EXPERIMENTAL ANALYSIS OF DIFFUSER PERFORMANCE …acumen.lib.ua.edu/content/u0015/0000001/0002183/u0015_0000001_0002183.pdfFigure 16 – ANSYS FLUENT flow simulation 2-D contour non–dimensionalized

EXPERIMENTAL ANALYSIS OF DIFFUSER PERFORMANCE

FOR THE SUBSONIC AERODYNAMIC RESEARCH

LABORATORY WIND TUNNEL

by

DEVON CRAIG MILLER

SEMIH M. ÖLÇMEN, COMMITTEE CHAIR

MUHAMMAD ALI ROB SHARIF

KEITH WILLIAMS

A THESIS

Submitted in partial fulfillment of the requirements

for the degree of Master of Science

in the Department of Aerospace Engineering and Mechanics

in the Graduate School of

The University of Alabama

TUSCALOOSA, ALABAMA

2015

Copyright Devon Craig Miller 2015

ALL RIGHT RESERVED

ii

ABSTRACT

This research is driven by the desire to improve efficiency of the Subsonic Aerodynamic

Research Laboratory (SARL) at the Wright-Patterson Air Force Base, Dayton, OH. Previous

research indicates a 30% loss of pressure occurring at the exit of the tunnel. A 60:1 scaled model

of the SARL tunnel and four different diffuser geometries were tested to determine the most

efficient diffuser for reducing overall losses. Experimental results were compared against

computational simulation analysis results obtained using the same diffuser models by King

(2012) to validate the computational results.

Four cases were studied experimentally using a Kiel Probe and Netscanner pressure

scanner. The inlet velocity profile entering the 60:1 scaled diffuser models was a fully

developed velocity profile with an average velocity of 60 m/s and a center velocity of 72.5 m/s

Total pressure losses downstream of the diffuser models were measured to determine the most

efficient geometry to reduce pressure losses and decrease operational cost of the SARL system.

Both the experimental and CFD results show that the “3.5 Base + Flat + Conical” diffuser

results in the least total pressure loss throughout the system. The experimental results indicate a

37% percent reduction in the total pressure losses while the CFD results gave a 45% reduction in

the total pressure losses in comparison to the pressure losses measured for the existing “7.5 base”

diffuser on the small scale. Implementing this diffuser model could improve the overall

efficiency of the full scale SARL tunnel by 11%

iii

LIST OF ABBREVIATIONS AND SYMBOLS

P𝑙𝑜𝑐𝑎𝑙 Static Pressure at a specified location within the SARL tunnel

𝑞𝑙𝑜𝑐𝑎𝑙 = P𝑙𝑜𝑐𝑎𝑙 +𝜌𝑉𝑙𝑜𝑐𝑎𝑙

2

2

�̅� Inlet Uniform Velocity

A1 Inlet Area, b*W1

a1 Speed of Sound at the inlet, 𝑎 ≡ √𝛾𝑅𝑇

A2 Exit Area, b2*W2

ABL Boundary Layer Area

Alocal Area at a specified location in the SARL tunnel

AR Aspect Ratio 𝐴𝑅 =𝐴2

𝐴1

Ats Area at the Test Section of the SARL Tunnel

b Diffuser Width

B1 Inlet Boundary Layer Blockage Factor

CFD Computational Fluid Dynamics

Cp Pressure Loss Coefficient

D Inner Diameter of PVC pipe, D=1.61 inches

D Diffuser Diameter

dmax Maximum deviation

EI Entrance Length Number

iv

ER Overall Circuit Energy

ft Feet

g Gravitational Force

HL Head Loss

HLc Center-line Non – Dimensionalized Pressure Losses

HVAC Heating, Ventilating, Air Conditioning

Ie Fully Developed Entrance Length

K Local Total Pressure Loss Coefficient

Ko Section Total Pressure Loss Coefficient

L Characteristic Length of the pipe, L=4.4 feet

M Mach Number

Mq1 Diffuser Inlet Mach Number,

n Power Law Velocity Distribution Coefficient

NUSS NetScanner Unified Startup Software

P Static Pressure

P0 Total Pressure

PIV Particle Image Velocimetry

PVC Polyvinyl chloride

qlocal Dynamic Pressure at a specified location in the SARL tunnel,

qts Dynamic Pressure at the Test Section of the SARL tunnel

R Radius of PVC pipe

r Relative Radius to location in distribution

Re Reynold’s Number

v

SARL Subsonic Aerodynamic Research Laboratory

T Absolute Temperature of Fluid

u Relative Velocity in the distribution

Vc Center Velocity

Vlocal Velocity Magnitude at a specified location in the SARL tunnel

Vts Velocity Magnitude at the Test Section of the SARL tunnel

W1 Inlet Diffuser Height

W2 Exit Diffuser Height

ΔP0 Change in Total Pressure across a given location

ΔP0 Change in Total Pressure across a given location

θ Diffuser Divergence Angle

λ Skin Coefficient

μ Dynamic Viscosity

ρ Air Density

σε Computational constant for turbulent dissipation

υ Kinematic Viscosity

vi

ACKNOWLEDGMENTS

I would sincerely like to thank Dr. Semih Ölçmen for motivating me to complete my

Master’s thesis. Dr. Semih Ölçmen’s guidance and patience was a driving force aiding me in

accomplishing my goals. Without the assistance of Chris King with the modifications in the

CFD results this thesis would not be possible and I would like to thank him for taking time to

give me the much needed assistance. I would also like to express appreciation to my fellow

students Narendra Chaganti, Alex Few, and Chaize DeSio for their assistance with completing

experimental measurements. In addition, many thanks go to The University of Alabama

Department of Aerospace Engineering for giving me the opportunity to earn my Master’s

Degree.

For spending long nights with me in the lab and supporting me in the pursuit of my

degree, I would like to thank my girlfriend, Susan Walmsley. Finally, I would like to express my

greatest appreciation and gratitude to my parents, Sheryl Randol and Gary Miller, for giving me

much needed motivation and encouragement to keep pushing forward. In addition, I would like

to thank my brothers Brent Randol for his wisdom and knowledge, and Logan Miller for his

support to finalize my thesis.

vii

CONTENTS

LIST OF ABBREVIATIONS AND SYMBOLS .......................................................................... iii

ACKNOWLEDGMENTS ............................................................................................................. vi

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

LIST OF FIGURES ........................................................................................................................ x

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

1.1 Diffusers .............................................................................................................................. 1

1.2 Subsonic Aerodynamics Research Laboratory Tunnel Background .................................. 6

1.3 Diffuser Design ................................................................................................................. 11

1.4 CFD Analysis .................................................................................................................... 13

1.5 Computational Diffuser Results ANSYS FLUENT ......................................................... 16

EXPERIMENTAL SETUP ........................................................................................................... 28

2.1 Pipe length selection and Diffuser Inlet Velocity Profile ................................................. 28

2.2 Experimental Instrumentation ........................................................................................... 31

2.3 Data Reduction.................................................................................................................. 39

RESULTS ..................................................................................................................................... 40

3.1 Experimental Diffuser Data .............................................................................................. 40

3.2 Uncertainty Analysis ......................................................................................................... 52

viii

3.3 Comparison of Experimental and CFD Pressure Losses for Diffuser Geometries ........... 59

3.4 Experimental and CFD total pressure loss Comparison at Station 3 ................................ 65

3.5 Comparison of Experimental Results and CFD simulations ............................................ 66

CONCLUSION ............................................................................................................................. 74

4.1 Conclusion ........................................................................................................................ 74

4.2 Future Work ...................................................................................................................... 77

REFERENCES ............................................................................................................................. 79

APPENDIX A ............................................................................................................................... 81

APPENDIX B ............................................................................................................................... 92

APPENDIX C ............................................................................................................................... 94

APPENDIX D ............................................................................................................................... 99

APPENDIX E ............................................................................................................................. 110

APPENDIX F ............................................................................................................................. 122

APPENDIX G ............................................................................................................................. 128

ix

LIST OF TABLES

Table 1 – Performance factor of Diffusers (White, 1980) .............................................................. 4

Table 2 – Atmospheric Conditions and Inlet Center Velocities ................................................... 41

Table 3 – Chauvenet’s criterion uncertainty No Diffuser and 7.5 Base Models .......................... 56

Table 4 - Instruments Measurement Uncertainty .......................................................................... 57

Table 5 – Uncertainty of Velocity Measurements for the 4 Diffusers and No Diffuser Cases .... 58

Table 6 – Experimental Head Losses of Diffuser Models – Fully Developed Flow

– Small Scale................................................................................................................................. 60

Table 7– Experimental Percentage Improvement in efficiency from the 7.5 Base Model for the

entire SARL tunnel – Fully Developed Flow - Small Scale. ........................................................ 62

Table 8 - ANSYS FLUENT Head Losses by Diffuser Geometry (King, 2012) .......................... 63

Table 9 – Pressure loss scale factor between the small scale model and the full scale tunnel

calculated using CFD results, hl_small/hl_full ............................................................................. 63

Table 10 – Experimental Approximation of total pressure losses – Fully Developed Flow – Full

Scale .............................................................................................................................................. 64

Table 11 - CFD simulation of Total Head Losses by Diffuser Model - Fully Developed Flow –

Small Scale.................................................................................................................................... 65

x

LIST OF FIGURES

Figure 1 - Diffuser Model for Ubertini and Desideri diffuser analysis (Ubertini and Desideri,

2000) ............................................................................................................................................... 3

Figure 2 – Subsonic Diffuser geometries with straight centerline (Farokhi, 2009) ........................ 4

Figure 3 - Diffuser Schematic with performance factors (White, 1980). ....................................... 5

Figure 4 – Flat-Walled-Diffuser Stability Map (Kline, 1955) ........................................................ 5

Figure 5 – Full Model of the Subsonic Aerodynamic Research Laboratory Tunnel (Presdorf,

1992) ............................................................................................................................................... 7

Figure 6 - Drawing of Fan Duct and Exit Diffuser Section of the SARL Wind Tunnel (Olcmen,

2011) ............................................................................................................................................... 8

Figure 7 – SARL tunnel velocity and pressure distributions with no losses (Britcher, 2011) ....... 8

Figure 8 – Revised Cumulative Losses Coefficient Analysis (Britcher, 2011) ............................ 10

Figure 9 – Static Pressure Distribution Analysis (Britcher, 2011) ............................................... 11

Figure 10 – Various SolidWorks models tested for loss reduction in the SARL tunnel (King,

2013) ............................................................................................................................................. 12

Figure 11 – Cross-section of diffusers (a) 7.5 Base, (b) 3.5 Base, (c) 3.5 Base + Flat, (d) 3.5 Base

