NUREG/IA-0239

 International 

Agreement Report

Development of Horizontal Off-Take 

Model for Application to Reactor 

Headers of CANDU Type Reactors

Prepared by:

Yong Jin Cho, Seung-Hoon Ahn, In-Goo Kim/KINS

Gyoo Dong Jeon/HYU

Korea Institute of Nuclear Safety (KINS)

19 Gusung-dong, Yusong,gu

Daejeon, 305-338, Korea

Hanyang University

17 Haengdang-dong, Seongdong-gu

Seoul, 133-791, Korea

A. Calvo, NRC Project Manager 

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

June 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
AVAILABILITY OF REFERENCE MATERIALS 

IN NRC PUBLICATIONS

NRC Reference Material 

As of November 1999, you may electronically access 

NUREG-series publications and other NRC records at 

NRC’s Public Electronic Reading Room at 

http://www.nrc.gov/reading-rm.html. Publicly 

released records include, to name a few, 

NUREG-series publications; Federal Register noti

applicant, licensee, and vendor documents and 

correspondence; NRC correspondence and inter

memoranda; bulletins and information notices; 

inspection and investigative reports; licensee even

reports; and Commission papers and their a

ces; 

nal 

t 

ttachments. 

NRC publications in the NUREG series, NRC 

regulations, and Title 10, Energy, in the Code of 

Federal Regulations may also be purchased from one 

of these two sources. 

1. The Superintendent of Documents 

 U.S. Government Printing Office 

 Mail Stop SSOP 

 Washington, DC 20402-0001 

 Internet: bookstore.gpo.gov 

 Telephone: 202-512-1800 

 Fax: 202-512-2250 

2. The National Technical Information Service 

 Springfield, VA 22161-0002 

 www.ntis.gov 

 1-800-553-6847 or, locally, 703-605-6000 

A single copy of each NRC draft report for comment is 

available free, to the extent of supply, upon written 

request as follows: 

Address: Office of the Chief Information Officer, 

 Reproduction and 

Distribution 

 Services Section 

 U.S. Nuclear Regulatory 

Commission 

 Washington, DC 20555-0001 

E-mail: DISTRIBUTION@nrc.gov 

Facsimile: 301-415-2289 

Some publications in the NUREG series that are 

posted at NRC’s Web site address 

http://www.nrc.gov/reading-rm/doc-collections/nuregs 

are updated periodically and may differ from the last 

printed version. Although references to material found 

on a Web site bear the date the material was accessed, 

the material available on the date cited may 

subsequently be removed from the site. 

Non-NRC Reference Material

Documents available from public and special technical 

libraries include all open literature items, such as 

books, journal articles, and transactions, Federal 

Register notices, Federal and State legislation, and 

congressional reports. Such documents as theses, 

dissertations, foreign reports and translations, and 

non-NRC conference proceedings may be purchased 

from their sponsoring organization. 

Copies of industry codes and standards used in a 

substantive manner in the NRC regulatory process are 

maintained at— 

The NRC Technical Library 

Two White Flint North 

11545 Rockville Pike 

Rockville, MD 20852-2738 

These standards are available in the library for 

reference use by the public. Codes and standards are 

usually copyrighted and may be purchased from the 

originating organization or, if they are American 

National Standards, from— 

American National Standards Institute 

11 West 42nd Street 

New York, NY 10036-8002 

www.ansi.org 

212-642-4900 

Legally binding regulatory requirements are stated only 

in laws; NRC regulations; licenses, including technical 

specifications; or orders, not in 

NUREG-series publications. The views expressed in 

contractor-prepared publications in this series are not 

necessarily those of the NRC. 

The NUREG series comprises (1) technical and 

administrative reports and books prepared by the staff 

(NUREG–XXXX) or agency contractors 

(NUREG/CR–XXXX), (2) proceedings of conferences 

(NUREG/CP–XXXX), (3) reports resulting from 

international agreements (NUREG/IA–XXXX), 

(4) brochures (NUREG/BR–XXXX), and 

(5) compilations of legal decisions and orders of the 

Commission and Atomic and Safety Licensing Boards 

and of Directors’ decisions under Section 2.206 of 

NRC’s regulations (NUREG–0750). 

DISCLAIMER: This report was prepared as an account of work sponsored by an agency of the U.S. 

Government. Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, 

expressed or implied, or assumes any legal liability or responsibility for any third party=s use, or the results of such 

use, of any information, apparatus, product, or process disclosed in this publication, or represents that its use by 

such third party would not infringe privately owned rights. 
NUREG/IA-0239

Development of Horizontal Off-Take 

Model for Application to Reactor 

Headers of CANDU Type Reactors 

Manuscript Completed: April 2010 

Date Published: June 2010 

Yong Jin Cho, Seung-Hoon Ahn, In-Goo Kim/KINS 

Gyoo Dong Jeon/HYU 

Korea Institute of Nuclear Safety (KINS) 

19 Gusung-dong, Yusong-gu 

Daejeon, 305-338, Korea 

Hanyang University 

17 Haengdang-dong, Seongdong-gu 

Seoul, 133-791, Korea 

Antony Calvo, NRC Project Manager 

Prepared for:

Division of Systems Analysis 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001

iii

ABSTRACT

In the CANDU accident analysis the header is one of the important components to be well 

modeled, because it has great impact on the fuel channel behavior during some accidents. The 

feeder void fraction, affected by thermal-hydraulic behavior in the headers, may affect the fuel 

bundle coolability. The liquid entrainment and vapor pull-through (off-take) phenomena in the 

header are considered highly important, in case where horizontal stratification is achieved inside 

the header. 

To generalize the model for application to various branch angles, a critical height correlation 

was reconstructed by using the point skin method, and then the constants were determined so 

the correlation can fit well with the previous large number of experimental data. The new model 

considers the effects of different branch angles on the off-take, and tested against the 

experimental data of various branch angles in a Separate Effect Test (SET). 

The verification analysis results in a conceptual blowdown problem showed that the new 

model gives better accuracy than the original. The new model also provided an enhancement in 

prediction of the experimental data selected for validation. 
iv
v

FOREWORD 

RELAP5 is one of the best-estimate thermal-hydraulic system codes to date. It was 

developed by United States Nuclear Regulatory Commission (USNRC) and its latest version, 

RELAP5/MOD3.3 (patch 03) was released in 2006. Though USNRC has been moving most of 

their developmental efforts from RELAP5 to TRACE, the RELAP5 code is still widely applied to 

analyses of various transients in Light Water Reactors (LWRs), including the postulated large 

break loss-of-coolant accident (LBLOCA). 

In Korea, four CANDU (CANada Deuterium Uranium)-type heavy water reactors are in 

operation, which have design peculiarities, especially the reactor core composed of many small 

separated horizontal fuel channels and the moderator separated from the coolant. For purpose 

of a regulatory auditing calculation, the RELAP5 code has been adapted to the CANDU reactor 

design by model modifications and developments. As part of such an effort, an effort was made 

to generalize the RELAP5 off-take model to various angled branches. This report is to extend 

the previous study by developing the new off-take model in angled branch line configurations of 

a large pipe, applicable to the header of the CANDU reactor. 

