NUREG/IA-0457

Assessment of Critical Subcooled Flow 

Through Cracks in Large and Small 

Pipes Using TRACE and RELAP5

Prepared by: 

Andrew Oussoren; J. Riznic; S.T. Revankar* 

Canadian Nuclear Safety Commission

280 Slater Street 

P.O. Box 1046 Station B

Ottawa, ON, Canada

*School of Nuclear Engineering, Purdue University

W. Lafayette, IN, USA

Kirk Tien, NRC Project Manager

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: November 2015

Date Published: August 2017

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

NUREG/IA-0457

Assessment of Critical Subcooled Flow 

Through Cracks in Large and Small 

Pipes Using TRACE and RELAP5

Prepared by: 

Andrew Oussoren; J. Riznic; S.T. Revankar* 

Canadian Nuclear Safety Commission

280 Slater Street 

P.O. Box 1046 Station B

Ottawa, ON, Canada

*School of Nuclear Engineering, Purdue University

W. Lafayette, IN, USA

Kirk Tien, NRC Project Manager

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: November 2015

Date Published: August 2017

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

iii

ABSTRACT

The thermal hydraulics system code TRACE has been used to predict subcooled critical flow in 

crack geometries. Three different experimental data sets were modelled in this study. The first 

experiment, performed at Purdue University, measured critical flow in slits with small section 

thicknesses similar to steam generator tubing. These results are also compared to model 

predictions using the RELAP5 code. The second experiment, conducted by Ontario Hydro (OH), 

measured critical flow rates in simulated circumferential cracks in thick-walled piping. The third 

experiment, from Atomic Energy of Canada Ltd. (AECL), measured critical flow through pressure 

cycling-induced fatigue cracks in thick walled vessels. 

For the Purdue tests, TRACE predictions were similar to those obtained with RELAP5. For the thin 

walled samples in these tests a junction nodalization was found to be more suitable than explicitly 

modelling the section thickness of the samples. TRACE predictions for both the Purdue and OH 

tests were in reasonable agreement with measured leak rates, with calculated discharge 

coefficients of between 0.5 and 1.0 for most cases. However, the model of the OH tests showed a 

trend towards under prediction as pressure dropped below 8 MPa. There was no clear trend 

demonstrated with respect to subcooling. For the AECL experiments the flow rate was significantly 

over predicted, with discharge coefficients as low as 0.1. This result is consistent with the modelling 

performed by the original experimenters and is likely due to the complexity of the flow pathway in 

the fatigue cracks used in this test, as compared to the machined geometries of the other samples.

In general TRACE appears to be a suitable tool for prediction of critical flow rates in crack 

geometries. Comparison against additional experimental data is recommended.

v 

TABLE OF CONTENTS

 Page

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

LIST OF FIGURES..............................................................................................................................vii

LIST OF TABLES................................................................................................................................. ix

ACKNOWLEDGMENTS......................................................................................................................xi

ABBREVIATIONS...............................................................................................................................xiii

SYMBOLS...........................................................................................................................................xv

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

2 CHOKED FLOW MODELS ............................................................................................................. 3

2.1 Choked Flow.............................................................................................................................. 3

2.2 Choked Flow Models................................................................................................................. 3

2.2.1 Modified Burnell Model.................................................................................................... 4

2.2.2 Henry-Fauske Model....................................................................................................... 5

2.2.3 Discharge Coefficients .................................................................................................... 5

3 PURDUE THIN WALLED CRITICAL FLOW TESTS..................................................................... 7

3.1 Facility Description..................................................................................................................... 7

3.2 Experiment Results.................................................................................................................... 9

3.3 Modelling..................................................................................................................................10

3.3.1 RELAP5 Model..............................................................................................................10

3.3.2 TRACE Model ...............................................................................................................11

3.4 Results .....................................................................................................................................12

3.5 Modelling Options and Sensitivity Studies ..............................................................................13

3.5.1 TRACE Sensitivity Studies............................................................................................13

3.5.2 RELAP...........................................................................................................................13

4 ONTARIO HYDRO THICK WALLED CRITICAL FLOW TESTS.................................................15

4.1 Facility Description...................................................................................................................15

4.2 Experimental Results...............................................................................................................16

4.3 Modelling..................................................................................................................................17

4.4 Results .....................................................................................................................................18

5 AECL FATIGUE CRACK CRITICAL FLOW TESTS....................................................................21

5.1 Facility Description...................................................................................................................21

5.2 Experimental Results...............................................................................................................22

5.3 Modelling..................................................................................................................................23

5.4 Results .....................................................................................................................................24

6 DISCUSSION AND CONCLUSIONS............................................................................................27

7 REFERENCES...............................................................................................................................29

vii

LIST OF FIGURES

 Page

Figure 1 Schematic of test facility [18].......................................................................................... 7

Figure 2 Sample mounting to test section [18] ............................................................................. 8

Figure 3 Slit crack test specimen # 2............................................................................................ 9

Figure 4 Critical mass flux as a function of subcooling................................................................. 9

Figure 5 RELAP channel nodalization (top) and junction nodalization (bottom)......................... 10

Figure 6 TRACE channel nodalization (top) and junction nodalization (bottom)........................ 11

Figure 7 TRACE and RELAP mass flux predictions vs. measurements for Purdue tests .......... 12

Figure 8 TRACE and RELAP calculated discharge coefficient for Purdue tests ........................ 13

Figure 9 Test section showing shim and the flared and rectangular crack geometries [7]......... 16

Figure 10 Measured flow rates for OH tests................................................................................. 17

Figure 11 TRACE nodalization for OH tests samples (cell sizing not to scale) ............................ 18

Figure 12 Model results for OH test samples ............................................................................... 19

Figure 13 Discharge coefficients for the OH test samples ........................................................... 19

Figure 14 Pressure cycling rig [19]............................................................................................... 21

Figure 15 TRACE nodalization for the AECL tests (cell sizes not to scale).................................. 23

Figure 16 Discharge coefficients for the AECL tests .................................................................... 25

ix

LIST OF TABLES

 Page

Table 1 Geometry of test samples [18]......................................................................................... 8