+ Flat + Conical (King, 2013) ....................................................................................................... 13

Figure 12 – (Left) Mesh Design for the Full Computational Domain of the 7.5BT. (Right) Mesh

Design of the 7.5BT diffuser (King, 2011). .................................................................................. 14

Figure 13 – Inlet Velocity Profile calculated using ANSYS FLUENT solver (King, 2011) ....... 16

Figure 14 – ANSYS FLUENT flow simulation 2-D contour plot non–dimensionalized Total

Pressure Distribution at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow ..... 18

xi

Figure 15 – ANSYS FLUENT flow simulation 2-D Contour non–dimensionalized Velocity

Profile at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow ............................ 19

Figure 16 – ANSYS FLUENT flow simulation 2-D contour non–dimensionalized Total Pressure

Distribution at Exit for 3.5 Base + Flat Geometry – Small Scale – Fully Developed Flow ......... 20

Figure 17 – ANSYS FLUENT flow simulation 2-D contour plot non–dimensionalized Velocity

Profile at the Exit for the 3.5 Base + Flat Geometry – Small Scale – Fully Developed Flow ..... 21


Pressure Distribution at Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully

Developed Flow ............................................................................................................................ 22


Profile at Exit for 3.5 Base + Flat + Conical Geometry – Small Scale

– Fully Developed Flow................................................................................................................ 23


Pressure Distribution at Exit for 7.5 Base Geometry – Small Scale

– Fully Developed Flow................................................................................................................ 25


Profile at Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow ............................ 26

Figure 22 – Exponent, n, power law velocity profile (Munson, 1990) ......................................... 29

Figure 23 – Power Law Velocity distribution for ‘n’ = 7.5 compared to Experimental Results

with no diffuser attachment .......................................................................................................... 30

Figure 24 – VACCON CDF 750H-EPT107 Air Amplifier .......................................................... 31

Figure 25 – Schematic of Coanda Effect using the VACOON Air Amplifier ............................. 32

Figure 26 – Front Panel of NetScanner Pressure Scanner (Left), Bottom Panel of NetScanner

Pressure Scanner (Right)............................................................................................................... 33

Figure 27 – Example of grid locations used to acquire pressure readings.................................... 34

Figure 28 - Diagram of Kiel Probe Design ................................................................................... 35

Figure 29 – Experimental Setup ................................................................................................... 36

Figure 30 – Experimental 2-D contour plot of total pressure distribution for no diffuser

– Small Scale – Fully Developed Flow......................................................................................... 37

xii

Figure 31 – Experimental 2-D contour plot of velocity distribution for no diffuser

– Small Scale – Fully Developed Flow......................................................................................... 38

Figure 32 – Experimental 2-D contour plot non–dimensionalized Total Pressure Distribution

at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow ........................................ 42

Figure 33 – Experimental 2-D non–dimensionalized Velocity Profile at Exit for 3.5 Base

Geometry – Small Scale – Fully Developed Flow........................................................................ 43

Figure 34 – Experimental 2-D contour plot Total Pressure Distribution at Exit for 3.5 Base

+ Flat Geometry – Small Scale – Fully Developed Flow ............................................................. 44

Figure 35 – Experimental 2-D contour plot Velocity Profile at Exit for 3.5 Base +

Flat Geometry – Small Scale – Fully Developed Flow ................................................................ 45

Figure 36 – Experimental 2-D contour plot non–dimensionalized Total Pressure Distribution at

Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully Developed Flow ................ 47

Figure 37 – Experimental 2-D contour plot non–dimensionalized Velocity Profile at

Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully Developed Flow ................ 47

Figure 38 – Experimental 2-D contour plot non–dimensionalized Total Pressure

Distribution at Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow ................... 49

Figure 39 – Experimental 2-D contour plot non–dimensionalized Velocity Profile at

Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow ........................................... 50

Figure 40 - – SolidWorks Flow Simulation Total Pressure Distribution through tunnel Cross-

Section for 7.5 Base Tunnel - Small Scale - Uniform Flow (King, 2012) ................................... 51

Figure 41 – Experimental Velocity Deviation from the Mean - No Diffuser – Vc = 72.5 m/s,

D = 1.61 inches ............................................................................................................................. 53

Figure 42 – Experimental Velocity Deviation from the Mean - 7.5 Base – Vc = 72.5 m/s, D =

1.61 inches .................................................................................................................................... 54

Figure 43 – Experimental Chauvents’s Criterion Uncertainty of Velocity - No Diffuser

– Vc = 72.5 m/s, D = 1.61 inches .................................................................................................. 55

Figure 44 – Experimental Chauvents’s Criterion Uncertainty of Velocity -

7.5 Base Diffuser – Vc = 72.5 m/s, D = 1.61 inches ..................................................................... 56

Figure 45 - General Locations for Power Loss Calculations relative to the SARL Wind Tunnel

Fan Duct and Diffuser Sections (King, 2011) .............................................................................. 60

xiii

Figure 46 - Percent Difference between Experimental and CFD results - 3.5 Base

- Small Scale ................................................................................................................................. 67

Figure 47 - Experimental and CFD Non-dimensionalized Velocity comparison

at Y/D = 0.155 .............................................................................................................................. 69

Figure 48 – Percent Difference of Experimental and CFD results - 3.5 Base + Flat

- Small Scale ................................................................................................................................. 70

Figure 49 - Percent Difference of Experimental versus CFD results - 3.5 Base +

Flat + Conical - Small Scale ......................................................................................................... 71

Figure 50 – Percent Difference of Experimental and CFD results - 7.5 Base - Small Scale ........ 72

Figure 51 – ANSYS FLUENT flow simulation Normalized Velocity of Section 1 at Exit

for 3.5 Base Geometry – Small Scale – Fully Developed Flow ................................................... 81






for 3.5 Base + Flat Geometry – Small Scale – Fully Developed Flow ......................................... 84






for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully Developed Flow ........................ 87









xiv



Figure 63 – NetScanner United Software Startup screenshot for extracting raw

data to Excel .................................................................................................................................. 92

Figure 64 - Experimental contour plot of uncertainty for velocity results of no diffuser

– small scale – fully developed flow – Vc = 72.5 m/s, D = 1.61 inches ....................................... 94

Figure 65 - Experimental contour plot of uncertainty for velocity results of 3.5 Base

– small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches ........................................ 95

Figure 66 - Experimental contour plot of uncertainty for velocity results of 3.5 Base + Flat –

small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches ........................................... 96

Figure 67 - Experimental contour plot of uncertainty for velocity results of 3.5 Base + Flat +

Conical – small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches .......................... 97

Figure 68 - Experimental contour plot of uncertainty for velocity results of 7.5 Base

– small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches ........................................ 98

Figure 69 – Experimental Normalized Velocity of Section 1 at Exit for 3.5 Base Geometry –

Small Scale – Fully Developed Flow............................................................................................ 99


Small Scale – Fully Developed Flow.......................................................................................... 100



Figure 72 – Experimental Normalized Velocity of Section 1 at Exit for 3.5 Base +

Flat Geometry – Small Scale – Fully Developed Flow .............................................................. 102






Flat + Conical Geometry – Small Scale – Fully Developed Flow .............................................. 105



xv









Figure 81 – Scatter plots of Experimental and CFD comparison for 3.5 Base

Diffuser model ............................................................................................................................ 112

Figure 82 – Scatter plots of Experimental and CFD comparison for 3.5 Base + Flat Diffuser

model........................................................................................................................................... 115

Figure 83 - Scatter plots of Experimental and CFD comparison for 3.5 Base + Flat + Conical

Diffuser model ............................................................................................................................ 118

Figure 84 - Scatter plots of Experimental and CFD comparison for 7.5 Base

Diffuser model ............................................................................................................................ 121

1

CHAPTER 1

INTRODUCTION

The United States Air Force expressed interest in improving the efficiency of the

Subsonic Aerodynamics Research Laboratory (SARL) Wind tunnel. With this in mind, different

diffusers have been tested to determine the effect of the diffusers on the overall tunnel efficiency.

Diffusers are used downstream of tunnel test sections to decrease flow speed, increase pressure

and improve overall efficiency of the system by reducing the total pressure losses. Experimental

and CFD results were compared to determine the extent of improvements on a small scale model

of the SARL tunnel. The results of the small scale research is then extended to determine the

effects of the diffuser on the full scale model. CFD analysis made both on the small and the full

scale models is used for this purpose.

1.1 Diffusers

The use of diffusers in fluid mechanic applications has had a great impact on the overall

performance of systems. Diffusers are typically designed with an area increase along the flow

direction with the purpose of decreasing the exit velocity, thereby recovering pressure and

decreasing total pressure losses throughout the system. Diffuser use is a common practice in many

applications including HVAC systems, many types of aircraft engines, and wind tunnels.

2

The earliest known use for diffusers dates back to the Roman aqueducts in 100 A.D.

Water supply systems were constant area pipes until it was discovered that an increased flow rate

could be created using a flared exit pipe (White, 1986). Previous research by Mehta and

Bradshaw (1979) has shown that the exit area to the entrance area ratio and diffuser angles are

the main factors affecting the performance of flow through diffusers. This research provides

design parameters to follow when designing a diffuser. Additional design factors affecting the

performance of diffusers were determined to be the inlet conditions, screen positioning, wall

shape, screen shape, and cross sectional shape. Conical diffusers were tested for incompressible

flows by McDonald and Fox (1965). Their results indicate that the diffuser performance is a

function of the Reynolds number. However, they also stated that once the Reynolds number

exceeds 75,000; the pressure recovery, diffuser effectiveness, and flow regime become

independent of the Reynolds number. In addition to the Reynolds number, McDonald and Fox

state the maximum effectiveness for conical diffusers does not align with the maximum

effectiveness from plane-walled diffusers. The conical diffuser can be designed for maximum

pressure recovery while maintaining a non-separated flow inside the diffuser (McDonald and

Fox, 1965). Shuja and Habib (1995) tested the effects and improvements gained by using

axisymmetric annular diffusers on heat transfer, showing a large improvement with a decrease of

the average convective heat transfer coefficient in the separated flow regions. Annular diffusers

were tested for experimental performance in cases with struts and without struts for gas turbines.

Ubertini and Desideri (2000) showed a 10–15% lower efficiency for the model with truncated

struts in the duct, which largely reduced the overall efficiency of the system. Figure 1 shows the

diffuser model used in the research by Ubertini and Desideri (2000), and the location of the struts

within the diffuser.