The authors acknowledge the financial support of the National Research Foundation under the 

national mid- and long-term nuclear research and development program of the Ministry of 

Education, Science and Technology of the Republic of Korea.
vi
vii

CONTENTS

Page

Abstract ........................................................................................................................... iii 

Foreword ....................................................................................................................... v 

Executive Summary ........................................................................................................ix 

Nomenclatures ................................................................................................................xi 

1. Introduction .............................................................................................................. 1-1 

2. Model Review ........................................................................................................... 2-1

 2.1 RELAP5 Model ................................................................................................... 2-1 

 2.2 State of the art .................................................................................................... 2-2

3. Theoretical Analysis ................................................................................................. 3-1 

 3.1 Theoretical Analysis ............................................................................................ 3-1 

 3.2 Experimental Assessment .................................................................................. 3-3 

3.3 Model Verification and Validation ........................................................................ 3-6 

4. Conclusions .............................................................................................................. 4-1 

5. References ............................................................................................................... 5-1 

Appendices

A Description of Canadian Experimental Facility used in SET Validation ............. A-1 

B Lists of Subprogram Changes ........................................................................... B-1 

C Input deck for Model Verification....................................................................... C-1 

D Input deck for Model Validation ........................................................................ D-1 
viii

List of Figures

Figure Page

1. Conceptual Sketches for Liquid and Vapor Pull-Through Model ........................................... 1-1 

2. Schematic Drawing for Theoretical Approach ....................................................................... 3-1 

3. Angled Branch Correlation Comparison ................................................................................ 3-5 

4. Vertical Downward Branch Correlation Comparison ............................................................. 3-5 

5. Vertical Upward Branch Correlation Comparison .................................................................. 3-6 

6. Modeling for New Model Verification (90o

~-90o) .................................................................... 3-7 

7. Upstream Pressure Behavior for Verification ........................................................................ 3-7 

8. Branch Line Liquid Fraction Results for Verification .............................................................. 3-8 

9. Branch Line Mass Flowrate Results for Verification .............................................................. 3-8 

10. Modeling for New Model Validation ...................................................................................... 3-9 

11. New Model Validation for -45o

 branch line ......................................................................... 3-10 

12. New Model Validation for 0o

 branch line ............................................................................ 3-10 

13. New Model Validation for -90o

 branch line ......................................................................... 3-11 

List of Tables

Table Page

1. Experimental Data used to determining correlation constants ..................................... 3-3 

2. Constants of Critical Height Correlation by Nonlinear Fitting Methods........................ 3-4 
ix

Executive Summary 

 

The header of CANDU nuclear power plant is the important component to simulate the fuel 

channel behavior because the headers' hydraulic behavior controls the feeder void fraction 

which affects on the fuel bundle coolability. In CANDU accident analyses, the liquid entrainment 

and vapor pull-through (off-take) phenomena should be considered when horizontal stratification 

achieved inside the header. The current RELAP5 off-take model can treat only 3 directions; 

vertical upward, downward, and side oriented junctions. The onset of liquid entrainment and 

vapor pull-through model, represented by the critical height were studied in the angled branch 

line configurations in a large pipe. 

In the CANDU accident analysis the header is one of the important components to consider 

when simulating the fuel channel behavior. The hydraulic behavior in the header controls the 

feeder void fraction which may affect the fuel bundle coolability. The liquid entrainment and 

vapor pull-through model (off-take model) becomes strongly influences the coolant flow of 95 

feeders connected to the reactor header component where the horizontal stratification may 

occur [6]. The current RELAP5 includes the off-take models only for the junctions of three 

angles, vertically upward and downward, and side oriented, and thus an improvement was 

needed to model the exact angles for simulation the branch lines from the CANDU header. 

The new model was applied to RELAP5/MOD3. For verification, conceptual problem 

calculations have been performed for a conceptual blowdown problem with different connection 

angles of branch in a horizontal pipe. The calculated void fraction and mass flow rate of different 

location of branches shows the validity of implemented model. As validation, the Canadian 

experiment was adopted and this experiment was performed in a horizontal pipe with a branch 

and different orientations using air-water mixture. The data for the angles of zero, -45 and -90 

degrees were selected among many data sets. The modified RELAP5 with new model gave 

improved results for the horizontal and vertical downward and angled branch line. 
x
Nomenclatures

C1 , C2 , : Coefficients C3

xi

 : Diameter of branch, (meter) 

D ter) 

 (kg/sec) 

n /sec) 

, z nates (meter) 

reek Letters 

d

 : Upstream Pipe Diameter (me

g : Gravitational Force (m/sec2

) 

h : Height (meter) 

m& : Mass Flow Rate

 : Strength of Point Sink (m3

P : Pressure (Pascal) 

s : Distance 

V : Velocity (m/sec) 

x, y : Cartesian Coordi

G

α : Void Fraction 

θ : Inclination Angle 

ρ : Density (kg/m3) 

Δρ : Density Differences (kg/m3

) 

φ : Potential Function (m2

/sec) 

ubscripts 

tical Height, usually used as hb 

E 

t 

S

b : Cri

B : Edge Point of Heavier Fluid Level 

BG : Beginning of Gas Entrainment 

BLE : Beginning of Liquid Entrainmen

L : Liquid Phase 

G : Gas Phase 
xii
1. INTRODUCTION

In many industrial applications, especially those in nuclear power plant, two-phase flow 

discharging from a stratified region through a branch need to be examined [1]. Examples 

include the flow through a small break in a horizontal channel of a nuclear power plant during 

loss of coolant accident, the flow distribution in CANDU header-feeder system [2] during 

accident scenarios, and two-phase distribution headers in general, where a certain incoming 

stream fed into a large header is divided among a number of discharging streams. 

The liquid entrainment and vapor pull-through model (off-take model) becomes strongly 

influences the coolant flow of 95 feeders connected to the reactor header component where the 

horizontal stratification may occur [3]. Studies of two-phase flow through small branches in 

horizontal pipes under stratified flow conditions have gained importance due to their relevance 

to many engineering applications. In the field of nuclear safety, the loss of coolant accident 

(LOCA) caused by a small break in a horizontal pipe is of great importance. During such a 

LOCA, a stratified flow may occur in the horizontal pipe, which strongly influences the mass flow 

rate through the break. The flow characteristics in an off-take phenomenon are shown in Fig. 1. 

The current RELAP5 model is able to treat only vertically upward, downward, and side oriented 

junctions, and thus improvements for the off-take model was needed for modeling the exact 

angles [4]. 

In this study, a base formulation for a new model was developed based on a point-sink method 

to consider the feeder pipe angle and the new models for vertical upward, downward and 

angled branch were developed and the verification/validation were performed using separate 

effect test data. 

Figure 1 Conceptual Sketches for Liquid and Vapor Pull-Through Model 

1-1
1-2
2. MODEL REVIEW 

2.1 RELAP5 Model 

RELAP5/MOD3 horizontal stratification entrainment/pull-through model [4] accounts for phase 

separation phenomena and computes the flux of mass and energy through an off-take attached 

to a horizontal pipe. When stratification occurs in a large horizontal pipe, the quality of a branch 

line can be calculated by “upward off-take,” “downward off-take,” and “horizontal off-take” 

models according to connection angle between a large horizontal and branch pipes. These 

models were developed from experimental studies where the inception height on liquid 

entrainment and vapor pull-through were measured. 

The inception height, , associated with the onset of liquid entrainment or vapor pull-through is 

represented as follows [4]. 

hb

 2-1

[ ( )] , 2.0

4.0

gfk

k

b

g

CW h − ρρρ = (1) 

Where the subscript k represents the phase properties of a continuum flowing in a branch pipe 

before the onset of liquid entrainment or vapor pull-through. For example, k rep sents liquid 

properties for downward oriented off-take. W the flow rate of a continuum. C is a 

coefficient determined by experiments. 

re

is 

 (2) 

⎪

⎪

⎩

⎪

⎪

⎨

⎧

−

− −

− −

−

=

for horizontal liquidtakeoff entrianmen t

for horizontal pullgastakeoff through

for downward pullgastakeoff through

liquidtakeoffupwardfor entrianmen t

75.0

75.0

50.1

67.1

C

The correlations used for calculation of flow quality, X , at the branch entrance with off-take are 

dependent on the connection angle between a large horizontal and branch pipes, and 

represented as follows; 

( ) ( ) [ ]

( ) ( ) ( ) [ ] ⎪

⎩

⎪

⎨

⎧

+− −

+− −

−

=

+ −

−

−

afor horizontal takeoff branch

afor downward takeoff branch

upwardanfor takeoff branch

5.0 1 1

5.0 5.2 1

)1(25.3

15.01

15.01

R

o

CR

o

R

o

R

o

R

X XRR

X XRR

R

X , (3) 

where, 0.5

1.15 ,

1

o

b f

g

h R X

h ρ

ρ

= = ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠

h = distance from the stratified liquid level to junction 

1.09

1.00

for gas pull through C

for liquid entrainment

⎧ − = ⎨

⎩ − 
2.2 State of the art 

In the field of nuclear safety, the loss of coolant accident (LOCA) caused by a small break in a 

horizontal pipe is of great importance. During such a LOCA, a stratified flow may occur in the 

horizontal pipe, which severely influences the mass flowrate through the break. Generally, 

break is simulated by T-junctions with small ratio d/D of branch to main pipe diameter. However 

the investigation was concentrated on flow and geometrical parameters quite different from 

those applying to the situations of interest in nuclear reactors. These situations were described 

by Zuber [1]. If a break is located above horizontal interface, liquid from the interface can be 

entrained due to the pressure drop produced by the vapor acceleration in the vicinity of the 

break (Bernoulli effect). Similarly, with a break located below the interface, vapor can reach the 

break due to vortex formation or can be pulled through in the vortex-free flow. 