Table 2 OH test fixture geometries [7]........................................................................................ 15

Table 3 Test specimen properties and measured flow rates [19]............................................... 22

Table 4 TRACE predicted leak rates and calculated discharge coefficients .............................. 24

Table 5 Predicted flow rate for sample 4, different edges selected as the choking plane.......... 25

xi

ACKNOWLEDGMENTS

The analysis in this report is based on the experimental work of Dr. Brian Wolf (formerly of Purdue 

University), the Ontario Hydro Research Division and Atomic Energy of Canada Limited.

xiii

ABBREVIATIONS

AECL Atomic Energy of Canada Limited

ASTM American Society for Testing and Materials

CAMP Code Applications and Maintenance Program

CNSC Canadian Nuclear Safety Commission 

COD Crack Opening Displacement

LOCA Loss of Coolant Accident

NRC United States Nuclear Regulatory Commission

OH Ontario Hydro

RELAP Reactor Excursion and Leak Analysis Program

SETS Stability-Enhancing Two-Step

SG Steam Generator

TRACE TRAC/RELAP Advanced Computational Engine

xv

SYMBOLS

At throat area

Aup upstream cell area

CNE non-equilibrium coefficient (default = 0.14)

Cp,v vapour heat capacity

DP/Dt substantial derivative of pressure

Gc critical mass flux

N non-equilibrium factor = xeq,t / CNE

Psat saturation pressure

Pt throat pressure

Pup pressure upstream of break

T upstream fluid temperature

Tc critical temperature

TR T / Tc

Vl liquid specific volume

Vl,0 upstream liquid specific volume

Vv vapour specific volume

dsl,eq/dP derived from liquid property tables

kB Boltzmann constant

sl,0 upstream liquid entropy

sl,eq equilibrium liquid entropy

sv,0 upstream vapour entropy

sv,eq equilibrium vapour entropy

vt throat velocity

x0 upstream quality

γ specific heat ratio of vapour

σ surface tension

η thermal equilibrium polytrophic exponent

ρl liquid density

1 

1 INTRODUCTION

Choked or critical flow is a phenomenon which occurs in a wide range of high pressure industrial

systems. It is especially important in pressurized water-cooled nuclear reactors where high 

pressure subcooled water is used to generate steam. The discharge rate of coolant from a broken 

primary coolant pipe controls the rate of heat transfer in the core and determines the requirements

for emergency core cooling and safety equipment as well as the containment structure design to

remedy reactor loss of coolant accident [1]. Therefore, in the event of a Loss Of Coolant Accident

(LOCA), choked flow determines the rate at which coolant inventory leaves the reactor cooling 

system. If choking were not to occur, the reactor water inventory would be depleted rapidly. This

is not the case however because, as the pressurized subcooled water nears the break, it flashes to 

vapor which limits the mass flow rate. Therefore, the coolability and structural integrity of the core

during a LOCA is strongly dependent on critical flow discharge. 

A LOCA from a small or large break to the containment building is not the only place in a reactor 

where coolant could be escaping the primary side of the reactor. Steam generator (SG) tubes have 

a history of small cracks and even ruptures, which cause a loss of coolant from the primary to the 

secondary coolant loop and provide a pathway outside of containment. In the case of leakage 

through SG tubes to the secondary side of the plant, radiation detection measurements of the 

secondary flow are taken and calibrated to predict an increase or decrease of leakage through the 

SG tubes. If excessive leakage occurs, the plant must shut down or the operator must take 

appropriate action. It is therefore of great interest to be able to quantitatively predict such flow rates 

with great accuracy. 

Reactor system safety codes were originally developed for simulation of single and two-phase flow 

of reactor coolant in nuclear power plants. Computer codes can be categorized in two broad 

groups: (i) one and limited three-dimensional system codes, and (ii) computational fluid dynamics 

codes. Computational fluid dynamics codes are generally based on commercial software and have 

the capability of modelling the flow in three dimensional space. Computational power and 

applicable models of turbulence are the main limitations of this type of code [2]. System codes, 

including TRACE and RELAP, are commonly used in nuclear industry for safety analysis of watercooled reactors. These codes in general use non-homogeneous, non-equilibrium models to 

describe behaviors of single and two-phase flow. They have been validated against experimental 

data from separate effects tests and integral tests, and are generally accepted for accident 

simulations in light water reactors. Recently, there have been efforts to use these codes for order 

of magnitude smaller geometries such cracks in pipes and vessel walls [2] [3] [4] [5] [6]. Leak rate 

calculations on this scale are traditionally performed by purpose-built codes (e.g. LEAK_RATE [7], 

SQUIRT [8]) which are validated against critical flow leak rate experimental measurements for 

example [9] [10] [11]). 

The Canadian Nuclear Safety Commission (CNSC), as a member of the Code Applications and 

Maintenance Program (CAMP), is evaluating the TRACE thermal hydraulic system code. This 

report details the modelling of three experiments measuring critical flow rates in crack geometries: 

one experiment recently sponsored by the CNSC as well as two earlier tests performed by Canadian 

researchers. 

The first data set analyzed in this report comes from a CNSC sponsored research program 

conducted at Purdue University to measure critical subcooled flow through samples with a section 

thickness which approaches the wall thickness of steam generator tubing. The pressure drop across 

the samples was 6.9 MPa, which is close to the pressure difference between the primary and 

secondary coolant loops of a pressurized water reactor. Flow rates were measured for different 
2

levels of subcooling at constant pressure. Modelling results for RELAP5 were also available for this 

test; therefore, these results are compared against TRACE predictions.

The second set of data comes from tests conducted by Ontario Hydro involving prepared 

circumferential cracks in thick walled piping. Flow rates through flared and straight crack sections 

were measured over a range of temperatures and pressures.

The last set of data comes from tests conducted by Atomic Energy of Canada Limited (AECL) in 

which a vessel representing a large diameter pipe with a simulated internal defect was pressure 

cycled until a through wall failure occurred. Flow rates were measured through defects in five 

different test specimens at a pressure of 8.5 MPa and temperature of 260 °C. A unique aspect of 

these tests is the use of fatigue cracks, which are likely more representative of cracks which could 

potentially develop in operating reactors compared to the more stylized, machined geometries of 

cracks used in the other two tests.