3

Figure 1 - Diffuser Model for Ubertini and Desideri diffuser analysis (Ubertini and

Desideri, 2000)

The pressure recovery was largely improved for diffusers with un-truncated struts in the duct

region. Overall their experiments demonstrate that presence of struts increase the overall losses

in a diffuser. Norris and Smith (1998) showed that in S-shaped diffusers a 28% efficiency

reduction was observed. A significant rise in the pressure loss coefficient due to regions with

large separation bubbles is observed when struts are present in the diffuser duct.

The focus of this thesis is on determining the effectiveness of different subsonic diffusers

on the overall performance of wind tunnels. Figure 2 shows three separate subsonic diffuser

geometries.

4

Figure 2 – Subsonic Diffuser geometries with straight centerline (Farokhi, 2009)

The pressure recovery coefficient, Cp, is a significant factor in relation to diffuser performance.

Using Bernoulli’s equation the value for Cp can be defined as:

𝑝 + 1

2𝜌𝑉2 = 𝑝𝑜 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (1.1.1)

𝐶𝑝 =𝑃𝑜−𝑃1

2𝜌𝑉2

(1.1.2)

where Po is total pressure, P is static pressure, ρ is air density, and V is velocity. A higher value

for the pressure recovery coefficient indicates better diffuser performance. The ideal diffuser

would have a Cp value equal 1. Many factors impact the value of Cp and effects the performance

of the diffuser, and some of these factors are listed in Table 1 and Figure 3 (White, 1980).

Table 1 – Performance factor of Diffusers (White, 1980)

Area Ratio AR = A1/A2

Divergence Angle 2θ

Slenderness L/D

Inlet Reynolds Number Re1 = V1W1/υ

Inlet Mach Number Mq1 = V1/a1

Inlet Boundary Layer Blockage Factor B1 = ABL/A1

Aspect Ratio AS = b/W1

The predominant performance factors impacting the diffusers are: area ratio, divergence angle,

and boundary-layer blockage factor. Boundary- layer blockage factor is defined as the area of

the boundary layer divided by the area of the diffuser inlet. Lengths and angles used to define

the performance factors are illustrated in Figure 3.

5

Figure 3 - Diffuser Schematic with performance factors (White, 1980).

Flow separation impacts diffuser performance highly. This is due in part to the increased

pressure drag at the wall where the flow separation occurs.

Flow patterns in diffusers were very unpredictable until 1955, until Kline demonstrated

flow patterns using flow visualization. Flat-walled diffuser stability map is shown in Figure 4.

Figure 4 – Flat-Walled-Diffuser Stability Map (Kline, 1955)

b2

6

This map shows the importance of both the divergence angle and diffuser length versus the width

of the diffuser. In addition to the pressure recovery coefficient, another way to determine the

efficiency of a diffuser is to evaluate the pressure head losses throughout the tunnel. Head loss

coefficient gives a relative value to the power loss from the inlet of the diffuser to the exit

(Farokhi, 2009). The head loss coefficient can be defined as:

ℎ𝐿 =(𝑃1−𝑃2)+

1

2𝜌(𝑉1

2−𝑉22)

𝜌𝑔 (1.1.3)

1.2 Subsonic Aerodynamics Research Laboratory Tunnel Background

The SARL tunnel was originally designed for efficiency and low cost of operation to

measure static pressure distribution and drag force of large vehicles. Figure 5 below

demonstrates a full schematic of the SARL tunnel. In 1983, the United States Air Force

approved the construction of the tunnel with the purpose of acquiring a low (< 0.05%) turbulence

wind tunnel that could allow employing flow visualization and laser-based diagnostic techniques

(Britcher, 2011). The tunnel is equipped to conduct both laser velocimetry measurements and

smoke visualization over complex models. The SARL tunnel is a large wind tunnel with an inlet

measuring 46 x 50 feet with a contraction ratio of 35:1, which helps turbulence reduction.

Screens installed at the inlet eliminate foreign object ingestion and act as a flow straightener,

ensuring a uniform inlet flow. Honeycombs and screens installed reduce the turbulence levels to

less than 0.05% throughout the tunnel (Presdorf, 1992).

7

Figure 5 – Full Model of the Subsonic Aerodynamic Research Laboratory Tunnel

(Presdorf, 1992)

Maximization of flow visualization capabilities of the tunnel are utilized by the side walls of the

test section, which include a 7 x 10 ft2 window to allow visual sight to the model. Maximum

design velocity of the tunnel was Mach 0.6, but due to natural frequency issues, the tunnel can

only operate up to Mach 0.5. A significant benefit of the SARL wind tunnel is the Air Force can

conduct advanced testing on vehicles at large angles of attack.

The tunnel diffuser section consists of the access, transition, and expansion cone. At

first, the cone expands with a 3.25° half angle to prevent the chance of flow separation and, in

the last four feet, changes to a half angle of 8.82 ° and can be viewed in Figure 6 (Presdorf,

1992).

8

Figure 6 - Drawing of Fan Duct and Exit Diffuser Section of the SARL Wind Tunnel

(Olcmen, 2011)

Figure 7 shows velocity and pressure distributions, with no pressure losses, of the SARL tunnel.

Figure 7 – SARL tunnel velocity and pressure distributions with no losses (Britcher, 2011)

9

Cost of operating the SARL tunnel is significant. One method to improve efficiency of

the operation is to add a diffuser to the tunnel exit. Previous analysis by Britcher concluded that

30% of the losses occurring in the SARL tunnel are generated within the diffuser and at the

tunnel exit. These total pressure losses from the diffuser and tunnel exit contributes to a high

cost of operation (Britcher, 2011). In Britcher’s research, the SARL tunnel was split into

separate sections where the losses were predicted and analyzed. The sections are as follows:

intake, settling chamber, contraction, test chamber, diffuser, catch screen, fan section, and

exhaust. Each section of the tunnel for the loss coefficient, in terms of entry dynamic pressure, is

expressed as

𝐾 = 𝐿𝑜𝑐𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 =∆𝑝𝜊

𝑞𝑙𝑜𝑐𝑎𝑙 (1.2.1)

𝐾0 = 𝑆𝑒𝑐𝑡𝑖𝑜𝑛 𝑇𝑜𝑡𝑎𝑙 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑙𝑜𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 =∆𝑝0

𝑞𝑡𝑠= 𝐾

𝑞𝑙𝑜𝑐𝑎𝑙

𝑞𝑡𝑠= 𝐾 (

𝑉𝑙𝑜𝑐𝑎𝑙

𝑉𝑡𝑠)

2

(1.2.2)

This loss coefficient for the system can then be applied to the overall circuit energy as

∆𝐸 = 1

2𝐾𝜌𝑉𝑙𝑜𝑐𝑎𝑙

3𝐴𝑙𝑜𝑐𝑎𝑙 = 𝐾𝜊1

2𝜌𝑉𝑡𝑠

3𝐴𝑡𝑠 (1.2.3)

𝐸𝑅 =1

2𝜌𝑉𝑡𝑠

3𝐴𝑡𝑠

Σ𝑙𝑜𝑠𝑠𝑒𝑠=

1

Σ𝐾𝜊 (1.2.4)

Considering the diffuser and the exit section has been predicted to be the largest contributor to

the losses throughout the system, the loss formula for the diffuser section can be approximated in

Equation (1.2.5), where 𝜆 is defined as the section skin friction coefficient.

𝐾 ≈ (𝜆

8 sin 𝜚+ 0.6 tan 𝜚) (1 −

1

𝐴𝑅2) (1.2.5)

10

The formulas for losses in the remaining sections of the tunnel are published by Britcher (2011).

In a preliminary study, Britcher’s research indicated that the cumulative loss coefficient was

approximately 0.237. This research indicated that both the diffuser and exit sections generate

sizeable losses. However, revised methods were applied to the sections, to calculate the losses

such as the test section strut losses, and to the diffuser section upstream of the fan duct. Britcher

concluded that overall cumulative loss should be increased to 0.245 from the previous 0.237. The

revised losses can be seen in Figure 8. Figure 9 displays the static pressure distribution

throughout the tunnel.

Figure 8 – Revised Cumulative Losses Coefficient Analysis (Britcher, 2011)

11

Figure 9 – Static Pressure Distribution Analysis (Britcher, 2011)

Conclusively, the diffuser duct and exit losses are major contributors of losses throughout the

circuit. Modifications via attachments can be made to the diffuser exit improving the overall

cumulative loss. Enhancements to the diffuser exit could decrease the loss coefficient from

0.245 to 0.2055, resulting in a potential 16% less total pressure loss across the entire circuit

(Britcher, 2011). A more realistic power savings of 13% could be achievable with improvements

at the exit of the tunnel (Schmidt 1986).

1.3 Diffuser Design

The desired efficiency improvement of the SARL tunnel required testing many diffuser

geometries to discover the best geometry for reducing the losses. Several models were tested

using computational methods and SolidWorks FloWorks fluid mechanics add-on tool.

Efficiency improvements achieved by different models were determined. Among the 30 models

designed using previous knowledge on diffuser effectiveness in loss reduction, four were

selected. These models were then used in experimental testing and CFD simulations. Models

12

not selected included diffusers that redirected flow upwards and away from the ground, diffusers

with splitter plates to direct the flow in two directions, conical and annular diffusers of varying

lengths, and constant area diffusers of different lengths, which are shown in Figure 10.

Figure 10 – Various SolidWorks models tested for loss reduction in the SARL tunnel (King,

2013)

The four selected models were all designed using SolidWorks. CFD calculations on these

models were made using the FloWorks add-on flow analysis tool. Figure 10 shows the cross-

sectional cut-out CAD drawings of the four diffusers selected. The selected four geometries

consist of the base model diffuser currently being utilized in the SARL tunnel, 8ᵒ half-apex angle

labeled as “7.5 Base”, 3.5ᵒ half-apex angle labeled as “3.5 Base”, a modified version of the “3.5

Base” with the addition of a constant area flat diffuser labeled as “3.5 Base + Flat”, and a

modification of the “3.5 Base + Flat” with the addition of an annular conical attachment labeled

as “3.5 Base + Flat + Conical”. The annular conical attachment consists of truncated cones with

respective angles of 60ᵒ; 34.7ᵒ; and 17.2ᵒ (King, 2013). Conical diffusers were designed to

13

achieve a large area variation in a short distance. Diffuser designs took into account several

parameters. Due to space limitations between the gearbox and diffuser exit, the diffuser length

was limited to 14 ft. The diffuser could not include moving parts, and could not be overly

complex as this would have increased the production cost. Both during the computational and

experimental studies, no moving parts, such as fan blades were incorporated.

