Laminar Hydraulic Analysis of 

a Commercial Pressurized 

Water Reactor Fuel Assembly

Office of Nuclear Regulatory Research

NUREG/CR-7144

SAND 2008 - 3938
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p 

Laminar Hydraulic Analysis 

of a Commercial Pressurized 

Water Reactor Fuel Assembly

Manuscript Completed: August 2008

Date Published: January 2013

Prepared by

E. R. Lindgren and S. G. Durbin

Sandia National Laboratory

Albuquerque, NM 87185

G. A. Zigh, NRC Project Manager

NRC Job Code Y6758

Prepared for

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

 

NUREG/CR-7144

SAND 2008 - 3938

iii

Abstract

To the knowledge of the authors, these studies are the first hydraulic characterizations of 

a full length, highly prototypic 17×17 pressurized water reactor (PWR) fuel assembly in 

low Reynolds number flows. The advantages of full scale testing of prototypic 

components are twofold. First, the use of actual hardware and dimensionally accurate 

geometries eliminates any issues arising from scaling arguments. Second, many of the 

prototypic components contain intricacies by design that would not be reproduced by 

using simplified flow elements. While this approach yields results that are inherently 

specific to the fuel assembly under testing, the differences in commercial designs are 

considered minor, particularly when considering the hydraulics of the entire assembly. 

This report summarizes the findings of the pressure drop experiments conducted using a 

highly prototypic PWR fuel assembly. The stated purpose of these investigations was to 

determine hydraulic coefficients, namely frictional loss coefficient (SLAM ) and inertial 

loss coefficient Σk values, for use in determining the hydraulic resistance in these 

assemblies within various numerical codes. Additionally, velocity profiles were acquired 

to estimate the partitioning of flow through the bundle and annular regions within the 

assembly. The apparatus was tested in the laminar regime with Reynolds numbers 

spanning from 10 to 1000, based on the average assembly velocity and hydraulic 

diameter.

v 

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

TABLE OF CONTENTS

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

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

EXECUTIVE SUMMARY.......................................................................xi

ACKNOLEDGEMENTS..................................................................... . xiii

ABBREVIATION AND DEFINITIONS .................................................... .xv

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

1.1 Background .........................................................................................................1

1.2 Objective ..............................................................................................................2

2 EXPERIMENTAL APPARATUS AND PROCEDURES ......................................................3

 2.1 Fuel Assembly .....................................................................................................3

2.2 Storage Cells ........................................................................................................5

2.3 Air Flow Control .................................................................................................5

2.4 Pressure Drop Measurements ...........................................................................7

 2.4.1 Hydraulic Loss Coefficients ....................................................................10

2.5 Laser Doppler Anemometry Measurements ..................................................12

 2.5.1 LDA Experimental Setup ........................................................................13

3 PRESSURE DROP RESULTS .......................................................................................15

3.1 217.5 mm Storage Cell ......................................................................................15

 3.1.1 Overall Pressure Drop .............................................................................15

 3.1.2 Hydraulic Loss Coefficients ....................................................................16

3.2 221.8 mm Storage Cell .....................................................................................20

 3.2.1 Overall Pressure Drop .............................................................................20

 3.2.2 Hydraulic Loss Coefficients ....................................................................23

3.3 226.6 mm Storage Cell .....................................................................................27

 3.3.1 Overall Pressure Drop .............................................................................27

 3.3.2 Hydraulic Loss Coefficients ....................................................................28

3.4 Boiling Water Reactor Assembly ....................................................................30

 3.4.1 Hydraulic Loss Coefficients ....................................................................30

3.5 PWR Storage Cell Size Dependence ..............................................................32

 3.5.1 Full Flow Range ......................................................................................32

4 VELOCITY PROFILE RESULTS .................................................................................35

4.1 226.6 mm Storage Cell .....................................................................................38

 4.1.1 Mid-Bundle Velocity Measurements ......................................................38

 4.1.2 Pre-Spacer Velocity Measurements ........................................................43

 4.1.3 Post-Spacer Velocity Measurements .......................................................47

4.2 221.8 mm Storage Cell .....................................................................................50

 4.2.1 Mid-bundle Velocity Measurements .......................................................50

4.3 217.5 mm Storage Cell .....................................................................................54

 4.3.1 Mid-bundle Velocity Measurements .......................................................54

5 SUMMARY .................................................................................................................57
vi

5.1 Pressure Drop Measurements .........................................................................57

5.2 Assembly Velocity Measurements ...................................................................58

6 REFERENCES ............................................................................................................61

APPENDIX A. ANALYTIC VALIDATION .............................................................................63

APPENDIX B. ERROR ANALYSIS .......................................................................................69

 B.1 Uncertainty in Assembly Velocity for the Apparatus ...................................69

 B.1.1 Uncertainty in Volumetric Flow Rate Q .................................................70

 B.1.2 Uncertainty in Ambient Air Temperature ...............................................71

 B.1.3 Uncertainty in Ambient Air Pressure ......................................................71

 B.1.4 Uncertainty in Assembly Cross Sectional Area ......................................71

 B.2 Uncertainty in Pressure Drop Measurements ...............................................71

 B.3 Uncertainty in SLAM and Σk Coefficients .......................................................71
vii

FIGURES

Figure 2.1 Prototypic 17×17 PWR components. ..........................................................3

Figure 2.2 Rod configuration of a typical 17×17 PWR assembly. ...............................4

Figure 2.3 Diagram and photographs of the flow control and flow straightening 

systems. ........................................................................................................6

Figure 2.4 Experimental PWR apparatus showing as-built port locations. ...................8

Figure 2.5 Lower detail of the PWR guide tube. ...........................................................9

Figure 2.6 Pressure traces recorded during a typical flow profile for 

measurements across 34–36, 30–34, and A–36. ..........................................9

Figure 2.7 Experimental BWR apparatus showing as-built port locations. ................10

Figure 2.8 Dual-beam backscatter LDA system components and principles..............13

Figure 2.9 Schematic of the LDA system for measuring velocity profiles in the 

PWR 17×17 assembly. ...............................................................................14

Figure 2.10 Photographs showing the LDA probe system in relation to the fuel 

assembly. ....................................................................................................14

Figure 3.1 Assembly pressure drop as a function of Reynolds numbers for 

analogous PWR and BWR fuel bundles. ...................................................15

Figure 3.2 Assembly pressure drop as a function of axial height for analogous 

PWR and BWR fuel bundles. ....................................................................16

Figure 3.3 Pressure drop as a function of average assembly velocity for the PWR 

fuel mockup inside the 217.5 mm storage cell. .........................................17

Figure 3.4 Overall assembly (A–36) hydraulic loss coefficients as a function of 

Reynolds number for the 217.5 mm storage cell. ......................................20

Figure 3.5 Pressure drop as a function of Reynolds numbers across the BWR fuel 

assembly and the PWR fuel assembly in the 221.8 mm storage cell. ........21

Figure 3.6 Pressure drop as a function of Reynolds numbers across the PWR fuel 

assembly in the 221.8 mm storage cell with blocked and unblocked 

guide tubes. ................................................................................................22

Figure 3.7 Pressure drop as a function of volumetric flow rate across the PWR 

fuel assembly in the 221.8 mm storage cell with blocked and 

unblocked guide tubes................................................................................22

Figure 3.8 Fraction of flow in guide tubes as a function of total flow through the 

PWR fuel assembly in the 221.8 mm storage cell with unblocked guide 

tubes. ..........................................................................................................23

Figure 3.9 Overall assembly (A–36) hydraulic loss coefficients as a function of 

Reynolds number for the 221.8 mm storage cell and blocked guide 

tubes. ..........................................................................................................26

Figure 3.10 Overall assembly (A–36) hydraulic loss coefficients as a function of 

Reynolds number for the 221.8 mm storage cell and unblocked guide 

tubes. ..........................................................................................................27

Figure 3.11 Pressure drop as a function of Reynolds numbers across the BWR fuel 

assembly and the PWR fuel assembly in the 226.6 mm storage cell. ........28

Figure 3.12 Overall assembly (A–36) hydraulic loss coefficients as a function of 

Reynolds number for the 226.6 mm storage cell. ......................................30
viii

Figure 3.13 Overall assembly (1–B) hydraulic loss coefficients as a function of 

Reynolds number for the BWR with blocked water rods. .........................32

Figure 3.14 Dependence of overall assembly (A–36) SLAM and Σk on the hydraulic 

diameter for full data range (Re = 10 to 1000). The validity of this 

correlation is limited to 17×17 PWR fuel. .................................................33

Figure 4.1 Definition of interior and annular cells for determining the partitioning 

of flow inside the assembly........................................................................35

Figure 4.2 Schematic showing the definition of the bundle (shaded) and annular 

(white) flow paths in the PWR assembly. ..................................................36

Figure 4.3 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 50. Note: the definitions of the 

bundle and annular regions are shown on the graph. .................................39

Figure 4.4 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 100. ....................................................39

Figure 4.5 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 200. ....................................................40

Figure 4.6 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 350. ....................................................41

Figure 4.7 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 500. ....................................................41

Figure 4.8 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell for Re = 900. ....................................................42

Figure 4.9 Percentages of total flow in the bundle (blue diamonds) and in the 

annulus (red squares) as a function of Reynolds number for the 226.6 

mm storage cell. .........................................................................................43

Figure 4.10 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell before a spacer for Re = 100. ...........................44

Figure 4.11 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell before a spacer for Re = 350. ...........................45

Figure 4.12 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell before a spacer for Re = 900. ...........................45

Figure 4.13 Percentages of total flow in the bundle (blue diamonds) and in the 

annulus (red squares) as a function of Reynolds number for the 226.6 

mm storage cell before a spacer. ................................................................46

Figure 4.14 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell after a spacer for Re = 100. ..............................48

Figure 4.15 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell after a spacer for Re = 350. ..............................48

Figure 4.16 Normalized velocity as a function of position inside the assembly in 

the 226.6 mm storage cell after a spacer for Re = 900. ..............................49

Figure 4.17 Percentages of total flow in the bundle (blue diamonds) and in the 

annulus (red squares) as a function of Reynolds number for the 226.6 

mm storage cell after a spacer. ...................................................................50

Figure 4.18 Normalized velocity as a function of position inside the assembly in 

the 221.8 mm storage cell for Re = 100. ....................................................51
ix

Figure 4.19 Normalized velocity as a function of position inside the assembly in 

the 221.8 mm storage cell for Re = 350. ....................................................52

Figure 4.20 Normalized velocity as a function of position inside the assembly in 

the 221.8 mm storage cell for Re = 900. ....................................................52

Figure 4.21 Percentages of total flow in the bundle (blue diamonds) and in the 

annulus (red squares) as a function of Reynolds number for the 221.8 

mm storage cell. .........................................................................................53

Figure 4.22 Normalized velocity as a function of position inside the assembly in 

the 217.5 mm storage cell for Re = 100. ....................................................54

Figure 4.23 Normalized velocity as a function of position inside the assembly in 

the 217.5 mm storage cell for Re = 350. ....................................................55

Figure 4.24 Normalized velocity as a function of position inside the assembly in 

the 217.5 mm storage cell for Re = 900. ....................................................55

Figure 4.25 Percentages of total flow in the bundle (blue diamonds) and in the 

annulus (red squares) as a function of Reynolds number in the 217.5 

mm storage cell. .........................................................................................56

 

TABLES 

Table 2.1 Dimensions of assembly components in the 17×17 PWR. .........................4

Table 2.2 Internal dimensions of commercial cask, pool cells, and areas of asbuilt experimental cells. ...............................................................................5

Table 2.3 Summary of the reference flow areas and hydraulic diameters of the 

laminar flow characterization experiments. ...............................................11

Table 2.4 Detailed list of the LDA system components. ...........................................14

Table 3.1 SLAM and Σk coefficient analysis data for pressure drops between 34–

36, 30–34, and A–36 for the 217.5 mm storage cell. .................................17

Table 3.2 Full flow range SLAM and Σk coefficients for the PWR assembly in the 

217.5 mm storage cell. ...............................................................................19

Table 3.3 Full flow range SLAM and Σk coefficients for the PWR assembly in the 

221.8 mm storage cell with blocked guide tubes. ......................................24

Table 3.4 Full flow range SLAM and Σk coefficients for the PWR assembly in the 

221.8 mm storage cell with unblocked guide tubes. ..................................25

Table 3.5 Full flow range SLAM and Σk coefficients for the PWR assembly in the 

226.6 mm storage cell. ...............................................................................29

Table 3.6 Full flow range SLAM and Σk coefficients for the BWR assembly with 

blocked water rods. ....................................................................................31

Table 4.1 Bundle cell values of area. .........................................................................35

Table 4.2 Annular and assembly hydraulic values for the different storage cells. ....36

Table 4.3 Velocity values from CFD simulations of the PWR fuel assembly...........37

Table 4.4 Velocity values from transitional and turbulent CFD simulations of the 

217.5 mm storage cell. ...............................................................................37

Table 4.5 Comparison of measured and equivalent, assembly average velocities 

for the 226.6 mm storage cell. ...................................................................43
x 

Table 4.6 Comparison of measured and equivalent assembly average velocities 

for the 226.6 mm storage cell before a spacer. ..........................................47

Table 4.7 Comparison of measured and equivalent assembly average velocities 

for the 226.6 mm storage cell after a spacer. .............................................50

Table 4.8 Comparison of measured and equivalent assembly average velocities 

for the 221.8 mm storage cell. ...................................................................53
xi

EXECUTIVE SUMMARY

The information in this report contains hydraulic characteristics of both Pressurized 

Water Reactor (PWR) and Boiling Water Reactor (BWR) assemblies, which were 

eventually used as input data to MELCOR to perform thermal-hydraulics analysis. 

Among these analyses are investigations of Zirconium fire in spent fuel pool. As such, 

these information was considered sensitive. 

The objective of this project was to provide hydraulic data to characterize the flow 

behavior in both the BWR and PWR assemblies. These assemblies were highly 

prototypical to eliminate scaling issues. Testing included pressure drop and velocity 

profile measurements throughout the two assemblies. These data can be further used to 

obtain inputs to several thermal-hydraulics codes such as MELCOR, Computational 

Fluid Dynamics (CFD) codes and others. These hydraulic data are useful to perform 

scenarios ranging from basic thermal response without accidents to severe accident cases 

involving Zirconium fire. 

These studies found the resistance to flow through the assembly was significantly greater 

than predicted by generally assumed and accepted best estimate “textbook” flow 

parameters. Use of best estimate flow parameters may significantly underestimate the 

resistance to laminar flow in the assembly, which leads to an overestimate of the cooling 

effects of naturally induced flows that develop in dry casks under normal storage 

conditions or wet spent fuel pool cells during complete loss of coolant accidents. Early 

on, the underestimation of these parameters was balanced by the large safety margin in 

the evaluation of peak cladding temperature due to the low decay heat. As the applicants 

continue to increase the stored fuel decay heat, the correct estimation of these parameters 

became important to the analysis. As such, these parameters were estimated using CFD 

which was validated using the data in this report. 

xiii

ACKNOWLEDGEMENTS 

To identify all of the individuals who participated in the success of this program would 

be impossible. The authors would like to acknowledge their hard work and commitment 

to excellence, albeit anonymously.

This work was conducted under Nuclear Regulatory Commission contract JCN# N6456. 

