The Pennsylvania State University

The Graduate School

Department of Mechanical and Nuclear Engineering

CRITICAL HEAT FLUX MODEL IMPROVEMENT IN CTF FOR NATURAL

CIRCULATION TYPE REACTORS

A Thesis in

Nuclear Engineering

by

Caleb Jernigan

©2016 Caleb Jernigan

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2016

ii

The thesis of Caleb Jernigan was reviewed and approved* by the following:

Maria Avramova

Adjunct Professor of Nuclear Engineering

Thesis Advisor

Kostadin Ivanov

Adjunct Professor of Nuclear Engineering

Jordan Rader

Mentor from Holtec International

Special Signatory

Arthur Motta

Professor of Nuclear Engineering and Materials Science and Engineering

Chair of Nuclear Engineering

*Signatures are on file in the Graduate School

iii

ABSTRACT

The objective of this study was to enhance the capabilities of the subchannel

thermal-hydraulics analysis code CTF for modeling critical heat flux (CHF) conditions

within natural circulation type of nuclear reactors such as the Holtec small modular reactor

SMR-160. The SMR-160 is a pressurized water reactor (PWR) characterized by core

coolant flow driven by natural circulation at relatively low mass flow rates and high inlet

subcooling as in compared to a typical PWR. Identifying a CHF model appropriate for

these conditions is required for an accurate thermal-hydraulics performance analysis.

Several CHF models available in the open literature, including those already

implemented in CTF, were studied for their applicability to SMR-160. This includes the

CHF models by Westinghouse (W-3), Electric Power Research Institute (EPRI-1), Biasi,

Bowring, and Groeneveld. Since the models were developed within a certain validity range

of operating conditions (mass flow rate, equilibrium quality, pressure, hydraulic diameter,

and others), these ranges were used as a measure of acceptability when compared to the

standard or expected SMR-160 operating conditions. It was found that the existing CHF

models in CTF, excluding the models by Bowring and Groeneveld, were not fully

applicable to the unique SMR-160 rated conditions. Therefore, the models by Bowring and

Groeneveld were selected for SMR-160 safety analysis.

The Bowring model consists of a set of empirical equations. The Groeneveld model

is in the form of a 15×21×23 multi-dimensional table of CHF values discretized in pressure,

mass flux and equilibrium quality, along with several “K” factors adjusting for additional

physical affects. These two models were implemented in CTF for CHF and DNB

calculations of SMR-160.

iv

Table of Contents

List of Abbreviations .............................................................................................................. vi

List of Figures .......................................................................................................................... vii

List of Tables .......................................................................................................................... viii

Acknowledgments ................................................................................................................... ix

Chapter 1: Introduction ..................................................................................................... 1

Problem Overview .............................................................................................................................. 1

Holtec SMR-160 Overview ............................................................................................................... 4

CTF Subchannel Analysis Code ...................................................................................................... 5

Research Objectives ........................................................................................................................... 6

Chapter 2: Test Case Descriptions .................................................................................. 7

SMR-160 Test Case ............................................................................................................................. 7

CTF Test Model .................................................................................................................................... 9

Chapter 3: Critical Heat Flux Models .......................................................................... 12

Westinghouse-3 Critical Heat Flux Model ............................................................................... 12

Biasi Critical Heat Flux Model ..................................................................................................... 14

The EPRI-1 Critical Heat Flux Model ......................................................................................... 16

EPRI-1 Cold Wall Effects .......................................................................................................................... 16

EPRI-1 Spacer Grid Effects ...................................................................................................................... 17

EPRI-1 Non-uniform Axial Heat Flux Effects ................................................................................... 17

Combined EPRI-1 Model .......................................................................................................................... 18

The Bowring Critical Heat Flux Model ..................................................................................... 20

The Groeneveld Critical Heat Flux Model ............................................................................... 22

v

Chapter 4: Critical Heat Flux Model Scoping ........................................................... 24

SMR-160 Test Case Results .......................................................................................................... 24

Parameter Comparison of Critical Heat Flux Models ......................................................... 27

CHF Model Scoping Results .......................................................................................................... 28

Chapter 5: Critical Heat Flux Model Implementation in CTF ............................. 29

Overview of the CTF Treatment of the Critical Heat Flux .................................................. 29

Fluidcell vs. Surface Type Calculations .............................................................................................. 30

Overview of CTF Source Modifications .................................................................................... 32

CTF Encoded Bowring Function ................................................................................................. 34

CTF Encoded Groeneveld Function ........................................................................................... 35

Look-up Table CHF Interpolation Scheme ........................................................................................ 35

Groeneveld Implementation ................................................................................................................... 36

Chapter 6: CTF Test Model Results.............................................................................. 46

Bowring CHF Model CTF Test Results ...................................................................................... 46

Groeneveld CHF Model CTF Test Results ................................................................................ 49

CHF Model Comparison ................................................................................................................. 52

Chapter 7: Conclusion and Future Work ................................................................... 53

Computer Files ........................................................................................................................ 55

References ................................................................................................................................ 57

vi

List of Abbreviations

ALHR – average linear heat rate

CHF – critical heat flux

DNB – departure from nucleate boiling

DNBR – departure from nucleate boiling ratio

EPRI – Electric Power Research Institute

FCT – Fuel centerline temperature

LWR – Light water reactor

LB-LOCA – Large breakloss of coolant accident

MDNBR – minimum departure from nucleate boiling ratio

OSB – onset of saturated boiling

PWR – pressurized water reactor

PZ – Pressurizer

RCS – reactor coolant system

RPV – reactor pressure vessel

SMR – small modular reactor

W3 – Westinghouse-3

vii

List of Figures

Figure 1: Fuel rod heat circuit analogy ............................................................................... 1

Figure 2: Boiling curve for pool boiling conditions at atmospheric pressure ..................... 3

Figure 3: SMR-160 test model top and bottom peaked axial power profiles ..................... 9

Figure 4: CTF test case numbered channels and rods ....................................................... 10

Figure 5: Combined CHF results for top shifted axial power ........................................... 24

Figure 6: Combined DNBR results for top shifted axial power ....................................... 25

Figure 7: Combined CHF results for bottom shifted axial power .................................... 25

Figure 8: Combined CHF results for bottom shifted axial power .................................... 26

Figure 9: Execution flow of CHF function call ................................................................ 29

Figure 10: Fluidcell and surface type illustration ............................................................. 30

Figure 11: Groeneveld CHF handling in CTF .................................................................. 31

Figure 12: Bowring model - equilibrium quality results for selected channels ................ 46

Figure 13: Bowring model - void fraction results for selected channels .......................... 47

Figure 14: Bowring model - CHF results ........................................................................ 47

Figure 15: Bowring model - MDNBR results................................................................... 48

Figure 16: Groeneveld model - equilibrium quality results for selected channels ........... 49

Figure 17: Groeneveld model - void fraction results for selected channels ..................... 50

Figure 18: Groeneveld model – CHF results ................................................................... 50

Figure 19: Groeneveld model – MDNBR results ............................................................. 51

viii

List of Tables

Table 1: SMR-160 steady state operating conditions ......................................................... 7

Table 2: SMR-160 internal channel parameters ................................................................. 7

Table 3: CTF test model operating parameters ................................................................. 10

Table 4: CTF test model spacer grid data ......................................................................... 10

Table 5: CTF test model normalized radial pin powers .................................................... 11

Table 6: W3 model variable definitions............................................................................ 13

Table 7: W3 range of parameters ...................................................................................... 13

Table 8: Biasi model variable definitions ......................................................................... 14

Table 9: Biasi range of parameters ................................................................................... 15

Table 10: EPRI-1 model constants ................................................................................... 18

Table 11: EPRI-1 model variable definitions ................................................................... 18

Table 12: Combined EPRI-1 range of parameters ............................................................ 19

Table 13: Bowring model variable description ................................................................. 21

Table 14: Bowring range of parameters............................................................................ 21

Table 15: Groeneveld model variable description ............................................................ 22

Table 16: Groeneveld range of parameters ....................................................................... 23

Table 17: CHF model limiting parameter comparison to SMR-160 conditions ............... 27

Table 18: Results comparison based on CHF model ........................................................ 52

Table 19: Computer files .................................................................................................. 55

ix

Acknowledgments

Firstly, I would like to thank my advisor Dr. Maria Avramova for her support and

advice throughout my graduate career. I would like to thank Dr. Kostadin Ivanov who has

provided guidance on multiple occasions. I would also like to thank Holtec International

for providing this research and funding my graduate studies through my mentors, Jordan

Rader and Tom Carter, who were pivotal in completing this project. Finally, I would like

to thank my wife and family for their continued patience and support.

1

Chapter 1: Introduction

Problem Overview

For a typical PWR type reactor, it is desirable for the working fluid to remain in

single phase throughout operation. This ensures consistent and reliable heat transfer from

the fuel rods and moderation of neutrons. Consider the following heat circuit analogy of a

fuel rod (Ref. 1, pg. 427):

Figure 1: Fuel rod heat circuit analogy

Demonstrated here is the fuel’s thermal dependence on heat transfer between the

rod and working fluid. As the fuel pellet generates heat by fission, adequate heat transfer

out of the fuel element is necessary to prevent excess heat storage in the fuel, which could

potentially cause fuel failure. Rod to fluid heat transfer is heavily dependent on the flow

regime of the working fluid. Heat transfer at the rod surface is enhanced in the early stages

of two-phase flow due to increased mixing from bubble detachment and vapor production.