Figure 11 – Cross-section of diffusers (a) 7.5 Base, (b) 3.5 Base, (c) 3.5 Base + Flat, (d) 3.5

Base + Flat + Conical (King, 2013)

During preliminary computational tests using SolidWorks FlowWorks code, the “3.5 Base +

Flat” and “3.5 Base + Flat + Conical” geometries exhibited the greatest pressure recovery

improving the overall efficiency of the SARL tunnel by 16%.

1.4 CFD Analysis

Computational studies using FLUENT CFD code were conducted prior to the

experimental studies to validate results obtained by the SolidWorks FloWorks CFD tool, as

FLUENT is a more accurate CFD solver than SolidWorks FloWorks. This section summarizes

14

CFD results obtained in another study (King, 2012). CFD results are included prior to the

discussion of experimental methods to aid in fully understanding the flow in the SARL tunnel

and how diffusers impact overall efficiency.

To solve governing equations for flow simulations, a computational mesh is needed.

ANSYS FLUENT uses a meshing package allowing for an unstructured grid designed for

complex non-uniform geometries. Calculations were completed by using different size meshes

in order to show that the solutions obtained did not depend on the mesh selection. The grid

independence study assures the most accurate results. Refined mesh settings were applied to all

diffuser geometries except the conical diffuser case, which required a separate mesh structure

entirely. A more detailed explanation of the mesh design is found in the study by King (2012).

Two examples of the mesh designs used for the ANSYS FLUENT simulations are shown in

Figure 12.

Figure 12 – (Left) Mesh Design for the Full Computational Domain of the 7.5BT. (Right)

Mesh Design of the 7.5BT diffuser (King, 2011).

15

Computational studies require defining boundary conditions to start running the code. Due to

program’s limitations the ANSYS FLUENT program did not contain a fully developed flow

boundary condition as it was available in SolidWorks program. The fully developed boundary

conditions used in ANSYS FLUENT were separately calculated using a constant diameter pipe

of a certain length and calculating the exit flow field by imposing a uniform flow at the pipe

entrance. The length of the pipe was determined using the following equations.

𝐸𝐼 = 4.4𝑅𝑒1

6 (1.4.1)

where the Reynolds number is defined as

𝑅𝑒 =𝑉𝐷

𝜐 (1.4.2)

The variables in these equation represent inlet conditions where EI is then entrance length

number, V is the velocity, D is the diameter, and 𝜐 is to the kinematic viscosity. The pipe inlet

uniform velocity was set to 60 m/s. The Reynolds number used for the small scale models is

1.674 x 105. Once the entrance length number is calculated, the pipe length needed for the fully

developed flow was calculated as 𝐼𝑒 = 1.34 meters (4.4 feet), using Equation (1.4.3).

𝐼𝑒 = 𝐸𝐼 ∗ 𝐷 (1.4.3)

The velocity distribution obtained from the computation is a fully developed turbulent flow. The

velocity distribution obtained from the calculations for the pipe flow is shown in Figure 13.

This velocity distribution is then used as the inlet velocity profile at the entrance to the diffuser

models for the CFD results.

16

Figure 13 – Inlet Velocity Profile calculated using ANSYS FLUENT solver (King, 2011)

Computations were completed both on the full scale and small scale models using SolidWorks

Flow Simulation and ANSYS FLUENT. For this thesis, only results from ANSYS FLUENT for

the small scale fully developed flow cases are included. Thesis results will focus on the static

and dynamic pressure of the flow, with the greatest interest in total pressure distribution at the

exit. With this information, head losses throughout the tunnel can be directly related to the

change in total pressure from the inlet to the exit.

1.5 Computational Diffuser Results ANSYS FLUENT

As mentioned previously, King (2012) completed CFD calculations on the four selected

diffuser geometries using both SolidWorks Flow Simulation and ANSYS FLUENT. It was

decided to use the ANSYS FLUENT results for the small scale fully developed flow cases since

17

the experimental data was obtained for such configurations. In order to compare the CFD results

with the experimental data, CFD results were restudied to determine the velocity and the total

pressure distributions at the locations where the experimental data were obtained. Previous

ANSYS FLUENT mesh techniques were used to create velocity and total pressure profiles 1/8”

downstream of the drive shaft with a fully developed flow of 60 m/s downstream of the diffuser

inlet.

Velocity profiles and pressure distributions were plotted using contour plots illustrating

geometric trends for each diffuser geometry. The CFD velocity results were non-

dimensionalized with a center line velocity of 60 m/s and the pressure results were non-

dimensionalized with a center line pressure of 2,131.2 Pa. In addition, both the X and Y axis

were non-dimensionalized with the pipe diameter, D = 1.61 inches. Figure 14 shows the

pressure distribution for the ANSYS FLUENT simulation for the ‘3.5 Base’ geometry.

18


Pressure Distribution at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow

The pressure distribution has shown a very symmetric distribution with peaks at 0ο, 120ο, and

240ο from the top of the exit. This is as expected considering those locations are where the flow

is least obstructed. As anticipated, minimums occur along the edges and in the center. Pressure

is expected to drop as it moves away from the center line; the zero pressure reading in the center

of the distribution is attributed to the drive shaft at that location. In addition, there is a drop in

total pressure at 60°, 180°, and 300°, attributed to struts connecting the diffuser wall to the center

drive shaft. Figure 15 shows the velocity profile for the “3.5 Base” geometry.

19

Figure 15 – ANSYS FLUENT flow simulation 2-D Contour non–dimensionalized Velocity

Profile at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow

Similar to the pressure distribution, the velocity profile demonstrates the same maximum and

minimum value trends. Viewable at the center location is a 0 non-dimensionalized velocity

reading, which can also be found at the four corners of the distribution outside the diffuser walls.

The maximum non-dimensionalized velocity value recorded for this case was 0.799 located at (0,

0.388).

20

The total pressure distribution for the “3.5 Base + Flat” geometry is illustrated in Figure 16.

Figure 16 – ANSYS FLUENT flow simulation 2-D contour non–dimensionalized Total

Pressure Distribution at Exit for 3.5 Base + Flat Geometry – Small Scale – Fully Developed

Flow

The figure shows that there is a symmetric distribution present. The highest pressure readings

were recorded closest to the center of the distribution at 0ο, 120ο, and 240ο from the top of the

exit. The reason there is a break in the high pressure ring surrounding the center of the exit is

due to the struts which obstruct the flow and cause a decrease in the pressure reading. Similarly

to the all the cases there is a 0 pressure reading in the center which is due to the drive shaft.

Finally at the wall of the diffuser geometry, or as the edge of the jet is approached the pressure

21

readings begin to decrease. Figure 17 shows the velocity profile for the “3.5 Base + Flat”

geometry.

Figure 17 – ANSYS FLUENT flow simulation 2-D contour plot non–dimensionalized

Velocity Profile at the Exit for the 3.5 Base + Flat Geometry – Small Scale – Fully

Developed Flow

The velocity distribution has a maximum non-dimensionalized velocity recording of

0.651 at (0.155, -0.776). The maximum velocity for this diffuser model is significantly lower

than the “3.5 Base” geometry. This begins to show the “3.5 Base + Flat” geometry has

significantly less pressure losses throughout the system. The minimum non-dimensionalized

velocity value recorded was along the edge of the distribution, where the lowest velocity was

22

expected to occur. At the center of the distribution at (0, 0) the velocity was recorded as 0.063

significantly lower than the rest of the velocity profile.

The total pressure distribution for the “3.5 Base + Flat + Conical” geometry is illustrated

in Figure 18.


Pressure Distribution at Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully

Developed Flow

Evident from the 2-D pressure distribution in Figure 19, the average total pressure for this case

is much lower than previous diffuser cases. An asymmetric flow is present for this pressure

distribution, with high pressure located at 0ο, 135ο, and 225ο from the top of the model. This high

pressure area appears to form a ring around the center of the distribution, where the high pressure

23

area correlates to the truncated cones of the conical diffuser attachment. In the high pressure

ring it is shown that at the location of the struts, lower pressure was recorded. The remaining two

rings from the conical diffuser do not seem to be visible in this distribution. An asymmetric flow

may be present due to flow separation in the diffuser. Similar to the all diffuser geometries,

there is nearly a 0 reading at the center due to the drive shaft. Total pressure readings were used

to calculate the velocity profile in Figure 19 for the “3.5 Base + Flat + Conical Diffuser”

geometry.


Velocity Profile at Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully

Developed Flow

24

The non-dimensionalized velocity profile has the same minimum and maximum locations similar

to the pressure distribution plots as before. Maximum non-dimensionalized velocity value was

recorded at (0.310, -0.233) with a value of 0.539 This model shows the smallest maximum

velocity simulated for all the models, indicating the most efficient diffuser attachment. The

average non-dimensionalized velocity across the profile is approximated to 0.373. Minimum

non-dimensionalized velocity simulated was located at (0, -0.077) with a value of 0.0215. This

is slightly shifted from the expected minimum velocity, which was assumed to be located at (0,

0). Finally, velocity decreases further away from the center and nearly zero in the corners of the

distribution.

The last diffuser model simulated was the original “7.5 Base” geometry that is currently

installed on the full scale SARL tunnel. Figure 20 includes the pressure distribution for the “7.5

Base” geometry.

25


Pressure Distribution at Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow

The pressure distribution contained three areas of high pressure values at 0ᵒ, 120ᵒ, and 250ᵒ.

These high pressure values in those locations are due to the geometric shape of the “7.5 Base”

geometry. At those locations the flow is the least obstructed from any struts, which allows for

higher pressure readings. The reason they are seem to be separated from each other by regions

of low pressure readings is due to the location of the struts on the model. These low pressure

readings around the center are located at 60°, 180°, and 300°, which correlates directly to the

location of the struts on the model. In addition, there is a low pressure region in the center of the

distribution due to the location of the drive shaft on the model. Finally, low pressure readings

were observed around the edges of the distribution and in the four corners an almost 0 pressure

26

reading was recorded. Velocities were calculated from these pressure values to show the rate of

the flow in these same locations in Figure 21.


Velocity Profile at Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow

Similar to the non-dimensionalized pressure distribution contour plot, the non-dimensionalized

velocity profile has the same trends across the distribution. The highest non-dimensionalized

velocities were simulated at angles of 0ᵒ, 120ᵒ, and 240ᵒ from the top of the model. The highest

non-dimensionalized velocity recorded in those regions was approximately 0.750. The highest

non-dimensionalized velocity simulated for this distribution was at (0,-0.466) with a magnitude

of 0.755 and the lowest was located at (0, -0.077) with a magnitude of 0.075.

27

Additional line plots of the data presented in this section can be found in Appendix A.