The authors gratefully acknowledge the technical guidance and support of Jorge Solis, 

Abdelghani Zigh, and Donald Helton at the NRC. 

The authors would also like to thank Greg Koenig, Shane Adee, Glen Cannon, John 

Bentz, Billy Martin, Brandon Servantes, and the support staff of 6763 for their tireless 

efforts and dedication to service, which made the success of this project possible. 

In addition, K.C. Wagner and Charles Morrow are to be commended for their outstanding 

technical support of the program. 

xv

ABBREVIATIONS/DEFINITIONS

AVG average

BWR boiling water reactor

CFD computational fluid dynamics

CYBL cylindrical boiling

DAQ data acquisition

EPA error propagation analysis

equiv. equivalent

ID inside diameter

IFM intermediate fluid mixer

LDA laser Doppler anemometer

meas. measured

MELCOR severe accident analysis code

NPT national pipe thread

NRC Nuclear Regulatory Commission

OD outside diameter

PCT peak cladding temperature

PWR pressurized water reactor

Ref. reference

RMS root mean square

SFP spent fuel pool

slpm standard liters per minute (standard defined at 0oC and 1 atm)

SNL Sandia National Laboratories

TC thermocouple

1 

1 INTRODUCTION 

1.1 Background

To the knowledge of the authors, these studies are the first hydraulic characterizations of a full 

length, highly prototypic pressurized water reactor (PWR) fuel assembly in low Reynolds 

number flows. The advantages of full scale testing of prototypic components are twofold. First, 

the use of actual hardware and dimensionally accurate geometries eliminates any issues arising 

from scaling arguments. Second, many of the prototypic components contain intricacies by 

design that would not be reproduced by using simplified flow elements. While this approach 

yields results that are inherently specific to the fuel assembly under testing, the differences in 

commercial designs are considered minor, particularly when considering the hydraulics of the 

entire assembly.

In a previous study under JCN Y6758 titled “Spent Fuel Pool Heatup and Propagation 

Phenomena Experiments”, the hydraulic characterization of a full scale, highly prototypic boiling 

water reactor (BWR) assembly mockup was conducted using a state-of-the-art quartz crystal 

differential pressure gauge.

1

 These pressure gauges have an unprecedented resolution of ± 0.02 

N/m2 (±0.000003 psi) that allows accurate measurement of the pressure drops across assembly 

segments at very low Reynolds numbers (Re = 60 to 900). 

These studies found the resistance to flow in the BWR assembly was significantly greater than 

predicted by generally assumed and accepted best estimate “textbook” flow parameters. Use of 

best estimate flow parameters may significantly underestimate the resistance to laminar flow in 

the assembly, which leads to an overestimate of the cooling effects of naturally induced flows 

that develop in dry casks under normal storage conditions or wet spent fuel pool cells during 

complete loss of coolant accidents. Early on, the underestimation of these parameters was 

balanced by the large safety margin in the evaluation of peak cladding temperature due to the 

low decay heat. As the applicants continue to increase the stored fuel decay heat, these 

parameters became important to the analysis. As such, the correct estimation of these parameters 

were estimated using CFD which was validated using the data in this report.

Overestimating the cooling effects of naturally induced flows may lead to non-conservative 

analyses of dry cask performance and spent fuel pool accident consequences. Two geometric 

aspects unique to the prototypic BWR assembly somewhat mitigate this problem: 1) water rods 

in the center of the assembly carry a significant fraction of the total natural circulation flow and 

aid in cooling and 2) eight of the seventy-two rods in the 9×9 BWR assembly are partial length 

and end 1.32 m (52 in.) below the top of the assembly. The increased void space in this upper 

portion greatly reduces flow resistance in this region. These geometric aspects were not fully 

appreciated until close inspection of the prototypic 9×9 BWR components, whose specifications 

are concealed in proprietary vender drawings. This is one of the benefits obtained by the Sandia 

National Laboratories (SNL) spent fuel pool (SFP) experimental program’s use of full-scale, 

prototypical vender hardware.

The flow resistance issue is expected to be more acute in a pressurized water reactor (PWR) 

assembly. A PWR assembly is fully populated with rods along the entire length (i.e. no partial 

length fuel rods) and there are no water rods. Thus, the mitigating geometric factors found in the 

BWR assembly are not present in a typical PWR assembly. Furthermore, the PWR assembly has 
2 

more spacers, and the spacers are hydraulically longer than in a BWR assembly. All of these 

factors may lead to significantly higher resistance to naturally convective flow as compared to a 

BWR assembly. The characterization of a highly prototypic PWR assembly, especially with 

respect to the design and placement of the spacers, is vitally important to provide prototypic 

hydraulic conditions for use in the analysis of dry cask performance.

1.2 Objective 

The objective of this project is to hydraulically characterize a full length, highly prototypic 

17×17 PWR fuel assembly in low Reynolds number laminar flows expected in dry casks under 

normal storage conditions or wet spent fuel pool cells during complete loss of coolant accidents. 

Testing includes pressure drop measurements and the quantification of velocities inside the 

assembly.
3 

2 EXPERIMENTAL APPARATUS AND PROCEDURES

These experiments were constructed and operated in the cylindrical boiling (CYBL) vessel 

located in Building 6585C in Technical Area III of Sandia National Laboratories (SNL) in 

Albuquerque, New Mexico. The CYBL facility houses a 4.9 m diameter × 8 m tall stainless steel 

vessel with 51 viewports. The vessel is open at the top with a 1 m diameter access port near the 

vessel floor. This facility was previously used for both the separate and integral effects testing in 

the BWR experimental program.1

2.1 Fuel Assembly

The highly prototypic fuel assembly was modeled after the 17×17 PWR. Commercial 

components were purchased to create the assembly including the top and bottom nozzles, 

spacers, intermediate fluid mixers (IFM), 24 guide tubes, one central instrumentation tube, and

all related assembly hardware. Many of these components are pictured in Figure 2.1. The 

central instrumentation tube and guide tubes are permanently attached to the spacers to form the 

structural skeleton of the assembly. The top and bottom nozzles are removable. The 24 guide 

tubes are completely open through the top nozzle and completely blocked in the bottom nozzle. 

The outer diameter of the 24 guide tubes changes from 11.2 mm to 12.2 mm at an axial location 

0.61 m from the bottom nozzle. Immediately above the guide tube diameter change are four 2.31 

mm holes in the tube wall. The central instrumentation tube is the same diameter as the upper 

guide tubes and is the same diameter along the entire length. There are no holes in the 

instrumentation tube wall. The instrument tube is completely open through the bottom nozzle 

but is mostly blocked by the top nozzle with only a single 2.6 mm hole centered on the tube. If 

not blocked, the holes in the guide tube wall would allow some flow through the guide tubes. 

The vast majority of spent PWR have the guide tubes blocked by a special thimble plug or spent 

control rod assembly. Unless noted otherwise, the data presented in this report are for blocked 

guide tubes. 

Figure 2.1 Prototypic 17×17 PWR components.

Stainless steel tubing was substituted for the fuel rod pins for hydraulic testing. The diameter of 

the stainless steel rods was slightly larger than prototypic pins, 9.525 mm versus 9.500 mm. 

Prototypic fuel rod end plugs were press fit into the ends of the stainless tubing. The dimensions 

of the assembly components are listed in Table 2.1. 

Top 

Grid Spacers Nozzle

8 Places

Mixing Spacers

3 Places

Bottom 

Nozzle

Guide 

Tubes

Top 

Nozzle

Grid 

Spacer

Guide 

Tubes
4 

Table 2.1 Dimensions of assembly components in the 17×17 PWR. 

Description Lower Section Upper Section

Number of Pins 264 264

Pin Diameter (mm) 9.525 9.525

Pin Pitch (mm) 12.6 12.6

Pin Separation (mm) 3.025 3.025

Number of Instrument Tubes 1 1

Number of Guide Tubes (G/T) 24 24

G/T Diameter (mm) 11.2 12.2

Axial Length (m) 0.704 3.268

Figure 2.2 shows the rod configuration of a typical 17×17 PWR assembly. Three different 

storage cells characterized by an inner dimension Dcell were studied. These cells are discussed 

next.

Figure 2.2 Rod configuration of a typical 17×17 PWR assembly.

x

y

z

G/T G/T G/T

G/T G/T

G/T G/T G/T G/T G/T

G/T G/T G/T G/T

G/T G/T G/T G/T G/T

G/T

G/T G/T G/T

G/T

Lmin

Dcell
5 

2.2 Storage Cells

A major difference between BWR and PWR assemblies is the absence of the channel box in the 

PWR. Without a channel box component, the pool or cask storage cell defines the peripheral 

flow boundaries for the PWR assembly (i.e., similar to a BWR canister). The extent of the gap 

between the outer row of rods and the inside cell wall influences the nature of flow inside the 

bundle. In order to study this effect, three different sized storage cells were tested. The three 

sizes were chosen to represent two common commercial sizes and one small cell size that 

minimized the annular flow much like the BWR canister. Table 2.2 lists the dimensions of cells 

used in three Holtec dry casks and one pool rack. The outer dimension of the 17×17 spacer is

214.0 mm (8.43 in.) and represents the smallest possible storage cell that would fit on the 

assembly. The internal dimensions of the commercial cells range considerably from a low of 

222.2 mm (8.75 in.) to a high of 229.9 mm (9.05 in.). 

Since there is variation in the size of the cells used commercially, three different sized pool cells 

were tested as indicated in gray in Table 2.2 and depicted in Figure 2.2 as dimension Dcell. The 

base case was the 217.5 (8.56 in.) cell with minimal annular flow area. Although this size is not 

found commercially, it is an important case for comparison purposes as it minimizes the 

complexity of the annular gap flow. The two other experimental storage cell sizes are 221.8 mm 

(8.73 in.) similar to that found in the Holtec MPC-24E/EF cask and 226.6 mm (8.92 in.) like 

found in the Holtec MPC-24 cask. This span of sizes includes the size used in a typical Holtec 

spent fuel pool rack. 

Table 2.2 Internal dimensions of commercial cask, pool cells, and areas of as-built experimental cells. 

 

 

Number

in Cask

Length 

(mm)

Width 

(mm)

Experimental Storage

Cell Dimension, Dcell (mm)

Minimum Annular

Gap, Lmin (mm)

17×17 spacer - 214.0 214.0 217.5 1.75

MPC-32 22 223.3 223.3

 8 223.3 227.1

2 227.1 227.1

MPC-24E/EF 20 222.2 222.2 221.8 3.9 

 4 229.9 229.9

MPC-24 24 226.6 226.6 226.6 6.3

 

Holtec pool - 224.8 224.8

2.3 Air Flow Control

Air was metered into the bottom of the assembly with eight mass flow controllers (MKS 

Instruments Inc. Model 1559A). The upper flow ranges in standard liters per minute (slpm) of 

each controller are listed in the table inset in Figure 2.3. Figure 2.3 also shows a diagram of the 

flow metering and flow straightening components as well as photographs of the equipment used. 

The metered air was conditioned to produce a uniform velocity profile at the inlet to the 

assembly. The flow from all the flow controllers was routed through a baffled manifold to mix 
6 

the flows and equally distribute flow to the bottom of a square flow straightener. The flow 

straightener consisted of a course screen, followed by a plastic honeycomb, followed by a fine 

screen. The selection of straightening components and their placement are based on the results 

of Farell and Youssef.2

 

Figure 2.3 Diagram and photographs of the flow control and flow straightening systems. 

Air in

Primary Manifold

Secondary

Manifold

Course Screen

Plastic Honey Comb

Fine Screen

Table

Storage 

Cell

Bottom Nozzle

Debris Catcher

Tube Bundle

Flow Straightener

Mass Flow

Controllers

Baffle

Air in

Air in

MKS 1559A 

Flow Controller Max Flow (slpm)

MF1 100

MF2 200

MF3 300

MF4 300

MF5 300

MF6 300

MF7 400

MF8 400

MF 7

MF 6

MF 3

MF 4

MF 5

MF 2

MF 1

MF 8

Secondary

ifld

Secondary

Manifold

Primary

Manifold

Flow

Controllers

Flow

Straightener
7 

2.4 Pressure Drop Measurements

Figure 2.4 shows the layout of the PWR pressure drop experimental assembly, including all 

available pressure port locations. Three Paroscientific Digiquartz differential pressure 

transducers (Model 1000-3D) were plumbed directly to the desired pressure ports. These 

pressure gauges use a highly sensitive quartz crystal to measure slight changes in differential 

pressure (resolution ~0.02 Pa). For this report the pressure drop across two ports is reported as 

the low side port first followed by the high side port, e.g., the overall pressure drop across the 

entire assembly is reported as A–36 (where “A” denotes ambient). Unless noted otherwise, the 

measurements described hereafter were taken with the guide tubes blocked. These guide tubes 

were blocked at the top, which is open, by inserting tapered rubber plugs into each tube. Figure 

2.5 shows the lower section of the guide tube including the transition in the outer diameter and 

the location of the drain holes. 

Measurements were recorded directly to the hard drive of a PC-based data acquisition system 

every 2 seconds using a LabView 8.2 interface. These measurements included the air flow rate 

through the assembly, ambient air temperature, ambient air pressure, and the assembly pressure 

drops. The LabView interface was used to automatically change the air flow rate according to a 

prescribed program which allowed a greater number of flow rate settings than in previous 

testing. 

With each pressure transducer plumbed to two set port locations and with the air flow off, 

pressure drop measurements were recorded for a period of roughly 1 minute. These 

measurements were termed zero flow measurements and allowed for correction of any zero drift

in the transducer. Next, the air flow was set to the desired rate with pressure drop readings 

subsequently acquired for 2 minutes. The air flow was then stopped, and zero flow 

measurements were again taken for 1 minute. This procedure was repeated for different air flow 

rates. A typical set of pressure traces are shown in Figure 2.6. The pressure spikes 

in this figure evident during the reestablishment of flow are discarded before averaging for the 

pressure drops. Also, the slight zero drift of the transducer was corrected by subtracting the 

average of the zero flow measurements taken prior to and after each respective flow test. The 

zero corrections of the pressure drops were less than 0.92 N/m2

, which occurred during an 

overall A–36 pressure drop measurement. 

Additionally, the BWR characterized in a previous study documented in SAND2007-2270 was 

re-tested using the improved automated procedures described previously.1

 The pressure port 

locations for the BWR assembly are shown in Figure 2.7. 
8 

Figure 2.4 Experimental PWR apparatus showing as-built port locations.

Bottom nozzle/Debris 

catcher

B

C

D

E

F

G

H

I

J

K

1

2

3

4

5

6

7

8

10

9

11

12

14

15

17

18 19

21

13

22

23 24 25 26 27 28 29

16

34

35

32

20

30 31

33

36

z

“A” = Ambient Top nozzle

Port z (m)

A 4.047

1 3.972

2 3.914

3 3.849

4 3.621

5 3.398

6 3.331

7 3.132

8 3.078

9 2.875

10 2.810

11 2.612

12 2.557

13 2.353

14 2.287

15 2.088

16 2.034

17 1.831

18 1.767

19 1.613

20 1.536

21 1.461

22 1.307

23 1.242

24 1.165

25 1.086

26 1.006

27 0.928

28 0.849

29 0.771

30 0.704

31 0.532

32 0.444

33 0.353

34 0.180

35 0.106

36 0.011
9 

Figure 2.5 Lower detail of the PWR guide tube. 