The importance of two-phase flow through small branches in horizontal pipes under 

stratified-flow conditions has motivated significant research, conducted mostly during the past 

twenty years. Smoglie and Reimann [5] performed experiments using stratified air-water flow 

at 200 to 500 kPa in a horizontal pipe (20.6cm in diameter) with different branch sizes (d=6,8,12 

and 20 mm) and different orientations (top, bottom and side) for each branch. The branches 

were simulated by pipe stubs (0.055m in length) with sharp-edged entrances and the flow 

through the branch was controlled by throttle valve. These results indicated an insignificant 

effect of the branch size on the onsets of gas and liquid entrainment. 

Correlations were developed by Smoglie and Reimann [5] based on their experimental data to 

predict the onsets of entrainment and quality of discharge. For the side and bottom orientation 

cases the critical heights corresponding to the onset or beginning of gas entrainment (BGE) and 

beginning of liquid entrainment were given in terms of Froude number as follows; 

For side orientation case 

0.4 0.681 BGE

BGE

h Fr

d = (4) 

0.4 0.626 BLE

BLE

h

Fr

d = (5) 

For bottom orientation case 

0.4

0.4

1.816

0.626

BGE

BGE

BGE

h Fr for vortex flow d

Fr for vortex free flow

=

= −

 (6) 

 with , ,

5 5

4 4 , ( ) ( )

L BGE G BLE

BGE BLE

LL g GL g

m m

Fr Fr

π ρ gd ρ ρ π gd ρ ρ ρ = = − −

& &

where h is the vertical distance between the water surface and the centerline of the branch 

(positive in the upward direction ρ g is the density of the gas, ρ L is the density of liquid, g is 

the gravitational acceleration and m is the mass flow rate at the onset. &

 2-2
The quality of discharge was correlated for the region BLE BGE h hh ≤ ≤ = ,0( BLE h for the bottom 

break). For the side branch, it was given by 

0.5

1.0 1.0

1.0 0.5 1.0 b b

h h c c

h

b b

h h X r r

h h

⎛ ⎞ ⎛ ⎞ ⎜ ⎟ + + ⎜ ⎟ ⎝ ⎠ ⎝ ⎠

⎡ ⎤ ⎛ ⎞⎛ ⎞

=− + ⎢ ⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎝ ⎠⎝ ⎠ ⎣ ⎦

h ⎥ (7) 

with 1.15

1.0 L

G

r

ρ

ρ

=

+

where c=1.09, where h>0, and c=1.00, h h b BG = E | | h h b BLE = when h<0. 

For the bottom branch, the quality was given by 

( )

0.5

1.0

2.5 / 1.0 0.5 1.0 BGE BGE

h c h h h

BGE BGE

h h X r r

h h

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

⎡ ⎤ ⎛ ⎞⎛ ⎞

=− + ⎢ ⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎝ ⎠⎝ ⎠ ⎣ ⎦

⎥ (8) 

Schrock et al. [6] performed experiments using both air-water and steam-water as the working 

fluid. The experiments were performed at system pressure up to 1.07 Mpa in a horizontal pipe 

(10.2cm in diameter) with different branch sizes (d=4, 6, and 10mm) and different orientations 

for each branch. The branches were simulated by 123 mm in length. Viewing windows were 

placed at the branch section and in the pipe just upstream and downstream of the branch to 

allow visual observation of the flow phenomena. They concluded that the BGE (side and bottom 

orientations) was affected by surface tension and viscosity in addition to Froude number. The 

BGE data for the side orientation did not agree with the data of Smoglie and Reimann [5]. No 

explanation was given for the disagreement. Their data on discharge quality, together with 

data from other studies were correlated in terms of normalized interface level. The correlations 

for , and hBGE BLE h X of the side branches were given by 

0.476

2 0.5

2

0.4

1

40.6

0.624

BGE

BGE

BLE

BLE

h Fr Bo N

d gd

h

Fr

d

μ

σ

ρ

−

−

⎛ ⎞ = ⎜ ⎟ Δ ⎝

=

⎠ (9) 

and 

 

0.7

1.0

0.06 1.0 1.0 b

h

h

b b

h h X c

h h

⎛ ⎞ ⎜ ⎟ +

⎝ ⎠ ⎡ ⎤ ⎛ ⎞⎛ ⎞ = − ⎢ ⎜ ⎟⎜ ⎟ ⎢ ⎥ ⎣ ⎦ ⎝ ⎠⎝ ⎠

+ ⎥ (10) 

with g Bo d ρ

σ

Δ = and ( )0.25

0.75 0.5

L

L

g Nμμ ρ

σ ρ

Δ =

where Bo is the Bond number, σ is the surface tension, Δρ is the density difference 

between the phases, μ L is the liquid viscosity, (c=0.5, hb = hBGE when h>0, and 

 2-3
c=0, b BLE = hh when h<0). For bottom branches, and hBGE X were given by 

0.454

2 0.5

2

1

19.4

BGE

BGE

h Fr Bo N

d gd μ

σ

ρ

⎛ − ⎞ = ⎜ ⎟ Δ ⎝ ⎠ (11) 

and 

3.5 2

1.0 exp 3.1

BGE BGE

h h X

h h

⎡ ⎤ ⎛⎞ ⎛⎞ ⎡ ⎤ =− − ⎢ ⎥ ⎜⎟ ⎜⎟ ⎢ ⎢ ⎥ ⎝⎠ ⎝⎠ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

⎥ (12) 

Yonomoto and Tasaka [7] developed a simple analytical model to study two-phase-flow 

through small branches. Air-water experiments at a maximum pressure of 700kPa were also 

conducted. A horizontal, square duct (19cm×19cm) was used in the experiments instead of 

a round pipe. The branch was simulated by a sharp-edged junction (d=10 and 20 mm). The 

characterization of BGE and BLE was determined by visual observation. Their model 

defined a two-phase interface profile having a conical sharp near the branch. Therefore, the 

mass flow rate and quality of the two-phase discharge through the branch were expressed 

as a function of void fraction α , defined as a ratio of gas flow area to total flow area in this 

conical region. 

mm m TP G BGE = +− α α , (1.0 ) L BGE && & , (13) 

and 

TP

BGEG

m

m

X &

& α , = (14) 

The void fraction α for the side branch was given by 

( ) 1.0

BLE

h

a

h

a α α α

⎛ ⎞

=− + ⎜ ⎟ ⎝ ⎠

 for h < 0 (15) 

and 

BGE

h

a

h

a α α α

⎛ ⎞

=− + ⎜ ⎟ ⎝ ⎠

 for h > 0 (16) 

where 

,

,

1.0

1.0 G BLE L

L BGE G

a

m

m

α

ρ

ρ

= ⎛ ⎞

+ ⎜ ⎟

⎝ ⎠

&

&

0.4 0.682 BGE

BGE

h Fr

d = and 0.4 0.558 BLE

BLE

h

Fr

d = (17) 

For the bottom branch, α was given by 

0.9 0 0.6

1.15 0.15 0.6 1.0

b for b

b for b

α

α α

α α

α

= ≤

= − ≤≤

≤

, (18) 

 2-4
where 

0.5 2.5

2 ,

,

1.0 G BLE L

L BGE G BGE

m h b cc

m h α αα

ρ

ρ

⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ =− + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦

&

& , 

with 

2.5

,

,

0.5 1.0 G BLE L

L BGE G BGE

m h

c

m h α

ρ

ρ

⎛ ⎞⎛ ⎞ = − ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

&

& and 0.4 0.909 BGE

BGE

h Fr

d = . 