The CFD results were non-dimensionalized for comparison purposes. The X and Y axes were

normalized using the inlet diameter of the diffuser, D = 1.61 inches. The magnitude of the

velocity was non–dimensionalized with the inlet center velocity, of approximately 60 m/s, from

the inlet velocity boundary conditions found in Figure 13. Non–dimensionalized velocity

profiles were plotted on three separate line plots showing velocity trends across the X –axis.

Each plot refers to a different “Y” location where velocity was simulated as indicated in the

legend.

28

CHAPTER 2

EXPERIMENTAL SETUP

Experimental research included setting up a test stand for carrying out the experiments,

printing the four selected models and carrying out the Pitot tube measurements at selected

locations. The four selected models were 3D printed at the WPAFB-AFRL facilities. The models

printed were attached to the exit of a pipe long enough to result in a fully developed velocity

profile at the exit of the pipe. The pipe flow was generated using an ejector pump. Total pressure

measurements were made using a Pitot tube at the exit of the diffusers on a plane 1/8”

downstream of the drive shaft extension. This section gives the details of the test stand and the

equipment used in the research.

2.1 Pipe length selection and Diffuser Inlet Velocity Profile

The selection of the diameter and the length of the pipe that is used to obtain a fully

developed velocity profile, and velocity profile obtained at the exit of the pipe is discussed in this

section. The pipe used was a schedule 40 PVC pipe with an inner diameter of D=1.61 inches

(0.04 m) to match the entrance diameter of the 3D printed nozzles. The length of the pipe was

determined using the analysis discussed in Chapter 1, Section 1.4. An entrance length leading to

the diffuser was calculated using Equations (1.4.1), (1.4.2), and (1.4.3). A Reynolds number

based on the pipe diameter of Re=153,617 was calculated using the Equation (2.1.3), with ρ

=1.184 kg/m3; V= 60 m/s, D=0.04 m, and μ=1.85 x 10-5 kg/(s*m). The Reynolds number was

29

used to find an entrance length number of EI=32.202. The entrance length number along with a

tube diameter D=0.04 m was used to determine the length, Ie=1.29 m (4.23 ft) required to

achieve fully developed flow. During the experiments a five foot PVC pipe was employed to

ensure that a fully developed flow was achieved. The center velocity of the velocity profile at

the exit of the pipe was determined using a power law such that the average velocity at the exit

would be 60 m/s. The power law velocity distribution equation is given by Equation (2.1.1).

First a value for the exponent, n=7.5 was obtained from Figure 22 using Re= 153,617.

Figure 22 – Exponent, n, power law velocity profile (Munson, 1990)

The exponent was next utilized in Equation (2.1.2) to calculate the center velocity. Center

velocity for a fully developed flow at the entrance of the diffuser models was calculated as 72.5

m/s. The equations below represents the power law distribution.

𝑢

𝑉𝑐= (1 −

𝑟

𝑅)

1

𝑛 (2.1.1)

30

𝑢

𝑉𝑐=

2𝑛2

(𝑛+1)(2𝑛+1) (2.1.2)

𝑅𝑒 =𝜌𝑢𝑑

𝜇 (2.1.3)

In addition, the power law velocity distribution was compared against the experimental

results obtained for the bare PVC pipe flow. Figure 23 shows the comparison of the power law

distribution for ‘n’ equal to 7.5 and the experimental results at specific Y-locations along the

center line of the distribution.

Figure 23 – Power Law Velocity distribution for ‘n’ = 7.5 compared to Experimental

Results with no diffuser attachment

The comparison shows a good correlation between the two sets of center line velocity

distributions. In can be stated from this figure that the approximation of ‘n’ from Figure 22 was

correct and that a uniform velocity of 60 m/s was indeed set at the entrance of the PVC pipe.

00.10.20.30.40.50.60.70.80.9

11.1

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Norm

aliz

ed V

eloci

ty

Y/D

Power Law Model Experimental Results

31

2.2 Experimental Instrumentation

Motive air required for the experiments was supplied from a 1000 ft3 tank capable of

being pressurized up to 200 psi absolute. The sought after flow velocity at the flow tube

entrance was a uniform flow of 60 m/s. The air from the tank was channeled to the experimental

setup using a 50 feet Tygon tubing. The pressurized air was lead to a pressure regulator. This

pressure regulator was necessary to set the pressure leading to the inlet, allowing for a constant

flow during the experiments. The pressure regulator used was a Wilkerson regulator with a

maximum inlet pressure of 300 psi gage and an adjustable range from 0 to 160 psi gage.

Regulator output was directed to the air amplifier using additional Tygon tubing. The air

amplifier used was a VACCON CDF 750H-EPT107, and it is shown in Figure 24.

Figure 24 – VACCON CDF 750H-EPT107 Air Amplifier

32

The air amplifier generates a high output flow using a smaller volume of compressed air utilizing

the Coanda Effect. As pictured in Figure 25, air passes into the amplifier, passing over two

curved surfaces causing a low pressure area. This action prompts air flow into the throat

resulting in a high output flow.

Figure 25 – Schematic of Coanda Effect using the VACOON Air Amplifier

By rotating the main body of the air amplifier, the distances between the curved surfaces can be

manipulated. This allowed controlling the amount of air pulled into the throat, enabling variable

exhaust velocity. Following the air amplifier, was the inlet section of the PVC pipe where a

uniform velocity of �̅� =60 m/s was needed for operation. The air amplifier was inserted into the

pipe to obtain a fully developed flow leading to the entrance of the diffuser.

The flow velocity in the pipe was adjusted using pressure values read from a Pitot and a

static port located close to the exit of the pipe. An inch upstream of the exit of the PVC pipe a

Pitot tube was installed. A port was opened near the Pitot tube port to be used as the static port.

Pressure difference between the Pitot tube and the static port readings was used to monitor the

pipe center velocity. At this axial location the center velocity was set to 72.5 m/s by adjusting

the Wilkerson pressure regulator to ensure a constant velocity. This Pitot tube was connected to

33

the NetScanner pressure scanner to accurately set the velocity to 𝑉𝑐 =72.5 m/s. Two of the

sixteen ports available on the Netscanner were used to measure the total and the static pressure at

the inlet of the diffuser models. The NetScanner reads the pressure from the selected ports and

outputs them on the NetScanner United Startup Software. This software is where all the pressure

readings were recorded for the final data. The front and back panel of the NetScanner pressure

scanner is displayed in Figure 26.

Figure 26 – Front Panel of NetScanner Pressure Scanner (Left), Bottom Panel of

NetScanner Pressure Scanner (Right)

34

The diffuser attachments were connected to the exit of the PVC pipe and secured in place using

hose clamps. The data was taken on a XY plane 1/8 of an inch downstream of the drive shaft of

the diffuser. Figure 27 shows an example grid used to obtain the pressure readings downstream

of the diffuser attachments.

Figure 27 – Example of grid locations used to acquire pressure readings

The total pressure was measured with a Kiel probe connected to a manual traversing system with

traversing capabilities both in the X and Y directions. Kiel probe design includes a Pitot tube

within a shroud resulting in pressure readings less sensitive to changes in the flow angularity up

to 20ο. Figure 28 shows the Kiel probe (United Sensor, KBC-12-F-10-C) used during the

experiments.

X

Y

Dinner = 1.61 in

1/8”

1/8”

35

Figure 28 - Diagram of Kiel Probe Design

The manual traverse was positioned at each XY grid point to obtain total pressure and

subsequently the velocity profiles for each diffuser geometry. The measurement points were

spaced 1/8 inch apart in both the X and Y directions. The Kiel probe output was connected to

the NetScanner to obtain a pressure reading from the Kiel probe. A schematic of the

experimental setup is shown in Figure 29.

36

Figure 29 – Experimental Setup

Velocity at the inlet of the diffusers required adjustment to a center velocity of 72.5 m/s

before any of the pressure and velocity profiles could be obtained for each diffuser geometry.

Total and static pressures were read one inch upstream of the inlet to the diffusers for one minute

using the Pitot and the static ports. Readings were averaged to determine the centerline velocity.

The pressure regulator was adjusted and the process was repeated until a 72.5 m/s was obtained

for each case. In addition, once center velocity was set, the Pitot tube was removed and replaced

with screws to fill the port opening to eliminate any possible causes for irregularity in the flow.

This process was repeated for each of the four diffusers. To determine the inlet conditions for

the four diffuser models, velocity measurements were made at the exit of the circular cylinder

pipe as a calibration case. Figure 30 and Figure 31 show the 2-D contour plot for both total

pressure and velocity at the exit of the pipe without any attachments

37

Figure 30 – Experimental 2-D contour plot of total pressure distribution for no diffuser –

Small Scale – Fully Developed Flow.

38

Figure 31 – Experimental 2-D contour plot of velocity distribution for no diffuser – Small

Scale – Fully Developed Flow.

Pressure and velocity profiles are very symmetric across both the X and Y axes as expected. The

maximum value is 0.977 and was recorded at (-0.077, 0). That location is just left of center

where velocity value is 0.971. The maximum and center value difference of 0.006 is within the

experimental uncertainty of the measurements. As stated previously, the velocity and pressure

profiles were measured to determine the inlet conditions for all diffusers cases used during

experimentation. With the velocity set to 72.5 m/s from the Pitot tube, it is shown the inlet

velocity profile for the four other cases also have a centerline velocity decrease of approximately

2 m/s in the one inch distance from the Pitot tube to the tube exit.

39

2.3 Data Reduction

Once data taking is completed pressure readings from the NetScanner had to be translated

into an Excel spreadsheet file. The raw data is converted from the raw file into an Excel readout

with pressure in psi units. To convert the raw data, each data point was converted one-by-one

into Excel file format using the NetScanner Unified Startup Software (NUSS). For each point on

the grid 30 data points were collected over 15 seconds. Each grid location recording necessitated

using NUSS for conversion to an Excel spreadsheet file. Appendix B gives the steps taken to

obtain the Excel spreadsheet files from the NUSS software.

40

CHAPTER 3

RESULTS

The main point of interest for this data will be the total pressure data obtained 1/8 inch

downstream of the motor drive shaft. Total pressure obtained at this location will be used to

determine the overall pressure losses, which will determine the diffuser model best suited for

improving the efficiency of the SARL tunnel. 2-D contour plots for both the total pressure and

velocity will be discussed for each of the diffuser geometries. These results will be compared

against the CFD results to show the validity of experimental and computational results.

Research results indicate that the “3.5 Base + Flat + Conical” is expected to have the largest

reduction in pressure losses and best suited for SARL tunnel power improvements.