0

20

40

60

80

100

120

140

0 2000 4000 6000 8000 10000 12000

Time (sec)

∆P (N/m2

)

34-36 30-34 A-36

 Figure 2.6 Pressure traces recorded during a typical flow profile for measurements

 across 34–36, 30–34, and A–36. 

Bottom tie plate

Grid spacer “J”

Debris catcher “K”

OD = 11.2 mm

OD = 12.2 mm

GT Drain holes –

4 places, ∅ = 2.31 mm
10

Figure 2.7 Experimental BWR apparatus showing as-built port locations.

2.4.1 Hydraulic Loss Coefficients

As discussed previously, one goal of this research was to determine the SLAM and Σk coefficients 

for use with thermal-hydraulic codes. The cross-sectional areas and hydraulic diameters used in 

the hydraulic analyses to follow are presented in Table 2.3. These reference hydraulics are 

computed from the bundle cross sections in the assemblies and do not account for contractions 

encountered at spacers and nozzle/tie plate elements. The reference hydraulic diameter is 

defined according to convention, or four times the flow area divided by the wetted perimeter. 

Cross section 

below partial 

Cross section 

above partial 

Port “B”

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

z

Port z (m)

1 4.19

2 4.15

3 3.73

4 3.69

5 3.45

6 3.22

7 3.18

8 2.71

9 2.66

10 1.68

11 1.64

12 1.41

13 1.17

14 1.13

15 0.66

16 0.62

17 0.13

B 0.00
11

 Table 2.3 Summary of the reference flow areas and hydraulic diameters of the laminar flow 

characterization experiments. 

Description Storage Cell Dimension, 

Dcell (mm)

Flow Area, 

AAssembly (m2) DH, Ref. (m)

PWR Upper Bundle 217.5 0.0256 0.0105

PWR Lower Bundle 217.5 0.0260 0.0108

PWR Upper Bundle 221.8 0.0275 0.0113

PWR Lower Bundle 221.8 0.0279 0.0116

PWR Upper Bundle (Unblocked Guide Tubes) 221.8 0.0299 0.0113

PWR Lower Bundle (Unblocked Guide Tubes) 221.8 0.0279 0.0116

PWR Upper Bundle 226.6 0.0296 0.0121

PWR Lower Bundle 226.6 0.0301 0.0124

BWR Upper (Partially Populated) 132.6 0.0106 0.0141

BWR Lower (Fully Populated) 132.6 0.0098 0.0119

Curve fits to the pressure drop data were used to determine the SLAM and Σk coefficients of the 

assembly. The technique used to determine these coefficients was successfully validated by 

investigation of flow in a simple annulus for which an analytic value of SLAM is known, see 

Appendix A for details. The determination of these coefficients is discussed next. The major, 

or viscous, pressure loss is expressed in Equation 1 as a function of the average z-component of 

velocity in the assembly, WAssembly. 

2

Assembly

major

H, Ref.

L ρ W P

D 2 f

   ⋅ ∆ =   

  

1 

The friction factor for laminar flow is written explicitly as

flow) (bundle 100 

, where flow) (pipe 64 S S

LAM

LAM

=

= = Re f 2 

Reynolds number is defined for these studies as

Assembly H, Ref. ρW D

μ

Re ⋅ ⋅ = 3 

Substituting for the Reynolds number yields 

Assembly

major LAM 2

H, Ref.

L Wμ P S

D 2

   ⋅ ∆ =      

4 

The minor, or form, pressure drops across the assembly are given by 
12

2

Assembly

minor

ρ W P k

2

  ⋅ ∆ =  

  ∑ 5 

Curve fits to pressure drop data are presented in the following format. In Equation 6, the 

quadratic term accounts for the minor losses and the linear term for the major losses. 

2 PW W total 2 Assembly 1 Assembly ∆ = ⋅ +⋅ a a 6 

The assembly velocity is determined from the measurement of the volumetric flow of air through 

the assembly as detailed in Section 2.3. The assembly velocity is computed by the following 

conversion in Equation 7. The standard density is taken at 0°C and 1 atm. The measured density 

is determined from local temperature and atmospheric pressure using the ideal gas law.

( )

( )

( )

std tot 3

meas.

Assembly 2

Assembly

ρ Q slpm ρ 1 m 1 min W ms

A m 1000 liters 60 sec

 

⋅        = ⋅⋅        

7 

Because the total pressure drop is simply the sum of the major and minor pressure drops, the 

SLAM and Σk coefficients may now be determined explicitly.

2

H, Ref.

LAM 1

2

D

S 2

Lμ

2 k

ρ

a

a

  = ⋅   ⋅  

⋅ ∑ =

8 

2.5 Laser Doppler Anemometry Measurements

Laser Doppler anemometry (LDA) is a non-intrusive, optical technique used to measure the 

instantaneous velocity in a flow field at the intersection of two coherent laser beams. The most 

common method of LDA used at present is the dual-beam anemometer system. Typically, a 

single laser beam is split into two mutually coherent polarized light waves, which intersect to 

form a spheroid-shaped region called the measuring volume. Particles passing through the 

measuring volume with a given velocity scatter light from the light beams to produce the LDA 

signal. For the investigations detailed herein, a dual-beam system operating in backscatter mode 

as shown in Figure 2.8 was used. The photodetector was a photomultiplier (PM), and a Bragg 

cell was used to introduce a reference frequency, allowing the measurement of near-zero 

velocities. The signal was then processed in a burst analyzer and sent to a PC-based data 

acquisition system.
13

Figure 2.8 Dual-beam backscatter LDA system components and principles.

A visual interpretation of the operation of the dual-beam LDA is given by the fringe model. This 

model avoids reference to the Doppler shift effect and instead makes use of the interference 

fringes created in the probe volume by the crossing of two incident coherent light beams. The 

wave fronts of the two beams form interference fringes with spacing dfr. The bright fringes are 

created from the constructive interference of the incident light beams and the dark fringes are a 

result of destructive interference. The fringe spacing dfr is a function of the half angle of the 

beam intersection and the wavelength of the incident light beams. The velocity of a particle 

passing perpendicular between fringes is then the division of the fringe spacing and the time 

between subsequent signal peaks. This model represents an oversimplification of the actual 

physics and signal processing involved in the LDA technique but is presented to give the 

unaccustomed reader some understanding of the instrument capability and functionality. Further 

information on the LDA technique can be found in Durst and Melling as well as Albrecht, et 

al.

3,4

2.5.1 LDA Experimental Setup

The average velocity and root-mean-square (RMS) velocity fluctuations were measured in these 

experiments by a single-component laser-Doppler anemometer (Dantec 1-D FlowExplorer). 

This LDA system is composed of the FlowExplorer probe head, a photomultiplier, a burst 

analyzer, a motorized stage and controller unit, a PC-based data acquisition (DAQ) system, and 

data processing software. These components are listed in Table 2.4. 

Figure 2.9 shows the layout of the test components for LDA measurements. The LDA probe is 

mounted externally to the PWR assembly on a motorized stage. The laser beams pass through 

the optical window into the assembly and measure the velocity at the intersection of the beams. 

In this manner the local velocity can be measured across the assembly in between rod banks. 

Figure 2.10 gives two photographs of the LDA setup. These photographs depict a measurement 

just inside the optical window. 

t (measured)

Signal

Time

Measuring volume Backscattered light

Flow with particles

dfr (known)

Bragg Laser

cell

Processor

Photomultiplier
14

Table 2.4 Detailed list of the LDA system components. 

Description Manufacturer Serial Number

FlowExplorer probe head Dantec Dynamics 0115

BSA F60 – Burst analyzer Dantec Dynamics 437

Photomultiplier Dantec Dynamics 119

1-D Stage Isel Automation 505

1-D Stage controller Isel Automation 502

DAQ – PC Dell F51KYD1

Figure 2.9 Schematic of the LDA system for measuring velocity profiles in the PWR 17×17 assembly.

Figure 2.10 Photographs showing the LDA probe system in relation to the fuel assembly.

z

y

x

Direction of 1-D 

automatic stage travel

Optical window 

Velocity 

profile along 

dashed line 

LDA probe head

PWR 17×17 assembly
15

3 PRESSURE DROP RESULTS 

3.1 217.5 mm Storage Cell

Since there is variation in the size of the cells used commercially for storing spent PWR 

assemblies, three different sized storage cells were tested. The base case is the 217.5 (8.56 in.) 

cell with minimal annular flow area. Although this size is not found commercially, this size cell

is an important case for comparison purposes as it minimizes the complexity of the annular gap 

flow. The base case PWR storage cell is analogous to the BWR canister.

3.1.1 Overall Pressure Drop

3.1.1.1 Overall Pressure Drop Dependence on Reynolds Number

Figure 3.1 shows the overall assembly pressure drop as a function of Reynolds number in the 

bundle of the PWR (A–36) and BWR (1–B) assemblies. The Reynolds number for the PWR is 

determined from the upper bundle, reference hydraulic diameter and the assembly velocity. The 

Reynolds number for the BWR is determined from the lower bundle, reference hydraulic 

diameter and the assembly velocity. The BWR data is added for comparison and includes the 

new data collected in the present study along with the data collected in the previous study.1 The 

PWR assembly is contained inside of the smallest, 217.5 mm storage cell that is sized to be 

analogous to the BWR canister. The water rods in the BWR and the guide tubes in the PWR are 

blocked to flow. At all Reynolds numbers, the pressure drop across the PWR is significantly 

larger than across the BWR assembly. 

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re

∆P (N/m2

)

PWR-217.5mm BWR-2008 BWR-2005

Figure 3.1 Assembly pressure drop as a function of Reynolds numbers for analogous PWR and BWR fuel 

bundles.
16

3.1.1.2 Pressure Drop with Axial Position

Figure 3.2 shows the axial pressure drop in a PWR assembly for three different flows when 

placed inside the smallest storage cell. The size of this storage cell is comparable to the canister 

on a BWR assembly. The pressure drop measured in the BWR assembly is shown for 

comparison. The pressure drop in the PWR is significantly higher than in the BWR assembly. 

The pressure drop along the PWR bundle and across the PWR spacers is slightly greater than the 

corresponding locations in the fully populated lower section of the BWR assembly and 

significantly greater than in the upper partially populated section of the BWR assembly. 

Figure 3.2 Assembly pressure drop as a function of axial height for analogous PWR and BWR fuel 

bundles.

3.1.2 Hydraulic Loss Coefficients

3.1.2.1 Full Flow Range SLAM-Σk Analysis

The following is an example SLAM-Σk analysis of the curve fit to pressure drop data for the full 

range of laminar flows. Please refer to Figure 2.4 for the location of the pressure ports described 

next. The data in Figure 3.3 refer to the pressure drops across pressure ports 34–36, 30–34, and 

A–36 for the assembly inside the 217.5 mm storage cell. The following analysis assumes that 

the hydraulic loss coefficients are not significant functions of the laminar flow Reynolds number. 

In the Section 3.1.2.2, the same data are analyzed in a partitioned fashion to show the Reynolds 

number dependence. The technique used to determine the hydraulic loss coefficients was 

successfully validated by investigation of flow in a simple annulus for which an analytic value 

for SLAM is known, see Appendix A for details. 

Note

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

z (m)

∆P (N/m2

)

: The pressure drops are plotted versus the corresponding assembly velocity for each 

section. The reference hydraulic diameter and flow area of the upper portion of the assembly 

  PWR  BWR Re = 150 450 900

∆P (N/m2) 

z
17

were used to calculate SLAM and Σk coefficients for the A–36 data, since these hydraulically 

characterize the bulk of the assembly. 

y = 2.47E-01x2

 + 3.46E+00x

R2

 = 1.00E+00

y = 1.43E+01x2 + 4.56E+01x

R2

 = 1.00E+00

y = 2.48E+00x2 + 4.10E+00x

R2

 = 1.00E+00

0

20

40

60

80

100

120

140

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Vbundle (m/s)

∆P (N/m2

)

34-36 30-34 A-36

Figure 3.3 Pressure drop as a function of average assembly velocity for the PWR fuel mockup inside the 

217.5 mm storage cell. 

The relevant information for the calculation of the overall SLAM and Σk coefficients are given in

Table 3.1. Uncertainties in the SLAM and Σk coefficients listed in this report are taken as ±5 and 

±1.4, respectively. See Appendix B for details. 

Table 3.1 SLAM and Σk coefficient analysis data for pressure drops between 

34–36, 30–34, and A–36 for the 217.5 mm storage cell. 

Pressure 

Drop L(m) AAssembly (m2) DH, Ref. (m) a1 (N·s/m3) a2 (N·s2/m4) SLAM Σ k

34–36 0.1688 0.0260 0.0108 4.10 2.48 305 5.0

30–34 0.5244 0.0260 0.0108 3.46 0.247 83.0 0.50

A–36 4.0472 0.0256 0.0105 45.6 14.3 135 29

This analysis assumes air properties at local ambient conditions, typically ρ = 0.98 kg/m3 and 

μ = 1.85×10-5 N·s/m2

. Changes in air temperature and pressure are taken into account for 

measurements collected during different experimental runs.

A summary of the SLAM and Σk coefficients for the 217.5 mm storage cell testing is shown in

Table 3.2. These values were determined from the full experimental flow rate range of 30 to 

2100 slpm, or Reynolds numbers of 10 to 1000, respectively. The reference hydraulic diameter 

and flow area of the upper section was used to calculate the SLAM and Σk values for any span 

including the upper section, e.g., A–36. Values of SLAM and Σk for segments 34–36 and 30–34 

WAssembly (m/s)
18

are calculated in two ways: 1) using the reference hydraulics of upper bundle section (DH, Ref. = 

0.0105 m) and 2) using the reference hydraulics of lower bundle section (DH, Ref. = 0.0108 m).

The second set of SLAM and Σk represent the actual local hydraulic conditions. The first set of 

SLAM and Σk parameters are needed to appropriately integrate the segment results for comparison 

with the overall (A–36) results as described next.

The single section/spacer SLAM and Σk values can be manipulated to recreate the values observed 

in the multiple section/spacer data. To accomplish this, the values of SLAM and Σk must be 

calculated with the same hydraulic parameters (i.e., DH, Ref. and flow area) as used in the overall 

analysis. Additionally, SLAM values must be weight averaged based on flow length. Equation 9 

shows the general format for calculating the effective SLAM coefficient of an assembly span with 

an overall flow length of Ltot, “I” number of spacers (including flow nozzles and IFMs), and “J” 

number of bundle sections. This effective SLAM coefficient is tabulated near the lower right hand 

corner of Table 3.2. The directly observed value of SLAM for the overall pressure drop was 

132.9, which denotes an error of less than 0.2% from the length-averaged value of 132.7. 

I J

sp,i LAMsp,i sect,j LAMsect,j

i 1 j 1

LAM,eff

tot

LS L S

S

L

= =

    ⋅+ ⋅

  =

∑ ∑

9 

The form loss coefficients will simply be the total of the Σk values for the individual segments. 

This value of 30.7 is provided near the bottom of the “Σk” column in Table 3.2. The directly 

measured value of Σk for the overall assembly pressure drop was 30.6, which indicates an error 

of about 0.3%. These two comparisons provide a measure of assurance that the values of SLAM

and Σk presented here provide a consistent set of data. 
19

Table 3.2 Full flow range SLAM and Σk coefficients for the PWR assembly in the 217.5 mm storage cell. 