2

Conversely, it is impeded by extended contact with vapor, which provides weaker heat

transfer capabilities.

Subcooled boiling is the first two-phase flow regime encountered in heated

conditions. It occurs when the fuel rod surface exceeds the local saturation temperature of

the fluid. The single-phase liquid in immediate contact with the heated surface is at the

same temperature and small bubbles will begin to develop that are only stable at the heated

surface. If detachment of the bubbles occurs in this flow regime, they will collapse once

encountering the subcooled bulk fluid conditions. As the rod surface temperature continues

to increase and exceed the fluid saturation temperature (this amount of excess is termed the

“wall superheat”), the production and size of these bubbles increases. With sufficient rod

superheat the bubbles will detach and inhabit the bulk fluid volume, a state termed nucleate

boiling. Nucleate boiling enhances heat transfer by inducing mixing at the rod surface. Rod

superheat will remain stable as long as the rod surface has sufficient contact with the liquid

fluid. As the fluid continues to absorb heat, vapor production increases and bubbles

increase in size or agglomerate into large voids. This flow regime will approach slug flow,

which is defined by the presence of a large void (or “slug”) in the center of the subchannel

with smaller bubbles entrained. A fluid film may still cover the rod surface, but with

sustained heat addition, the vapor development overcomes the presence of the liquid fluid,

covering the rod in a vapor blanket. Once covered in a vapor blanket, the rod superheat as

well as the fuel centerline temperature (FCT) will increase to critical levels, commonly

resulting in the melting of fuel.

3

These post-nucleate boiling flow regimes occur when liquid fluid is no longer in

contact with the rod surface. Monitoring the fluid conditions to ensure they never exceed

nucleate boiling conditions is essential. This is done by developing an expression for the

critical heat flux (CHF), which is the heat flux corresponding to a departure from nucleate

boiling (DNB) state. The following boiling curve illustrates the progression of the CHF in

pool boiling conditions (Ref. 1, pg. 707):

Figure 2: Boiling curve for pool boiling conditions at atmospheric pressure

The critical point C represents the CHF, which separates nucleate boiling behavior from

more extreme two-phase flow and heat transfer regimes. Post-CHF, the outer fuel rod heat

flux will drop as indicated here due to the loss in heat transfer, and excess energy will be

absorbed in the fuel.

The CHF is a necessary parameter to establish thermal margins or operating limits

in nuclear reactor analysis. It is used frequently to determine the departure from nucleate

boiling ratio (DNBR), defined as the ratio of the CHF to the local heat flux. The CHF

phenomena is extremely complicated, and cannot be truly determined from first principals.

4

It is primarily determined via empirical models, which are developed from experimental

data. Models used to determine the CHF are readily available for typical pressurized water

reactors (PWRs). One exception to this are reactors which are driven by natural circulation,

as they typically exhibit lower mass flow rates and have more widely varying fluid

conditions between the inlet and outlet due to the large temperature gradients required to

induce a sufficient thermal driving head.

Holtec SMR-160 Overview

The Holtec SMR-160 is a small modular reactor (SMR) which incorporates the

design aspects of modern light water reactors (LWRs). One unique feature of the reactor is

that mass flow through the core during normal operation is driven entirely by natural

circulation. A large temperature gradient is required in order to induce sufficient driving

head for the flow. In order to achieve this, the active length of the core is longer than typical

for PWRs, and the inlet conditions are more highly subcooled.

The SMR-160 system boasts passive safety capabilities in that mass flow is driven

by gravity, making it immune to loss of flow (LOF) accidents. The reactor coolant system

(RCS) design employs an integrated pressurizer and steam generator (PZ and SG,

respectively), which is connected to the reactor pressure vessel (RPV) through a single

interconnecting nozzle. The single connection between the RPV and PZ/SG makes the

system immune to large break loss of coolant accidents (LB-LOCA).

5

CTF Subchannel Analysis Code

The subchannel analysis code under consideration for this study is CTF, a rebranded

and improved version of COBRA-TF (COolant Boiling in Rod Arrays – Two Fluid/Three

Field). CTF has treatment for three separate fluid fields: liquid film, liquid droplets and

vapor (Ref. 2). A total of eight conservation equations in mass, momentum and energy are

used to capture the thermal-hydraulic contributions of each fluid field. Assuming thermal

equilibrium between the liquid film and droplets fields removes consideration for a third

energy conservation equation. The code was validated thoroughly, as described in Ref. 3.

Most notable, validation was performed there against two NUPEC benchmarks: BWR Full-

size Fine-mesh Bundle Tests (BFBT) and the PWR Subchannel and Bundle Tests (PSBT).

Previous to this study, the code used two very common PWR type CHF models: the

Westinghouse-3 (W3) and Biasi models. These two models are likely not applicable for

the SMR-160 core, which is an atypical PWR characterized by natural circulation with the

same features mentioned previously. As CTF is used to model the thermal-hydraulic

behavior of the SMR-160 core, it should be modified for CHF models that are appropriate

for the core’s thermal-hydraulic conditions.

6

Research Objectives

The main objective of this study is to enhance the CTF capability of performing

SMR-160 design and safety analyses by implementing suitable CHF correlations. A

scoping study is required in order to determine which, of several candidate CHF models,

are most appropriate considering the SMR-160 unique operating conditions. This will also

require a description of the SMR-160 expected range of operating conditions and

comparison to ranges of validity for the CHF models under consideration.

A hand calculation is provided to present results for the CHF models using SMR-

160 operating conditions applied to single heated channel theory. The intent is to develop

SMR-160 relevant fluid conditions to demonstrate results for the CHF models under

investigation. This should aid in scoping out the most suitable CHF models for

implementation in CTF.

Once the correct model(s) is (are) selected, the numerical implementation of the

CHF models in CTF will be described. A CTF model for testing is also provided here to

present results from the encoded CHF models for comparison.

7

Chapter 2: Test Case Descriptions

SMR-160 Test Case

The Holtec SMR-160 test case is developed by modeling a single heated channel

with a hand calculation. Steady-state operating conditions characteristic of the SMR-160

are required for the test case, and are as follows (Ref. 4):

Table 1: SMR-160 steady state operating conditions

Parameter SMR-160

Average linear heat rate 11.388 kW/m

Pressure 2283 psi 15.74 MPa

Core Mass Flux 0.701 Mlb/ft2hr 950.28 kg/m2s

Core Inlet Temperature 384.5 oF 195.83 oC

Core Outlet Temperature 600 oF 315.56 oC

The average linear heat rate (ALHR) and core mass flux are calculated using parameters

from Ref. 4 as follows:

ALHR =Core Power

Number of Assemblies × Number of Pins × Active Length

Core Mass Flux =Assembly Average Mass Flow Rate

∑ Subchannel Flow Areas

The methods used to determine the thermal-hydraulic conditions of the model are described

hereafter, using these SMR-160 operating conditions and channel parameters given in

Table 2 (Ref. 4):

Table 2: SMR-160 internal channel parameters

Parameter Value

Heated length [m] 4.267

Fuel pin diameter [m] 0.0102

Subchannel hydraulic diameter [m] 0.0081

Subchannel heated diameter [m] 0.0109

8

This simplified SMR-160 single channel test case is used primarily to determine the

parameters necessary for calculating the CHF. The results from this test case are presented

later in Chapter 4: Critical Heat Flux Model Scoping as a measure of acceptability for the

CHF models. The local enthalpy is determined based on local linear heat rate:

ℎ(𝑧) = ℎ𝑖𝑛 +1

�̇�∫ 𝑞′(𝑧′)𝑑𝑧′𝑧

0,

Where local linear heat rate is defined by the ALHR and some axial peaking distribution,

𝑞′(𝑧) = 𝐴𝐿𝐻𝑅 × 𝐹𝑧(𝑧)

Therefore, the local equilibrium quality is calculated as

𝜒𝑒(𝑧) =ℎ(𝑧)−ℎ𝑓

ℎ𝑓𝑔.

The fuel pin is treated as a heater rod, and therefore inner fuel dimensions or

properties are not necessary. For simplicity, pressure is considered as constant along the

axial length (no pressure drop) and the water/steam properties are determined at the system

pressure only.

The axial power profile is arbitrarily set to top- and bottom-peaked distributions.

This non-uniformity will exploit the differences of the CHF models for varying power. The

two axial power profiles are displayed in Figure 3. Results are also displayed for DNBR,

which is calculated as:

𝐷𝑁𝐵𝑅(𝑧) =𝑞𝑐′′(𝑧)

𝑞′′(𝑧),

Where the subscript “c” indicates the critical heat flux.

9

Figure 3: SMR-160 test model top and bottom peaked axial power profiles

CTF Test Model

This section describes the CTF model used to develop the CHF results once the

models are encoded into CTF. The operating parameters are arbitrarily established to

ensure that saturated boiling (𝜒𝑒 > 0) occurs in the model. The intent is to model some

unique assembly features to check the robustness of the developed CHF functions. For

example, a central guide thimble is included to check that the CHF functions appropriately

identify the guide tube apart from a heated or nuclear fuel rod. The CTF model can then be

described as a simple 3x3-pin array with a central guide thimble. The operating parameters

and dimensions are given in Table 3 and Table 4.