The following chapters describe the critical flow models used in the TRACE and RELAP5 codes, 

the experimental setup and results for each of the three tests, the development of nodalization for 

those tests and comparisons of predicted flow rates against experimentally measured values.
3 

2 CHOKED FLOW MODELS

2.1 Choked Flow

Pressurized systems with high fluid velocities have the potential for flow to become choked. This 

occurs when fluid’s velocity is equal to its sonic velocity (speed of sound). The sonic velocity is the 

maximum speed at which pressure waves may propagate in a fluid, therefore when flow becomes 

choked pressure waves can no longer travel upstream. This causes the flow rate to become 

independent of the downstream pressure. In liquid systems such as water-cooled nuclear reactors, 

choked flow may occur due to localized vapour generation, which significantly reduces the mixture 

sonic velocity. 

Consider a small hypothetical crack in the piping of a nuclear reactor cooling system where the 

coolant is at high pressure. If the coolant flowing out of the break is at sufficiently low temperature 

(highly subcooled), it will remain in a liquid state as it exits the break. The sonic velocity of liquid 

water is high enough that choked conditions will not occur.

If, however, the coolant is at high temperature (low subcooling), as is typically the case in an 

operating reactor, as the coolant exits the break and the pressure drops rapidly, the saturation 

temperature will fall below the temperature of the liquid. This causes some of the water to flash into 

steam. The sonic velocity of steam is much lower than that of water; therefore the speed of sound 

of the liquid/steam mixture will drop rapidly. This creates the conditions for flow exiting the break to 

become choked. 

2.2 Choked Flow Models

Prediction of critical flow rates in an important component of any safety analysis system codes. 

Special process models are required in thermal hydraulic system codes to provide realistic 

estimates of flow rates in choked flow conditions. 

The TRACE and RELAP5 model for critical flow employs a modified form of the Burnell model for 

critical flow of liquid which is initially subcooled. For initially two-phase mixtures the model developed 

by Ransom and Trapp is used. Since the tests described in this report consist only of initially 

subcooled flow, only the modified Burnell model will be described in detail. 

RELAP5 also allows the user to select the Henry-Fauske model for critical flow; therefore this model 

is also described.
4

2.2.1 Modified Burnell Model

A modified version of the choked flow model originally proposed by Burnell [12] is used in both 

TRACE and RELAP5. In this model, subcooled critical flow is idealized using the Bernoulli equation. 

Because the choking flow rate is independent of the downstream pressure, the choking flow velocity 

at the throat is given as a function of the pressure difference between the upstream conditions, Pup, 

and the pressure at the choking plane, Pt. TRACE compares this velocity to the speed of sound for 

the homogeneous mixture; the velocity at the choking throat, vt, is then given as:

vt = Max �αHE, vup

2 +

2(Pup − Pt)

ρ �

1

2

(1)

Where ααHHHH is the homogeneous equilibrium speed of sound and vup is the upstream velocity. The 

pressure Pt is the pressure at the choking throat, where vaporization first occurs. Due to nonequilibrium effect Pt does not necessarily equal the local saturation pressure. The existence of 

superheated liquid results in a delay in the onset of nucleation at the throat, such that Pt may be 

significantly lower than the local saturation pressure [13]. A correlation is then required to determine 

the throat pressure at which vaporization will occur.

Both RELAP5 and TRACE employ the model described above for single phase critical flow; 

however they employ different correlations to derive Pt.

In RELAP5 Pt is given by a correlation developed by Alamgir and Lienhard [14] and Jones [15]:

Pt = Psat − Max �0 , 0.258 σ

3

2TR

13.76

�kBTc

Vv

Vv − Vl

� 1 + 2.078x10−8(ρl

1

At

dAt

dx vt

3)0.8�

0.5

− 6.9984x10−2 � At

Aup�

2

ρlvt

2�

(2)

where Psat is saturation pressure, σ is surface tension, TR = T / Tc, T is upstream fluid temperature, 

Tc is critical temperature, kB is Boltzmann’s constant, Vv is vapour specific volume, Vl is liquid 

specific volume, At is throat area, Aup is upstream cell area, and ρl is liquid density,.
5

In TRACE Pt is given by the correlation of Jones and Abuaf [13] [16]:

Pt = Psat − Max � 0 , 0.258 σ

3

2TR

13.76

�kBTc

Vv

Vv − Vl

� 1 + 13.25 � −1

1.01325x1011

Dp

Dt�

0.8

�

0.5

− 27(0.072)2 � At

Aup�

2 ρlvt

2

2 �

(3)

where Dp/Dt = substantial derivative of pressure. 

Equation (1) and equation (2) or (3) form a coupled set which are solved iteratively to determine the 

velocity which will result in choked flow. By comparison to the solution to the momentum equation 

the codes then determine whether choked flow conditions will occur.

2.2.2 Henry-Fauske Model

The Henry-Fauske model is the default model for choked flow in RELAP5. The model defines the 

critical mass flux at a choking plane as: [17]

Gc

2 = �

x0Vv

ηP + (Vv − Vl,0) � (1 − x0)N(sv,eq − sl,eq)

dsl,eq

dP −

x0Cp,v �

1

η − 1γ�

Pt�sv,0 − sl,0�

��

−1

(4)

In the tests described in this report the test fluid is subcooled liquid. In this case the upstream quality 

x0 = 0, and equation (4) reduces to:

Gc

2 = � (Vv − Vl,0) � N

(sv,eq − sl,eq)

dsl,eq

dP ��

−1

(5)

where Vv,eq is the equilibrium vapour specific volume, Vl,0 is upstream liquid specific volume, N is the 

non-equilibrium factor = xeq,t / CNE, xeq,t is equilibrium quality at the throat, CNE is the non-equilibrium 

coefficient (default = 0.14), sv,eq is equilibrium vapour entropy, sl,eq is equilibrium liquid entropy, 

dsl,eq/dP is derived from liquid property tables.