3.1 Experimental Diffuser Data

Experimental diffuser results will be shown as non-dimensional pressure and velocity

distributions. The experimental results were non-dimensionalized with a center line velocity of

72.5 m/s and a center line pressure readings of 3,111.7 Pa. In addition, the X axis and Y axis

grid point coordinates were non-dimensionalized with the inlet diameter, D=1.61 inches. Lastly,

the raw velocity results for these models can be viewed in Appendix G.

The initial inlet boundary conditions and the daily atmospheric conditions for each

diffuser geometry are listed in Table 2.

41

Table 2 – Atmospheric Conditions and Inlet Center Velocities

Diffuser

Geometries

Atmospheric

Pressure

[Pa]

Atmospheric

Temperature

[K]

Inlet Center

Velocity

[m/s]

Air Density

[kg/m3]

No Diffuser 101,118 293 72.61 1.202

3.5 Base 101,302 289 72.31 1.223

3.5 Base + Flat 100,798 292 72.64 1.204

3.5 Base + Flat +

Conical 101,236 293 72.51 1.205

7.5 Base 101,070 294 72.28 1.251

The first diffuser for discussion will be the “3.5 Base”. Figure 32 and Figure 33 show

the 2-D non–dimensionalized pressure and velocity distributions obtained at 1/8 inch

downstream of the drive shaft.

42


Distribution at Exit for 3.5 Base Geometry – Small Scale – Fully Developed Flow

43

Figure 33 – Experimental 2-D non–dimensionalized Velocity Profile at Exit for 3.5 Base

Geometry – Small Scale – Fully Developed Flow

The pressure and velocity contour plots show asymmetric behavior at 45ᵒ, 190ᵒ, and 330ᵒ

orientations. It is believed that these regions are formed mostly due to the effect of the nacelle

on the flow field. Considering that the struts are located at 60ᵒ, 180ᵒ, and 300ᵒ, it can be

concluded the drop in pressure is due to the struts. The highest velocities recorded are located in

the dark red ring around the center of the diffuser. The highest recorded non-dimensionalized

velocities are in the 0.897 range, which is 0.0828 lower than the velocities taken for the no

diffuser case. The maximum velocity was recorded at (0.233, 0) where magnitude was

calculated as 0.899. The flow is slowed down considerably along the wall of the diffuser and

can be viewed in the figures above. It is also observed at the (0, 0) location, the non-

44

dimensionalized velocity recorded was practically zero, which was caused by the drive shaft

protruding from the exit of the diffuser.

Illustrated below in Figures 34 and Figure 35 are the 2-D contour plots for the “3.5 Base

+ Flat Tunnel” non–dimensionalized total pressure and velocity distributions.

Figure 34 – Experimental 2-D contour plot Total Pressure Distribution at Exit for 3.5 Base

+ Flat Geometry – Small Scale – Fully Developed Flow

45

Figure 35 – Experimental 2-D contour plot Velocity Profile at Exit for 3.5 Base + Flat


As seen from the 2-D non–dimensionalized pressure and velocity contour plots it can be stated

that the asymmetric shape observed for the “3.5 Base” geometry is still very apparent with the

“Flat” attachment. The pressure and velocity drop at 60ᵒ, 180ᵒ, and 300ᵒ orientations. Similar to

the previous model, these drops are due to the effect of the struts on the flow. It can also be

observed that the highest pressure and velocity values were recorded on the top half of the

model, where both non–dimensionalized velocity and pressure distributions reach their maxima.

This could indicate flow separation on the bottom half of the diffuser, causing higher velocities

above the X axis. The highest non-dimensionalized velocity value was recorded at (0.310, 0)

with a value of 0.84. The minimum values recorded were along the wall at 45ᵒ, 135ᵒ, 225ᵒ, and

46

315ᵒ. The center velocity was 0.84, this lower value is due to the drive shaft located on the “3.5

Base” geometry. The maximum value along the negative X axis was 0.783 and the maximum

along the positive X axis was 0.840. It can also be observed that with the addition of the “Flat”

attachment on the “3.5 Base” geometry the maximum non–dimensionalized velocities and

pressures were reduced at the exit for the same inlet conditions. This indicates a reduction in the

pressure losses for the “3.5 Base + Flat” geometry in comparison to the “3.5 Base” geometry.

Figure 36 and Figure 37 illustrate the 2-D contour plots for both non–dimensionalized

pressure and velocity distributions for the “3.5 Base + Flat + Conical” geometry.

47


Distribution at Exit for 3.5 Base + Flat + Conical Geometry – Small Scale – Fully

Developed Flow

Figure 37 – Experimental 2-D contour plot non–dimensionalized Velocity Profile at Exit for

3.5 Base + Flat + Conical Geometry – Small Scale – Fully Developed Flow

The “3.5 Base + Flat + Conical” geometry figures show an irregular non–dimensionalized

velocity and pressure distributions with truncated rings resulting from the “conical” attachments.

The truncated rings in from the conical attachment associate with a pressure decrease in the

pressure distribution. The maximum value occurs in a circle around the center of the model as

well as at 45ᵒ, 180ᵒ, and 315ᵒ orientations, as seen in Figure 36 and Figure 37. The nacelle

48

causes an almost zero velocity reading at the 0ᵒ, 135ᵒ, and 215ᵒ orientations, which in comparison

to the previous two models is a much lower non–dimensionalized velocity reading at the same

locations. The lower pressure readings at those orientations are most likely due to the two sets of

struts that are present in this model. The “3.5 Base” diffuser has struts oriented at 60ᵒ, 180ᵒ, and

300ᵒ and the “conical” attachment has struts located at 0ᵒ, 120ᵒ, and 240ᵒ. These struts cause a

disturbance in the flow and result in lower pressure readings. The maximum value for this

diffuser is located at (0.310, 0.310) with a magnitude of 0.753. The lowest maximum velocity

value was recorded in this diffuser in comparison to the other geometries. Similar to previous

cases, lower velocities occur around the center drive shaft and along the walls of the diffuser.

The distribution is symmetric with respect to Y axis. For the positive side of the X-axis, the

maximum value was 0.647 and the maximum for the first peak on the negative side of the X-axis

was 0.637. The next two peaks show a larger difference in the values. The value for the positive

side of the X-axis for the second peak was 0.537 and the maximum value for the negative side of

the X-axis for the second peak was 0.590. These peaks show a difference of 0.055 from the

positive side to the negative side of the X-axis. Lastly, the third peaks from about the Y axis are

symmetrical. The maximum for the positive side was 0.394 and the negative side was 0.387,

which only shows a 0.007 difference. This shows that any type of flow separation can be ruled

out for this case.

Lastly Figure 38 and Figure 39 display both non–dimensionalized pressure and velocity

distribution plots for the “7.5 Base Tunnel’ geometry.

49


Distribution at Exit for 7.5 Base Geometry – Small Scale – Fully Developed Flow

50

Figure 39 – Experimental 2-D contour plot non–dimensionalized Velocity Profile at Exit for

7.5 Base Geometry – Small Scale – Fully Developed Flow

The “7.5 Base” diffuser case has the least amount of symmetry both for the non–dimensionalized

velocity and pressure distributions. Unlike the previous case figures, this case has a more oval

shaped distribution compared to the symmetric circular distributions observed for the first three

diffusers. The asymmetrical shape for this distribution could be due to flow separation upstream

of the exit of the diffuser. Previous research by King (2012) concluded that simulation for this

same case had flow separation. This affect can be seen in Figure 40.

51

Figure 40 - – SolidWorks Flow Simulation Total Pressure Distribution through tunnel

Cross-Section for 7.5 Base Tunnel - Small Scale - Uniform Flow (King, 2012)

This figure shows a large difference in pressures simulated from the top of the diffuser to the

bottom of the diffuser, proving flow separation is evident. In addition at the half angle on this

figure it is shown that the flow is separating from the wall further indicating this geometry has

separation. It can be stated from Figure 38 and Figure 39 that the maximum values for both the

pressure and velocity are located at the 90ᵒ and 270ᵒ locations. The maximum value is located at

(0.465, 0) with a value of 0.924. This is the highest value obtained including all four diffuser

models. From the 2-D pressure contour plot, it can be observed that there is a drop in pressure

due to the struts at 60ᵒ, 180ᵒ, and 300ᵒ. The centerline non–dimensionalized velocity depicts the

asymmetry in this case, although the peaks for the velocity are very similar. The positive side of

the X-axis has a maximum of 0.924 and the negative side of the X-axis has a maximum value of

0.879. The issue is on the positive side of the X-axis where the value at (0.621, 0) is 0.692 and

the value at (-0.621, 0) is 0.385. With this much of a discrepancy, it is most likely that a

52

separated flow is present in this region, causing the values on the positive side of the Y-axis to be

larger than the values on the opposite side of the axis.

3.2 Uncertainty Analysis

In order to determine the uncertainty in the measurements two data sets were taken twice.

The two data sets that were repeated were the “No Diffuser” and “7.5 Base” geometries. The

uncertainty in the data were calculated both using the Chauvenet’s criterion (Coleman and

Steele, 1999; Reddy, 2011) and the method described by Kline and McClintock (1953).

The uncertainties in the data collected for this research was determined by analyzing

pressure measurements repeated on different days under the same experimental conditions for

two separate diffuser cases and using the Chauvenet’s criterion. Chauvenet’s criterion is a very

commonly used technique to eliminate the outlier data points from a set of data points (Coleman

and Steele, 1999; Reddy, 2011). The criterion states that for a data set consisting of N

observations with a normal distribution and a constant variance the outlier points can be

identified and rejected. The outlier points are identified as the points with deviations from the

mean such that the probability of occurrence of such deviations exceeds 1/(2N).This description

allows defining a ratio of acceptable deviation to standard deviation, 𝑑𝑚𝑎𝑥/𝜎 for a given the

number of data points as small as N=2. In the current research an average 𝑑max was calculated

using two separate data sets taken at an axial location. The two sets were used to calculate the

deviations as the half the difference between two data values at the same radial location. The

average deviation was then calculated and used as the 𝑑max. The standard deviation, 𝜎 was then

calculated using the 𝑑𝑚𝑎𝑥/𝜎 given by the Chauvenet’s criterion. The calculated 𝜎 value was then

used to define the uncertainty associated with a quantity as ±2σ.

53

For two readings, the standard deviation given by Chauvenet’s criterion is:

𝑑𝑚𝑎𝑥

𝜎= 1.15. (3.2.1)

The first step for using this criterion was to calculate the mean value and maximum deviation for

the two sets of data points. The standard deviation was then found between the two sets of data

for each point. Figure 41 and Figure 42 show the maximum deviation from the mean for the

‘No Diffuser’ and ‘7.5 Base’ geometries.