The test model can be represented as shown in Figure 4, with numbered

subchannels and rods or guide tube.

The radial power data is developed to be corner-peaked (Table 5).

0 2 4 6 8 10 12 140

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Top and Bottom Shifted Axial Peaking Distributions for the SMR-160

Axial Location [ ft ]

Pe

ak-t

o-A

ve

rag

e R

atio

[ -

]

Top Shifted Distribution

Bottom Shifted Distribution

Peak Value = 1.67

10

Table 3: CTF test model operating parameters

Parameter Value

Mass flow rate [kg/s] 2.677

Average linear heat rate [kW/m] 27.0

Inlet temperature [C] 292.78

Outlet temperature [C] 326.94

Pressure [bar] 155.13

Fuel pellet diameter [mm] 8.192

Cladding inner diameter [mm] 9.500

Cladding thickness [mm] 0.570

Pin pitch [mm] 12.60

Inner diameter of guide tube [mm] 11.22

Outer diameter of guide tube [mm] 12.04

Active length [mm] 3657.6

Table 4: CTF test model spacer grid data

Spacer grid # Initial height [mm] Final height [mm] Minor loss coefficient

1 0 38.66 0.9070

2 613.44 651.54 0.9065

3 1135.44 1173.54 0.9065

4 1657.44 1695.54 0.9065

5 2179.44 2217.54 0.9065

6 2701.44 2739.54 0.9065

7 3223.44 3261.54 0.9065

Figure 4: CTF test case numbered channels and rods

11

Table 5: CTF test model normalized radial pin powers

Pin number Normalized radial power

1 1.125

2 1.500

3 1.875

4 0.750

5 0.000

6 1.500

7 0.375

8 0.750

9 1.125

12

Chapter 3: Critical Heat Flux Models

Westinghouse-3 Critical Heat Flux Model

The W3 CHF model, one of the two exiting CHF models in CTF, is commonly used

for PWRs safety margin evaluations. Developed by L. S. Tong [5], the model provides an

empirical method to determine the CHF for a non-uniformly heated subchannel. The

equation for CHF from uniform heating is as follows (see also Table 6):

𝑞𝑈′′ = 𝐾1(𝑃, 𝜒𝑒) × 𝐾2(𝜒𝑒 , 𝐺) × 𝐾3(𝜒𝑒 , 𝐷𝑒) × 𝐾4(ℎ𝑓 , ℎ𝑖𝑛),

Where the individual functions are given as follows:

𝐾1 = (2.022 − 0.06238𝑃) + (0.1722 − 0.01427𝑃) exp[(18.177 − 0.5987𝑃)𝜒𝑒]

𝐾2 = [(0.1484 − 1.596𝜒𝑒 + 0.1729𝜒𝑒 |𝜒𝑒|)2.326𝐺 + 3271]

𝐾3 = [1.157 − 0.869𝜒𝑒][0.2664 + 0.8357exp(−124.1𝐷𝑒)]

𝐾4 = [0.8258 + 0.0003413(ℎ𝑓 − ℎ𝑖𝑛)]

The corrective factor, which scales the uniform CHF to a CHF with non-uniform heat flux

considerations, is originally expressed as

𝐹 =𝑞𝑈′′

𝑞𝑁𝑈′′ ;

𝐹 =𝐶

𝑞′′(𝑙𝐷𝑁𝐵)[1 − exp(−𝐶𝑙𝐷𝑁𝐵)]∫ 𝑞′′(𝑧) exp[−𝐶(𝑙𝐷𝑁𝐵 − 𝑧)] 𝑑𝑧

𝑙𝐷𝑁𝐵

𝑙𝑂𝑁𝐵

With an empirically determined coefficient C given as:

𝐶(𝑙𝐷𝑁𝐵) = 185.6[1 − 𝜒𝑒(𝑙𝐷𝑁𝐵)]

4.31

𝐺0.478

The location of the onset of nucleate boiling, 𝑙𝑂𝑁𝐵, is treated as the inlet location of the

core. This causes the lower limit of integration to become zero. This approximation is

13

negligible for PWRs, where nucleate boiling occurs in close proximity to the core inlet. It

also inserts conservatism by making the corrective factor, F, larger due to integrating over

more length. For simplicity, 𝑙𝐷𝑁𝐵 also is treated as the distance from the core inlet, z.

Table 6: W3 model variable definitions

Variable Description Units

𝑞𝑈′′ CHF from uniform heat flux kW/m2

𝑞𝑁𝑈′′ CHF from non-uniform heat flux kW/m2

𝑙𝐷𝑁𝐵 Location of departure from nucleate

boiling m

𝑙𝑂𝑁𝐵 Location of the onset of nucleate boiling m

𝑃 Pressure MPa

𝜒𝑒 Local equilibrium quality -

𝐷𝑒 Equivalent hydraulic diameter m

𝐺 Mass flux kg/m2s

ℎ𝑖𝑛 Inlet enthalpy kJ/kg

ℎ𝑓 Saturated liquid enthalpy kJ.kg

The W3 model was developed for, and is only valid in the range of operating conditions

and geometry characteristics given in Table 7:

Table 7: W3 range of parameters

Parameter W3 Range

Pressure [MPa] 5.5 – 16.0

Mass Flux [𝑘𝑔/𝑚2𝑠] 1,356 – 6,800

Equivalent Heated Diameter [m] 0.015 – 0.018

Equilibrium Quality [ - ] -0.15 – 0.15

Length of Assembly [m] 0.254 – 3.70

Heated to Wetted Perimeter Ratio

[ - ]

0.88 – 1.00

14

Biasi Critical Heat Flux Model

The Biasi model [6] was an improvement on several prior existing models for

circular ducts. The intent of the improvement was to extend the validity range of the

parameters (pressure, mass flux, etc.), to improve accuracy and to simplify the governing

equation. The model utilizes a set of two empirical CHF equations: for low quality regions

and for high quality regions. This model uses the maximum of the low quality and high

quality CHF results as its local CHF value. The low quality and high quality forms of the

empirical CHF equations are, respectively, as follows (see also Table 8):

𝑞𝑐,0′′ =

1.883 × 104

𝐷𝑒𝛼𝐺

16

[𝑦(𝑃)

𝐺0.2− 𝜒𝑒(𝑧)]

𝑞𝑐,1′′ =

3.78 × 104 ℎ(𝑃)

𝐷𝑒𝛼𝐺0.6

[1 − 𝜒𝑒(𝑧)]

Where the pressure and hydraulic diameter dependent constants are given as:

𝑦(𝑃) = 0.7249 + 0.099𝑃 exp(−0.032𝑃)

ℎ(𝑃) = −1.159 + 0.149𝑃 exp(−0.019𝑃) +8.99𝑃

10 + 𝑃2

𝛼 = {0.4 𝑓𝑜𝑟 𝐷𝑒 ≥ 1 𝑐𝑚0.6 𝑓𝑜𝑟 𝐷𝑒 < 1 𝑐𝑚

Table 8: Biasi model variable definitions

Variable Description Units

𝑞𝑐,0′′ Critical heat flux of low quality region kW/m2

𝑞𝑐,1′′ Critical heat flux of high quality region kW/m2

𝐷𝑒 Hydraulic diameter cm

𝐺 Mass flux g/cm2s

𝑃 pressure atm

𝜒𝑒 Local equilibrium quality -

15

The range of conditions, at which the Biasi model was developed, limits its applicability -

using the model for a subchannel with operating conditions outside this validity envelope

would introduce error. The validity envelope for the Biasi model is given Table 8:

Table 9: Biasi range of parameters

Parameter Biasi Range

Pressure [MPa] 0.27 to 14.00

Mass Flux* [𝑘𝑔/𝑚2𝑠] 100 to 6,000

Inlet Equilibrium Quality [ - ] < 0

Outlet Quality [ - ] [𝜌𝑔 (𝜌𝑔 + 𝜌𝑙)⁄ ] to 1

Length of Assembly [m] 0.20 to 6.00

Hydraulic Diameter [m] 0.003 to 0.0375

16

The EPRI-1 Critical Heat Flux Model

The EPRI-1 CHF model is first considered as a candidate for implementation in

CTF. Developed by Columbia University’s Heat Transfer Research Facility for the Electric

Power Research Institute [7], the EPRI-1 CHF model was intended to accurately calculate

CHF within a wide range of operating conditions. This model shows consistent behavior

in both PWR and BWR operating conditions, making it potentially suitable for the SMR-

160.

The EPRI CHF model is a simple empirical formula that has four general CHF

considerations:

1. Base case

2. Cold wall effects

3. Spacer grid effects

4. Non-uniform axial heat flux effects

EPRI-1 Cold Wall Effects

The model for cold wall effects takes into account CHF that could occur in

subchannels which are in contact with non-heated surfaces (corner, side or water rod

subchannels) and, therefore, requiring more detailed mass flow treatment. Since BWR-like

assemblies generally experience uniform, corner or center peaked radial power

distributions, cold wall effects are considered only for the corner subchannel. The model

is as follows:

𝑞𝑐′′(𝑧) =

𝐴𝐹𝑎−χin

𝐶𝐹𝑐+[𝜒(𝑧)−𝜒𝑖𝑛𝑞′′(𝑧)

].