Segment Description DH, Ref. (m) SLAM Σk L (m) SLAM·(L/Ltot)

A–3 Top Nozzle 0.0105 107.1 1.5 0.2097 5.5

3–5 Long Bundle 0.0105 76.1 1.4 0.4509 8.5

5–6 Spacer 0.0105 418.4 2.0 0.0667 6.9

6–7 Short Bundle 0.0105 82.4 1.0 0.1990 4.1

7–8 IFM 0.0105 283.2 1.4 0.0545 3.8

8–9 Short Bundle 0.0105 77.0 0.4 0.2021 3.8

9–10 Spacer 0.0105 466.3 1.9 0.0656 7.6

10–11 Short Bundle 0.0105 81.1 0.8 0.1979 4.0

11–12* IFM 0.0105 290.8 1.4 0.0545 3.9

12–13* Short Bundle 0.0105 77.2 0.7 0.2043 3.9

13–14 Spacer 0.0105 432.1 2.0 0.0661 7.1

14–15 Short Bundle 0.0105 72.1 0.8 0.1995 3.6

15–16 IFM 0.0105 294.2 1.5 0.0534 3.9

16–17 Short Bundle 0.0105 73.3 0.3 0.2027 3.7

17–18 Spacer 0.0105 492.5 1.9 0.0646 7.9

18–22 Long Bundle 0.0105 80.7 1.0 0.4604 9.2

22–23 Spacer 0.0105 480.0 1.6 0.0646 7.7

23–29 Long Bundle 0.0105 77.2 1.5 0.4710 9.0

29–30 Spacer 0.0105 424.3 2.2 0.0667 7.0

30–34 Long Bundle 0.0105 77.4 0.5 0.5244 10.0

30–34 Long Bundle 0.0108 83.0 0.5† -- --

34–36 Bottom Nozzle 0.0105 284.7 4.9 0.1688 11.9

34–36 Bottom Nozzle 0.0108 305.3 5.0† -- --

Summation Overall (equiv.) 0.0105 -- 30.7 4.0472 132.7

A–36 Overall (meas.) 0.0105 132.9 30.6 4.0472 -- * Due to a blockage in port 12, segments 11–12 and 12–13 values are averages of the remaining 

IFM spacers and short bundle segments, respectively.

† These form losses are not included in the sum total.

3.1.2.2 Partitioned Flow Range SLAM-Σk Analysis

The previous analysis assumed that the hydraulic loss coefficients are not significant functions of 

the laminar flow Reynolds number. In this section, the same overall assembly (A–36) pressure 

drop data are analyzed in a partitioned fashion to show the Reynolds number dependence. The 

data were divided into three partitions of approximately equal number of data points. Each 

partition of data was analyzed for SLAM and Σk using the same approach described in the 

previous section. 

Figure 3.4 shows the SLAM and Σk for the three-partition analysis of data for the 217.5 mm cell. 

The points represent the SLAM and Σk for the corresponding average Reynolds number for the

data included in the partition. The horizontal bars represent the range of Reynolds numbers over 

which the hydraulic loss coefficients were calculated. The vertical bars represent the error for 

the SLAM and Σk calculated by the method detailed in Appendix B. The error is large for small 

Reynolds numbers and decreases as the Reynolds number increases. The dashed black lines 

represent the overall SLAM and Σk values reported in Table 3.2. The yellow shading about the 

black dashed lines represents the experimental error associated with the overall SLAM and Σk
20

values. The error range for all the partitioned data overlaps with the error range of the overall 

SLAM and Σk. The hydraulic loss coefficients appear to exhibit negligible Reynolds number 

dependence especially when considering the magnitude of the error at the lowest Reynolds 

number. 

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re mid

SLAM,

Σ

k

SLAM k

Figure 3.4 Overall assembly (A–36) hydraulic loss coefficients as a function of Reynolds number for the 

217.5 mm storage cell. 

3.2 221.8 mm Storage Cell

The 221.8 mm (8.743 in.) size storage cell can be found in the Holtec MPC-24E/EF cask. This 

size of storage cell is the smallest used in Holtec PWR storage casks.

3.2.1 Overall Pressure Drop

3.2.1.1 Overall Pressure Drop Dependence on Reynolds Number with Blocked Guide Tubes

Figure 3.5 shows the overall assembly pressure drop as a function of Reynolds number in the 

bundle of the PWR and BWR assemblies. The PWR assembly is contained inside of the midsized, 221.8 mm storage cell. This size storage cell represents the smallest commonly found in 

commercial dry storage casks. The water rods in the BWR and the guide tubes in the PWR are 

plugged. At all Reynolds numbers, the pressure drop across the PWR is similar to the pressure 

drop across the BWR assembly. The pressure drop across the BWR assembly is slightly lower 

than the pressure drop across the PWR assembly at low Reynolds numbers and nearly equal at 

higher Reynolds numbers. 
21

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

∆P (N/m2

)

PWR-221.8mm BWR-2008 BWR-2005

Figure 3.5 Pressure drop as a function of Reynolds numbers across the BWR fuel assembly and the PWR 

fuel assembly in the 221.8 mm storage cell. 

3.2.1.2 Overall Pressure Drop Dependence on Reynolds Number with Unblocked Guide 

Tubes

Figure 3.6 shows the overall assembly pressure drop as a function of Reynolds number across the 

PWR assembly in the 221.8 mm storage cell with blocked and unblocked guide tubes. With the 

guide tubes open to flow, the flow area of the assembly increases from 0.0275 m2 to 0.0299 m2

but the hydraulic diameter remains unchanged (see Table 2.3). At all Reynolds numbers, the 

pressure drop across the unblocked PWR is greater than to the pressure drop across the blocked

PWR assembly. The increase in flow area provided by the unblocked guide tubes reduces the 

average flow velocity and Reynolds number for any given volumetric flow rate. 

Figure 3.7 presents the same pressure drop data for blocked and unblocked guide tubes but now 

as a function of total flow rate through the assembly. At any given flow rate, the pressure drop 

across the assembly with unblocked guide tubes is less than the pressure drop across the 

assembly with blocked guide tubes. The difference is due to the increased flow through the 

unblocked guide tubes. 

The two data sets in Figure 3.7 were each fit to a quadratic equation with excellent correlation 

results. The quadratic correlations were solved for flow at a number of pressure drops and

differenced to calculate the flow rate through the guide tubes. Figure 3.8 shows the fraction of 

flow through the guide tubes as a function of total flow through the PWR assembly with 

unblocked guide tubes. The fraction of flow in the guide tubes drops from about 9% at low 

flows to about 5% at high flows. 
22

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

∆P (N/m2

)

Blocked Unblocked

Figure 3.6 Pressure drop as a function of Reynolds numbers across the PWR fuel assembly in the 221.8 mm 

storage cell with blocked and unblocked guide tubes. 

∆P = 1.734E+04Q2

 + 1.070E+03Q

R2

 = 9.998E-01

∆P = 1.821E+04Q2 + 1.181E+03Q

R2

 = 9.998E-01

0

10

20

30

40

50

60

70

80

90

100

0.00 0.01 0.02 0.03 0.04 0.05

Q (m3/s)

∆P (N/m2

)

Unblocked Blocked

Figure 3.7 Pressure drop as a function of volumetric flow rate across the PWR fuel assembly in the 221.8 

mm storage cell with blocked and unblocked guide tubes. 
23

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 0.01 0.02 0.03 0.04 0.05

Qtot (m3

/s)

QGT / Qtot

Figure 3.8 Fraction of flow in guide tubes as a function of total flow through the PWR fuel assembly in the 

221.8 mm storage cell with unblocked guide tubes. 

3.2.2 Hydraulic Loss Coefficients

3.2.2.1 Full Flow Range SLAM-Σk Analysis with Blocked Guide Tubes 

A summary of the SLAM and Σk coefficients for the 221.8 mm storage cell tested with blocked 

guide tubes is shown in Table 3.3. These values were determined from the full experimental 

flow rate range of 30 to 2100 slpm, or Reynolds numbers of 10 to 1000, respectively. The 

reference hydraulic diameter and flow area of the upper section was used to calculate the SLAM

and Σk values for any span including the upper section, e.g., A–36. Values of SLAM and Σk for 

segments 34–36 and 30–34 are again calculated in two ways: 1) using the reference hydraulics 

of upper bundle (DH, Ref. = 0.0113 m) section and 2) using the reference hydraulics of lower 

bundle section (DH, Ref. = 0.0116 m). The second set of SLAM and Σk represent the actual local 

hydraulic conditions. The first set of SLAM and Σk parameters are needed to appropriately 

integrate the segment results for comparison with the overall assembly (A–36). The directly 

observed value of SLAM for the overall pressure drop was 109.9, which denotes an error of less 

than 0.5% from the length-averaged value. The directly measured value of Σk for the overall 

assembly pressure drop was 27.7, which indicates an error of about 0.7%.
24

Table 3.3 Full flow range SLAM and Σk coefficients for the PWR assembly in the 221.8 mm storage cell with 

blocked guide tubes. 

Segment Description DH, Ref. (m) SLAM Σk L (m) SLAM·(L/Ltot)

A–3 Top Nozzle 0.0113 113.2 1.4 0.2097 5.9

3–5 Long Bundle 0.0113 65.6 1.2 0.4509 7.3

5–6 Spacer 0.0113 357.6 1.9 0.0667 5.9

6–7 Short Bundle 0.0113 57.7 0.9 0.1990 2.8

7–8 IFM 0.0113 231.2 1.1 0.0545 3.1

8–9 Short Bundle 0.0113 56.0 0.5 0.2021 2.8

9–10 Spacer 0.0113 364.6 1.5 0.0656 5.9

10–11 Short Bundle 0.0113 68.3 0.9 0.1979 3.3

11–12 IFM 0.0113 237.2 1.1 0.0545 3.2

12–13 Short Bundle 0.0113 50.7 0.5 0.2043 2.6

13–14 Spacer 0.0113 394.9 1.9 0.0661 6.5

14–15 Short Bundle 0.0113 57.4 0.7 0.1995 2.8

15–16 IFM 0.0113 276.7 1.4 0.0534 3.7

16–17 Short Bundle 0.0113 47.5 0.3 0.2027 2.4

17–18 Spacer 0.0113 383.5 1.8 0.0646 6.1

18–22 Long Bundle 0.0113 62.4 1.2 0.4604 7.1

22–23 Spacer 0.0113 366.7 1.8 0.0646 5.8

23–29 Long Bundle 0.0113 65.4 1.5 0.4710 7.6

29–30 Spacer 0.0113 314.5 1.3 0.0667 5.2

30–34 Long Bundle 0.0113 73.0 1.6 0.5244 9.5

30–34 Long Bundle 0.0116 77.9 1.7† -- --

34–36 Bottom Nozzle 0.0113 238.7 3.4 0.1688 10.0

34–36 Bottom Nozzle 0.0116 255.0 3.5† -- --

Summation Overall (equiv.) 0.0113 -- 27.9 4.0472 109.4

A–36 Overall (meas.) 0.0113 109.9 27.7 4.0472 -- † These form losses are not included in the sum total.

3.2.2.2 Full Flow Range SLAM-Σk Analysis with Unblocked Guide Tubes

A summary of the SLAM and Σk coefficients for the 221.8 mm storage cell testing with unblocked 

guide tubes is shown in Table 3.4. These values were determined from the full experimental 

flow rate range of 30 to 2100 slpm, or Reynolds numbers of 10 to 1000, respectively. The 

reference hydraulic diameter and flow area of the upper section was used to calculate the SLAM

and Σk values for any span including the upper section, e.g., A–36. The increased flow area and 

wetted perimeter for the inside of the guide tubes is included in these calculations. As in the 

previous sections, values of SLAM and Σk for segments 34–36 and 30–34 are again calculated in 

two ways: 1) using the reference hydraulics of upper bundle (DH, Ref. = 0.0113 m) section and 2) 

using the reference hydraulics of lower bundle section (DH, Ref. = 0.0116 m). The second set of 

SLAM and Σk represent the actual local hydraulic conditions. The first set of SLAM and Σk 

parameters are needed to appropriately integrate the segment results for comparison with the 

overall assembly (A–36). Since the lower guide tube section does not carry flow, the lower 

bundle hydraulics are the same in the blocked and unblocked cases. The directly observed value 

of SLAM for the overall pressure drop was 108.6, which denotes an error of less than 1.3% from 
25

the length-averaged value. The directly measured value of Σk for the overall assembly pressure 

drop was 31.7, which indicates an error of about 0.6%.

At a value of 108.6, the SLAM for the unblocked case is not significantly lower than SLAM = 109.9 

for the blocked guide tube case. However, the difference in the form loss parameter, Σk, is more 

significant. For the unblocked case, the form losses are 31.7. This represents a substantial 

increase from the blocked case of 27.7 and is well above the experimental uncertainty of uk = 

1.4. 

Table 3.4 Full flow range SLAM and Σk coefficients for the PWR assembly in the 221.8 mm storage cell with 

unblocked guide tubes. 

Segment Description DH, Ref. (m) SLAM Σk L (m) SLAM·(L/Ltot)

A–3 Top Nozzle 0.0113 116.7 1.5 0.2097 6.0

3–5 Long Bundle 0.0113 60.6 1.6 0.4509 6.8

5–6 Spacer 0.0113 339.8 2.2 0.0667 5.6

6–7 Short Bundle 0.0113 58.9 0.9 0.1990 2.9

7–8 IFM 0.0113 235.7 1.2 0.0545 3.2

8–9 Short Bundle 0.0113 52.0 0.6 0.2021 2.6

9–10 Spacer 0.0113 335.6 1.9 0.0656 5.4

10–11 Short Bundle 0.0113 59.9 1.0 0.1979 2.9

11–12 IFM 0.0113 239.9 1.2 0.0545 3.2

12–13 Short Bundle 0.0113 49.4 0.6 0.2043 2.5

13–14 Spacer 0.0113 389.1 2.1 0.0661 6.4

14–15 Short Bundle 0.0113 56.9 0.8 0.1995 2.8

15–16 IFM 0.0113 263.8 1.6 0.0534 3.5

16–17 Short Bundle 0.0113 46.6 0.4 0.2027 2.3

17–18 Spacer 0.0113 358.1 2.0 0.0646 5.7

18–22 Long Bundle 0.0113 62.3 1.5 0.4604 7.1

22–23 Spacer 0.0113 364.0 1.9 0.0646 5.8

23–29 Long Bundle 0.0113 61.9 1.9 0.4710 7.2

29–30 Spacer 0.0113 293.5 1.5 0.0667 4.8

30–34 Long Bundle 0.0113 78.2 1.7 0.5244 10.1

30–34 Long Bundle 0.0116 76.5 1.5† -- --

34–36 Bottom Nozzle 0.0113 248.5 4.0 0.1688 10.4

34–36 Bottom Nozzle 0.0116 243.2 3.5† -- --

Summation Overall (equiv.) 0.0113 -- 31.9 4.0472 107.3

A–36 Overall (meas.) 0.0113 108.6 31.7 4.0472 -- † These form losses are not included in the sum total.

3.2.2.3 Partitioned Flow Range SLAM-Σk Analysis with Blocked Guide Tubes

Figure 3.9 shows the SLAM and Σk for the three-partition analysis of data for the 221.8 mm cell. 