Figure 41 – Experimental Velocity Deviation from the Mean - No Diffuser – Vc = 72.5 m/s,

D = 1.61 inches

0.543

0.388

0.232

0.077

-0.077-0.232

-0.388-0.543

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4

54

Figure 42 – Experimental Velocity Deviation from the Mean - 7.5 Base – Vc = 72.5 m/s, D =

1.61 inches

For the ‘No Diffuser’ geometry, most of the large deviations from the mean fall along the edges

of the distribution. In the ‘7.5 Base’ case the maximum deviation falls at the center of the

distribution. There are also some high deviations along the edges for this case as well. To obtain

the average uncertainty in terms of change in velocity for the entire data set Equation (3.3.2) was

utilized.

∆𝑉 = ±2 (𝑑𝑚𝑎𝑥𝑑𝑚𝑎𝑥

𝜎

) ; ∆𝑉 = ±2𝜎 (3.2.2)

Nondimensional velocity uncertainty 3D contour plots for both the ‘No Diffuser’ and ‘7.5 Base’

are shown in Figure 43 and Figure 44.

0.543

0.310

0.077

-0.155

-0.388

0

0.05

0.1

0.15

0.2

0.25

0.3

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3

55

Figure 43 – Experimental Chauvents’s Criterion Uncertainty of Velocity - No Diffuser – Vc

= 72.5 m/s, D = 1.61 inches

0.543

0.388

0.232

0.077

-0.077

-0.232

-0.388-0.543

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7

56

Figure 44 – Experimental Chauvents’s Criterion Uncertainty of Velocity - 7.5 Base Diffuser

– Vc = 72.5 m/s, D = 1.61 inches

The average uncertainty was calculated for both cases and is listed in Table 3. The percent

uncertainty was calculated from the average velocity uncertainty in relation to the inlet center

velocity of 72.5 m/s.

Table 3 – Chauvenet’s criterion uncertainty No Diffuser and 7.5 Base Models

No Diffuser 7.5 Base

Velocity Uncertainty, ∆𝑉 ±5.39% ±6.95%

Uncertainty analysis was also determined using the Kline and McClintock (1953)

method, which is based on the specific uncertainites from the experimental measurements. To

obtain the final velocity profile for each diffuser case Bernoulli’s equation was used to solve for

the velocity shown in Equation (3.3.3).

0.543

0.310

0.077

-0.155

-0.388

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3 0.3-0.35 0.35-0.4 0.4-0.45 0.45-0.5

57

𝑃𝑜 − 𝑃 = 1

2∗ 𝜌𝑈2 ; 𝑈 = √

2(𝑃𝑜−𝑃)

𝜌 (3.2.3)

The measurements needed to solve for the velocity were the total pressure (𝑃𝑜), atmospheric

pressure (𝑃), and temperature (T). Using these values, the air density was solved for and was

used to make the final velocity calculations. The accuraccies of each instrument is listed in

Table 4. The full scale range of the transducers for the NetScanner is 10” of water (2,500 Pa)

and the uncertainty of the NetScanner was reported from the manual as 0.05%.

Table 4 - Instruments Measurement Uncertainty

∆𝑃𝑜 ∆𝑃 ∆𝑇

Uncertainty ±12.5 𝑃𝑎 ±12.5 𝑃𝑎 ±0.1 𝐾

Using these uncertainties the uncertainty for the calculated velocity value can be obtained by

using Equation (3.2.3).

∆𝑈 = √(𝜕𝑈

𝜕𝑃𝑜∆𝑃𝑜)

2+ (

𝜕𝑈

𝜕𝑃∆𝑃)

2+ (

𝜕𝑈

𝜕𝜌∆𝜌)

2 (3.2.3)

The partial derivative of the Bernoulli’s equation, with respect to the independent variables total

pressure, atmospheric pressure, and density were taken and shown below in Equation (3.2.4).

𝜕𝑈

𝜕𝑃𝑜=

1

𝜌𝑈 ;

𝜕𝑈

𝜕𝑃= −

1

𝜌𝑈 ;

𝜕𝑈

𝜕𝜌= −

𝑈

2𝜌 (3.2.4)

Since the density was not actually measured, the uncertainty must be determined in the same

manner as the velocity. Atmospheric pressure and temperature were measured and inserted into

Equation (3.2.5) to solve for the air density.

𝑃 = 𝜌𝑅𝑇 ; 𝜌 =𝑃

𝑅𝑇 (3.2.5)

58

Since the atmospheric pressure and temperature have uncertainty in their measurements, as

stated above, the partial derivatives were taken with respect to both measurements using

Equation (3.2.5) and are displayed below in Equation (3.2.6).

𝜕𝜌

𝜕𝑃= −

1

𝜌𝑈 ;

𝜕𝜌

𝜕𝑇= −

𝜌

𝑇 (3.2.6)

The partial derivatives and uncertainties were factored into Equation (3.27) to solve for the

uncertainty in the density measurement.

∆𝜌 = √(𝜕𝜌

𝜕𝑃∆𝑃)

2+ (

𝜕𝜌

𝜕𝑇∆𝑇)

2 (3.2.7)

The final velocity uncertainty was then determined using Equation (3.2.8).

∆𝑈 = √(1

𝜌𝑈∗ ∆𝑃𝑜)

2

+ (−1

𝜌𝑈∗ ∆𝑃)

2

+ (−𝑈

2𝜌∗ √(−

1

𝜌𝑈∆𝑃)

2

+ (−𝜌

𝑇∆𝑇)

2

)

2

(3.2.8)

The values for the velocity uncertainty for each of the five diffuser cases are listed in Table 5.

The average velocity uncertainty for each distribution in relation to the inlet center velocity of

72.5 m/s has given the percent uncertainty for each diffuser geometry.

Table 5 – Uncertainty of Velocity Measurements for the 4 Diffusers and No Diffuser Cases

No

Diffuser

3.5 Base

3.5 Base +

Flat

3.5 Base + Flat +

Conical

7.5 Base

Uncertainty ±1.42% ±1.13% ±2.03% ±1.05% ±0.84%

The graphs for the velocity uncertainty for each case can be viewed in Appendix D.

59

3.3 Comparison of Experimental and CFD Pressure Losses for Diffuser Geometries

Comparison of the experimental and CFD results were made using nondimensional data.

Velocities for the experimental data were non-dimensionalized using the V𝑐 = 72.5 𝑚/𝑠. The

pipe exit diameter, D = 1.61 inches was used to non-dimensionalized the traversing distances

both in the X and Y axes for each diffuser velocity profile. Each diffuser velocity distributions

were presented using 2-D and 3-D contour plots. In addition to the contour plots, line plots of

the data corresponding to the Y stations at each X measurement location were generated. These

graphs were generated to show the geometric trends of the data. Each graph included five line

plots representing the X location of the data to allow for clear representation of the Y station

data. The graphs were labeled by sections showing where the data was obtained. Each of the

four diffuser models’ velocity distributions were plotted with three graphs for each location

along the X-axis. These plots can be viewed in Appendix E. Some of the unique plot trends will

be discussed in detail in the next chapter.

To quantify the relative loss of power the head loss coefficient through the diffuser was

calculated. Locations used for power loss calculations are illustrated in Figure 45.

3

60

Figure 45 - General Locations for Power Loss Calculations relative to the SARL Wind

Tunnel Fan Duct and Diffuser Sections (King, 2011)

The head loss coefficient through the diffuser can be expressed as

ℎ𝐿 =(𝑃1−𝑃2)+

1

2𝜌(𝑉1

2−𝑉22)

𝜌𝑔 (3.3.1)

Locations 1 and 2 on Figure 45 refer to the inlet and exit of the diffuser. Due to geometrical

access limitations velocities were not measured at these locations. Instead location 3 was

used to calculate the pressure losses for each diffuser model. Location 3 is the location 1/8”

downstream of the drive shaft where the experimental results were recorded. Pressure losses

at location 3 were calculated using the following equation.

ℎ𝐿3 = 1

2𝜌𝑉3

2

𝜌𝑔 (3.3.5)

An average pressure loss for each diffuser was calculated using the individual pressure loss

calculated at each X and Y position. Table 6 gives the total averaged pressure losses

obtained using the experimental results at location 3.

Table 6 – Experimental Head Losses of Diffuser Models – Fully Developed Flow –

Small Scale

Diffuser Geometry

Pressure Losses

Small Scale, hL3

(m)

Non-dimensionalized

Pressure Losses Small

Scale, Vc = 72.5 m/s,

ℎ𝐿3/𝑉𝑐

2

2𝑔

Percentage

Improvement in Losses

in comparison to 7.5

base case,

61

(hL3-hL3-7.5Base)/hL3-7.5Base

3.5 Base 95.174 0.3553 2.9715

3.5 Base + Flat 83.745 0.3077 14.6234

3.5 Base + Flat

+ Conical

61.607 0.2266 37.1927

7.5 Base 98.089 0.3661

For comparison purposes against the CFD results the losses were normalized using the equations

below.

ℎ𝐿𝑐 = 1

2𝜌𝑉𝑐

2

𝜌𝑔 (3.3.6)

𝑁𝑜𝑛 − 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙𝑖𝑧𝑒𝑑 ℎ𝐿3 = ℎ𝐿3

ℎ𝑙𝑐 (3.3.7)

Results indicate that the most efficient diffuser is the “3.5 Flat + Conical” model showing head

losses of 61.6 m. With a head loss of 83.7 m the “3.5 Base + Flat” diffuser ranks second best

followed by the “3.5 Base” model. Table 6 also tabulates the percentage improvement from the

original “7.5 Base” diffuser. As stated previously the “3.5 Base + Flat + Conical” provides the

largest percentage increase in reducing the losses by 37.1%. All the diffuser cases show an

improvement compared to the base model, with a 14.6% increase for the “3.5 Base + Flat” model

and a 2.97% increase for the “3.5 Base” model. From a previous study by Britcher (2011) it was

stated that 30% of the losses occurring throughout the SARL tunnel occur at the exit. With 30%

of the losses occurring at the exit, the pressure losses of the SARL tunnel from each diffuser can

62

be calculated to show the impact of each diffuser case on the overall performance of the tunnel.

Table 7 consists of the percentage improvements for each diffuser case for the overall tunnel.

Table 7– Experimental Percentage Improvement in efficiency from the 7.5 Base Model for

the entire SARL tunnel – Fully Developed Flow - Small Scale.

Diffuser Geometry

Percentage Improvement for SARL

tunnel,

(hL3-hL3-7.5Base)/hL3-7.5Base*30%

3.5 Base 0.891

3.5 Base + Flat 4.387

3.5 + Flat + Conical 11.157

The “3.5 Base + Flat + Conical” geometry shows the largest improvement for the entire tunnel

with approximately an 11.1% improvement. This large improvement in overall efficiency could

be significant in reducing the cost of operations.