17

With constants for the Cold Wall effects in terms of the mass flux:

𝐹𝑎 = 𝐺0.1

𝐹𝑐 = 1.183𝐺0.1

EPRI-1 Spacer Grid Effects

The original model showed errors when spacer-grids were present. To fix this, the

model was modified with a spacer grid correction factor given as

𝑞𝑐′′(𝑧) =

𝐴−χin

𝐶𝐹𝑔+[𝜒(𝑧)−𝜒𝑖𝑛𝑞′′(𝑧)

].

The constant for the spacer grid effects in terms of a grid loss coefficient as

𝐹𝑔 = 1.3 − 0.3𝐶𝑔.

EPRI-1 Non-uniform Axial Heat Flux Effects

Enforced by R. W. Bowring’s studies [8], the model for non-uniform axial heat flux

effects scales the non-uniformity with the ratio of averaged heat flux to local heat flux. The

model is as follows:

𝑞𝑐′′(𝑧) =

𝐴−χin

𝐶𝐶𝑛𝑢+[𝜒(𝑧)−𝜒𝑖𝑛𝑞′′(𝑧)

].

The correction factor for a non-uniform heat flux is

𝐶𝑛𝑢 = 1 +(𝑌−1)

(1+𝐺);

𝑌 =1

𝐿∫

𝑞′′(𝑧)

𝑞′′(𝐿)𝑑𝑧

𝐿

0.

18

Combined EPRI-1 Model

The cold wall effects should only be considered for a subchannel in contact with a

non-heated surface such as the corner channel. Therefore, for these analyses the cold wall

effects are neglected, because an internal subchannel is being considered. The spacer grid

effects are also neglected for this study for the sake of simplicity.

The combined expression for the EPRI-1 CHF model is then as follows:

𝑞𝑐′′(𝑧) =

𝐴−χin

𝐶𝐶𝑛𝑢+[𝜒𝑒(𝑧)−𝜒𝑖𝑛𝑞′′(𝑧)

].

The empirical constants for the base case in terms of reduced pressure and mass flux (see

also Table 10 and Table 11):

𝐴 = 𝑃1𝑃𝑅𝑃2𝐺(𝑃5+𝑃7𝑃𝑅)

𝐶 = 𝑃3𝑃𝑅𝑃4𝐺(𝑃6+𝑃8𝑃𝑅)

Table 10: EPRI-1 model constants

Constant Value Constant Value

𝑃1 0.5328 𝑃5 -0.3040

𝑃2 0.1212 𝑃6 0.4843

𝑃3 1.6151 𝑃7 -0.3285

𝑃4 1.4066 𝑃8 -2.0749

Table 11: EPRI-1 model variable definitions

Variable Description Units

𝑞𝑐′′ Critical heat flux MBtu/ft2hr

𝜒𝑖𝑛 Inlet equilibrium quality -

𝜒𝑒 Local equilibrium quality -

𝑃𝑅 Reduced pressure (𝑃 𝑃𝑐𝑟𝑖𝑡⁄ ) -

𝐺 Mass flux Mlbs/ft2hr

𝐶𝑛𝑢 Form factor for non-uniform heat -

19

The EPRI-1 CHF model is valid in the range of operating conditions and geometry

characteristics given in Table 12:

Table 12: Combined EPRI-1 range of parameters

Parameter EPRI-1 Range

Pressure [MPa] 1.5 – 17

Mass flux [kg/m2s] 270 – 5560

Local quality [ - ] -0.25 – 0.75

Inlet quality [ - ] -1.10 – 0.00

Length [m] 0.80 – 4.27

Hydraulic diameter [m] 0.009 – 0.014

Rod diameter [m] 0.0097 – 0.0160

20

The Bowring Critical Heat Flux Model

The Bowring CHF model [8] was developed for circular ducts for a large range of

pressure and mass flux.

The empirical formula for the critical heat flux is as follows (see also Table 13):

𝑞𝑐′′ =

𝐴−𝐵ℎ𝑓𝑔𝜒𝑒

𝐶.

The constants in the Bowring CHF equation are defined as:

𝐴 =2.317(ℎ𝑓𝑔𝐵)𝐹1

1+0.0143𝐹2𝐷1 2⁄ 𝐺;

𝐵 =𝐷𝐺

4;

𝐶 =0.077𝐹3𝐷𝐺

1+0.347𝐹4(𝐺

1365)𝑛;

𝑝𝑅 = 0.145𝑝;

𝑛 = 2.0 − 0.5𝑝𝑅.

The pressure dependent constants are defined as:

For 𝑝𝑅 < 1 𝑀𝑃𝑎

𝐹1 =𝑝𝑅18.942 exp[20.89(1−𝑝𝑅)]+0.917

1.917;

𝐹2 =1.309𝐹1

𝑝𝑅1.316 exp[2.444(1−𝑝𝑅)]+0.309

;

𝐹3 =𝑝𝑅17.023 exp[16.658(1−𝑝𝑅)]+0.667

1.667;

𝐹4 = 𝐹3𝑝𝑅1.649.

For 𝑝𝑅 > 1 𝑀𝑃𝑎

𝐹1 = 𝑝𝑅−0.368 exp[0.648(1 − 𝑝𝑅)];

21

𝐹2 =𝐹1

𝑝𝑅−0.448 exp[0.245(1−𝑝𝑅)]

;

𝐹3 = 𝑝𝑅0.219;

𝐹4 = 𝐹3𝑝𝑅1.649.

Table 13: Bowring model variable description

Variable Description Units

𝑞𝑐′′ Critical heat flux W/m2

ℎ𝑓𝑔 Latent heat of vaporization J/kg

𝜒𝑒 Local equilibrium quality -

𝐺 Mass flux kg/m2s

𝐷 Fuel pin diameter m

The Bowring model is valid in the range of operating conditions and geometry

characteristics given in Table 14:

Table 14: Bowring range of parameters

Parameter Bowring Range

Pressure [MPa] 0.2 – 19

Mass flux [kg/m2s] 136 – 18,600

Length [m] 0.15 – 3.7

Rod diameter [m] 0.002 – 0.045

22

The Groeneveld Critical Heat Flux Model

The Groeneveld CHF model [9] is simply a series of look-up table for CHF as a

function of equilibrium quality, pressure and mass flux. As such, it often requires

interpolation between values. This current version is from 2006, and is an update from his

original CHF look-up tables determined with the same methods and corrective factors. The

form of the empirical equation for the Groeneveld CHF as well as applicable corrective

factors are taken from Ref. 1, page 783, and is as follows (see also Table 15):

𝑞𝑐′′ = (𝑞𝑐

′′)𝐿𝑈𝑇𝐾1𝐾4𝐾5.

There are eight total corrective factors, but only three are applicable for this analysis.

The corrective factor for subchannel geometry is given as:

𝐾1 = {(8

𝐷𝑒)1/2

for 3 < 𝐷𝑒 < 25 𝑚𝑚

0.57 for 𝐷𝑒 > 25 𝑚𝑚 .

The corrective factor for the heated length is for 𝐿 𝐷𝑒⁄ > 5:

𝐾4 = exp [(𝐷𝑒

𝐿) exp(2𝛼𝐻𝐸𝑀)];

𝛼𝐻𝐸𝑀 =𝜒𝑒𝜌𝑓

𝜒𝑒𝜌𝑓+(1−𝜒𝑒)𝜌𝑔.

The corrective factor for the axial heat flux:

𝐾5 = {1.0 for 𝜒𝑒 ≤ 0

𝑞′′ 𝑞𝐵𝐿𝐴′′⁄ for 𝜒𝑒 > 0

.

Table 15: Groeneveld model variable description

Variable Description Units

𝑞𝑐′′ Critical heat flux kW/m2

(𝑞𝑐′′)𝐿𝑈𝑇 Critical heat flux look-up value kW/m2

𝜒𝑒 Local equilibrium quality -

𝛼𝐻𝐸𝑀 Void fraction -

𝐷𝑒 Hydraulic diameter m

23

The Groeneveld model is valid in the range of operating conditions and geometry

characteristics given in Table 16:

Table 16: Groeneveld range of parameters

Parameter Groeneveld Range

Pressure [MPa] 0.1 – 21

Mass flux [kg/m2s] 0 – 8,000

Equilibrium quality [-] -0.50 – 1.0

Rod diameter [m] 0.003 – 0.025

24

Chapter 4: Critical Heat Flux Model Scoping

SMR-160 Test Case Results

This section utilizes the single heated channel model for the SMR-160 described

previously (Chapter 2: Test Case Descriptions) as a test case to calculate an axial

progression of CHF values using the CHF models. The intent is to expose weaknesses or

strengths by illustration and comparison.