Good agreement was obtained between their model and their experimental data for discharge 

quality on the liquid-entrainment side (h < 0) and an empirical correction factor was incorporated 

in the model on the gas entrainment side (h > 0). A modified mathematical model was 

developed later by Yonomoto and Tasaka [8] which improved the agreement with the 

experimental data. 

Micaelli and Memponteil[9] performed experiments using steam-water mixtures. A wide range 

of parameters was covered (system pressure of 2 to 7 MPa, main pipe diameters of 80 and 135 

mm and branch diameters of 12 and 20 mm). The correlations for the BGE and BLE were based 

on their experimental data as well as those of Smoglie and Reimann [5] and Schroch et al. [6]. 

A semi-empirical correlation was developed for the branch quality based on simple theoretical 

approaches adjusted by their own experimental data as well as other experimental data in the 

literature. 

In their final correlation, the quality x for the side-branch case was given as a function of void 

fraction α at the branch inlet over the whole range BLE < < hhh BGE as follows: 

( ) 1.0 L

G

x

α

ρ α α

ρ

=

+ −

 (19) 

where 

2

* 1.0 0.5 1.0

b

h

x

h

⎛ ⎞

=− + ⎜

⎝ ⎠⎟ for h < 0

 and 

2

* 0.5 1.0

b

h

x

h

⎛ ⎞ = − ⎜

⎝ ⎠⎟ for h > 0

 with ( )

0.2 2

* 0.69 TP

b

mL G

m h

gρρ ρ

⎡ ⎤ = ⎢ ⎥ − ⎣ ⎦

&

and ρ m is the homogeneous density given by ( ) 1

1.0 m

G L

x x

ρ

ρ ρ

−

⎡ − ⎤ = − ⎢ ⎥ ⎣ ⎦

For the bottom branch, X was also corrected by the equation of X with α given by 

1.0

BGE

h

h

α = − (20) 

 2-5
and 

0.4 0.2 * 2

, 1.0

( )

L L BGE

BGE

d LL G

V m

h

V gρρ ρ

⎡ ⎤ ⎛ ⎞ ⎡ ⎤ = − ⎢ ⎥ ⎜ ⎟ ⎢ ⎢ ⎥ ⎝ ⎠ − ⎣ ⎦ ⎣ ⎦

& ⎥ (21) 

where and are the mean liquid velocities in the branch and in the main pipe(downstream

from the branch), respectively.

Vd * Vd

 2-6
3. THEORETICAL ANALYSIS 

3.1 Theoretical Analysis 

The phenomena identified in the previous section can have a strong influence on discharge flow 

through branches. For these phenomena, a few theoretical formulae were reported recently to 

predict two phenomena, the discharge flow rate and quality [10, 11]. The phenomena are based 

on the two-phase flow, vapor and liquid phase. The simplified theoretical approach neglects the 

effects of viscosity and surface tension, assumed potential flow throughout the field and treated 

the branch as a point sink. 

The configuration under consideration in the present analysis is shown in Figure 2. Stratified 

layers of immiscible fluids with density ρ and ρ + Δρ are contained in large reservoir whose 

wall is inclined at an angle θ from vertical. Discharge is induced from the lighter fluid through 

the branch with mass flowrate . The purpose of the analysis is to predict the critical height h

at which the heavier fluid starts flowing into the branch. 

m&

Figure 2 Schematic Drawing for Theoretical Approach 

The point B is a linking point between the wall and the heavier fluid pulled by surface tension, 

and s is the distance from the elevation of B to the elevation of the point of contact between the 

centerlines of inner edges in the header outlet and the branch line. The present analysis 

assumes that the dominant forces are the inertia and gravity forces and the effect of viscosity 

and surface tension are negligible. Both fluids are assumed to be incompressible and 

steady-state potential flow is assumed in the lighter fluid, while the heavier fluid is stagnant. The 

present analysis follows Craya’s [12] approach, applied successfully by Armstrong et al. [13], 

and Hassan et al. [14] where equilibrium of interface and the velocity field in the lighter fluid are 

determined first and then equality of the velocity and its gradient at linking point B (see Figure 2) 

are later imposed as conditions for the onset of liquid entrainment. 

y 

x 

s 

t h 

Heavier Fluid ρ + Δρ

d 

Light Fluid ρ

Angleθ

m 

Interface 

B 

 3-1
The equilibrium condition is assumed at interface between light and heavy fluid. Applying 

Bernoulli equation on a stream line coincident with the interface from the side of the lighter fluid, 

the following equation can be introduced: 

2

2

V P gt ρ+ += ρ C (22) 

where C is an arbitrary constant, V is fluid velocity, g is gravitational constant, ρ is density, 

P is pressure and t is distance between the liquid level and the liquid/wall contact point. 

Along the same streamline from the side of the heavier fluid, the Bernoulli equation gives: 

P g + +Δ = ( ) ρ ρ t C (23) 

Subtracting Eqn. (23) from Eq. (22), we get: 

2

2

V

gt ρ

ρ

Δ = (24) 

If we consider branch line point corresponding to the location on the interface where = − sht , 

Eqn. (24) gives: 

( 2

2

VB g h s) ρ

ρ

Δ = − (25) 

If we define n as a strength, the relation between n and m& are; 

2

n m

π ρ = & (26) 

In developing the velocity field in the lighter fluid, the presence of heavier stationary fluid is 

ignored. Therefore, the fluid field is treated as a semi-infinite medium extending over 0 ≤ x ≤ ∞ , 

−∞ ≤ ≤ ∞ y , and . The three dimensional flow is symmetric around the x-y plane 

which passes through the sink. Therefore, some analogy exists with the case of two-dimensional 

flow, thereby allowing the introduction of stream function and a velocity potential. Following 

Milne-Thomson [15], the potential function in the x-y plane, which is perpendicular to the 

reservoir wall, is given by : 

−∞ ≤ ≤ ∞ z

n

r

φ = − (27) 

where r is the radial distance from the sink. 

The radial velocity at any point in the x-y plane can be obtained as: Vr

r 2

n V

r r

∂φ =− =− ∂ (28) 

At front point of liquid surface, the velocity corresponds to VB r s = / cosθ is; 

( )

2 2

2

1

2 2 / cos

VB n

s θ

⎡ ⎤ = ⎢

⎢ ⎥ ⎣ ⎦

⎥ (29) 

Now, two expressions for given by 2 VB / 2 (25) and (29) are introduced. In order to get critical 

height, we combine two equations, (25) and (29) with Eqn.(26) as follows; 

( )

2

2

1 ( ) 2 / cosn gh s

s

ρ

ρ θ

⎡ ⎤ − = ⎢

Δ ⎢ ⎥ ⎣ ⎦

⎥ (30) 

 3-2
After differentiating the both sides of the above equation with respect to s and rearranging each 

term, the distance s in Figure 2 is obtained as follows. 

1

2 4 5 2 cos n

s

g

ρ θ

ρ

⎛ ⎞ = ⎜ ⎟ ⎝ Δ ⎠

 (31) 

The parameters of this equation are composed by physical parameters. Thus this equation 

introduce in Eqn. (30) and with some manipulation, we can get the critical height h : 

( )

0.4

m 2 ⎡ ⎤ & 1 h C cos

g

θ

ρ ρ = ⎢ ⎥

⎣ ⎦ Δ

 (32) 

.2 Experimental Assessments 

qn. (32) indicates that for single discharge with fixed flow rate and fluid properties, h varies with 

3

E

wall inclination θ according to cosθ . The exponent of cosθ was regarded as an unknown 

constant that should be determined by experiment and be compared with large number of 

experimental data. 

The experimental data were gathered from Smoglie and Reimann [5], Schrock et al. [6], Ibrahim 

G.Hassan et al. [14], J. L. Anderson et al.[16], and T.S.Andreychek, et al [17]. Over 500 

effective data points including vertical upward, vertical downward, horizontal side and angled 

branch with downward angle (θ =0o

, 45 o, 60 o) were produced. The detailed experimental 

parameters are shown in Table 1. 

