5535, Rev. 1, December 2001. 

4. V. H. Ransom and J. A. Trapp. “The RELAP5 Choked Flow Model and Application to a 

Large Scale Flow Test.” Proceedings of the ANS/ASME/NRC International Topical 

Meeting on Nuclear Reactor Thermal-Hydraulics, Saratoga Springs, New York, October 

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