The combined CHF results for the top shifted axial power case are as follows:

Figure 5: Combined CHF results for top shifted axial power

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4Combined CHF Results for the SMR-160, Top Shifted Heat Flux

Axial Position [ft]

He

at

Flu

x [

106

Btu

/hr-

ft2]

Actual q"

W3, uniform q"

W3, non-uniform q"

Biasi

EPRI-1, uniform q"

EPRI-1, non-uniform q"

Bowring

Groeneveld

25

Figure 6: Combined DNBR results for top shifted axial power

Lastly, the combined CHF results for the bottom shifted axial power case are as

follows:

Figure 7: Combined CHF results for bottom shifted axial power

0 2 4 6 8 10 12 141

5

10

15

20

25

30

35

40Combined DNBR Results for the SMR-160, Top Shifted Heat Flux

DN

BR

[-]

Axial Position [ft]

W3, uniform q"

W3, non-uniform q"

Biasi

EPRI-1, uniform q"

EPRI-1, non-uniform q"

Bowring

Groeneveld

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4Combined CHF Correlation Results for the SMR-160, Bottom Shifted Heat Flux

Axial Position [ft]

He

at

Flu

x [

106

Btu

/hr-

ft2]

Actual q"

W3, uniform q"

W3, non-uniform q"

Biasi

EPRI-1, uniform q"

EPRI-1, non-uniform q"

Bowring

Groeneveld

26

Figure 8: Combined CHF results for bottom shifted axial power

From the results, it can be seen that EPRI-1 behaves inconsistently in comparison

to the other CHF models, with a constant negative slope in the results. It also outlies the

other results, yielding much smaller CHF values. . Similarly, the Biasi model over-predicts

the CHF in comparison to the majority of the other CHF model results.

The W3, Bowring and Groeneveld models are similar in value, suggesting

consistency in results. The Groeneveld model, however, produces partial results for the

CHF as much of the test models fluid conditions are below the limits for which the model

is developed (equilibrium quality < -0.5). By nature of look-up tables, the Groeneveld

model cannot return CHF values outside of its prescribed range.

0 2 4 6 8 10 12 141

5

10

15

20

25

30

35

40Combined DNBR Correlation Results for the SMR-160, Bottom Shifted Heat Flux

DN

BR

[-]

Axial Position [ft]

W3, uniform q"

W3, non-uniform q"

Biasi

EPRI-1, uniform q"

EPRI-1, non-uniform q"

Bowring

Groeneveld

27

Parameter Comparison of Critical Heat Flux Models

This section displays the combined limiting parameters of the CHF models, and

compares them with the SMR-160 postulated ranges of operating conditions. The

comparison is as follows (Table 17):

Table 17: CHF model limiting parameter comparison to SMR-160 conditions

Parameter W3 Biasi EPRI-1 Bowring Groeneveld SMR-160

Pressure [MPa] 5.5 - 16.0 0.27 - 14.0 1.5 - 17.0 0.7 - 17.0 0.1 - 21.0 8 - 17

Mass flux [kg/m2s] 1356 - 6800 100 - 6000 270 - 5560 136 - 18600 0 - 8000 475 - 1425

Hydraulic dia [cm] 0.51 - 1.78 0.30 - 3.75 0.90 - 1.40 0.20 - 4.50 0.30 - 2.50 0.67 - 1.62

Local quality [-] -0.15 - 0.15 < 1.00 -0.25 - 0.75 - -0.5 - 1.0 -0.84 - 0.00

The postulated ranges, when provided, are calculated with extremes equal to

±50% of the nominal value. Green and red highlighted limits denote those that bound the

SMR-160 operating conditions, and those that do not, respectively.

The results show that the Bowring and Groeneveld CHF models are the most

appropriate for the SMR-160 operating conditions. The Biasi model bounds all of the

operating conditions except for pressure, which is a necessity. Similarly for the EPRI-1

model, except that it fails to bound the lower limits of subcooling and the hydraulic

diameter of the internal channel, which is the most abundant channel in an assembly. The

W3 model fails to fully bind any SMR-160 operating parameter save the channel hydraulic

diameter.

28

CHF Model Scoping Results

Of the comparisons made in this section, the most informative are the CHF model

limiting parameter comparison to SMR-160 conditions (Table 17). The empirical

correlations or look-up tables, which comprise the CHF models, are developed for specific

ranges of operating conditions. Using these outside of their prescribed ranges of conditions

is inappropriate as they simply have no meaning at non-included operating conditions.

With these considerations, it is apparent that the Bowring and Groeneveld CHF models are

the only ones appropriate for the SMR-160. Results from the single heated channel test

case enforce this by displaying inconsistencies in results, particularly with the EPRI-1 and

Biasi models.

For these reasons, the Bowring and Groeneveld CHF models are selected for

implementation in CTF. These two CHF models should yield meaningful results for the

Holtec SMR-160 project.

29

Chapter 5: Critical Heat Flux Model Implementation in CTF

Overview of the CTF Treatment of the Critical Heat Flux

The flow of information, from input to output, as pertains to the CHF calculation

in CTF can be described in Figure 9:

The variable iw3chf is read from the

input in card group 8. It is a flag for which

CHF function will be called.

This module calculates various fluid cell

conditions. It calls the appropriate CHF

correlation based on the iw3chf flag.

Parameters needed to calculate the CHF

are passed to the function, and qchf is

passed back as the function result.

The CHF is calculated here from one of

the available CHF functions, and returned

to the Mod_heat module.

Figure 9: Execution flow of CHF function call

Many more steps actually occur between “CTF input” and “Fluid cell heat

calculations”, but they do not affect the CHF function call. The process between “Fluid

cell heat calculations” and “CHF functions calculations” occurs at least once for every axial

fluid cell or node.

CTF input

Mod_read_card_group_8

- iw3chf

Fluid cell heat calculations

Mod_heat

CHF functions calculations

Heatfunctions

- qchf

30

Prior to this study, the iw3chf flag was only capable of calling one of three choices:

W3, Biasi, or no correlation. The obvious first step in the code development was to add the

additional CHF function flags, making the options for iw3chf as follows:

iw3chf =

{

0 Biasi 1 W3 2 Bowring 3 Groeneveldelse no correlation.

This was done by modifying the if-then structure in the Mod_heat module to accept

the new iw3chf flags as well as the previous ones. This encoding is trivial, and is therefore

not described. The flow of information then follows that described in the previous figure.

Fluidcell vs. Surface Type Calculations

Before the encoded CHF functions are described, an explanation is needed as to

what type of calculations they are. This requires a distinction to be made between the

“fluidcell” and “surface” type calculations in CTF. The following illustrates the difference

for an internal channel connected to four pins (Figure 10):

Figure 10: Fluidcell and surface type illustration

In an arbitrary axial node and channel, the above illustrates the fluidcell calculation

type (F1) versus the corresponding four surface calculation types (S1 – S4) for an internal

31

subchannel. The fluidcell calculation types are defined for the fluidcell, which is bound by

the four surfaces and gaps (blue lines). The fluidcell would obviously contain data

describing the channel fluid properties: density, temperature, mass flux, hydraulic diameter,

etc. The surface types which connect to this fluid cell contain data specific to the rods: heat

flux, cladding temperature (in the case of modelling fuel rods), etc.

The CHF is calculated and stored in CTF as the surface type. In the absence of

surface specific CHF models (the W3 model, for instance, uses the Tong factor which is

specific to the fuel or heater rod), the surface type CHF is defined by the fluid-cell

conditions, meaning all the surfaces in contact with the fluid cell all have the same CHF

value. It is very simple to calculate CHF with the Bowring function because it only requires

fluidcell defined parameters (channel coolant density, enthalpy, etc.). The Groeneveld

function, however, requires surface specific parameters (rod heat flux and axial and radial

power profiles). This is handled within the Mod_heat module, which calls the surface-

specific and fluid-cell-specific data for the Groeneveld CHF as follows (Figure 11):

Figure 11: Groeneveld CHF handling in CTF

As explained later, the Groeneveld CHF implementation into CTF requires a

function to be added to the Heatfunctions module for the fluid-cell-specific data (which

includes the interpolated CHF, K1 and K4), and a subroutine to the Surface_type

module for the rod-specific K5 factor. See the Groeneveld Implementation section for

32

details. This implementation calls the Groeneveld K5 subroutine in Surface_type once

for every rod, and the main CHF function in Heatfunctions once for every fluid cell,

reducing overall computational effort.

Overview of CTF Source Modifications

Implementing the chosen CHF models into CTF is performed in such a way that

preserves CTF’s coding style, accuracy and stability in calculations. The CHF models are

added to the CTF module Heatfunctions as functions. Similar to object oriented coding

techniques, the Fortran module allows separate code to be written with defined inheritance

from other modules, making the coding technique “modular”. A typical module is outlined

Code Block 1.

The CHF models under consideration are added to the “functions” section to

calculate CHF values. Parameters required for the CHF models (e.g., subchannel

hydraulic diameter) are taken in from the “use” section. For this module, all functions are

public so that they can be called from others parts of CTF. Therefore, the CHF model

function names must be added to the “public” section. The remaining sections describe

the CHF model functions individually.

33

Code Block 1: Example Fortran module

Code Section Comment

module <module_name> Declares the present module

name and begins scope.

use <outside_module>

A declaration for what functions

or subroutines from outside of

this module are to be imported.

private :: <some_function>

List of functions from within this

module’s scope that are private,

i.e., they cannot be imported into

other modules.

public :: <some_function>

List of functions from within this

module’s scope that are public,

i.e., they ae able to be imported

into other modules.

real function <function_name>(...)

result(...)