Table 1 Experimental Data used to determining correlation constants 

Experimental Smoglie/ 

Reimann [5] 

Schrock Hassan 

e

Anderson Andreychek 

Conditions et al.[6] t al. [14] et al. [16] et al. [17] 

1. Tank/Branch 

) 

- d/D 

0o

, 0o, -90o 

.029~0.097 

o

, -90o 

.396, 

0.03 

o

, 45o, 90o 

.0228 

o

, 90o 

.034~0.052 

o

, 45o, 60o, 90o 

17,0.32 

 - Angle 

 - Size(mm

9

0.6, 0.8, 1.2 

0

0

0.375, 0

0.632 

0.021~

0

0.635 

0

0

0.81 

0

0

31.75, 57.15, 

69.85 

0.12,0.

2. T/H condition 

 - Pressure(MPa) .2~0.5 .109~0.913 .316, 0.517 .45, 4.4, 6.2 .1 

 - Temperature(o

C)

0

20 

0

20~Saturation

0

20 

3

Saturation 

0

20 

3. Simulant Air/Water Air/Water 

ter Air/Water Steam/Water Air/Water Steam/Wa

4. No.of Data/used 264 174 6 9 50 

The ratio of correlation and experimental results according to the diameter ratio were 

investigated. Due to the lack of experimental results for angled branch, the results from 

T.S.Andreychek, et al. [17] were used, but this experiment could be characterized by large 

diameter ratio between branch line and main horizontal pipe. In previous section, the point sink 

was assumed and the point sink means that the sink has no area. Because the experimental 

 3-3
data with large diameter ratio should be used, the non-dimensional compensation factor should 

be needed and considered in the model and defined as follows; 

/ R dD d = , (33) 

where d is 

Thr ined, based on the 

branch line diameter, and D is main line pipe diameter. 

ough these evaluations, the basic correlation form had been determ

previous analysis, as follows; 

( )( ) 2 3 cos C C hC R h = θ

( )( ) 2 3

1

0.4

1 cos

b d

C C

d

k

mk C R

g

θ

ρ ρ = Δ

⎡ ⎤

⎢ ⎥ ⎢ ⎥ ⎣ ⎦

& (34) 

where 3 are constants, h is introduced from Eqn. (34) and subscript k represent the

 co phase. 

in Eqn. (34), a statistical methodology was used. In this study, 

 was pe

, NLIN in SAS 6.12, was 

l upward, vertical downward, and 

Table 2 Constants of Critical Height Correlation by Nonlinear Fitting Methods 

Constants Upward Orientation Downward Orientation Angled Orientation 

1 2 CCC , ,

ntinuous 

To get the constants, 123 CCC , ,

all statistical analysis rformed using the commercial program, SAS 6.12 (Statistical 

Analysis System) for windows [18]. Above all, the correlation among variables was analyzed by 

procedure CORR in SAS 6.12, using various correlation coefficient. The results of procedure 

CORR showed that the critical height, h was strongly correlated with the cosine term, the area 

ratio, and main form of Eqn. (34) because Pearson correlation coefficients of those parameters 

are relatively larger than other parameters in CORR analysis results. 

Next step is the nonlinear regression analysis and the procedure

utilized. The procedure NLIN can analyze the nonlinear regression analysis using nonlinear 

least-square method. In this procedure, the all options in NLIN were studied for sensitivity 

analysis and the differences among their results were found to be negligible. The studied options 

were the Newton, modified Gauss-Newton, and DUD method. 

The experimental results were divided into three groups, vertica

other angles including side branch (0o). For each of the three groups, the above procedures 

were applied. The resulting coefficients C1 , C2 and C3 in Eqn. (34) are listed in Table 2. 

C1 0.5146 0.8286 0.3416 

C2 0. 0. -0.34 

C3 -0.24198 -0.07012 -0.115 

Figure 3 shows that the RELAP5 [4] correlation results could not predict the critical height at 

angled branch line but the new model could predict the experimental results with reasonable 

accuracy. The critical height value of zero calculated by RELAP5 indicates RELAP5 can not 

treat the angled branches. Also, the new model shows to give more accurate results than 

those of RELAP5 for all cases. For the case of vertical upward and downward cases, the results 

were shown in Figures 4 and 5. The Figures also show that new model can better predict 

compared with that of RELAP5. 

 3-4
0.00 0.02 0.04 0.06 0.08 0.10

0.00

0.02

0.04

0.06

0.08

0.10

0% -10%

10%

New Correlation 20%

RELAP5 Correlation

Calculated Critical Height (meter)

Measured Critical Height (meter)

-20%

Figure 3 Angled Branch Correlation Comparison 

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

N

New New Correlation

 RELAP5 Correlation

Calculated Critical Height (meter)

Measured Critical Height (meter)

0% -10%

10%

20%

-20%

Figure 4 Vertical Downward Branch Correlation Comparison 

 3-5
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Calculated Critical Height (meter)

Measured Critical Height (meter)

New Correlation

RELAP5 Correlation

0% -10%

10%

20%

-20%

Figure 5 Vertical Upward Branch Correlation Comparison 

3.3 Model Verification and Validation 

The developed models described in previous section, were applied to RELAP5/MOD3 [5]. In 

order to simulate the general angled branch, the liquid entrainment and vapor pull-through model 

of RELAP5 was modified in the stratified liquid level, angled branch elevation, and Critical Depth 

Correlation for angled branch configuration. Implementing the above new model into RELAP5, 

the subprogram, HZFLOW which calculate the fluid flow characteristics under horizontal 

stratification conditions was modified. For the related branch angle input processing, the input 

subroutines RBRANCH, RSNGLJ, and RVALVE were modified and the new model can be used 

in single junction, branch and valve components [19]. 

For validation of the modified model, two approaches were followed; the first one is a conceptual 

problem and the second is a limited SET (Separate Effect Test) problem. The objective of the 

conceptual problem is to investigate whether the errors were induced by the modifying 

procedure and whether the new model gives physically reasonable prediction of the off-take 

phenomena. The SET problem is selected to evaluate the performance of the new model in 

comparison with the experimental results. 

As a conceptual problem, a discharge from a reservoir was selected [19]. The reservoir has 

saturated 100 bar heavy water and 7 branches are connected to the reservoir at various angles 

(-90o

 ~ 90 o). This problem can be defined as the higher branch flow transition occurred from 

liquid to vapor earlier than that of lower branch, as the reservoir level decreased. Modeling of 

this problem is shown in Figure 6, and the results are also shown in Figure 7, 8 and 9. 

As shown in Figure 7, at about 200 seconds after the initiation of flow through seven branches, 

the reservoir is completely depressurized. Comparisons of liquid fractions and mass flow rate for 

each branch line are shown in Figure 8 and 9, respectively. The transition starts at upper 

branches and propagates to lower branches. In Figure 8, the differences among each vapor 

entrainment timings of branches become larger as the reservoir level decreases. Initially, the 

liquid leaks out through all 7 branches and the pressure including water head is large. As the 

 3-6
pressure decreases, the rate of level reduction became slower and the amount of time increased 

after upper branch was uncovered. The vapor pull-through occurs before the water level reaches 

the entrance of branch. For example, in the case of 0o branch, the vapor pull-through was 

observed at 0.34 void fractions before the void fraction reaches 0.5. These results show that the 

geometric modeling concept is reasonably accurate and consistent with the physical 

phenomena. 

Figure 6 Modeling for New Model Verification (90o

~-90o) 

0 50 100 150 200

0.0

2.0x106

4.0x106

6.0x106

8.0x106

1.0x107

1.2x107

Pressure (Pa)

Time (seconds)

 Upstream

Figure 7 Upstream Pressure Behavior for Verification 

 3-7
0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

Liquid Fraction

Time (seconds)

 Up

 90o

 60o

 30o

 0o

 -30o

 -60o

 -90o

Figure 8 Branch Line Liquid Fraction Results for Verification 

0 50 100 150 200

0

1

2

3

4

5

6

7

8

9

10

Mass Flowrate (kg/sec)

Time (seconds)

 90o

 60o

 30o

 0o

 -30o

 -60o

 -90o

Figure 9 Branch Line Mass Flowrate Results for Verification 

For the SET (Separate Effect Test) validation, Canadian experimental facility [14] was selected 

as the SET assessment. Hassan et al. [14] performed the experiment about off-take 

 3-8
phenomena, and this experiment is characterized by angled branch line. The experiment was 

performed in a horizontal pipe (58mm in diameter) with one branch size (d=0.635mm) and 

different orientations (0, 45, and 90 degrees) at system pressures of 316 kpa and 517 kpa using 

air-water mixture. This experimental facility was described in Appendix A. The test section of the 

facility had a semicircular shape of 50.8mm diameter and 50.8mm length. The 0, -45 and -90 

degrees data were selected among many data sets. RELAP5/MOD3 model is shown in Figure 

10. 