The points represent the SLAM and Σk for the corresponding average Reynolds number of the data 

used in the analysis. The horizontal bars represent the range of Reynolds numbers over which 

the hydraulic loss coefficients were calculated. The vertical bars represent the error for the SLAM

and Σk calculated by the method detailed in Appendix B. The error is large for small Reynolds 

numbers and decreases as the Reynolds number increases. The dashed black lines represent the 

respective overall SLAM and Σk values reported in Table 3.3. The yellow shading about the black 
26

dashed lines represents the experimental error associated with the overall SLAM and Σk values. 

The error range for all the partitioned data overlaps with the error range of the overall SLAM and 

Σk. The hydraulic loss coefficients appear to exhibit negligible Reynolds number dependence. 

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re mid

SLAM, Σ

k

SLAM k

Figure 3.9 Overall assembly (A–36) hydraulic loss coefficients as a function of Reynolds number for the 

221.8 mm storage cell and blocked guide tubes. 

3.2.2.4 Partitioned Flow Range SLAM-Σk Analysis with Unblocked Guide Tubes

Figure 3.10 shows the SLAM and Σk for the three-partition analysis of data for the 221.8 mm cell 

with unblocked guide tubes. The points represent the SLAM and Σk for the corresponding average 

Reynolds number of the data used in the analysis. The horizontal bars represent the range of 

Reynolds numbers over which the hydraulic loss coefficients were calculated. The vertical bars 

represent the error for the SLAM and Σk calculated by the method detailed in Appendix B. The 

error is large for small Reynolds numbers and decreases as the Reynolds number increases. The 

dashed black lines represent the respective overall SLAM and Σk values reported in Table 3.4. 

The yellow shading about the black dashed lines represents the experimental error associated 

with the overall SLAM and Σk values. The error range for all the partitioned data overlaps with 

the error range of the overall SLAM and Σk. The hydraulic loss coefficients appear to exhibit 

negligible Reynolds number dependence. 
27

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re mid

SLAM, Σ

k

SLAM k

Figure 3.10 Overall assembly (A–36) hydraulic loss coefficients as a function of Reynolds number for the 

221.8 mm storage cell and unblocked guide tubes. 

3.3 226.6 mm Storage Cell

The 226.6 mm (8.920 in.) size storage cell can be found in the Holtec Holtec MPC-24 cask. This 

size storage cell is among the largest used in Holtec dry casks. All of the 24 cells in the MPC-24 

cask are this size. There are a few large cells in other Holtec casks, but they are not significant in 

number. The MPC-32 casks has two (of 32) cells that are 227.1 mm and the MPC-24E/EF has 

four (of 24) cells that are 229.9 mm. 

3.3.1 Overall Pressure Drop

3.3.1.1 Overall Pressure Drop Dependence on Reynolds Number

Figure 3.11 shows the overall assembly pressure drop as a function of Reynolds number in the 

bundle of the PWR and BWR assemblies. The PWR assembly is contained inside of the largest 

sized, 226.6 mm storage cell. This size storage cell represents the largest commonly found in 

commercial dry storage casks. The water rods in the BWR and the guide tubes in the PWR are 

blocked. At all Reynolds numbers, the pressure drop across the PWR is significantly less than 

the pressure drop across the BWR assembly.
28

0

10

20

30

40

50

60

70

80

0 200 400 600 800 1000

Re

∆P (N/m2

)

PWR-226.6mm BWR-2008 BWR-2005

Figure 3.11 Pressure drop as a function of Reynolds numbers across the BWR fuel assembly and the PWR 

fuel assembly in the 226.6 mm storage cell. 

3.3.2 Hydraulic Loss Coefficients

3.3.2.1 Full Flow Range SLAM-Σk Analysis

A summary of the SLAM and Σk coefficients for the 226.6 mm storage cell testing is shown in 

Table 3.5. These values were determined from the full experimental flow rate range of 30 to 

2100 slpm, or Reynolds numbers of 10 to 1000, respectively. The reference hydraulic diameter 

and flow area of the upper section was used to calculate the SLAM and Σk values for any span 

including the upper section, e.g., A–36. Values of SLAM and Σk for segments 34–36 and 30–34 

are calculated in two ways: 1) using the reference hydraulics of upper bundle (DH, Ref. = 0.0121 

m) section and 2) using the reference hydraulics of lower bundle section (DH, Ref. = 0.0124 m). 

The second set of SLAM and Σk represent the actual local hydraulic conditions. The first set of 

SLAM and Σk parameters are needed to appropriately integrate the segment results for comparison 

with the overall (A–36). The directly observed value of SLAM for the overall pressure drop was 

98.5, which denotes an error of about 1% from the length-averaged value. The directly measured 

value of Σk for the overall assembly pressure drop was 27.4, which indicates an error of about 

1.1%.
29

Table 3.5 Full flow range SLAM and Σk coefficients for the PWR assembly in the 226.6 mm storage cell. 

Segment Description DH, Ref. (m) SLAM Σk L (m) SLAM·(L/Ltot)

A–3 Top Nozzle 0.0121 89.9 1.4 0.2097 4.7

3–5 Long Bundle 0.0121 65.7 1.4 0.4509 7.3

5–6 Spacer 0.0121 303.4 1.6 0.0667 5.0

6–7 Short Bundle 0.0121 52 0.7 0.1990 2.6

7–8 IFM 0.0121 227.7 1.0 0.0545 3.1

8–9 Short Bundle 0.0121 51.7 0.5 0.2021 2.6

9–10 Spacer 0.0121 269.2 1.6 0.0656 4.4

10–11 Short Bundle 0.0121 57.3 1.1 0.1979 2.8

11–12 IFM 0.0121 194.3 1.0 0.0545 2.6

12–13 Short Bundle 0.0121 53.3 0.6 0.2043 2.7

13–14 Spacer 0.0121 302.1 1.8 0.0661 4.9

14–15 Short Bundle 0.0121 53.9 0.8 0.1995 2.7

15–16 IFM 0.0121 223.1 1.2 0.0534 2.9

16–17 Short Bundle 0.0121 45.7 0.4 0.2027 2.3

17–18 Spacer 0.0121 341.9 1.8 0.0646 5.5

18–22 Long Bundle 0.0121 56 1.2 0.4604 6.4

22–23 Spacer 0.0121 322.7 1.6 0.0646 5.1

23–29 Long Bundle 0.0121 60 1.7 0.4710 7.0

29–30 Spacer 0.0121 296.7 1.6 0.0667 4.9

30–34 Long Bundle 0.0121 68.1 1.5 0.5244 8.8

30–34 Long Bundle 0.0124 72.4 1.5† -- --

34–36 Bottom Nozzle 0.0121 223.5 3.3 0.1688 9.3

34–36 Bottom Nozzle 0.0124 237.8 3.4† -- --

Summation Overall (equiv.) 0.0121 -- 27.7 4.0472 97.5

A–36 Overall (meas.) 0.0121 98.5 27.4 4.0472 -- † These form losses are not included in the sum total.

3.3.2.2 Partitioned Flow Range SLAM-Σk Analysis

Figure 3.12 shows the SLAM and Σk for the three-partition analysis of data for the 226.6 mm cell. 

The points represent the SLAM and Σk for the corresponding average Reynolds number of the data

used in the analysis. The horizontal bars represent the range of Reynolds numbers over which 

the hydraulic loss coefficients were calculated. The vertical bars represent the error for the SLAM

and Σk calculated by the method detailed in Appendix B. The error is large for small Reynolds 

numbers and decreases as the Reynolds number increases. The dashed black lines represent the 

respective overall SLAM and Σk values reported in Table 3.5. The yellow shading about the black 

dashed lines represents the experimental error associated with the overall SLAM and Σk values. 

The error range for almost all the partitioned data overlaps with the error range of the overall 

SLAM and Σk. The hydraulic loss coefficients appear to exhibit a slight Reynolds number 

dependence but the magnitude of the error at the lowest Reynolds numbers casts doubt on this 

interpretation.
30

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re mid

SLAM, Σ

k

SLAM k

Figure 3.12 Overall assembly (A–36) hydraulic loss coefficients as a function of Reynolds number for the 

226.6 mm storage cell. 

3.4 Boiling Water Reactor Assembly

3.4.1 Hydraulic Loss Coefficients

3.4.1.1 Full Flow Range SLAM-Σk Analysis with Blocked Water Rods

A summary of the SLAM and Σk coefficients for the BWR assembly with blocked water rods is 

shown in Table 3.6. These measurements repeat those conducted in 2005 at SNL but include a 

more refined flow control capability. The reference hydraulic loss coefficients calculated in the 

present investigations are within the experimental error from those documented in SAND2007-

2270 (2005 – SLAM = 106, Σk = 37).

1

 These values were determined from the full experimental 

flow rate range of 15 to 600 slpm, or Reynolds numbers of 20 to 850, respectively. The 

hydraulic diameter and flow area of the upper and lower sections of the BWR assembly are listed 

in Table 2.3. The hydraulic diameter and flow area of the lower fully populated bundle section 

were used to calculate the SLAM and Σk values for any span including the lower section, e.g., 1–

B. Values of SLAM and Σk for segments in the upper section are calculated in two ways: 1) using 

the reference hydraulics of lower section (DH, Ref. = 0.0119 m) section and 2) using the reference

hydraulics of upper section (DH, Ref. = 0.0141 m). The second set of SLAM and Σk represent the 

actual local hydraulic conditions. The first set of SLAM and Σk parameters are needed to 

appropriately integrate the segment results for comparison with the overall assembly (1–B). The 

directly observed value of SLAM for the overall pressure drop was 104.2, which denotes an error 

of less than 1% from the length-averaged value. The directly measured value of Σk for the 

overall assembly pressure drop was 37.8, which also indicates an error of less than 1%. 
31

Table 3.6 Full flow range SLAM and Σk coefficients for the BWR assembly with blocked water rods. 

Segment Description DH, Ref. (m) SLAM Σk L (m) SLAM·(L/Ltot)

1–2 Top Tie 0.0119 44.4 0.4 0.040 0.4

1–2 Top Tie 0.0141 66.7 0.4† -- --

2–3 Long Bundle 0.0119 34.8 0.3 0.411 3.4

2–3 Long Bundle 0.0141 52.3 0.3† -- --

3–4 Spacer 0.0119 313.3 2.6 0.044 3.3

3–4 Spacer 0.0141 471.0 3.1† -- --

4–6 Long Bundle 0.0119 38.5 0.9 0.468 4.3

4–6 Long Bundle 0.0141 57.8 1.0† -- --

6–7 Spacer 0.0119 298.6 2.6 0.042 3.0

6–7 Spacer 0.0141 448.9 3.0† -- --

7–8 Long Bundle 0.0119 48.0 0.5 0.469 5.4

7–8 Long Bundle 0.0141 72.2 0.5† -- --

8–9 Spacer 0.0119 733.6 3.4 0.044 7.8

9–10 2×Long Bundles + Spacer 0.0119 105.4 5.0 0.980 24.7 

10–11 Spacer 0.0119 707.7 3.4 0.044 7.5

11–13 Long Bundle 0.0119 77.2 0.9 0.467 8.6

13–14 Spacer 0.0119 720.3 3.3 0.044 7.6

14–15 Long Bundle 0.0119 75.1 0.8 0.468 8.4 

15–16 Spacer 0.0119 739.1 3.3 0.043 7.5

16–17 Long Bundle 0.0119 73.0 0.7 0.470 8.2

17–B Bottom Tie 0.0119 124.5 10.0 0.127 2.3

Summation Overall (equiv.) 0.0119 -- 38.1 4.190 103.4 

1–B Overall (meas.) 0.0119 104.2 37.8 4.190 --

3.4.1.2 Partitioned Flow Range SLAM-Σk Analysis with Blocked Water Rods

Figure 3.13 shows the SLAM and Σk for the three-partition analysis of data for the BWR 

assembly. The horizontal bars represent the range of Reynolds numbers over which the 

hydraulic loss coefficients were calculated. The vertical bars represent the error for the SLAM and 

Σk calculated by the method detailed in Appendix B. The error is large for small Reynolds 

numbers and decreases as the Reynolds number increases. The dashed black lines represent the 

respective overall SLAM and Σk values reported in Table 3.6. The yellow shading about the black 

dashed lines represents the experimental error associated with the overall SLAM and Σk values. 

The hydraulic loss coefficients appear to exhibit a Reynolds number dependence. The SLAM

increases from 94 to 109 at Remid = 75 to 770, respectively. Similarly, the Σk decreases from 69 

to 35 at Remid = 75 to 770, respectively. 
32

0

20

40

60

80

100

120

140

160

0 200 400 600 800 1000

Re mid

SLAM, Σ

k

SLAM k

Figure 3.13 Overall assembly (1–B) hydraulic loss coefficients as a function of Reynolds number for the 

BWR with blocked water rods. 

3.5 PWR Storage Cell Size Dependence

Three different sized PWR storage cells were tested to determine the effect of the storage cell 

size on the hydraulic viscous and form loss parameters. The smallest storage cell tested was 

217.5 mm and is constrained by the size of the spacer, which is 214 mm. The other two storage 

cells tested were 221.8 mm and 226.6 mm, which span the sizes of the most common storage 

cells. The largest storage cell found in the three dry casks considered is approximately 230 mm 

(see Table 2.2). 

3.5.1 Full Flow Range 

The geometry of the annular flow path is fundamentally different in each of the storage cells. 

The hydraulic diameter of the storage cell increases as the flow area of the annular region 

increases. This change in annular flow areas between different storage cells affects the 

distribution of flow between the bundle and annular regions. The hydraulic loss parameters are 

also affected. Figure 3.14 shows the dependence of the SLAM and Σk on the storage cell 

hydraulic diameter based on data from the full range of laminar flows (Re = 10 to 1000). 

The full-flow-range SLAM drops from 134.0 at DH, Ref. = 0.0105 m (217.5 mm cell) to 110.7 at DH, 

Ref. = 0.0113 m (221.8 mm cell) to 98.6 at DH, Ref. = 0.0121 m (226.6 mm cell). An empirical 

power law correlation was developed to aid in assigning hydraulic parameters to storage cell 

sizes not tested. The validity of this correlation is limited to 17×17 PWR fuel. In the limit as the 

cells size increases, the SLAM asymptotically approaches the value of 57 for a square duct [Kays 

and Crawford, Fig 6-4, p. 63].5

 A power law correlation was chosen because it could be forced 

to approach this limiting value.
33

The full-flow-range form loss coefficient, Σk, shows less dependence on cell size. For DH, Ref. = 

0.0105 m (217.5 mm cell), Σk is 30.9 and drops to 28.0 at DH, Ref. = 0.0113 m (221.8 mm cell) 

and 27.8 at DH, Ref. = 0.0121 m (226.6 mm cell). A power law correlation was also used to fit the 

form loss data. 

0

20

40

60

80

100

120

140

160

0.01 0.011 0.012 0.013 0.014

DH (m)

SLAM, Σ

k

SLAM k

SLAM = 57 + 1.891E-7 · DH

-4.348E+0

R2 = 0.994

Σk = 9.872E-1 · DH

-7.527E-1

R2 = 0.817

Figure 3.14 Dependence of overall assembly (A–36) SLAM and Σk on the hydraulic diameter for full data 

range (Re = 10 to 1000). The validity of this correlation is limited to 17×17 PWR fuel.
34

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35

4 VELOCITY PROFILE RESULTS 

Velocity profiles were measured across the bundle for the three pool cells included in this study. 