Header for function within the

module scope. Included here are

variables that are taken into

function, frequently taken from

the “use” section, and calculated

variables passed back from this

function. ... Body of function. end function <function_name> Ends the function scope. end module <module_name> Ends the module scope.

34

CTF Encoded Bowring Function

The Bowring CHF model is encoded into CTF as a function, with the following

function header.

Code Block 2: Bowring CHF model function header

real function Calc_qchf_Bowring (de,hfg,p,g,xaeq) result (qchf)

! Arguments -------------------------------------------------------------

real, intent(in) :: de,hfg,p,g,xaeq

! Local variables -------------------------------------------------------

real :: pr,n,F1,F2,F3,F4,B,C,A

!------------------------------------------------------------------------

As previously mentioned, the function declaration (first line) declares the function

name, input variables and the output or result. The next line of code (not including

comments) declares variables taken in from outside of the function. The flag intent(in)

only allows local changes to the input variables. This prevents possible errors in parent

modules due to altering the input. Following this, local variables used in the function

calculations are declared.

The body of the function follows the CHF model as described in The Bowring

Critical Heat Flux Model section to calculate the CHF.

Code Block 3: Bowring CHF model function body

pr = 0.001*p

n = 2.0-0.5*pr

if (pr<=1) then

F1 = (pr**18.942*exp(20.89*(1-pr))+0.917)/1.917

F2 = 1.309*F1/(pr**1.316*exp(2.444*(1-pr))+0.309)

F3 = (pr**17.023*exp(16.658*(1-pr))+0.667)/1.667

F4 = F3*pr**1.649

else

F1 = pr**(-0.368)*exp(0.648*(1-pr))

F2 = F1/(pr**(-0.448)*exp(0.245*(1-pr)))

F3 = pr**0.219

F4 = F3*pr**1.649

end if

B = (de*12)*(g/1e6)/4.0

C = 104.4*F3*(de*12)*(g/1e6)/(1+0.347*F4*((g/1e6)**n))

A = 2.317*hfg*B*F1/(1+3.092*F2*(g/1e6)*((de*12)**0.5))

qchf = (A-B*hfg*xaeq)/C*1e6 ! [BTU/hr-ft^2]

end function Calc_qchf_Bowring

35

CTF Encoded Groeneveld Function

Look-up Table CHF Interpolation Scheme

The Groeneveld CHF model as previously described is a 21x23x15 look-up table

of CHF values discretized in equilibrium quality, pressure and mass flux. This is initialized

into CTF in a separate module which creates the 3D array of CHF values. The interpolation

scheme used to calculate a local Groeneveld CHF is described in the following steps:

1. From the original 21x23x15 Groeneveld CHF look-up array, select a 2x2x2 CHF

array that bounds the local fluidcell conditions (described in pressure, mass flux

and equilibrium quality).

2. Reduce the 2x2x2 CHF array in pressure, mass flux and equilibrium quality to a

1x2x2 array in mass flux and equilibrium quality by interpolating in pressure.

3. Reduce 1x2x2 CHF array in mass flux and equilibrium quality to 1x1x2 array in

equilibrium quality by interpolating in mass flux

4. Determine local Groeneveld CHF value by interpolating 1x1x2 CHF array in

equilibrium quality

36

Groeneveld Implementation

Groeneveld 3D CHF Array Initialization

The Groeneveld CHF array is initialized within Mod_Groeneveld as follows:

Code Block 4: Groeneveld CHF array initialization module

module Groeneveld

...

implicit none

integer, parameter :: chf_arr(9775) = (/ ... /)

real, parameter :: Gro(23,25,17) = reshape(chf_arr,(/23,25,17/),Order=(/2,1,3/))

real, parameter :: xelim(25) = (/ -5.00,-0.50,-0.40,-0.30,-0.20,-0.15,-0.10,-0.05,&

0.00,0.05,0.10,0.15,0.20,0.25,0.30,0.35,0.40,0.45,&

0.50,0.60,0.70,0.80,0.90,1.0,5.0/)

real, parameter :: xe_interval(32) = (/1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11,&

12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 20,&

21, 21, 22, 22, 23, 23, 24/)

real, parameter :: glim(23)= (/-50,0,50,100,300,500,750,1000,1500,2000,2500,3000,&

3500,4000,4500,5000,5500,6000,6500,7000,7500,8000,&

40000000/)

real, parameter :: g_interval(162) = (/1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, &

6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, &

9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11,&

11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13,&

13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15,&

15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17,&

17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19,&

19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21,&

21, 21, 21, 22/)

real, parameter :: plim(17) = (/0,100,300,500,1000,2000,3000,5000,7000,10000,&

12000,14000,16000,18000,20000,21000,40000000/)

real, parameter :: p_interval(211) = (/1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, &

5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, &

7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, &

8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, &

9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, &

9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,&

10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,&

11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,&

12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,&

13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,&

14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16/)

end module Groeneveld

The variable chf_arr is a linear array of all of the Groeneveld CHF values, which

is reshaped into the 3D array Gro. The 3D CHF array is padded with repeated values at the

37

boundaries. This is done so that interpolation performed outside of the boundary will return

the boundary value.

Included in this module are arrays used to intelligently select the 2x2x2 array

element used for interpolation. The array xelim is an array of the equilibrium quality

values that discretize the Groeneveld CHF look-up tables. This array is padded with

extreme values which are used to ensure that extreme conditions return the boundary values.

The CHF array is non-uniformly discretized in equilibrium quality, so in order to

select the appropriate bounding conditions without a logic searching function, an additional

array xe_interval is provided to return the array location of the bounding equilibrium

quality value from xelim, but using a uniform discretization step. For example, a local

equilibrium quality value of 0.42 is bound by the equilibrium quality values 0.40 and 0.45

in the Groeneveld CHF array. The location of the lower bounding value is selected as

follows using the smallest equilibrium quality discretization step used by the Groeneveld

CHF array, which is 0.05:

ceiling (𝜒𝑒,𝑙𝑜𝑐∆𝜒𝑒

) + 11 = ceiling (0.42

0.05) + 11 = 20

xe_interval(20) = 17

Where “11” is the number of negative values in the xelim array, and the 17th element of

the xelim array is indeed 0.4. This functionality is used in the main Groeneveld function.

Something similar is performed for the mass flux and pressure arrays.

38

Groeneveld CHF Interpolation

The Groeneveld function is housed in the module Heatfunctions. The function header

is as follows:

Code Block 5: Groeneveld CHF model function header

real function Calc_qchf_Groeneveld (ichan,jlev,z,de,p,g,xaeq,L,rhof,rhog)

result (qchf)

! Arguments --------------------------------------------------------------

real, intent(in) :: de,p,g,xaeq,z,L,rhof,rhog

integer, intent(in) :: jlev,ichan

! Local variables --------------------------------------------------------

real :: gsi,psi,xelow,xeup,glow,gup,plow,pup,Gro_int,&

desi,zsi,Lsi,qint,K1,K2,K3,K4,K6,K7,K8,alpha

real, dimension(2,2,2) :: Gro_red

real, dimension(2,2) :: Gro_redp

real, dimension(2) :: Gro_redpg

integer :: n1,n2,n3

!-------------------------------------------------------------------------

gsi = abs(g)*t_lbm_kg/(t_hr_s*t_ft_m**2) ![kg/m^2s]

psi = p*t_psi_MPa*t_MPa_kPa ![kPa]

desi = de*t_ft_m ![m]

zsi = z*t_ft_m ![m]

Lsi = L*t_ft_m ![m]

The “local variables” are defined for the variables used locally in the function.

Three arrays are declared for the reduction of the Groeneveld CHF array: first the selected

2x2x2 from the original array, the array reduced in pressure, and then the array reduced in

mass flux (Gro_red, Gro_redp and Gro_redpg, respectively). The last section are

simply conversions to SI units, required for the Groeneveld empirical correlations.

The first calculations in the Groeneveld function are used to select the 2x2x2 from

the original Groeneveld CHF array that bounds the local fluid condition. This uses the same

method as mentioned in the previous section to select the array indices for the Groeneveld

CHF array that correspond to the reduced 2x2x2.

39

Code Block 6: 2x2x2 CHF array selection

! Setting equilibrium quality limits for the reduced 2x2x2

n1 = xe_interval(max(1,min(size(xe_interval),ceiling(xaeq/0.05)+11)))

xelow = xelim(n1)

xeup = xelim(n1+1)

! Setting mass-flux limits for the reduced 2x2x2

n2 = g_interval(min(size(g_interval),ceiling(gsi/50)+1))

glow = glim(n2)

gup = glim(n2+1)

! Setting pressure limits for the reduced 2x2x2

n3 = p_interval(min(size(p_interval),ceiling(psi/100)))

plow = plim(n3)

pup = plim(n3+1)

! Develops 2x2x2 matrix from original 17x23x25 using pressure, xe and

! mass flux boundaries

Gro_red = real(Gro(n2:n2+1,n1:n1+1,n3:n3+1))

This selects the lower and upper bounds of the reduced 2x2x2 CHF array for

equilibrium quality, mass flux and pressure, and then selects the reduced array.

The interval and lim (short for limit) variables are taken in from the previously

described module, Mod_Groeneveld. They are used to intelligently select the 2x2x2

without the use of logical loops, as previously described.