In Figures 11, 12, and 13, the reservoir level and branch mass flow rate are shown and the 

experimental results are predicted well by the RELAP5 with new model. As shown in Figure 11, 

the calculated results for -45o show that the new model can predict the experimental results with 

reasonable accuracy and void appeared in branch line before the level reached the branch 

elevation. Figure 12 and 13 show that the results of the original RELAP5 and RELAP5 with new 

model provide good predictions with almost same accuracy. Also, the above void appearance 

behavior in branch line before the level reached the branch elevation is also shown in the results 

of 0 and -90 degrees in Figure 12 and 13. Moreover, in the cases of 0 and -90 degrees, the 

results with new model show better and more stable agreement with experiments than those 

with the original RELAP5/MOD3. 

Figure 10 Modeling for New Model Validation 

 3-9
0.00 0.01 0.02 0.03 0.04 0.05

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Branch Line Mass Flowrate (Kg/sec)

Header Water Level (m)

 New Model

 -45o Branch Location

 Experiment

Figure 11 New Model Validation for -45o

 branch line 

0.00 0.02 0.04 0.06

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Branch Line Mass Flowrate (Kg/sec)

Header Water Level (m)

 New Model

 Original Model

 Experiment

Figure 12 New Model Validation for 0o

 branch line 

3-10
0.00 0.01 0.02 0.03 0.04

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Branch Line Mass Flowrate (Kg/sec)

Header Water Level (m)

 New Model

 Original Model

 Experiment

 Figure 13 New Model Validation for -90o

 branch line 

3-11
3-12
4. CONCLUSIONS 

The onset of liquid entrainment and vapor pull-through model, represented by the critical height 

were studied in the angled branch line configurations in a large pipe. The new model was 

introduced based on the point sink method, considering branch line connection angle, as 

theoretical approach, and the constants of new model were determined using the previous large 

number of experimental data. The new model was applied to vertical upward, downward and 

angled branches, and new model provides more accurate calculations compared with original 

RELAP5. 

The new model was applied to RELAP5/MOD3. For verification, conceptual problem calculations 

have been performed for a conceptual blowdown problem with different connection angles of 

branch in a horizontal pipe. The calculated void fraction and mass flow rate of different location 

of branches shows the validity of implemented model. As validation, the Canadian experiment 

was adopted and this experiment was performed in a horizontal pipe with a branch and different 

orientations using air-water mixture. The data for 0, -45 and -90 degrees were selected among 

many data sets. The modified RELAP5 with new model gave improved results for the horizontal 

side and vertical downward and angled branch line. 

 4-1
 4-2
5. REFERENCES

1. Zuber, N., “Problems in Modeling of Small Break LOCA," Nuclear Regulatory Commission Report, 

NUREG-0724, 1980. 

2. Korea Electric Power Company, "Wolsong Nuclear Power Plant Unit 2, 3, 4 Final Safety Analysis 

Report," May 1995. 

3. B.D.Chung et al., "Development of Preliminary PIRT (Phenomena Identification and Ranking 

Table) of Thermal-Hydraulic Phenomena for 330Mwt SMART Integral Reactor," KAERI/TR-912/97, 

September 1997. 

4. Thermal Hydraulics Group "RELAP5/MOD3 Code Manual Volume 4: Models and Correlations", 

Scientech, Inc., NUREG/CR-5535, 1998. 

5. C. Smoglie, “Two-Phase Flow Through Small Branches in a Horizontal Pipe with Stratified 

Flow,“ KfK 3861, Kernforschungszentrum Karlsruhe GmbH (KfK), Karlsruhe, FRG, December 

1984. 

6. V. E. Schrock, S. T. Revankar, R. Mannheiner, and C. H. Wang, “Small Break Critical Discharge 

The Role of Vapor and Liquid Entrainment in a Stratified Two-Phase Region Upstream of the 

Break,” NUREG/CR-4761, LBL-22024, Lawrence Berkeley Laboratory, December 1986. 

7. Yonomoto, T. and Tasaka, K., "New Theoretical Model for Two-Phase Flow Discharged from 

Stratified Two-Phase Flow Discharged from Stratified Two-Phase Region Through Small Break," J. 

Nuclear Science Technology, 25, 441-455, 1988 

8. Yonomoto, T. and Tasaka, K., "Liquid and Gas Entrainment to Small Break Hole from a Stratified 

Two-Phase Region," International Journal of Multiphase Flow, 17, 745-765, 1991 

9. T. Maciaszek and A. Menponteil, Experimental Study on Phase Separation in a Tee Junction for 

Steam-Water Stratified Inlet Flow, Paper C2, European Two-Phase Flow Working Group Meeting, 

Munich, FRG, June 10-13, 1986. 

10. Y.J.Cho, et al., "Modeling of Liquid Entrainment and Vapor Pull-Through in Header-Feeder Pipes 

of CANDU," Journal of Korean Nuclear Society, 36, No.6, April 2004 

11. Yong Jin Cho, Gyoo Dong Jeun, "A Study of the Liquid Entrainment and Vapor Pull-Through in an 

Angled Branch Line," Nuclear Technology, 58 No.3, 2007. 

 5-1
 5-2

12. Craya, A., "Theoretical Research in the Flow of Non-Homogeneous Fluids," La Houille Blanche, 

pp. 44-55, January-February 1949. 

13. Armstrong,K.F., et al., "Theoretical and Experimental Study of the Onset of Liquid Entrainment 

During Dual Discharge from Large Reservoirs," International Journal of Multiphase Flow, 18, 

217-227, 1992. 

14. Ibrahim G.Hassan, Hassan M. Soliman, Grant E. Sims and Janusz E. Kowalski, "The Onset of 

Liquid Entrainment during Discharge from Two Branches on an Inclined Wall," The Canadian 

Journal of Chemical Engineering, 77, June 1999. 

15. Milne-Thomson, L.M., "Theoretical Hydrodynamics," 5th Ed., MacMillan and Company Ltd., 

London, UK (1968) 

16. J. L. Anderson and R. L. Benedetti, Critical Flow Through Small Pipe Breaks, EPRI NP-4532, 

Idaho National Engineering Laboratory, May 1986. 

17. T.S.Andreychek, et al, "Loss of RHRS cooling while the RCS is partially filled," WCAP-11916, July 

1988. 

18. SAS User’s Guide, Version 6, Fourth Edition, Volume 1 and 2, Cary NC, USA, SAS Institute Inc., 

1989. 
Appendix A 

Description of Canadian Experimental Facility used in SET Validation 

A- 1
A- 2
Canadian experimental facility was adopted for SET validation: This facility is small 

facility which was designed for CANDU header-feeder system. A schematic diagram 

of the flow loop is shown in Figure A.1. An immersion-type circulating pump was used 

to supply distilled water to the test section at a rate adjusted by a by-pass line. The 

temperature of the water was held steady during the experiment by a cooling coil as 

shown in Figure A.1. The large reservoir was connected to an air supply equipped 

with a feed-back pressure controller which maintained a steady pressure Po in the test 

section throughout the experiment. 

The two-phase flows leaving the test section through the branches were directed to 

their respective separators where the air and water were split by centrifugal 

action. The flow rates of air and water leaving the measuring separators were each 

measured by a bank of four variable-area type flow meters with overlapping 

ranges. Each of these flow-measuring stations covered the range of 15cm3/min to 

0.0415m3/min on the water side and 198 cm3/min to 1.3m3/min at standard conditions 

on the air side. The temperature and pressure within the large reservoir, as well as 

other location within the loop, were recorded during the experiment. All flow meters, 

thermocouples and pressure gauges were calibrated before testing began. 