These profiles are valuable in estimating the flow partition between the bundle and annular 

regions within the assembly. These measurements also indicated a redistribution of flow after 

spacers and intermediate flow mixers (IFMs) at higher flow rates, suggesting significant wake 

effects. The wake disturbances in the flow as shown in Section 4.1.3 were generally not 

apparent in the mid-bundle measurements, which may suggest that the flow has reestablished a 

fully developed condition. 

Figure 4.1 shows the definition of interior and annular cells within the assembly. An interior cell 

is defined as the interstitial space formed between four fuel rods with an area of Aint. An interior 

cell formed by the interstitial space formed between three fuel rods and a guide tube has an area 

defined as Aint-GT. Similarly, an annular cell is the interstitial space formed by two fuel rods and 

the storage cell wall with an area of Aann, cell. The distance Lann is the length between the inner 

storage cell wall and the centerlines of the outermost rod bank. The dashed lines show a portion 

of the traverses captured by the LDA. 

Figure 4.1 Definition of interior and annular cells for determining the partitioning of flow inside the 

assembly. 

Table 4.1 shows the area and number of the two types of interior cells. The sum of these cells 

constitutes the area defined as the bundle in the following analyses. The definition of the bundle 

and annulus are shown schematically in Figure 4.2. This figure also shows the locations of the 

LDA traverses. The bundle is taken as the portion of the assembly inside the planes formed by 

the centerlines of the outer rods. The annular region is the portion of the assembly from this 

boundary to the inner cell walls. 

Table 4.1 Bundle cell values of area.

Interior Interior - GT

Area (m2) 8.75×10-5 7.61×10-5

Quantity 156 100

Abundle (m2) 0.02126

Interior cell Annular cell

Aint Aint-GT

Interior cell – GT

Lann

 

 

 

Aann, cell

GT =

Guide Tube
36

Figure 4.2 Schematic showing the definition of the bundle (shaded) and annular (white) flow paths in the 

PWR assembly.

Table 4.2 gives the annular values for the different storage cells used in this study. The annular 

area to total area ratio are 0.170, 0.227, and 0.282 for the 217.5, 221.8, and 226.6 mm storage 

cells, respectively. The flow partition between the bundle and annular regions is strongly 

influenced by this ratio. As the annular area ratio is increased, the amount of flow in this region 

increases significantly. This effect is discussed in more detail in the following sections.

Table 4.2 Annular and assembly hydraulic values for the different storage cells. 

Storage Cell (mm) Lann (mm) Aann, cell (m2) Aann (m2) Atot (m2)

217.5 7.96 6.47×10-5 0.00434 0.02560

221.8 10.11 9.18×10-5 0.00624 0.02750

226.6 12.51 1.22×10-4 0.00834 0.02960

The ratio of the integrated average velocity along the lines shown in Figure 4.1 to the area 

integrated average velocity is of particular importance in interpreting these results. Since only 

the line average is available from the LDA measurements, a limited number of computational 

fluid dynamics (CFD) runs were conducted to determine this ratio. A PWR bundle section with 

the same geometry was simulated in FLUENT with the laminar solution model to calculate this 

ratio as summarized in Table 4.3. The area to line ratios of both the interior and annular cells 

were averaged for the two Reynolds numbers in each storage cell for the LDA analysis. The 

resulting average ratios are 0.741 (interior) and 0.961 (annular) for the 217.5 mm cell, 0.739 

(interior) and 0.903 (annular) for the 221.8 mm cell, and 0.732 (interior) and 0.893 (annular) for 

the 226.6 mm cell. 

Abundle

Aann

x

y

y = 94.5 mm

z

z = 1.537 m

z = 1.326 m

z = 2.787 m
37

Table 4.3 Velocity values from CFD simulations of the PWR fuel assembly. 

Cell Size (mm)

217.5 221.8 226.6

Re 100 900 100 900 100 900

Winlet (m/s) 0.1690 1.6000 0.1570 1.4900 0.1460 1.3870

Interior: Warea, avg 0.1904 1.7398 0.1561 1.5022 0.1136 1.2889

Interior: Wline, avg 0.2570 2.3458 0.2109 2.038 0.1536 1.7793

Interior: area, avg

line, avg

W

W

      0.741 0.742 0.740 0.737 0.740 0.724

Interior: area, avg

line, avg avg

W

W

      0.741 0.739 0.732

Annular: Warea, avg 0.1256 1.3400 0.1961 1.7496 0.2467 1.8654

Annular: Wline, avg 0.1310 1.3923 0.2211 1.9041 0.2810 2.0530

Annular: area, avg

line, avg

W

W

      0.959 0.962 0.887 0.919 0.878 0.909

Annular: area, avg

line, avg avg

W

W

      0.961 0.903 0.893

Two additional CFD simulations were conducted to explore the appropriateness of the laminar 

model in interpreting the LDA results. These simulations are summarized in Table 4.4. Both of 

these turbulent simulations give similar area to line ratios as those determined from the laminar 

model. Since the Reynolds numbers for the rod bundle in the current study are within the 

accepted laminar regime as defined in Cheng and Todreas, the laminar model results are used in 

subsequent sections for interpretation of the LDA data.

6

Table 4.4 Velocity values from transitional and turbulent CFD simulations of the 217.5 mm storage cell. 

217.5 mm Cell

Turbulence model k-ω Realizable k-ε

Re 900 900

Winlet (m/s) 1.6 1.6

Interior: Warea, avg 1.7667 1.7400

Interior: Wline, avg 2.1963 2.1872

Interior: area, avg

line, avg

W

W

      0.804 0.795

Annular: Warea, avg 1.3445 1.3553

Annular: Wline, avg 1.4000 1.3800

Annular: area, avg

line, avg

W

W

      0.960 0.982

The volumetric flow rate of the bundle is estimated by taking the product of the bundle area, the 

integrated line average of the LDA data in the bundle, and the ratio of the area to line average 

velocity from the CFD calculations (see ( area, avg line, avg )avg W W in Table 4.3) as shown in Equation 

10. 
38

area, avg

bundle bundle bundle,LDA

line, avg avg,CFD-int

W

Q= W WA

  ⋅ ⋅     

10

Similarly, the volumetric flow in the annulus is estimated by taking the product of the annular 

area, the integrated line average LDA velocity in the annulus, and the CFD-derived area to line 

ratio for the annular region as shown in Equation 11. 

area, avg

ann ann ann,LDA

line, avg avg,CFD-ann

W

Q= W WA

  ⋅ ⋅ 

 

11

Finally, an equivalent, assembly-averaged velocity (i.e. inlet velocity assuming uniform 

distribution) is derived from these two calculated quantities (Equation 12) to compare with the 

value measured directly from the mass flow controllers (Equation 7). The value calculated in 

Equation 7 is termed the measured, assembly average velocity. Comparison of these values 

gives an estimate of the error in the flow partitioning calculated in these analyses.

bundle ann

avg, equiv.

tot

Q Q W =

A

+

12

4.1 226.6 mm Storage Cell

4.1.1 Mid-Bundle Velocity Measurements

The velocity measurements detailed in this section were taken at y = 94.5 mm and z = 1.537 m in 

between spacers “H” and “I” (see Figure 4.2) for the largest storage cell (226.6 mm). This 

location corresponds to the middle of a long bundle run in between the two rod banks closest to 

the storage cell wall. Figure 4.3 shows a typical, normalized velocity profile taken inside the 

assembly. This profile was acquired for Re = 50 and was normalized by the assembly average 

velocity. The definitions of the bundle and annular regions are marked on the graph (x = 100.8 

mm). The dashed black lines indicate the LDA integrated line average velocities for each region. 

A no-slip condition was added to the profile at the storage cell wall for all velocity profiles in 

this report. The velocities display a periodicity that corresponds to the rod pitch of the assembly, 

the maxima occurring in the centers of interstitial spaces and the minima at the narrowest points 

between the rods. The integrated average velocity in the annulus is over twice that of the 

assembly average, indicating a substantial amount of flow in the annulus despite accounting for 

only 28.2% of the flow area.

Figure 4.4 and Figure 4.5 show the normalized velocity distribution in the assembly for Re = 100 

and Re = 200, respectively. These profiles are quite similar to that presented in Figure 4.3. 

Again, the annular average velocity is nearly twice that of the assembly average. The velocity 

profile is also periodic with the rod pitch in the assembly. These two profiles imply that the flow 

in the annulus is increasing slightly with increasing Reynolds number. 
39

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.3 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

for Re = 50. Note: the definitions of the bundle and annular regions are shown on the graph.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.4 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell for 

Re = 100.

Bundle

Annulus

Bundle

Annulus
40

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.5 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell for 

Re = 200.

As Reynolds number continues to increase above Re = 200, a larger portion of the flow begins to 

partition towards the bundle. Figure 4.6 gives the normalized velocity profile for Re = 350. 

Possible shear effects are evident near the transition from the bundle to the annulus. The 

minimum velocity that existed at this location is now greater than the assembly average velocity 

and is also shifted further into the bundle. The integrated average velocities in the bundle and 

annulus indicate the flow partition is biasing towards the bundle. 

Figure 4.7 illustrates the same trends in the velocity profile for Re = 500 as shown in Figure 4.6. 

The first minimum closest to the cell wall is again greater than the assembly average velocity and 

slightly displaced into the bundle, away from the location of smallest rod separation. The 

integrated average velocity in the bundle is greater than the assembly average velocity, and the 

normalized annular velocity continues to decrease. 

Figure 4.8 gives the normalized velocity profile for the highest Reynolds number observed in the 

LDA measurements, Re = 900. This profile displays similar behavior to those for Reynolds 

numbers of 350 and above. The minimum at the boundary of the bundle and annulus is again 

greater than the assembly average velocity. As the Reynolds number increases, the normalized 

average annular and bundle velocities are decreasing and increasing, respectively.

Bundle

Annulus
41

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.6 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell for 

Re = 350.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.7 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell for 

Re = 500.

Bundle

Annulus

Bundle

Annulus
42

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.8 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell for 

Re = 900.

Figure 4.9 shows the percentages of the total flow in the bundle (blue diamonds) and the annulus 

(red squares) as a function of Reynolds number. These values were determined using Equation 

10 and Equation 11. The amount of flow initially increases in the annulus up to Re = 200 and 

then begins to decrease. The maximum flow in the annulus is 58.7% with 41.3% in the bundle. 

The maximum flow in the bundle is 56.3% with 43.7% in the annulus. The average flow 

percentages over the entire Reynolds number range are 48.6 and 51.4% in the bundle and 

annulus, respectively. These results indicate that the flow is nearly divided in equal parts 

between the bundle and annulus for the largest storage cell (226.6 mm). 

Bundle

Annulus
43

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

Flow Percentage (%)

Bundle

Annulus

Figure 4.9 Percentages of total flow in the bundle (blue diamonds) and in the annulus (red squares) as a 

function of Reynolds number for the 226.6 mm storage cell. 

Table 4.5 gives the comparison between the measured and equivalent, assembly average 

velocities. The absolute maximum and minimum errors are 5.4 and 0.6%, respectively. These 

velocities are all within the experimental uncertainty of 0.012 m/s except for Re = 350 and 500. 

Although the partitions of flow should be viewed with a certain level of uncertainty because they 

are subject to the validity of a number of assumptions, the reasonable comparison of the 

measured and equivalent assembly velocities does suggest that the divisions of flow reported are 

confirmed to some extent. 

Table 4.5 Comparison of measured and equivalent, assembly average velocities for the 226.6 mm storage 

cell. 

Re Wavg, meas (m/s) Wavg, equiv. (m/s) Error (%)

50 0.073 0.074 1.6

100 0.146 0.138 -5.4

200 0.292 0.281 -3.7

350 0.511 0.525 2.7

500 0.730 0.778 6.6

900 1.388 1.395 0.6

4.1.2 Pre-Spacer Velocity Measurements

The velocity measurements detailed in this section were taken at y = 94.5 mm and z = 2.787 m 

upstream of spacer “D” (Figure 4.2) for the largest storage cell (226.6 mm). This location 

corresponds to the end of a bundle run in between the two rod banks closest to the storage cell 

wall. Figure 4.10 shows the normalized velocity profile for Re = 100. As in the previous 
44

section, the local velocity was normalized by the assembly average velocity. The definitions of 

the bundle and annular regions are marked on the graph (x = 100.8 mm). The dashed black lines 

indicate the LDA integrated line average velocities for each region. The velocities display a 

periodicity that corresponds to the rod pitch of the assembly, the maxima occurring in the centers 

of interstitial spaces and the minima at the narrowest points between the rods. The integrated 

average velocity in the annulus is higher prior to the spacer than at the mid-bundle location 

shown in Figure 4.4, suggesting that the flow is redistributing preferentially to the annulus. This 

result is not surprising because the spacer presents a flow contraction and would naturally deflect 

the approaching streamlines away from the bundle into a less constrained flow path, especially at 

the lowest Reynolds number. 

Figure 4.11 and Figure 4.12 show the normalized velocity distribution in the assembly for Re = 

350 and Re = 900, respectively. As in the mid-bundle profiles, these velocity measurements 

show evidence of the annular flow influencing the bundle flow near the partition. The minimum 

bundle flow at this point is greater than the assembly average velocity. The sample rate for the 

LDA was lower than nominal when capturing the annular region of the velocity profile in Figure 

4.11, which is the reason for the noise in the measurements. This condition was corrected once 

inside the bundle. 

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.10 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

before a spacer for Re = 100.

Bundle

Annulus
45

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.11 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

before a spacer for Re = 350.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.12 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

before a spacer for Re = 900.

Bundle

Annulus

Bundle

Annulus
46

The percentages of flow in the annulus and bundle at a z-location corresponding to just upstream 

of a spacer are presented in Figure 4.13. A redistribution of flow into the annulus is evident at 

the lowest Reynolds number, indicating the spacer may affect the upstream flow distribution. 

However, these effects are not as marked for Re > 200. Also, the CFD results used to interpret 

the LDA data were obtained for a fully developed laminar condition. This assumption of fully 

developed flow may not be appropriate with the addition of a flow contraction upstream of the 

measurements. The average flow percentages over the entire Reynolds number range are 48.4 

and 51.6% in the bundle and annulus, respectively. These results again indicate that the flow is 

nearly divided in equal parts between the bundle and annulus for the largest storage cell (226.6 

mm).

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

Flow Percentage (%)

Bundle

Annulus

Figure 4.13 Percentages of total flow in the bundle (blue diamonds) and in the annulus (red squares) as a 

function of Reynolds number for the 226.6 mm storage cell before a spacer. 

Table 4.6 gives the comparison between the measured and equivalent, assembly average 

velocities at the pre-spacer location. The absolute maximum and minimum errors are 25.2 and 

0.5%, respectively. These velocities are all within the experimental uncertainty of 0.012 m/s 

except for Re = 200 and 900. These comparisons again show reasonable agreement, particularly 

when considering the presence of the spacer may affect the distribution of flow at this location. 
47

Table 4.6 Comparison of measured and equivalent assembly average velocities for the 226.6 mm storage 

cell before a spacer. 