2.2.3 Discharge Coefficients

In the implementation of these critical flow models, both RELAP5 and TRACE allow the user to 

specify a discharge coefficient (referred to in TRACE as a critical flow multiplier). This is a multiplier 

allowing the user to adjust the predicted flow rate to account for inconsistencies between model 

predictions and experimental observation. For the models described in this report, in all cases a 

discharge coefficient or critical flow multiplier of 1.0 was implemented. 

Modelling results are presented in terms of a calculated discharge coefficient, defined as the 

experimental mass flow rate divided by the predicted mass flow rate. This value represents the 

multiplier which could be applied in the model to achieve perfect agreement with experimental 

results.

7 

3 PURDUE THIN WALLED CRITICAL FLOW TESTS

3.1 Facility Description

This set of experiments was conducted to measure critical flow rates through slits with section 

thicknesses similar to steam generator tubes. The tests were sponsored by CNSC and conducted 

at Purdue University. Figure 1 shows a schematic of the test facility. It consists of a vertical pressure 

vessel, an outlet pipe leading to a test specimen holder and a water tank where discharge from the 

test specimen is condensed.

The vessel is pressurized using compressed nitrogen bottles connected via stainless steel piping. 

Ceramic band heaters are used to control the temperature of the pressure vessel inventory. 

Pressure and temperature are measured in the vessel as well as upstream of the test section.

A valve upstream of the test specimen is used to initiate the experiment. As the subcooled water 

is discharged from the test section it flashes and a two-phase critical flow develops. The outlet of 

test section is submerged in a cool water bath which condenses the discharged mixture. The 

condensed steam and discharged water are collected in the bath volume, the mass of which is 

measured using two high precision strain gauge type load cells. This allows for a time averaged 

mass flow rate to be measured. 

Figure 1 Schematic of test facility [18]
8 

Flow rate tests were conducted using specimens consisting of a slit cut in a 3.175mm stainless steel 

disk. 

The sample disks were mounted on a stainless steel nipple and attached to pressure vessel outlet 

pipe as shown in Figure 2. 

Figure 2 Sample mounting to test section [18]

The dimensions of the samples are presented below in Table 1. The use of laser cutting resulted in 

a non-uniform cross sectional area; the average flow area for each sample was determined by 

optical measurement of the front and back surfaces and averaging the values. Hydraulic diameter 

was also determined through optical measurement. Figure 3 shows the front and back surface of 

sample 2.

Table 1 Geometry of test samples [18]

Sample # Area (m2) Dh (m) Thickness (m) L/D Roughness (m)

2 9.736E-07 7.086E-04 3.175E-03 4.5 3.75E-05

3 1.269E-06 6.996E-04 3.175E-03 4.5 3.75E-05

4 1.333E-06 6.589E-04 3.175E-03 4.8 3.75E-05

5 1.359E-06 6.468E-04 3.175E-03 4.9 3.75E-05

6 1.833E-06 5.859E-04 3.175E-03 5.4 3.75E-05

The test matrix for each sample consisted of varying the subcooling at near constant pressure. 

Pressures for the tests ranged from 6.87 MPa to 6.60 MPa, with a range of subcooling between 

48.1 and 24.7oC. Measurement error for mass flux values was less than 2%.

As the experiments were designed to simulate choking flow through steam generator tube cracks, 

the tests were carried out at 6.9 MPa (1000 psi), which approaches the pressure differential across 

the walls of steam generator tubes under normal operating conditions. However, the pressure 

differential in actual steam generators is approximately 15 MPa to 5.8 MPa in PWRs (10 MPa to 

4.7 MPa for CANDU reactors) as opposed to 7 MPa to 0.1 MPa in this experiment. Achieving 

prototype reactor conditions was not possible within the constraints of test apparatus. 
9 

 Front

 Back

Figure 3 Slit crack test specimen # 2 

3.2 Experiment Results

Figure 4 shows the measured mass flux as a function of subcooling for the 5 samples. In all cases 

the mass flux increases with subcooling; a more highly subcooled liquid results in less flashing at 

the choking plane and thus less restriction in flow rate. The mass flux does not show a clear trend 

with respect to the sample geometric parameters listed in Table 1. 

Figure 4 Critical mass flux as a function of subcooling
10

3.3 Modelling

The experiment was modelled using both RELAP5 and TRACE. Due to the very small section 

thickness of the samples, two nodalization schemes were investigated for each code:

1. Channel nodalization: The sample is modelled using discrete PIPE components with length

equal to the section thickness (3.175mm), with cell and junction flow area and hydraulic

diameters described as in Table 1.

2. Junction nodalization: The section thickness of the sample is not explicitly modelled; instead

the junction between the upstream piping and the outlet boundary condition is assigned the

flow area and hydraulic diameter of the test sample.

The nodalization for each code is described below.

3.3.1 RELAP5 Model

RELAP5/Mod3.3 Patch04 was used to model choked flow through the test specimens. The 

modelling was performed using the Symbolic Nuclear Analysis Package (SNAP) graphical interface. 

The SNAP representations of these two models are shown in Figure 5. 

Figure 5 RELAP channel nodalization (top) and junction nodalization (bottom)

Components 101 through 104 represent the piping upstream of the sample. Components 98 and 

108 are time dependent volumes which represent, respectively, the pressure vessel at test pressure 

and temperature and the condensing tank at standard atmospheric temperature and pressure.

In the channel nodalization the sample slit was represented by PIPE component 106 which consists 

of five hydraulic cells. Component 106, as well as junction components 105 and 107, was assigned 

the flow area and hydraulic diameter of the test specimen as given in Table 1. 

For the junction nodalization components 106 and 107 are removed, and the flow area and hydraulic 

diameter of the test specimen are represented solely by junction component 105. In this nodalization 

the length of the flow path through the specimen is not explicitly modeled. No minor loss coefficients 

were assigned in the model.
11

In both models choking was enabled on the junction immediately upstream of the outlet boundary 

condition. The RELAP5 model was tested in four different configurations:

1. Channel nodalization using the modified Burnell critical flow model 

2. Channel nodalization using the Henry-Fauske critical flow model

3. Junction nodalization using the modified Burnell critical flow model

4. Junction nodalization using the Henry-Fauske critical flow model

A critical flow discharge coefficient of 1.0 was used for all tests to facilitate comparison between 

models.