For two-phase reservoir, details of the large reservoir are shown in Figure A.2 with 

water entering through the bottom flange, air entering through the left flange and 

discharge through the right flange. The reservoir was manufactured from type 304 

stainless steel sections, except for a clear acrylic pipe section near the outlet flange for 

visual observation of the flow phenomena. The acrylic pipe was held firmly between 

two machined flanges by four tie-rods and sealed with an O-ring at each end. The air 

and water entering through the reservoir were dispersed into a number of streams to 

prevent any waves or ripples on the gas-liquid interface. The attainment of a smooth 

interface was essential in eliminating fluctuations in the differential pressure transducer 

signal used to measure the liquid level height. Details of the inlet air and water 

dispersers are shown in Figure A.3 and A.4, respectively. Each disperser was 

mounted onto the inner face of the corresponding flange. 

A schematics diagram of a test section used in group nos. 1 to 3 is shown in Figure 

A.5. The first part of the discharge branches were holes, 6.35mm in diameter and 

127mm long, machined in a brass block and bolted to the stainless-steel outlet 

flange. Thus, each branch had a straight length of 20 diameters before any bends or 

area changes were incorporated. Two brass blocks were machined to provide 

L/d=1.5, 2, 3 and 8. A surveying transit was used to ensure that the faces of the outlet 

A- 3
flange and the brass block were vertical and that the centerlines of the test branches 

fell on a straight (horizontal in group no.2 and vertical in group no.3) line. Only one 

branch was active in group no.1 experiments. 

 The test section used in group no.4 is shown in Figure A.6. A semicircular shape of 

diameter 50.8mm and length 50.8mm was machined in a brass block and three 

branches were drilled and connected to the semicircular surfaces at angles 0o, 45o 

and 90o from the horizontal as shown in the Figures. The branches started out with a 

diameter d=6.35mm, were maintained at this size for a length of at least 4 diameters 

were subsequently enlarged to a diameter 9.53mm, as shown in Figure A.6. The 

brass block was bolted to a stainless-steel blind flange and the semicircular surface 

and branches were exposed to a large, stratified, air-water region. 

In the early stages of the investigation, consideration was given to a circular (full 

header) test section with 5 branches. However, a careful analysis of the expected 

flow conditions revealed that the flowrates leaving the branches would have to be kept 

fairly small if stratified conditions were to be maintained in the header. Due to the 

interest in a wide range of branch flow rates, a semicircular (half header) test section 

that is opened to a large volume was adopted instead. Certain conditions would have 

to be satisfied if the results of the semicircular section are to be considered applicable 

to the circular geometry. 

A- 4
Figure A.1 Schematic diagram of experimental test facility 

Figure A.2 Cross-sectional view of two-phase reservior 

A- 5
Figure A.3 Details of air disperser 

Figure A.4 Details of water disperser 

A- 6
Figure A.5 Details of the test section for group no. 1-3 

Figure A.6 Details of the test section for group no. 4 

A- 7
A- 8
Appendix B 

Lists of Subprogram Changes 

B- 1
B- 2
Changes in ‘hzflow’ 

SUBROUTINE hzflow(ichoke) 

!define win32dvf 

!define erf 

!define fourbyt 

!define hconden 

!define impnon 

!define in32 

!define newnrc 

!define ploc 

!define sphaccm 

. 

. 

. 

INCLUDE 'voldat.h' 

! candu HDR i1 

 INCLUDE 'cons.h' 

! Local variables. 

 INTEGER i,ik,j,k,kk,kx,ky,l,ll,lx,ly,m,nmap 

 LOGICAL countc 

 REAL(8) aj,ajth,alf,alg,alphef,alpham,arfg,argf 

. 

. 

. 

PARAMETER (grvmp2=0.634d0,grvp5=3.13d0) 

 REAL(8) psinq,pcosq 

! candu HDR i1 

 REAL(8) voidgs,hangle 

! 

! Data statements. 

 DATA ighsed,ighseh,ighsex/0,0,0/ 

. 

. 

. 

! Upward-oriented junction -- liquid entrainment. 

! Calculate critical depth, limiting to a diameter. 

! CANDU.CHO.START 

! Replace critical height correlation 

! Delete 3 line, Insert 5 line 

! hbf=(wgg*wgg/(rhog(kk)*max(rhof(kk)-& 

! rhog(kk),1.d-7)))**0.2d0*(1.67d0* & 

! grvmp2) 

 hbf=(wgg*wgg/(rhog(kk)*max(rhof(kk)- & 

 rhog(kk),1.d-7)))**0.2d0*(0.5146d0* & 

 grvmp2)*(min(diamv(kk),diamv(ll))/ & 

 max(diamv(kk),diamv(ll))**(-0.24198d0)& 

 *(max(cos(theta),1.d-7))**0.d0 

! CANDU.CHO.END! candu HDRIF(hbf.gt.diamv(kk))then 

 hbf=diamv(kk) 

 ELSE 

 hbfdw=1.0d0 

 ENDIF 

 IF((diamv(kk) * 0.5d0-hcll) & 

 .ge.hbf.and.vdg.lt.1.0d0)then 

! No entrainment possible with old gas flow, see if using pure gas 

! 

. 

. 

. 

! 

! Side or central junction. 

. 

. 

. 

! CANDU.CHO.START 

! Replace critical height correlation 

! Delete 3 line, Insert 5 line 

! RELAP5 ORIGINAL 

! hbf=(wgg*wgg/(rhog(kk)*max(rhof(kk)-& 

! rhog(kk),1.d-7)))**0.2d0*(0.69d0* & 

! grvmp2) 

! MODIFIED BY B.D.CHUNG 

! hbf=(wgg*wgg/(rhog(kk)*max(rhof(kk)-& 

! rhog(kk),1.d-7)))**0.2d0*(0.69d0* & 

! grvmp2) 

B- 3
B- 4

 hbf=(wgg*wgg/(rhog(kk)*max(rhof(kk)- & 

 rhog(kk),1.d-7)))**0.2d0*(0.3416d0* & 

 grvmp2)*(min(diamv(kk),diamv(ll))/ & 

 max(diamv(kk),diamv(ll))**(-0.115d0) & 

 *(max(cos(theta),1.d-7))**(-0.34d0) 

! CANDU.CHO.END 

. 

. 

. 

. 

. 

. 

! Downward-oriented junction -- gas pullthrough 

! Calculate critical depth, limiting to a diameter 

! CANDU.CHO.START 

! Replace critical height correlation 

! Delete 3 line, Insert 5 line 

! hbf=(wff*wff/(rhof(kk)*max(rhof(kk)-& 

! rhog(kk),1.d-7)))**0.2d0*(1.5d0* & 

! grvmp2) 

 hbf=(wff*wff/(rhof(kk)*max(rhof(kk)- & 

 rhog(kk),1.d-7)))**0.2d0*(0.8286d0* & 

 grvmp2)*(min(diamv(kk),diamv(ll))/ & 

 max(diamv(kk),diamv(ll))**(-0.07012d0)& 

 *(max(cos(theta),1.d-7))**0.d0 

! CANDU.CHO.END 

. 

. 

. 

. 

. 

. 
Appendix C 

Input Deck for Model Verification 

C- 1
C- 2
= Horizontal Stratification Take Off Model 

* running type 

*----------------------- 

* option 14 : turn off constitutive relation 

*1 14 

100 new transnt 

101 run 

102 si si 

105 2. 4. 