Re Wavg, meas (m/s) Wavg, equiv. (m/s) Error (%)

100 0.146 0.140 -4.3

200 0.292 0.219 -25.2

350 0.511 0.514 0.5

500 0.730 0.721 -1.2

900 1.388 1.300 -6.3

4.1.3 Post-Spacer Velocity Measurements

The velocity measurements detailed in this section were taken at y = 94.5 mm and z = 1.326 m 

downstream of spacer “I” (see Figure 4.2) for the largest storage cell (226.6 mm). This location 

corresponds to the beginning of a bundle run in between the two rod banks closest to the storage 

cell wall. Figure 4.14 shows the normalized velocity profile for Re = 100. As in previous 

sections, the assembly average velocity was used to normalize the local velocity. The definitions 

of the bundle and annular regions are marked on the graph (x = 100.8 mm). The dashed black 

lines indicate the LDA integrated line average velocities for each region. The velocities display 

a periodicity that corresponds to the rod pitch of the assembly, the maxima occurring in the 

centers of interstitial spaces and the minima at the narrowest points between the rods. The 

annulus to bundle ratio of integrated average velocity is considerably higher after the spacer than 

at the mid-bundle location, again suggesting that the flow is redistributing preferentially to the 

annulus at the spacers. The spacers present a flow contraction and would naturally deflect the 

approaching streamlines away from the bundle. The spacers are also designed to promote flow 

mixing in order to enhance heat transfer, which will strongly affect the flow distribution. 

Figure 4.15 and Figure 4.16 show the normalized velocity distribution in the assembly for Re = 

350 and Re = 900, respectively. These velocity measurements show evidence of the wake effects 

from the spacer. These effects are observed for Re ≥ 350 at this z-location. The initial effects 

are broadening and enhancement of every other maximum in the bundle velocity profile as 

shown in Figure 4.15. As Reynolds number increases, these wake structures become more 

pronounced as seen in Figure 4.16. This velocity profile may appear chaotic at first glance but is 

actually periodic at a frequency of twice the pitch, which corresponds to the repeating pattern of 

small turning vanes within the spacer. 
48

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.14 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

after a spacer for Re = 100.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.15 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

after a spacer for Re = 350.

Bundle

Annulus

Bundle

Annulus
49

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.16 Normalized velocity as a function of position inside the assembly in the 226.6 mm storage cell 

after a spacer for Re = 900.

Figure 4.17 shows the flow percentages in the bundle and annulus as calculated at the postspacer location for the largest storage cell (226.6 mm). These results suggest that the flow does 

redistribute into annulus around the spacers, particularly at lower Reynolds numbers. The 

average flow percentages over the entire Reynolds number range are 43.1 and 56.9% in the 

bundle and annulus, respectively. This flow partition indicates slightly higher flow in the 

annulus compared to mid-bundle location, 51.4%. However, the assumption of fully developed 

laminar flow in the CFD results is likely inappropriate as evidenced in the higher Reynolds 

velocity profiles and will lead to errors in the interpretation of the LDA data.

Bundle

Annulus
50

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

Flow Percentage (%)

Bundle

Annulus

Figure 4.17 Percentages of total flow in the bundle (blue diamonds) and in the annulus (red squares) as a 

function of Reynolds number for the 226.6 mm storage cell after a spacer. 

Table 4.7 gives the comparison between the measured and equivalent, assembly average 

velocities at the post-spacer location for the largest storage cell (226.6 mm). The absolute 

maximum and minimum errors are 20.2 and 10%, respectively. All the equivalent velocities are 

lower than the measured values. This discrepancy is most likely due to the use of fully 

developed CFD results to interpret velocity profiles that exhibit obvious wake effects from the 

spacer.

Table 4.7 Comparison of measured and equivalent assembly average velocities for the 226.6 mm storage 

cell after a spacer. 

Re Wavg, meas (m/s) Wavg, equiv. (m/s) Error (%)

50 0.073 0.059 -18.7

100 0.146 0.117 -20.2

200 0.292 0.234 -19.9

350 0.511 0.454 -11.2

500 0.730 0.657 -10

900 1.388 1.221 -12

4.2 221.8 mm Storage Cell

4.2.1 Mid-bundle Velocity Measurements

The velocity measurements detailed in this section were taken at y = 94.5 mm and z = 1.537 m in 

between spacers “H” and “I” (see Figure 4.2) for the middle-sized storage cell (221.8 mm). This 

location corresponds to the middle of a long bundle run in between the two rod banks closest to 
51

the storage cell wall. Figure 4.18 shows the normalized velocity profile taken inside the 

assembly for Re = 100. The definitions of the bundle and annular regions are marked on the 

graph (x = 100.8 mm). The dashed black lines indicate the LDA integrated line average 

velocities for each region. The ratio of the bundle to annulus integrated average velocity is 

greater than in the 226.6 mm storage cell, indicating more flow is now passing through the 

bundle rather than the annulus. 

Figure 4.19 and Figure 4.20 show the normalized velocity distribution in the assembly for Re = 

350 and Re = 900, respectively. These profiles also indicate that more flow is passing through 

the bundle than the annulus as compared to the 226.6 mm storage cell. The shear effects 

observed in Figure 4.6 at the bundle/annulus transition are not evident in Figure 4.19. These 

effects are apparent at the higher Reynolds number flow as shown in Figure 4.20, although not as 

pronounced. 

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.18 Normalized velocity as a function of position inside the assembly in the 221.8 mm storage cell for 

Re = 100.

Bundle

Annulus
52

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.19 Normalized velocity as a function of position inside the assembly in the 221.8 mm storage cell for 

Re = 350.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.20 Normalized velocity as a function of position inside the assembly in the 221.8 mm storage cell for 

Re = 900.

Bundle

Annulus

Bundle

Annulus
53

Figure 4.21 shows the percentages of the total flow in the bundle (blue diamonds) and the 

annulus (red squares) as a function of Reynolds number for the 221.8 mm storage cell. These 

values were determined using Equation 10 and Equation 11. The amount of flow is relatively 

constant across the entire flow range. The average flow percentages over the entire Reynolds 

number range are 65.0 and 35.0% in the bundle and annulus, respectively. These results indicate 

that more flow passes through the bundle than the annulus for the middle-sized storage cell 

(221.8 mm). 

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

Flow Percentage (%)

Bundle

Annulus

Figure 4.21 Percentages of total flow in the bundle (blue diamonds) and in the annulus (red squares) as a 

function of Reynolds number for the 221.8 mm storage cell. 

Table 4.8 gives the errors between the measured and equivalent average velocities for the 221.8 

mm storage cell. The average error of the equivalent velocity is -5.5%. While all the equivalent 

velocities are outside the experimental uncertainty with the exception of Re = 900, the relative 

agreement is again viewed as confirmation of the flow percentages calculated previously. 

Table 4.8 Comparison of measured and equivalent assembly average velocities for the 221.8 mm storage 

cell. 

Re Wavg, meas (m/s) Wavg, equiv. (m/s) Error (%)

50 0.079 0.064 -19.7

100 0.158 0.174 9.7

200 0.317 0.302 -4.5

350 0.554 0.506 -8.8

500 0.792 0.715 -9.6

900 1.504 1.504 0.0
54

4.3 217.5 mm Storage Cell

4.3.1 Mid-bundle Velocity Measurements

The velocity measurements detailed in this section for Reynolds numbers of 50, 100, 350, and 

900 were taken at y = 94.5 mm and z = 1.537 m in between spacers “H” and “I” (see Figure 4.2) 

for the 217.5 mm storage cell. The measurements for Re = 200 and 500 were taken at y = 18.9 

mm and the same z-location. Due to the close proximity of the annular wall to the first rod bank

and the resulting reflections, velocity measurements were not obtained in the annulus for the 

smallest storage cell. However, the annular velocity is estimated by subtracting the bundle flow 

from the assembly total and dividing by the annulus area. Figure 4.22 shows the normalized 

velocity profile in the 217.5 mm storage cell for Re = 100. Logically, the integrated average 

velocity in the bundle is greater than that observed in the two larger cells. This profile displays 

the same periodicity shown in previous sections. However, the difference in the maximum to 

minimum in the bundle is greater for the smallest cell.

Figure 4.23 gives the normalized velocity profile for Re = 350. The average velocity in the 

bundle has decreased slightly from the case of Re = 100, indicating more flow is going into the 

annulus as Reynolds number increases. This trend is also observed for Re = 900 in Figure 4.24. 

The average velocities in the annulus and bundle are nearly equal for this flow. The wake effects 

of the spacer are also evident in this profile indicating that the flow has not reestablished fully 

developed flow. These effects were not seen at the mid-bundle location for the two larger 

storage cells.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.22 Normalized velocity as a function of position inside the assembly in the 217.5 mm storage cell for 

Re = 100.
55

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.23 Normalized velocity as a function of position inside the assembly in the 217.5 mm storage cell for 

Re = 350.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120

x (mm)

w/W avg

Figure 4.24 Normalized velocity as a function of position inside the assembly in the 217.5 mm storage cell for 

Re = 900.
56

Figure 4.25 shows the percentages of flow in the bundle and annulus for the smallest storage cell 

(217.5 mm). These results indicate that flow in the bundle decreases with increasing Reynolds 

number. The average flow percentages were 88.8 and 11.2% in the bundle and annulus, 

respectively. These results are subject to greater uncertainty than the other storage cells because 

the annulus was not measured independently. The equivalent assembly average velocity 

therefore cannot be calculated.

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000

Re

Flow Percentage (%)

Bundle

Annulus

Figure 4.25 Percentages of total flow in the bundle (blue diamonds) and in the annulus (red squares) as a 

function of Reynolds number in the 217.5 mm storage cell. 
57

5 SUMMARY

These studies represent the first hydraulic characterizations of a full length, highly prototypic 

PWR fuel assembly in low Reynolds number flows. There are at least two advantages to the 

testing of full scale, prototypic components. First, the use of actual hardware and dimensionally 

accurate geometries eliminates any issues arising from scaling arguments. Second, many of the 

prototypic components contain intricacies by design that would not be reproduced by using 

simplified flow elements. While this approach yields results that are inherently specific to the 

fuel assembly under testing, the differences in commercial designs are considered minor, 

particularly when considering the hydraulics of the entire assembly.

The generic use of best estimate flow parameters available in the literature for the hydraulic 

analysis of a nuclear fuel assembly may significantly underestimate the resistance to laminar 

flow in the assembly. This underestimation leads to an overestimate of the cooling effects of 

naturally induced flows that develop in dry casks under normal storage conditions or wet pool 

cells during complete loss of coolant accidents. Early on, the underestimation of these 

parameters was balanced by the large safety margin in the evaluation of peak cladding 

temperature due to the low decay heat. As the applicants continue to increase the stored fuel 

decay heat, these parameters became important to the analysis. As such, the estimation of these 

parameters were estimated using CFD which was validated using the data in this report. 

A commercial 17×17 PWR fuel assembly was hydraulically characterized by measuring both 

pressure drops and velocities inside three different storage cells in the laminar regime. Two of 

the storage cell sizes (226.6 mm and 221.8 mm) were chosen to span the cell size commonly 

used in dry storage casks and the third size (217.5 mm) was chosen as a practical minimum that 

forced most the air flow through the tube bundle. These tests spanned Reynolds numbers from 

10 to 1000 based on the hydraulic diameter and average assembly velocity. The pressure drop 

results were used to calculate viscous and form loss coefficients, namely SLAM and Σk, 

respectively. The velocity profiles were used to estimate the partitioning of flow in the tube 

bundle and the annular region between the tube bundle and the storage cell wall. The velocity 

profile data also suggests that transition away from laminar flow behavior may begin at Reynolds 

numbers as low as 200. 

5.1 Pressure Drop Measurements

Pressure drop measurements were collected at 52 different flow rates between 25 and 2100 slpm. 

Three high precision quartz crystal differential pressure gauges collected data from 36 pressure 

ports. The pressure ports were positioned to allow characterization of all individual spacers and 

bundle runs along the axis of the assembly. Overall pressure drop data was used to calculate 

SLAM and Σk hydraulic loss coefficients. The technique used to determine these coefficients was 

successfully validated by investigation of flow in a simple annulus for which an analytic value 

for SLAM is known, see Appendix A for details. Hydraulic loss coefficients were also determined 

for individual assembly components by the same technique and integrated over the length of the 

assembly to determine equivalent overall coefficients. The equivalent overall coefficients were 

in excellent agreement with the directly measured overall coefficients in all cases tested. 
58

For reference, comparison was made with the BWR assembly characterized in a previous study. 

The BWR assembly was also re-tested, and the new pressure drop data is in excellent agreement 

with the previous study. 

The smallest PWR storage cell tested (217.5 mm) is analogous to a BWR canister. The overall 

pressure drop across the PWR assembly in this storage cell was significantly greater than the 

overall pressure drop across the BWR assembly. The BWR pressure drop is lower because the 

assembly has fewer grid spacers, and partial length rods result in a significant increase in flow 

area in the upper third of the assembly. The overall SLAM and Σk hydraulic parameters for the 

PWR assembly in the 217.5 mm storage cell were determined to be 132.9 and 30.6 respectively. 

The middle sized PWR storage cell (221.8 mm) tested represents the smallest cell typically used 

in commercial dry casks. The overall pressure drop across the PWR assembly in the 221.8 mm 

cell was found to be essentially the same as the overall pressure drop across the BWR assembly. 

The overall SLAM and Σk hydraulic parameters for the PWR assembly in the 221.8 mm storage 

cell were determined to be 109.9 and 27.7 respectively. 

The largest PWR storage cell tested (226.6 mm) represents the largest cell typically used in 

commercial dry casks. The overall pressure drop across the PWR assembly in the 226.6 mm cell 

was significantly lower than the overall pressure drop across the BWR assembly. The overall 

SLAM and Σk hydraulic parameters for the PWR assembly in the 226.6 mm storage cell were 

determined to be 98.5 and 27.4 respectively. 

The viscous loss coefficient, SLAM, exhibits a larger dependence on storage cell hydraulic 

diameter than the form loss coefficient, Σk. To aid in determining the appropriate coefficients to 

use with storage cell sizes not tested, empirical power law correlations were determined for SLAM

and Σk as a function of storage cell hydraulic diameter. The resulting correlations based on the

full range of flow rates tested (Re = 10 to 1000) are: 

SLAM = 57 + 1.891E-7 · DH, Ref.-4.348

Σk = 9.872E-1 · DH, Ref.-0.7527

where DH, Ref. is the storage cell hydraulic diameter in meters. The correlations should only be 

used for 17×17 PWR fuel assemblies with storage cells smaller than 230 mm. 

5.2 Assembly Velocity Measurements

Velocity profiles were measured across the PWR bundle using laser Doppler anemometry (LDA) 

These profiles are used in estimating the flow partition between the bundle and annular regions 

within the assembly. These measurements also indicated a redistribution of flow after spacers 

and intermediate flow mixers (IFMs) at higher flow rates, suggesting significant wake effects. 

The wake disturbances in the flow were not apparent in the mid-bundle measurements, which 

may suggest that the flow has reestablished a fully developed condition. 

The partitioning of flow between the bundle and annular regions showed a strong dependence on 

storage cell size and a weaker dependence on Reynolds number. For Re = 400 at the mid-bundle 

location, the percentage of annular flow was 12, 34, and 52% in the 217.5, 221.8, and 226.6 mm 
59

storage cells, respectively. In general the percentage of annular flow decreased with Reynolds 

number except in the 217.5 mm cell where the percentage increased from 5 to 20% at Re = 50 to 

900, respectively. 

61

6 REFERENCES

1. Lindgren, E.R. and Durbin, S.G., 2007, “Characterization of Thermal-Hydraulic and 

Ignition Phenomena in Prototypic, Full-Length Boiling Water Reactor Spent Fuel Pool 

Assemblies after a Complete Loss-of-Coolant Accident,” SAND2007-2270. 