3.3.2 TRACE Model

TRACE V5.830 was used for the simulation. The TRACE nodalization was created using the ‘Import 

RELAP’ function available in SNAP which translated the RELAP input deck into a TRACE input file. 

As with the RELAP analysis, two nodalization were evaluated: Modelling the test specimen as a 

channel or as a junction. Note that unlike RELAP, TRACE does not utilize discrete junction 

components; the flow area and hydraulic diameter of cell junctions are instead defined at the edge 

of each PIPE component. The resulting nodalization are shown in Figure 6. 

Figure 6 TRACE channel nodalization (top) and junction nodalization (bottom)

The TRACE model was tested for three different configurations:

1. Channel nodalization with critical flow enabled

2. Channel nodalization with critical flow disabled

3. Junction nodalization with critical flow enabled

Minor loss coefficients were calculated internally by TRACE by enabling the ‘abrupt area change’ 

model at the junctions between each component. 

As with the RELAP runs, default critical flow multipliers of 1.0 were used. The default critical flow 

relaxation constant of 2.0 was found to produce oscillations; this value was reduced to 1.1 which 

produced more steady results.
12

3.4 Results

Figure 7 shows the Modelling results in terms of predicted vs. measured mass flux for both TRACE 

and RELAP. 

Figure 7 TRACE and RELAP mass flux predictions vs. measurements for Purdue tests

The channel nodalization for each model predicts lower mass flux rates compared to the junction 

nodalization. This is likely due to the added wall friction losses in the channel nodalization compared 

to the junction nodalization. 

The modified Burnell models in RELAP and TRACE produce similar results for the junction 

nodalization. The Henry-Fauske model in RELAP is somewhat more accurate using the junction 

nodalization, however for the channel nodalization it does not appear to capture the trend. The 

TRACE model with choking disabled produces the results with the lowest absolute error, however 

the predicted flow rate is more or less constant; the most accurate data points correspond to tests 

with the highest subcooling, which approaches the un-choked condition.

A junction nodalization appears to be more suitable for Modelling critical flow through very thin 

walled samples such as the ones in this experiment: the junction models over predict flow, which is 

conservative in most cases, and a junction nodalization simplifies the model compared to a channel 

nodalization. This is particularly significant for RELAP5, where the numerical solving scheme is 

constrained by the Courant limit; the very short hydraulic cells of the channel nodalization result in 

a very small maximum time step and consequently long solving times.

From a Modelling perspective it is useful to present results in terms of a discharge coefficient, 

calculated as the measured mass flux divided by the predicted mass flux. These discharge 

coefficients are plotted as a function of subcooling in Figure 8. For the TRACE no choking model 

and the RELAP channel Henry-Fauske model the discharge coefficient increases with increasing 

subcooling, while the rest of the result are relatively consistent with respect to temperature. 
13

Figure 8 TRACE and RELAP calculated discharge coefficient for Purdue tests

3.5 Modelling Options and Sensitivity Studies

Several sensitivity studies were performed in both the TRACE and RELAP5 models to determine 

the impact of various modelling parameters. The results are detailed below.

3.5.1 TRACE Sensitivity Studies

Time Step Size: Reducing the time step from the 0.1s used in the analysis to 0.001s had no impact 

on results.

Numerical Scheme The default solver in TRACE is the SETS solver. Changing to the semi-implicit 

solver resulted in no appreciable change in predicted flow rates but produced some oscillations in 

the results.

Wall Roughness: Increasing wall roughness by 50% resulted in a decrease in predicted critical 

mass flow rate of less than 2%

Fineness of Nodalization: Doubling the number of hydraulic cells in the channel nodalization had a 

negligible impact on model results.

Critical Flow Relaxation Constant: As mentioned earlier, the relaxation constant for the critical flow 

model was reduced to 1.1. With the default 2.0 significant oscillations were observed in the flow 

rates.

3.5.2 RELAP

Time Step Size: The RELAP5 numerical solving scheme is subject to the material Courant limit, 

therefore the very short cell lengths in the channel nodalization results in a very small time step (on 

the order of 10-5 seconds). For the junction nodalization, reducing the time step from 0.1s to 0.001s 

had no impact on results.

Wall Roughness: Increasing the wall roughness by 50% reduced predicted critical mass flow rates 

by less than 3%.

Nodalization of Sample: Doubling the number of cells in the channel nodalization had a negligible 

impact on predicted mass flow rates.

15

4 ONTARIO HYDRO THICK WALLED CRITICAL FLOW TESTS

4.1 Facility Description

This series of tests was conducted by Ontario Hydro (OH) [7] in 1985 to support the use of a leakbefore-break approach for pipe failure analysis in CANDU reactors. The tests were designed to 

measure flow rates through circumferential cracks in large diameter pipes.

The experiment used a test fixture consisting of two stainless steel cylinders. An aluminum wire 

shim was placed between the two cylinders, which were then bolted together. The wire crushed 

down to provide a leak tight seal. The thickness of the crushed wire determined the width of the 

crack or crack opening displacement (COD), while the positioning of the wire was used to produce 

either a rectangular or flared crack cross section. 

Three tests were conducted using different parameters as outlined in Table 2. 

Table 2 OH test fixture geometries [7]

Test ID Crack Shape COD 

(mm)

Crack Length at Outer 

Surface (mm)

Average Surface 

Roughness (μm)

Crack Depth 

(mm)

SS-A1 Flare 75.2° 0.102 98.6 2.03 38.1

SS-A2 Rectangular 0.109 48.8 2.03 38.1

SS-A3 Flare 75.2° 0.508 98.6 2.03 38.1

The measured change in COD before and after the test was less than 5%.

A pressure vessel with a capacity of approximately 200 kg was used to supply water to the test 

fixture. The entire apparatus of the pressure vessel, nitrogen tanks and supply lines was mounted 

on a weight balance platform. A load cell located under the opposite end of the platform measured 

the loss of water mass from the pressure vessel, which was correlated to mass flow rate from the 

test fixture. The nitrogen tanks were situated to eliminate the effects of mass shift from the tanks to 

the pressure vessel. Experimental error in leak rate measurement was within +/- 0.005 kg/s. The 

experimental apparatus and test fixtures are illustrated in Figure 9. 