110 nitrogen 

115 1.0 

* 

120 100010000 0.0 d2o channel 

* 

201 100. 1.0e-6 0.1 3 10 1000 10000 

*201 500. 1.0e-6 0.1 3 10 1000 100000 

*201 10. 1.0e-6 0.1 3 10 10000 10000 

*201 300. 1.0e-6 0.01 7 200 50000 50000 

*************************************************** 

* minor edit volumes 

*----------------------- 

*300 70.2 70.8 

301 p 100010000 

302 p 100020000 

311 voidg 100010000 

312 voidg 100020000 

313 voidg 100030000 

331 quale 100020000 

332 quals 100020000 

334 xej 101000000 

341 voidgj 101000000 

342 voidgj 102000000 

343 voidgj 103000000 

344 voidgj 104000000 

345 voidgj 105000000 

346 voidgj 106000000 

347 voidgj 107000000 

348 voidgj 108000000 

361 mflowj 101000000 

362 mflowj 102000000 

363 mflowj 103000000 

364 mflowj 104000000 

365 mflowj 105000000 

366 mflowj 106000000 

367 mflowj 107000000 

368 mflowj 108000000 

* 

501 time 0 ge null 0 0.0 l 

* 

*************************************************** 

* Heated Section Pipe 

* 

1000000 chan1 pipe 

*1000000 chan1 canchan 

C- 3
1000001 3 

1000101 1.0 3 

1000201 0.0 2 

1000301 1.0 3 

1000401 0.0 3 

1000501 0.0 3 

1000601 0.0 3 

1000701 0.0 3 

1000801 0.0 0.0 3 

1000901 0.939 0.939 2 

1001001 100 3 

1001101 100 2 

1001201 002 10.69e6 0.0001 0. 0. 0. 3 

1001300 1 

1001301 0.0 0.0 0.0 2 

* Dj 

1001401 0.00 0.0 1.0 1.0 2 

************************************************ 

1010000 jun882 valve 

1010101 100020003 200000000 0.0001 0.00 0.00 10100 

1010102 1.00 0.14 *0.0 

1010201 1 0.0 0.0 0.0 

1010300 trpvlv 

1010301 501 

* 

************************************************ 

1020000 jun882 valve 

1020101 100020003 200000000 0.0001 0.00 0.00 40100 

1020102 1.00 0.14 80.0 

1020201 1 0.0 0.0 0.0 

1020300 trpvlv 

1020301 501 

* 

************************************************ 

1030000 jun882 valve 

1030101 100020003 200000000 0.0001 0.00 0.00 40100 

1030102 1.00 0.14 60.0 

1030201 1 0.0 0.0 0.0 

1030300 trpvlv 

1030301 501 

* 

************************************************ 

1040000 jun882 sngljun 

1040101 100020003 200000000 0.0001 0.00 0.00 40100 

1040102 1.00 0.14 40.0 

1040201 1 0.0 0.0 0.0 

*1040300 trpvlv 

*1040301 501 

* 

********************************************** 

1050000 jun882 sngljun 

1050101 100020003 200000000 0.0001 0.00 0.00 40100 

1050102 1.00 0.14 30.0 

1050201 1 0.0 0.0 0.0 

C- 4
************************************************ 

1060000 jun882 valve 

1060101 100020003 200000000 0.0001 0.00 0.00 40100 

1060102 1.00 0.14 20.0 

1060201 1 0.0 0.0 0.0 

1060300 trpvlv 

1060301 501 

* 

************************************************ 

1070000 jun882 valve 

1070101 100020003 200000000 0.0001 0.00 0.00 40100 

1070102 1.00 0.14 10.0 

1070201 1 0.0 0.0 0.0 

1070300 trpvlv 

1070301 501 

* 

************************************************ 

1080000 jun882 sngljun 

1080101 100020003 200000000 0.0001 0.00 0.00 30100 

1080102 1.00 0.14 *0.0 

1080201 1 0.0 0.0 0.0 

*1080300 trpvlv 

*1080301 501 

* 

2000000 system snglvol 

* Area Length Volume ANGLE Height Rough 

2000101 0.0 20.000 1000.000 0.0 -90.0 -20.000 0.00000 

2000102 0.0 000000 

2000200 002 1.0000e5 1.00 

* 

* termination card 

. 

C- 5
C- 6
Appendix D 

Input Deck for Model Validation 

D- 1
D- 2
= Horizontal Stratification Take Off Model 

* angle=45 degree 

* level decrease 

* running type 

*----------------------- 

* option 14 : turn off constitutive relation 

*1 14 

100 new transnt 

101 run 

102 si si 

105 2. 4. 

110 nitrogen 

115 1.0 

* 

120 100010000 0.0 h2o channel 

* 

*201 10. 1.0e-6 0.1 3 10 1000 10000 

202 10. 1.0e-11 0.01 3 1 100000 1000000 

*************************************************** 

* minor edit volumes 

*----------------------- 

301 p 100010000 0.0e+7 5.0e+5 1 1 * channel in pressure 

311 voidg 100010000 0.0 1.5 2 1 

341 voidgj 101000000 0.0 1.5 2 2 

342 voidfj 101000000 0.0 1.5 2 3 

343 voidgj 031000000 0.0 1.5 2 4 

344 voidfj 031000000 0.0 1.5 2 5 

361 mflowj 101000000 0.0 0.5 4 1 

372 mflowj 031000000 0.0 0.5 4 2 

375 voidg 200010000 0.0 1.5 5 1 

380 cntrlvar 005 0.0 0.06 6 1 

* 

501 time 0 ge null 0 3.0 l 

502 time 0 ge null 0 0.0 l 

* 

0300000 system snglvol 

* Area Length Volume ANGLE Height Rough 

0300101 0.0 5.500 5.5 0.0 90.0 5.5 0.00000 

0300102 0.0 000000 

0300200 004 0.316e6 300.0 1.00 

*0300200 004 0.316e6 300.0 1.00 

* 

0310000 jun882 sngljun 

0310101 030000000 100000000 0.0001 0.00 1.e0 020000 

0310201 1 0.0 0.0 0.0 

** 

**************************************************** 

* Heated Section Pipe 

* 

1000000 system snglvol 

* Area Length Volume ANGLE Height Rough 

1000101 0.0020258 0.2 0.0 0.0 0.0 0.0 0.00000 

1000102 0.0 000000 

1000200 003 0.316e6 300.0 0.0 

D- 3
************************************************ 

1010000 jun882 valve 

1010101 100010000 200000000 0.00003165 0.00 0.00 40100 

1010102 1.00 0.14 -45.0 

1010201 1 0.0 0.0 0.0 

1010300 trpvlv 

1010301 501 

* 

************************************************ 

* 

2000000 system snglvol 

* Area Length Volume ANGLE Height Rough 

2000101 0.00003165 0.1 0.0 0.0 -45.0 -0.07071 0.00000 

2000102 0.0 000000 

2000200 004 0.316e6 300.0 0.00 

************************************************ 

** 

2500000 jun882 sngljun 

2500101 200010000 300000000 0.00003165 1.5 0.00 00000 

2500201 1 0.0 0.0 0.0 

* 

3000000 system snglvol 

* Area Length Volume ANGLE Height Rough 

3000101 0.0 20.000 100000.0 0.0 -90.0 -20.000 0.00000 

3000102 0.0 000000 

3000200 004 0.19e6 300.0 1.00 

* 

20500100 lvl_hdr sum 1.0 0.0 1 

20500101 0.0 1.0 voidf 100010000 

20500500 isgzelvl function 0.0508 0.0 1 

20500501 cntrlvar 001 501 

* 

20250100 normarea 

20250101 0. 0. 

20250102 0.000140812 0.00190265 

20250103 0.001121358 0.00759612 

20250104 0.003755859 0.01703708 

20250105 0.00880828 0.030153677 

20250106 0.016969119 0.046846087 

20250107 0.028834425 0.066987271 

20250108 0.044887692 0.090423941 

20250109 0.065485162 0.116977732 

20250110 0.090845005 0.146446552 

20250111 0.121040688 0.178606126 

20250112 0.155998745 0.2132117 

20250113 0.195501005 0.249999906 

20250114 0.239191228 0.288690762 

20250115 0.286585921 0.328989809 

20250116 0.337089033 0.370590346 

20250117 0.390010069 0.413175768 

20250118 0.444585061 0.456421975 

20250119 0.499999792 0.499999837 

D- 4
D- 5

20250120 0.555414526 0.5435777 

20250121 0.609989528 0.58682391 

20250122 0.662910578 0.629409338 

20250123 0.713413712 0.671009884 

20250124 0.76080843 0.711308942 

20250125 0.804498682 0.749999811 

20250126 0.844000976 0.786788032 

20250127 0.878959068 0.821393624 

20250128 0.909154787 0.853553217 

20250129 0.934514666 0.883022058 

20250130 0.955112171 0.909575871 

20250131 0.97116547 0.933012566 

20250132 0.983030807 0.953153775 

20250133 0.991191671 0.969846211 

20250134 0.996244113 0.982962836 

20250135 0.998878629 0.992403823 

20250136 0.999859185 0.998097321 

20250137 1. 1. 

* 

. * termination card