Following this, the 2x2x2 CHF array is interpolated in pressure, mass flux and

finally in equilibrium quality using the previously determined limits.

The final interpolated value is converted locally to US units, as CTF uses that unit

system internally.

40

Code Block 7: CHF interpolation

! Develops 1x2x2 matrix reduced/interpolated in pressure

Gro_redp(1,1) = (Gro_red(1,1,2)-Gro_red(1,1,1))/(pup-plow)*(psi-plow)+&

Gro_red(1,1,1)

Gro_redp(1,2) = (Gro_red(1,2,2)-Gro_red(1,2,1))/(pup-plow)*(psi-plow)+&

Gro_red(1,2,1)

Gro_redp(2,1) = (Gro_red(2,1,2)-Gro_red(2,1,1))/(pup-plow)*(psi-plow)+&

Gro_red(2,1,1)

Gro_redp(2,2) = (Gro_red(2,2,2)-Gro_red(2,2,1))/(pup-plow)*(psi-plow)+&

Gro_red(2,2,1)

! Develops 1x2 matrix reduced/interpolated in pressure and mass flux

Gro_redpg(1) = (Gro_redp(2,1)-Gro_redp(1,1))/(gup-glow)*(gsi-glow)+&

Gro_redp(1,1)

Gro_redpg(2) = (Gro_redp(2,2)-Gro_redp(1,2))/(gup-glow)*(gsi-glow)+&

Gro_redp(1,2)

! Final interpolated chf value, reduced/interpolated in pressure,

! mass flux and xe

Gro_int = (Gro_redpg(2)-Gro_redpg(1))/(xeup-xelow)*(xaeq-xelow)+&

Gro_redpg(1)

qint = 1000*Gro_int*((1./t_btu_J)/(1./t_hr_s))/((1./t_ft_m)**2) ! [BTU/hr-

ft^2]

Groeneveld K-factors

The applicable Groeneveld K-factors, as described in the

41

The Groeneveld Critical Heat Flux Model section, are applied in the remaining

portion of the module.

Code Block 8: Subchannel geometry factor, K1

! Subchannel cross-section geometry factor

if (desi > 0.003 .AND. desi < 0.025) then

K1 = (0.008/desi)**0.5

else if (desi >= 0.025) then

K1 = 0.57

else

K1=1.633

end if

The subchannel geometry factor, K1, as described previously, accounts for the

effect of subchannel hydraulic diameters that differ from the 8 mm tubes used in

Groeneveld’s CHF studies.

Accounting for the effect of the heated length, the factor K4 is encoded as follows:

Code Block 9: Heated length factor, K4

! Heated length factor

if(xaeq > 0) then

alpha = xaeq*rhof/(xaeq*rhof+(1-xaeq)*rhog)

else

alpha = 0

end if

if (Lsi/desi > 5) then

K4 = exp((desi/Lsi)*exp(2*alpha))

else

K4 = 1.0

end if

The final K-factor, K5, which accounts for the effect of the non-uniform heat flux,

is calculated in a separate module, Surface_type. As its name suggests, this module is

used for calculating parameters unique to the heated surface of a rod, and defines a surface

class in Fortran to which the K5 factor and other parameters belong. Calculation of the K5

factor in this module saves computational effort as it is only performed once for every rod.

42

The header for the K5 subroutine is as follows:

Code Block 10: K5 subroutine header for the non-uniform axial heat flux factor

!=====================================================================

!> Updates the Groeneveld heated factor (K5). They account for

!! non-uniform heating.

!=====================================================================

subroutine Calc_Groeneveld_K5 (me)

class(Surface), intent(in out) :: me

real :: sum_q,num_sum,qbla

integer :: osb_j, j_int, j, jh

logical :: osb_exists=.false.

This subroutine, and likewise the result for the K5 factor, are initializes as instances

of the class Surface. Parameters with the flag j are axial nodes or heights.

The K5 factor is initialized only in post-saturated boiling conditions, as defined in

the description of the Groeneveld model. The following checks for the occurrence of the

onset of saturated boiling (OSB) at the rod as a condition for calculation.

Code Block 11: K5 subroutine check for OSB

! First find the axial location where OSB occurs

! We start at the bottom of the rod and move up until we

! encounter a non-negative xe, the onset of saturated boiling

! Initialize the location to the top of the rod

osb_j=me%jmax

osb_exists=.false.

do j=1,me%jmax

if (me%xe(j)>=0) then

osb_j=j

osb_exists=.true.

exit

end if

end do

The parameter xe is a local value for the equilibrium quality of the fluid in contact

with the rod. A non-negative value for the equilibrium quality is used as a flag for OSB,

which is searched for this section of code.

The last section of the subroutine calculates K5 in OSB conditions.

43

The boiling length averaged heat flux is calculated between the top axial node and the node

where OSB occurs. The integral is approximated numerically as the sum of the axial heat

flux values for each node divided by the number of nodes. Local values for K5 are

calculated as described in the section

44

The Groeneveld Critical Heat Flux Model.

Code Block 12: K5 subroutine initialization

! Determines K5 as the local heat flux divided by the boiling length

averaged

! heat flux

me%K5 = 1.0

if (osb_exists) then

do jh = osb_j,me%jmax

! Takes the sum of all the axial heat flux from the osb to the

! current axial location

sum_q = 0.0

num_sum = 0.0

do j_int = osb_j,jh

sum_q = sum_q + me%q(j_int)

num_sum = num_sum + 1.0

end do

! The boiling length averaged heat flux

if (jh /= osb_j) then

qbla = sum_q/num_sum

else

qbla = sum_q

end if

if (me%q(jh) > 0) then

me%K5(jh) = me%q(jh)/qbla

else

me%K5(jh) = 1.0

end if

end do

end if

45

Resulting Groeneveld CHF

The final value for the Groneveld CHF is initialized in the module Mod_heat. This

is the parent module that calls the previously mentioned modules and subroutines to

develop the final Groeneveld CHF:

𝑞𝑐′′ = 𝐶𝐻𝐹𝑖𝑛𝑡𝑒𝑟𝑝𝐾1𝐾4𝐾5

Where the interpolated CHF and the K-factors K1 and K4 comes from Heatfunctions,

and K5 from Surface_type. Here, the resulting CHF value is assigned to the appropriate

rod surface.

46

Chapter 6: CTF Test Model Results

Bowring CHF Model CTF Test Results

Results from the test model (described in the CTF Test Model section) for the

Bowring CHF model are presented in Figure 12 ÷ Figure 15.

As desired to test the robustness of the CHF model, the test model starts yielding

void around 1.5 meters. The effect of the spacer grids and mixing can also be seen in the

void-fraction valleys. The CTF test case results are extracted from the produced HDF5 file,

and are plotted using a MATLAB script. These and other files are described in the

Computer Files section. The CHF and MDNBR results taken from the same HDF5 file are

given for every pin. As such, they are taken as the limiting value from the pin surface at a

given axial height. Results are also displayed for the numbered subchannels and pins (see

Figure 4: CTF test case numbered channels and rods). CHF results are then as follows:

Figure 12: Bowring model - equilibrium quality results for selected channels

0 1 2 3 4-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1Channel Equilibrium Quality

Axial Position [ m ]

XE

[-]

Chan 4

Chan 7

Chan 10

Chan 13

47

Figure 13: Bowring model - void fraction results for selected channels

Figure 14: Bowring model - CHF results

0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35Vapor Void Fraction

Axial Position [ m ]

Void

[-]

Chan 4

Chan 7

Chan 10

Chan 13

0 1 2 3 41.5

2

2.5

3

3.5

4

4.5

5Pin Critical Heat Flux

Axial Position [ m ]

CH

F [

10

3 k

W/m

2]

Pin 1

Pin 2

Pin 3

Pin 4

Pin 6

Pin 7

Pin 8

Pin 9

48

Figure 15: Bowring model - MDNBR results

The CHF and MDNBR results from the CTF encoded Bowring model are

conceptually agreeable. The magnitude of CHF results are inversely proportional to the

heat flux; that is to say that the pin with the largest heat flux would also have the minimum

CHF. This is observed for pin number 3 in the model. Likewise, the MDNBR progression

for the same pin is the minimum in comparison to the others.

0 1 2 3 40

5

10

15

20

25

30

35Pin Minimum Departure From Nucleate Boiling Ratio

Axial Position [ m ]

MD

NB

R [

-]

Pin 1

Pin 2

Pin 3

Pin 4

Pin 6

Pin 7

Pin 8

Pin 9

49

Groeneveld CHF Model CTF Test Results

Results from the test model (described in the CTF Test Model section) for the

Groeneveld CHF model are presented in Figure 16 ÷ Figure 19. Slight disagreement is seen

between the fluid conditions produced here for the Groeneveld CHF model in comparison

to the previous Bowring model results. The deviation appears to occur in the higher void

region. This can be explained by CTF’s use of the CHF to select certain flow regimes,

which will have an effect on fluid conditions.

Similar to previous results though, the test model possesses a wide range of fluid

conditions which will be used to test the robustness of the CHF models.