During testing the pressure vessel was filled with deionized water and heated using 40 kW 

immersion heaters. Nitrogen cover gas was used to maintain the desired pressure throughout the 

test.
16

Figure 9 Test section showing shim and the flared and rectangular crack geometries [7]

4.2 Experimental Results

The measured flow rates for the three tests are shown in Figure 10. Flow rate was tested over a 

pressure range of 1 MPa to 12 MPa at temperatures between 177°C and 300°C. As the temperature 

increases (subcooling decreases) for each test the flow rate decreases. It is observed that for highly 

subcooled conditions the flow rate is strongly dependent on pressure, while at low subcooling the 

flow is less dependent on pressure.
17

Figure 10 Measured flow rates for OH tests

4.3 Modelling

The experimental setup was modelled using TRACE V5.830. The SNAP representation of the 

nodalization is presented in Figure 11. The simulated crack is represented by a 3 cell PIPE 

(component 30). The internal volume of the test fixture is modelled with a single hydraulic cell 

(component 20). Boundary conditions 10 and 40 represent the test pressure and temperature and 

atmospheric conditions, respectively.

Choking was enabled at the interface between component 30 and boundary condition 40, with a 

default critical flow multiplier of 1.0 applied for all model runs. Minor losses at the inlet and outlet 

edge were calculated internally by TRACE using the ‘abrupt area change’ modelling option.

For the flared crack geometry the flow areas at the inner and outer edge of component 30 were 

calculated as the COD multiplied by the crack length along the pipe inner and outer circumference, 

respectively. Internal edge and cell centered flow areas were linearly interpolated between these 

values. Hydraulic diameter was calculated in a similar manner. For the straight crack geometry the 

flow area was calculated simply as the COD multiplied by the width of the flow path.
18

Figure 11 TRACE nodalization for OH tests samples (cell sizing not to scale)

4.4 Results

Figure 12 show the predicted vs. measured mass flow rate for the three test specimens. For 

samples 1 and 2 the flow rates are mostly predicted within ±25% and tend towards over prediction. 

Sample 3 results are over predicted to a greater degree, up to +75%.

The results in terms of calculated discharge coefficients are shown in Figure 13. Discharge 

coefficients trend towards higher values at lower pressures, indicating a tendency towards under 

prediction at low pressure; above 8 MPa results are more consistent. Under prediction of critical 

flow rates for the low pressure conditions have also been reported for the RELAP5 implementation 

of the modified Burnell/Ransom-Trapp critical flow model [17]. 

Samples 1 and 2 represent flared and rectangular crack geometries, respectively, which have a 

similar COD. For pressures above 8 MPa the discharge coefficients for these samples are similar, 

with a range of 0.7 – 1.05 for sample 1 and 0.6-0.9 for sample 2. 

By comparison the discharge coefficients for sample 3 are both lower and fall in a narrower range 

of 0.52 – 0.64. The smaller range for sample 3 may be due to larger COD, which results in higher 

flow rates and thus lower relative error in experimental measurements. 

Modelling results show no clear trend with respect to test temperature.
19

Figure 12 Model results for OH test samples

Figure 13 Discharge coefficients for the OH test samples 

21

5 AECL FATIGUE CRACK CRITICAL FLOW TESTS

5.1 Facility Description

This series of tests was designed to measure flow rates through cracks in thick-walled pipes. A 

unique feature of these tests is the use of pressure cycling to produce fatigue cracks for flow rate 

measurements; the cracks produced by this method are expected to be more representative of 

through-wall defects which could potentially develop in reactors compared the machined, simulated 

crack geometries of the other tests.

A diagram of the pressure cycling rig used to produce cracks in the test specimens is shown in 

Figure 14. The pipe specimens consisted of 100 ASTM 106 Grade B pipes with diameters between 

305 and 610mm and L/D of approximately 2, with end caps welded to each end. In order to assist 

the cracking process a notch was introduced on the inner surface using electric discharge 

machining (EDM). For samples 3 and 5 a flange was welded on the inside surface of the pipe to 

further increase stress. One end cap was connected with a pipe coupling to the pressure cycling 

rig. 

Pressure cycling histories were different for each specimen; a typical regime involved cycling from 

5 MPa up to 29 MPa. Between 30,000 and 91,000 pressure cycles were required to produce a 

through wall crack. During pressure cycling the outside of the pipe was sprayed with water to 

maintain ambient temperatures and to reduce the number of cycles required to form cracks.

Figure 14 Pressure cycling rig [19]

Once a crack had been produced, the specimen was attached to a water supply at 260 oC and 8.5 

MPa. A single set of test pressure and temperature was used for the test series. Strap heaters and 

insulation were installed to maintain the temperature of the pipe at 260 oC. Steam discharged from 

the crack was collected and condensed in a tube-to-tube heat exchanger. The condensate was 

collected in a bucket, the weight of which was recorded with a load cell to determine the leak rate. 
22

Post testing, the cracks were examined by cutting out the crack section and measuring the crack 

length and crack opening displacement (COD) on both inside and outside surfaces. The section 

was then cooled with liquid nitrogen and cracked open to expose the leak path. The crack lengths 

were then re-measured and the surface roughness of the leak path was measured.

5.2 Experimental Results

The properties of the five test specimen are listed in Table 3. Several tests were performed for each 

sample using the same test conditions of 8.5 MPa and 260oC; the range of flow rates observed 

during the different tests is reported. Note that the location of the crack, where the pipe failed during 

pressure cycling, varied and in the case of specimens 2 and 4 occurred not at the EDM notch but 

in the end cap weld. 