2. Farell, C. and Youssef, S., 1996, “Experiments on Turbulence Management Using 

Screens and Honeycombs,” J. Fluids Eng., 118, 26-32. 

3. Durst, F., Melling, A., Whitelaw, J.H., 1981, Principles and Practice of Laser-Doppler 

Anemometry

4. Albrecht, H., Borys, M., Damaschke, N., and Tropea, C., 2003, 

, New York: Academic Press.

Laser Doppler and Phase 

Doppler Measurement Techniques

5. Kays, W.M. and M.E. Crawford, 1980, 

, Berlin: Spinger-Verlag.

Convective Heat and Mass Transfer

6. Cheng, S. and Todreas, N.E., 1986, “Hydrodynamic Models and Correlations for Bare 

and Wire-Wrapped Hexagonal Rod Bundles—Bundle Friction Factors, Subchannel 

Friction Factors and Mixing Parameters,” Nucl. Eng. Des., 92, 227-251. 

, Second 

Edition, New York, NY: McGraw- Hill.

63

APPENDIX A. ANALYTIC VALIDATION

The technique used to determine the hydraulic loss coefficients was successfully validated by the 

following investigation of flow in a simple annulus for which an analytic value for SLAM is 

known. The dimensions of the annulus were sized to represent flow in semi-infinite parallel 

plates and resulted in measurements that were within the normal operating range of the flow 

controllers and pressure gauges used in the larger PWR characterization study. The same flow 

controllers, pressure gauges, and control systems were used in the both this validation exercise 

and the PWR (and previous BWR) characterizations. 

The pressure drop in the annular flow area formed between two concentric sections of pipe was 

measured to compare with the known analytic solution. The outer and inner pipes were 4 in. and 

3 in. PVC, respectively. The average inner diameter (ID) of the 4 in. pipe was measured to be 

101.1 mm (3.980 in.), and the average outer diameter (OD) of the 3 in. pipe was measured to be 

89.0 mm (3.502 in.). Table A.1 summarizes the hydraulic characteristics of the annular flow 

region. The annulus has a hydraulic diameter of DH, Ref. = 12.1 mm (0.478 in.) and a flow area of 

1812 mm2 (2.809 in2).

Table A.1 Hydraulic characteristics of the annular flow region. 

Description Metric Value English Value

ID 89.0 mm 3.502 in.

OD 101.1 mm 3.980 in.

Area 1812 mm2 2.809 in2

Wetted perimeter 597.0 mm 23.505 in.

DH, Ref. 12.1 mm 0.478 in

Figure A.1 shows the flow area that was studied. Due to the manner of construction, the inner 

pipe ends 85.725 mm (3.375 in) below the outer pipe. However, all pressure ports were located 

below the top of the inner pipe. The inner pipe was centered by three screws at the top located at 

120° spacing (see the left photo in Figure 1) and by a 3 in. to 4 in. reducing coupling at the 

bottom. 
64

Figure A.1 Isometric and overhead views of the annular flow path. 

Figure A.2 shows the full length of the test section. A total of seven pressure ports were installed 

along the length of the outer pipe at intervals of 304.8 mm (12 in.). The bottom port, Port 7, was 

located 914.4 mm (36 in.) above the end of the outer pipe to ensure all measurements were taken 

after the flow was fully developed. As an added precaution, all measurements were taken at Port 

6 or above. 

Figure 2 Photographs of the annular test section. All dimensions are in millimeters.

Curve fits to the pressure drop data were used to determine the SLAM coefficient of the test 

assembly. The major, or viscous, pressure loss is expressed in Equation A.1. The length of the 

flow section, air velocity, and air density are denoted by L, V, and ρ, respectively.

Air 

inlet

Lentry = 

914.4

Port 7

Port 7

Port 6

Port 5

Port 4

Port 4

Port 3

Port 2

Port 1

304.8

304.8

304.8

304.8

304.8

304.8
65















 ⋅















 =∆

2

ρ V

D

L P

2

H

major f A.1

The friction factor for laminar flow from Kays and Crawford is written explicitly as5

, where (annular 96 S flow) S

LAM

LAM = = Re f A.2

Substituting for the Reynolds number yields 















 ⋅















 =∆

2

V μ

D

L SP 2

H

major LAM A.3

Curve fits to pressure drop data are presented in the format of Equation A.4. 

Pmajor a1 ⋅=∆ V A.4

The SLAM coefficient may now be determined explicitly.

















⋅ ⋅= L μ

D 2S

2

H

LAM a1 A.5

The following is an example SLAM analysis of the curve fit to pressure drop data. Please refer to 

Figure A.2 for the location of the pressure ports described next. The data in Figure A.3 refer to 

the pressure drops across pressure ports 6–1, 5–2, and 4–3 with lengths of 1524 mm (5 ft.), 914.4 

mm (3 ft.), and 304.8 mm (1 ft.), respectively. Using Equation A.5 and the linear curve fit 

coefficients, the SLAM coefficient was determined to be 95.7, 98.8, and 100.2 for the pressure 

flow length segments of 6–1, 5–2, and 4–3, respectively. The uncertainty in these coefficients is 

estimated to be uSLAM = ±3.4 based on the effects of uncertainties in the mass flow controller and 

pressure gauges on the curve fit coefficients.
66

y = 5.4914x

R2

 = 0.9967

y = 1.8906x

R2

 = 0.9927

y = 9.5821x

R2

 = 0.9969

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

V (m/s)

∆P (N/m2

)

6-1 (5 ft.)

5-2 (3 ft.)

4-3 (1 ft.)

Figure A.3 Pressure drop as a function of velocity in the annular region for different flow lengths. 

Table A.2 summarizes the data collected for this validation effort. All the SLAM’s determined 

from this analysis matched the analytic value of 96 (Kays and Crawford) within experimental 

uncertainty with the exception of the first run between ports 6–1.5 These ports were closest to 

the inlet and outlet, possibly encountering some secondary pressure losses. 

Table A.2 SLAM coefficient analysis data for pressure drops between ports 

 4–3, 5–2, and 6–1 in the annular flow region. 

Pressure 

Drop Run L(mm) a1 (N·s/m3) SLAM

4–3 1 304.8 1.8906 98.8

4–3 2 304.8 1.8621 97.4

4–3 3 304.8 1.8487 96.7

5–2 1 609.6 5.4914 95.7

5–2 2 609.6 5.4296 94.6

6–1 1 1524 9.5821 100.2

6–1 2 1524 9.4793 99.1

Finally, the pressure drop data were plotted against the analytic solution. Figure A.4, Figure A.5, 

and Figure A.6 show the pressure drop as a function of Reynolds number for the 4–3 (1 ft.), 5–2 
67

(3 ft.) and 6–1 (5 ft.) annular lengths, respectively. These data generally conform to the analytic 

solution with some noticeable deviation above a Reynolds number of approximately 1500. This 

increased pressure drop could indicate the beginning of the transition to turbulence. 

0

1

2

3

4

5

6

7

0 500 1000 1500 2000

Re

∆P (N/m2) 

Analytic Solution

Run 1

Run 2

Run 3

Figure A.4 Pressure drop as a function of Reynolds number across ports 4–3 (1 ft.). 
68

0

2

4

6

8

10

12

14

16

18

20

0 500 1000 1500 2000

Re

∆P (N/m2) 

Analytic Solution

Run 1

Run 2

Figure A.5 Pressure drop as a function of Reynolds number across ports 5–2 (3 ft.). 

0

5

10

15

20

25

30

35

0 500 1000 1500 2000

Re

∆P (N/m2) 

Analytic Solution

Run 1

Run 2

Figure A.6 Pressure drop as a function of Reynolds number across ports 6–1 (5 ft.). 
69

APPENDIX B. ERROR ANALYSIS

The error and uncertainty inherent to an experimental result are critical to the accurate 

interpretation of the data. Therefore, the uncertainties in the experimental measurements are 

estimated in this section. Results of this analysis are given, followed by a general description of 

the method used and a brief explanation of the source of each reported measurement uncertainty. 

The overall standard uncertainty of an indirect measurement y, dependent on N indirect 

measurements xi, is defined in Equation B.1. The standard uncertainty associated with an 

indirect measurement is analogous to the standard deviation of a statistical population. 

∑= 















∂

∂ =

N

i

i

i

u

x

y u

1

2

2 B.1

Here, u is used to define the standard uncertainty of a measurement and defines the bounds that 

include 95% of the possible data. 

B.1 Uncertainty in Assembly Velocity for the Apparatus

The uncertainty in the bundle velocity was determined using error propagation analysis (EPA) 

for the blocked guide tube measurements in the smallest storage cell (217.5 mm). The assembly

velocity was determined from Equation B.2 in which Qi is the volumetric flow rate in slpm for 

each flow controller, AAssembly is the cross sectional area of the assembly, R is gas constant for 

air, T is the ambient air temperature, and P is the ambient air pressure. The first term in the 

equation represents the conversion from slpm to kg/s. 

8

3

STP 1

Assembly

assembly

m Q 0.001ρ l R T W

60 s A P min

i

i=

  ⋅   ⋅ =          

∑

B.2

Equation B.3 gives the relation between the overall uncertainty of Wassembly and the contributions 

from the measurement uncertainties of Q, Τ, and P. 

Assembly

Assembly

2 2

8

tot 2 3 Q T

STP 1 Assembly Assembly 2

W 2 2

tot tot

2 2 P A

Assembly Assembly

RT Q R

0.001ρ

m P A P A l

s 60 min Q RT Q RT

P A P A

i

i

u u

u

u u

=

          +   ⋅   ⋅ ⋅    =  

       + +   

   ⋅ ⋅     

∑

B.3

Table B.1 summarizes the values used to determine the overall uncertainty of the assembly 

velocity. The overall uncertainty in WAssembly was found for the highest volumetric flow rate

achieved during testing, Qtot = 2300 slpm, at a typical ambient condition of T = 298 K, P = 

83,400 N/m2, and AAssembly = 0.0256 m2. The standard uncertainty was determined to be WAssembly

u

= 0.012 m/s. The uncertainty was most affected by the volumetric flow rate (Q) and air 
70

temperature (T) contributing 41 and 40% of the overall uncertainty, respectively. The 

uncertainty in the assembly hydraulic area contributed 14% to the overall uncertainty. The 

remainder was due to the uncertainty in the atmospheric pressure. 

Table B. 1 Measurement uncertainties and intermediate calculations for Vbundle. 

Measurement, xi Standard Uncertainty, ui

Influence Coefficient 

( ) Assembly

i

W

x

∂

∂

Section 

Containing 

Explanation

Volumetric Flow 

Rate, Q1

1.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q2

2.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q3

3.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q4

3.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q5

3.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q6

3.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q7

4.0 slpm

Assembly

RT

P A⋅

B.1.1

Volumetric Flow 

Rate, Q8

4.0 slpm

Assembly

RT

P A⋅

B.1.1

Ambient Air 

Temperature, Τ

1.1 K tot

Assembly

Q R

P A⋅

B.1.2

Ambient Air 

Pressure, P

110 Pa tot

2

Assembly

Q RT

P A⋅

B.1.3

Assembly Hydraulic 

Area, Aassembly

1.1 × 10-4 m2

tot

2

Assembly

Q RT

P A⋅

B.1.4

B.1.1 Uncertainty in Volumetric Flow Rate Q

The volumetric flow rate was controlled with eight MKS volumetric flow controllers operated in 

parallel (Model # 1559A-24174). The uncertainty of the volumetric flow rate was determined 

from the stated manufacturer’s upper uncertainty of 1% of full scale. The uncertainties in flow 

rate were 1 slpm for flow controller 1, 2 slpm for flow controller 2, 3 slpm for flow controllers 3 
71

through 6, and 4 slpm for flow controllers 7 and 8. The value shown in Table B.1 represents 

these standard uncertainties associated with the volumetric flow rate. 

B.1.2 Uncertainty in Ambient Air Temperature

The air temperature was measured with a standard k-type TC. The standard uncertainty for this 

type of TC is uT = 1.1 K. 

B.1.3 Uncertainty in Ambient Air Pressure

The air pressure was measured with a Setra Systems barometer (Model 276). The uncertainty of 

the ambient air pressure was taken from the manufacturer’s calibration sheet, which indicated an 

uncertainty in the instrument of ±0.1% of full scale (110,000 Pa). Therefore, the standard 

uncertainty in the pressure reading is uP = 110 Pa. 

B.1.4 Uncertainty in Assembly Cross Sectional Area

The inner dimension of the storage cell was measured to within ± 0.127 mm (0.005 in). The 

outer diameter of the simulated fuel rods was measured to within ± 0.0254 mm (0.001 in). This 

tolerance leads to a maximum uncertainty of 5.5 × 10-5 m

2 in the hydraulic area.

B.2 Uncertainty in Pressure Drop Measurements

The manufacturer of the Digiquartz pressure transducers used in these experiments lists a static 

error band of ±0.02% of full scale, or ±4.1 N/m2. This error band includes repeatability, 

hysteresis, and conformance. Furthermore, these error bands consider the zero-drift of the 

instrument over periods of up to 14 years. Conversations with the manufacturer indicate the 

experimental procedure followed for these investigations, namely the zero flow measurements to 

correct any zero drift and the relatively short experimental data collection times (~ 2 minutes), 

should place the uncertainty in any pressure data closer to the resolution of the instrument, or 1 

part per million of full scale. The largest observed zero drifts in the zero flow measurements 

were less than 0.92 N/m2, which is smaller than the plotted symbols in this report. 

B.3 Uncertainty in SLAM and Σk Coefficients

The following procedure was adopted to determine the uncertainty in the SLAM and Σk

coefficients. Because the greatest experimental uncertainty comes from the bundle velocity, the 

influence of the velocity on the quadratic curve fits was examined. The overall assembly 

pressure drops for the blocked guide tubes case were curve fit as a function of WAssembly ± 

WAssembly

u . Figure B.1 shows the resulting curve fits to the pressure drop data across the assembly 

in the smallest storage cell (217.5 mm). Using these curve fit coefficients, the error associated 

with the SLAM and and Σk coefficients may now be determined. This procedure was also 

followed for the pressure drops in the other two storage cells. 
72

0

20

40

60

80

100

120

140

160

0.0 0.5 1.0 1.5 2.0

VAssembly (m/s)

∆P (N/m2

)

Figure B.1 Overall assembly pressure drop as a function of velocity for the 217.5 mm storage cell. 

The two dashed curves represent the quadratic fits to the data shifted by ± WAssembly

u . 

Table B.2 summarizes the SLAM and Σk coefficients determined from this error analysis.

Table B.2 SLAM and Σk coefficients showing the effect of the uncertainty in assembly velocity.

Fitting velocity (m/s)

217.5 mm 221.8 mm 226.6 mm

SLAM Σ k SLAM Σ k SLAM Σ k 

WAssembly 133 31.2 110 27.5 99 27.3

WAssembly+ WAssembly

u 138 29.8 115 26.4 104 26.3

WAssembly - WAssembly

u 128 32.5 106 28.6 94 28.3

The uncertainty for SLAM and Σk coefficients appears to be slightly dependent on storage cell 

size. The maximum differences in the SLAM and Σk coefficients in Table B.2 are taken to be the 

uncertainty, SLAM u = 5 and uk = 1.4. These values represent the conservative limit.

WAssembly (m/s)



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