The CHF and MDNBR results from the CTF encoded Groeneveld model are

conceptually agreeable, for the same reason previously stated for the Bowring CHF model

Figure 16: Groeneveld model - equilibrium quality results for selected channels

0 0.5 1 1.5 2 2.5 3 3.5 4-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1Channel Equilibrium Quality

Axial Position [ m ]

XE

[-]

Chan 4

Chan 7

Chan 10

Chan 13

50

Figure 17: Groeneveld model - void fraction results for selected channels

Figure 18: Groeneveld model – CHF results

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35Vapor Void Fraction

Axial Position [ m ]

Vo

id [

-]

Chan 4

Chan 7

Chan 10

Chan 13

0 0.5 1 1.5 2 2.5 3 3.5 41

1.5

2

2.5

3

3.5

4

4.5

5Pin Critical Heat Flux

Axial Position [ m ]

CH

F [

10

3 k

W/m

2]

Pin 1

Pin 2

Pin 3

Pin 4

Pin 6

Pin 7

Pin 8

Pin 9

51

Figure 19: Groeneveld model – MDNBR results

0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

30

35Pin Minimum Departure From Nucleate Boiling Ratio

Axial Position [ m ]

MD

NB

R [

-]

Pin 1

Pin 2

Pin 3

Pin 4

Pin 6

Pin 7

Pin 8

Pin 9

52

CHF Model Comparison

The following is a table comparing results between the CHF models:

Table 18: Results comparison based on CHF model

CHF Model MDNBR Maximum Equilibrium Quality

Bowring 1.0574 0.0512

Groeneveld 1.0972 0.0512

Figure 12 ÷ Figure 19 and Table 18 show that the results between the two are

comparable. The Bowring CHF model yields a more conservative value for the MDNBR,

with equivalent maximum equilibrium qualities. The maximum equilibrium quality, in

view of Figure 13 and Figure 17, does not occur exactly at the exit but near it. This drop in

the equilibrium quality at the exit is a result of mixing from the spacer grid.

The CHF models are shown to have an unnoticeable effect on the fluid condition

results, namely equilibrium quality and void fraction. This is expected since at MDNBR >

1.0 for both cases, and post-CHF flow regimes are not encountered.

53

Chapter 7: Conclusion and Future Work

Analyzing a natural circulation type reactor like the SMR-160 is a challenging task

as it exhibits atypical behavior in comparison to a typical PWR. In order to facilitate

adequate flow from natural circulation, a large temperature gradient across the core is

necessary. This requires a high degree of subcooling at the inlet to maintain reasonable

outlet conditions. Flow by natural circulation also creates a strong coupling between power

and flow: a change in the heat absorbed from the fuel rods will create a proportional change

in flow due to the altered temperature gradient.

To enhance CTF capabilities of SMR-160 safety margins evaluations, two CHF

models were implemented: the Bowring CHF correlation and the Groeneveld CHF lookup

tables. The selection was based on the models’ availability in the open literature and on the

validity range of operating conditions under which the two models were developed. The

results from the single heated subchannel calculations and the comparison of limiting

ranges of applicability for the CHF models show that the Groeneveld and Bowring models

are the most applicable for SMR-160.

The Bowring CHF model is far simpler to implement than the Groeneveld model.

It also shows reasonable results in comparison to the other models, as is shown in Figure 5

÷ Figure 8, and meets the SMR-160 ranges of operating conditions as described in Table

17. In the interest of code use though, the Groeneveld model has more advantages. It also

shows close agreement in results compared to other models, and with the exception of the

inlet subcooling meets the SMR-160 range of operating conditions (Figure 5 ÷ Figure 8

and Table 17, respectively). By nature of a look-up table, the Groeneveld CHF model can

always return an interpolated CHF value. This is done by returning the boundary CHF

54

value in the case that fluid conditions are out of the Groeneveld range of valid operating

conditions. In doing so, this has two effects:

1. The Groeneveld CHF implementation is less prone to instabilities and should

always return a CHF value, even in extreme conditions

2. For highly subcooled flow, as is relevant to the SMR-160, the CHF values

returned at levels of subcooling lower than the range suggested for the

Groeneveld model are shown to be conservative in this context

In addition to this, the Groeneveld model is accompanied by form or K-factors which can

account for additional flow effects (subchannel geometry, heated length, and axial heat flux

factors as described in The Groeneveld Critical Heat Flux Model). For the above reasons,

the Groeneveld CHF model is deemed to be the most applicable of the two for use in core

analysis of the SMR-160.

Future work should applied towards analyzing the available K-factors to determine

which are applicable for use in CTF (see Ref. 1, page 783 for a description of all K-factors).

Several were designed to account for additional thermal-hydraulic effects which CTF is

already accounting for, making them unnecessary for use in a robust thermal-hydraulics

analysis code. Some also are not as accurate as factors developed from other works. Some

sources for example recommend using the Tong non-uniform axial heating factor rather

than the Groeneveld K5 factor.

55

Computer Files

Described here are the computer files used for this study.

Table 19: Computer files

File Checksum Description ctf_chf_test.inp 99c40175e6a9977d

6e8e477134b26e3b CTF input for the test model

described in CTF Test Model. The

flag iw3chf was modified to switch

back and forth between the Bowring

model and Groeneveld model. ctf_chf_test_bow.

h5

3b08be9e8f095a5d

3cfc6d817c7b9f63 CTF HDF5 output file for the CTF

test case using the Bowring model.

Used in Bowring CHF Model CTF

Test Results. ctf_chf_test_gro.

h5

042b1f260827870d

e388568d6601d42f CTF HDF5 output file for the CTF

test case using the Groeneveld

model. Used in Groeneveld CHF

Model CTF Test Results. Heatfunction.f90 47619095cda50602

dbbb553d815d58c9 CTF module where the Goeneveld

and Bowring CHF functions were

added. Described in

CTF Encoded Bowring Function

and CTF Encoded Groeneveld

Function. Mod_Groeneveld.f9

0

eb31abbf59f043d2

7a2363640dcbce5b CTF module where the Groeneveld

CHF array and other accompanying

arrays are imported. Described in

Groeneveld 3D CHF Array

Initialization. Surface_type.f90 d530ecd419c110cf

ef02fa0378b0c643 CTF class for rod or conductor

surfaces that was modified for the

Groeneveld K5 factor. Described in

Groeneveld K-factors. CombinedCHFBottom

ShiftSMR.m

6c98811efdbf1af0

9373d04ef2e28e87 Matlab file that performs the CHF

candidate comparisons using SMR-

160 relevant operating conditions

for a single subchannel with a

bottom shifted power distribution.

Results in SMR-160 Test Case

Results. CombinedCHFTopShi

ftSMR.m

abb0ed02bc1bc295

67f7cdf3797960e5 Matlab file that performs the CHF

candidate comparisons using SMR-

160 relevant operating conditions

for a single subchannel with a top

56

shifted power distribution. Results

in SMR-160 Test Case Results. axial_position.tx

t

983a8030bd46e1e2

86e042f7a3db9d4f Text file with axial position data

required for CombinedCHFBottomShiftSMR.

m and CombinedCHFTopShiftSMR.m

BottomPeak.txt 1864a6c78b389346

92e6d7533aa40ca3 Text file with bottom-peaked power

dist. data required for CombinedCHFBottomShiftSMR.

m and CombinedCHFTopShiftSMR.m

TopPeak.txt e5778dfc0d739c80

dc4edadf1047a92d Text file with top-peaked power

dist. data required for CombinedCHFBottomShiftSMR.

m and CombinedCHFTopShiftSMR.m

CTF_chan_read.m 83a73fbf6e93565c

4de750e0c4766465 Matlab file that reads CTF output

from HDF5 file and plots results.

Results in CTF Test Model Results.

57

References

1. Todreas and Kazimi. Nuclear Systems Volume I: Thermal Hydraulic

Fundamentals; CRC Press, 2nd edition, 2011.

2. Salko, R. K.; Avramova, M. N. CTF Theory Manual. The Pennsylvania State University.

http://www.casl.gov/vera-resources/Theory%20Manual%20CTF%20CASL-U-

2015-0054-000.pdf

3. Salko, R. K. et al. CTF Validation. The Pennsylvania State University.

http://www.casl.gov/vera-resources/Validation%20Manual%20CTF%20CASL-

U-2014-0169-000.pdf

4. Holtec International. Base CTF Model for the SMR-160 Single Assembly. HI-

2156823R0.

5. Tong, L. S., Heat transfer in water cooled reactors. Nuclear Engineering and

Design, Vol.6, 301-324, 1967.

6. Biasi, L., et al, Studies on Burnout, Part 3 – A new correlation for round ducts

and uniform heating and its comparison with world data. Energia Nucleare, Vol.

14, 530-536, 1967.

7. Reddy, D. G. and Fighetti, C. F., Parametric study of CHF data, volume 2: A

generalized subchannel CHF correlation for PWR and BWR fuel assemblies.

Electric Power Research Institute Report NP-2609, prepared by Heat Transfer

Facility, Department of Chemical Engineering, Columbia University, NY,

January 1983.

8. Bowring, R.W., A Simple but Accurate Round Tube, Uniform Heat Flux Dryout

Correlation over the Pressure Range 0.7 to 17 MPa. AEEW-R-789, U.K. Atomic

Energy Authority, Winfrith, UK, 1972.

9. Groeneveld, D. C., The 2006 CHF look-up table. Nuclear Engineering and

Design, Vol. 237, p 1909 – 1922, 2007.