Table 3 Test specimen properties and measured flow rates [19]

Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5

Pipe OD (mm) 324 457 324 324 610

Pipe Wall 

Thickness (mm)

21.2 26.7 19.7 21.4 38.9

Crack Location EDM notch Endcap weld Flange Endcap weld Flange

Crack Length on ID 

(mm)

58 10 14 20.2 115

Crack Length on 

OD (mm)

13.5 65 14 12.6 10.5

Approximate COD 

(mm)

0.1 0.2 0.3-0.7 0.35 0.17

Crack Surface 

Roughness (μm)

10.2 13-16 5-20 3.8-7.6 20.3

Measured Leak 

Rate (kg/h)

0.5-7 8-11 15-30 65-115 8-24

For comparison to Modelling results the highest observed flow rate is used. Specimen 1 has a 

particularly wide range of flow rates; the researchers noted that the loop had not been used prior to 

testing of specimen 1, and leak rates measured closer to the lower end of the reported range where 

likely impacted by crud deposition in the crack [19].
23

5.3 Modelling

The experiments were modeled using TRACE V5.830. The nodalization appears in Figure 15 and 

is essentially the same model used for the Ontario Hydro tests detailed in section 4.3. Boundary 

conditions 10 and 40 represent the test fluid conditions and atmospheric conditions, respectively. 

Pipe 20 represents the volume of the test specimen, while the through-wall crack is represented by 

component 30. 

The flow area and hydraulic diameter of the inlet and outlet of the crack are based on the crack 

length and COD values in Table 4. 

For this set of tests the crack shape is not reported. For the fatigue cracks in this set of tests the 

COD is likely not consistent along the crack length. For development of the nodalization it was 

assumed that the reported COD is the maximum value at the crack center, which tapers linearly to 

zero at the crack ends. This assumption yields a diamond shaped crack whereby the flow area is 

equal to COD x crack length / 2. Flow area between the inner and outer surface of the crack was 

linearly interpolated. Minor losses at the inlet and outlet edge of the crack were calculated internally 

by TRACE using the ‘abrupt area change’ modelling option. Choking was enabled on the edge 

between component 30 and boundary condition 40.

 

Figure 15 TRACE nodalization for the AECL tests (cell sizes not to scale) 
24

5.4 Results

Modelling results are presented in Table 4 and Figure 16. The discharge coefficient is calculated as 

the measured mass flow rate divided by the predicted mass flow rate. For the measured rate the 

highest value reported in Table 3 is used. 

In all cases TRACE significantly over predicts mass flow through the crack. Excluding specimen 4, 

the predictions are up to one order of magnitude higher than measured values. Specimen 4 

prediction is closer to the experimental value; this test showed a significantly higher measured flow 

rate that the other tests. Based on the specimen geometry reported in Table 4 the major difference 

between sample 4 and the others samples is a lower surface roughness. The high relative 

roughness of the other samples with respect to their COD may contribute to the very low flow rates 

seen in those test.

Flow rate predictions for this experimental are significantly over predicted compared to the other 

two experiments. Notable difference between these tests and the OH tests, which also used thick 

walled sections, is the use of fatigue cracks as opposed to stylized, machined crack geometries. 

The irregularities in flow path resulting from the fatigue cracking process likely have a strong impact 

on the low flow rates seen in the test.

Table 4 TRACE predicted leak rates and calculated discharge coefficients

Specimen 

Number

Measured leak 

rate (kg/hr)

TRACE predicted 

leak rate (kg/hr)

Discharge 

coefficient

1 7 62 0.11

2 11 59 0.19

3 30 287 0.10

4 115 241 0.48

5 24 217 0.11
25

Figure 16 Discharge coefficients for the AECL tests

For specimen 4 a sensitivity study was conducted by changing the location of the choking plane. 

Table 5 shows that as the choking plane was moved away from the outside edge towards the inside 

surface of the pipe the flow rate increased until at edge 1 non-critical flow conditions were predicted. 

Table 5 Predicted flow rate for sample 4, different edges selected as the choking plane

Location of 

Choking Plane

Predicted Flow 

Rate (kg/h)

Fluid 

Condition

Edge 5 241.2 Choked

Edge 4 257.4 Choked

Edge 3 273.2 Choked

Edge 2 282.6 Choked

Edge 1 322.9 Unchoked

27

6 DISCUSSION AND CONCLUSIONS

Based on the comparison of nodalization techniques for the Purdue tests, a junction nodalization

appears more suitable for modelling of cracks with low wall thicknesses. When this nodalization 

scheme is employed, the TRACE implementation of the modified Burnell critical flow model gives 

similar results to the RELAP5 implementation of that model. 

The Purdue tests and the OH tests both represent well defined, simulated crack geometries. The 

TRACE results for the OH tests at pressures above 8 MPa showed a range of discharge coefficients 

of 0.52 to 1.02, which bounds the results for the Purdue tests using the junction nodalization, where 

the range of discharge coefficients was 0.71 to 0.86. Modelling of the OH tests showed a tendency 

for TRACE to over-prediction critical flow at low pressures; in this case discharge coefficients began 

to rise at pressures below 8 MPa. There was no clear trend in model accuracy with respect to 

subcooling. 

The OH and AECL tests both used thick walled samples with similar section thicknesses. However 

there is up to an order of magnitude difference in model predictions for these samples, with 

discharge coefficients for four of the five samples in the range of 0.10 – 0.19. 

The major difference between the specimen sets is that the AECL tests have much higher surface 

roughness, on average 10-20 μm as opposed to 2 μm, for the AECL tests, likely due to production 

of the crack through a fatigue cracking process. For the very narrow cracks in these tests the surface 

roughness represents a significant fraction of the COD. This may introduce effects such as local 

changes in flow direction which are not accounted for in the model. It is notable that in the original 

report on the AECL tests a theoretical model for predicting leakage rate was described which 

produced good results only when a discharge coefficient of 0.07 was applied [19], indicating a more 

significant-over prediction of flow than the TRACE model.

In general, TRACE appears to be a suitable tool for modelling critical flow in thin and thick walled 

crack geometries. Modelling of additional leak rate tests should be performed to expand the code 

validation in this area.

29

7 REFERENCES

[1] J. Riznic, M. Ishii and N. Afgan, "Mechanistic Model for Void Distribution in Flashing Flow," 

in Hewitt, G., Mayinger, F., Riznic, J., (Eds), Transient Phenomena in Multiphase Flow, 

New York, NY, 1987. 

[2] A. Frisani and Y. Hassan, "Analysis of Leaks through Microchannel Cracks Using 

RELAP5-3D," Nuclear Technology, vol. 167, pp. 304-312, 2008. 

[3] V. Krungleviciute and A. Kaliatka, "Employing of RELAP5 Code for LBB Deterministic 

Analysis in the Ignalina NPP," 

http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/33/020/33020121.pdf.

[4] S. Majumdar, K. Kasza, J. Y. Park and S. Bakhtiari, "Prediction of Failure Pressure and

Leak Rate of Stress Cossosion Cracks," Argonne National Laboratory, Argonne, IL, USA, 

2002.

[5] S. Ghosh and S. K. Saha, "Experimental validation of RELAP5 predictions for subcooled 

leak flow through narrow circumferential slits," Annals of Nuclear Energy, vol. 75, pp. 507-

515, 2015. 

[6] S. T. Revankar, B. Wolf and J. R. Riznic, "Flashing Flow of subcooled liquid through small 

cracks," Procedia Engineering, vol. 56, pp. 454-461, 2013. 

[7] J. Nathwani, B. Kee, C. Kim and M. Kozluk, "Ontario Hydro's Leak Before Break Approach: 

Application to the Darlington (CANDU) Nuclear Generating Station A," Nuclear 

Engineering and Design, vol. 111, pp. 85-107, 1989. 

[8] D. Paul and e. al., "Evaluation and Refinement of Leak–Rate Estimation Models," 

NUREG/CR–5128, Rev. 1, 1994.

[9] S. Ghosh, D. Mukhopadhyay and S. K. Saha, "An experimental analysis of subcooled 

leakage flow through slits from high pressure high temperature pipelines," International 

Journal of Pressure Vessels and Piping, vol. 88, pp. 281-289, 2011. 

[10] Z. Yang, Q. Bi, G. Zhu, Q. Zhang and J. Liang, "Leak rates of high pressure steam–water 

across simulation crack," Experimental Thermal and Fluid Science, vol. 59, pp. 118-126, 

5014. 

[11] S. Majumdar, K. Kasza, S. Bakhtiari, J. Park, J. Oras, J. Franklin, C. Vulyak and W. Shack, 

"Steam Generator Tube Integrity Issues: Pressurization Rate Effects, Failure Maps, Leak 

Rate Correlation Models, and Leak Rates in Restricted Areas," NUREG/CR-6879, 2009.

[12] J. Burnell, "Flow of Boiling Water through Nozzles, Orifices, and Pipes," Engineering, pp. 

572-576, 1947. 

[13] US NRC Office of Nuclear Regulatory Research, "TRACE V5.435 Theory Manual," 

Washington, DC, USA, 2011.

[14] M. D. Alamgir and J. H. Lienhard, "Correlation of Pressure Undershoot During Hot Water," 

Transactions of ASME, Journal of Heat Transfer, vol. 103, pp. 52-55, 1981. 

[15] O. C. Jones, "“Flashing Inception in Flowing Liquids," Journal of Heat Transfer, vol. 102, 

pp. 439-444, 1980. 

[16] N. Abuaf, J. O. C. Jones and B. J. C. Wu, "Critical Flashing Flow in Nozzles with 

Subcooled Inlet Conditions, BNL-NUREG-27512," Brookhaven National Laboratory, 1980.

[17] Information Systems Laboratories Inc., "RELAP3.3 MOD3.3 Code Manual Volume IV: 

Models and Correlations," Division of Systems Research, United States Nuclear 

Regulatory Commission, Washington DC, 2010.
30

[18] S. T. Revankar, B. Wolf and A. Vadlamani, "Assessment of Leak Rates through Steam 

Generator Tubes," Purdue University School of Nuclear Engineering, West Lafayette, IN, 

USA, 2013.

[19] D. Scott and A. Cook, "Leakage Rate through Cracks in Thick Walled Pipes," AECL Report 

9003, available online: 

http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/19/068/19068504.pdf, 1985.
Assessment of Critical Subcooled Flow Through Cracks in Large and 

Small Pipes Using TRACE and RELAP5

NUREG/IA-0457

Andrew Oussoren; J. Riznic; S.T. Revankar*

Canadian Nuclear Safety Commission *School of Nuclear Engineering

280 Slater Street Purdue University

P.O. Box 1046 Station B W. Lafayette, IN, USA

Ottawa, Ontario, Canada

Kirk Tien, NRC Project Manager

Division of Systems Analysis

Office of Nuclear Regulartory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

The thermal hydraulics system code TRACE has been used to predict subcooled critical flow in crack geometries. Three 

different experimental data sets were modeled in this study. The first experiment, performed at Purdue University, measured 

critical flow in slits with small section thicknesses similar to steam generator tubing. These results are also compared to 

model predictions using the RELAP5 code. The second experiment, conducted by Ontario Hydro (OH), measured critical 

flow rates in simulated circumferential cracks in thick-walled piping. The third experiment, from Atomic Energy of Canada 

Ltd. (AECL), measured critical flow through pressure cycling-induced fatigue cracks in thick walled vessels. For the Purdue 

tests, TRACE predictions were similar to those obtained with RELAP5. For the thin walled samples in these tests a junction 

nodalization was found to be more suitable than explicitly modeling the section thickness of the samples. TRACE predictions 

for both the Purdue and OH tests were in reasonable agreement with measured leak rates, with calculated discharge 

coefficients of between 0.5 and 1.0 for most cases. However, the model of the OH tests showed a trend towards under 

prediction as pressure dropped below 8 MPa. There was no clear trend demonstrated with respect to subcooling. For the 

AECL experiments the flow rate was significantly over predicted, with discharge coefficients as low as 0.1. This result is 

consistent with the modelling performed by the original experimenters and is likely due to the complexity of the flow pathway

in the fatigue cracks used in this test, as compared to the machined geometries of the other samples.

Ontario Hydro (OH) 

Canadian Nuclear Safety Commission (CNSC)

Atomic Energy of Canada Limited (AECL)

Subcooled Critical Flow

Steam Generator pipe cracks

August 2017

Technical



NUREG/IA-0457 Assessment of Critical Subcooled Flow Through Cracks in Large and Small Pipes Using TRACE and RELAP5 August 2017