To extrapolate the experimental results to the full scale SARL tunnel scale factors were

required. These scale factors were determined using from the previous CFD work by King

(2012), in which he made CFD simulations of the small and full scale models. Using the CFD

head loss calculations for both the small scale and full scale models scale factors were

determined for all of the diffusers. These scale factors were then used with the experimental

results to estimate the head losses for the full scale tunnel with assumed diffuser attachments. It

should be noted here that the CFD total pressure loss calculations used in this section were

obtained using the CFD results obtained at stations 1 and 2 previously shown in Figure 45.

Results for the CFD simulations can be viewed in Table 8.

63

Table 8 - ANSYS FLUENT Head Losses by Diffuser Geometry (King, 2012)

Small Scale Models Full Size Models

Uniform Flow Fully Developed Flow Uniform Flow Fully Developed Flow

7.5 Base Tunnel 160.848472 m 126.8040263 m 113.0444985 m 106.2995676 m

3.5 Base Tunnel 198.9305041 m 159.0046268 m 153.7993301 m 136.1212656 m

3.5 + Flat 128.6798943 m 103.802302 m 108.2979733 m 94.53623618 m 3.5 + Flat +

Conical 139.3758639 m 104.8927772 m 96.23651085 m 84.12098481 m

Due to an error discovered in the CFD results, for the ‘3.5 + Flat’ fully developed small scale

flow, the scaling factor to the full scale model used is an estimated value and is used as a

representative number. The “3.5 + Flat” case small to full scale ratio was calculated using the

incorrect value for the small scale model head losses divided by the full scale model head losses.

For this case the CFD results were obtained with wrong size struts causing false results. The

ratio for the CFD simulations of small scale to full scale for each diffuser model are listed in

Table 9.

Table 9 – Pressure loss scale factor between the small scale model and the full scale tunnel

calculated using CFD results, hl_small/hl_full

Diffuser Geometry Small to Full Scale Ratio CFD simulations

3.5 Base 1.168

3.5 Base + Flat 1.098

3.5 + Flat + Conical 1.247

7.5 Base 1.193

64

Small to full scale ratios are used for an approximation for pressure losses for the full scale

SARL tunnel. Extrapolated approximate experimental total pressure losses for the full scale

model are listed in Table 10.

Table 10 – Experimental Approximation of total pressure losses – Fully Developed Flow –

Full Scale

Diffuser Geometry

Pressure Losses Full

Scale, hL3 (m)

Percentage

Improvement in

Losses in comparison

to 7.5 base case,

(hL3-hL3-7.5Base)/hL3-

7.5Base

Percentage

Improvement for

SARL tunnel,

(hL3-hL3-

7.5Base)/hL3-7.5Base

*30%

3.5 Base 81.489 0.893 0.268

3.5 Base + Flat 76.272 7.238 2.171

3.5 + Flat + Conical 49.404 39.915 11.974

7.5 Base 82.223

From these head loss approximations a percent increase in efficiency from the “7.5 Base”

original tunnel was calculated. The results have shown for the full scale approximations for the

“3.5 Base” and “3.5 Base + Flat” decreased in percent improvement from 2.9% to 0.892% and

14.6% to 7.2% in comparison to the small scale results.. The diffuser that showed the most

improvement for the overall efficiency for the small scale tunnel remained the same for the full

scale tunnel with improved results. The “3.5 Base + Flat + Conical” shows an increase from

65

37.1% to 39.9%. If the same relation is used from Britcher (2011), that 30% of the losses occur

at the exit. The overall increase of efficiency for the entire tunnel for each case is as follows in

Table 10. The approximation for the full scale efficiency improvements for the entire tunnel

show that a significant increase of 11.9% is possible with the “3.5 Base + Flat + Conical”

geometry. This shows an increase from the small scale model of 0.8%. Installation of the “3.5

Base + Flat + Conical” geometry on the full scale model would have a possible improvement in

efficiency of 11.9%.

3.4 Experimental and CFD total pressure loss Comparison at Station 3

The same calculations were made for the CFD results obtained 1/8 inch downstream of the

drive shaft for comparison against the experimental results. Table 11 contains the pressure losses

for the CFD results. To compare the CFD results to the experimental measurements the CFD

pressure losses were normalized with an inlet center velocity of 60 m/s.

Table 11 - CFD simulation of Total Head Losses by Diffuser Model - Fully Developed Flow

– Small Scale

Diffuser Geometry

Pressure Losses

Small Scale

(Pascal)

Normalized

Pressure Losses

Small Scale

Percentage

Improvement in

Losses

3.5 Base 57.966 0.3108 -8.862

3.5 Base + Flat 38.510 0.2064 27.706

3.5 + Flat + Conical 29.288 0.1569 45.044

7.5 Base 53.279 0.2855

66

As seen from Table 11 the most efficient diffuser model was the “3.5 Base + Flat + Conical” with

the lowest pressure loss of 29.288 m. This is consistent with the experimental results, where the

same model showed the least amount of losses. In addition, it can be seen that the “3.5 + Base +

Flat” decreased pressure losses from the “7.5 Base” model. The “3.5 + Base + Flat had an average

pressure loss of 38.510 m. Where the CFD results and the experimental results differ are in the

next two cases. The CFD results for the “3.5 Base” model did not actually show an improvement

from the “7.5 Base” model. The “3.5 Base” had an average pressure loss of 57.966 m, where the

“7.5 Base” model had an average pressure loss of 53.279 m. The experimental measurements

show that the “3.5 Base” geometry showed an improvement from the “7.5 Base” geometry

installed on the SARL tunnel currently. As stated previously is it shown that the greatest

improvement in pressure losses can be achieved from the “3.5 + Flat + Conical” geometry with an

improvement of 45.044%. With an improvement of 27.706% the “3.5 Base + Flat” model would

also greatly improve the pressure losses in the SARL tunnel. CFD results for the “3.5 Base”

geometry shows an increase in pressure losses and a percentage decrease of 8.862% from the “7.5

Base” geometry.

3.5 Comparison of Experimental Results and CFD simulations

This section discusses the comparison between non–dimensionalized experimental and

CFD results. Percent difference calculations were completed to quantify the differences between

to the two sets of results. Equation (3.4.1) was utilized to find the percent difference between the

results, where ER denotes the experimental result and CR denotes the computational result.

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =∑|𝐸𝑅−𝐶𝑅|

𝑁∗ 100 (3.4.1)

67

Difference calculations were made for each distribution at each XY location. These results were

added across the X axis and divided by N, which represent the number of points in the

summation. These percent difference calculations are presented at each Y location of each

distribution. The diffuser geometries were graphed using a scatter plot for the percent difference.

In addition, the experimental and CFD results were plotted as line plots at each Y – axis

location to so show the velocity distribution trends across the X – axis. The uncertainty of the

experimental results were included in these plots to show a better comparison to the CFD results.

15 plots were made for each diffuser geometry to compare the experimental and computations

results. These plots are presented in Appendix E.

The “3.5 Base” comparison shows the best correlation for all four diffusers models. The

largest differences lie at the Y/D = -0.543, Y/D = -0.465, and Y/D = -0.077. The percent

differences for each Y location can be viewed in Figure 46.

Figure 46 - Percent Difference between Experimental and CFD results - 3.5 Base - Small

Scale

0

2

4

6

8

10

12

14

16

18

20

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Per

cent

Dif

fere

nce

Y/D

68

It can be stated, that a large variance in percent difference across the entire distribution is

present. Outliers are present along the top edge of the diffuser at Y/D = -0.077 where the largest

difference is 17.6%, which is considerably higher than the average. The average percent

difference calculated across the entire distribution was 11.7%. It can be stated from Figure 46

that much higher percent difference seems to occur closer to the center of the distribution. The

lowest percent difference occurs at Y/D = 0.543 with a value of 3.19%. For the entire

distribution the two sets seem to have very similar trends but the difference comes mostly from

the magnitude of the velocity. For most of the Y – locations the CFD results have a considerably

lower velocity around the center of the distribution.

The “3.5 Base + Flat” diffuser geometry shows as the data approaches the center, at Y =

0, it begins to show a better agreement. This set of data shows the third best correlation for the

diffuser models. Similar to the “3.5 Base” model along the edge of the X – axis seems to give

best agreement of the data. There also seems to be an issue with the shapes of the distribution

across the X – axis. The experimental data shows maxima across the X – axis where the CFD

simulations show two maxima, which is be shown in Figure 47.

69

Figure 47 - Experimental and CFD Non-dimensionalized Velocity comparison at Y/D =

0.155

There is also another disagreement with the magnitude of the velocity approaching X/D = 0.

Excluding Y/D = 0.543 and Y/D = 0.465 the experimental results show a greater velocity and

begins to separate from the CFD simulations. To visualize the difference numerically a percent

difference calculation was completed for each of the Y – locations and are shown in Figure 48.

70

Figure 48 – Percent Difference of Experimental and CFD results - 3.5 Base + Flat - Small

Scale

It is shown that the majority of the high difference lies closer to the edges of the velocity

distribution. The distribution shows a large variance in correlation, with a maximum percent

difference of 27% at Y/D = 0.543 and a minimum percent difference of 5% at Y/D = -0.077.

From the percent difference calculations, with the outliers discarded, the average percent

difference for this distribution becomes 16.9%.

The next diffuser model is the comparison of the “3.5 Base + Flat + Conical” geometry.

This geometry seems to have the least agreeable distribution between the experimental and CFD

results, which is due to the complex velocity distribution created by the effects of re-directing the

flow from the conical attachment. Very similarly to the previous “3.5 Base + Flat” geometry, the

agreement between the two sets of data seems to increase as the data moves closer to the (0, 0)

location. The maximum and minimum peaks are reversed for the two sets of data for many of

the plots. This can be seen at Y/D = -0.232, where there is a maximum peak for the experimental

0

5

10

15

20

25

30

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Per

cen

t D

iffe

ren

ce

Y/D

71

results the same location for the CFD results show a minimum peak. The percentage difference

was calculated at each Y – location to show where the largest disagreement is located. The

values for percentage difference can be viewed in Figure 49.

Figure 49 - Percent Difference of Experimental versus CFD results - 3.5 Base + Flat +

Conical - Small Scale

Unlike the previous diffuser models where the large percent difference lies on the edge of the

distribution there is significant difference present throughout the entire model. The velocity

distribution at the location Y/D = 0.465 has a difference of 159%. Maximum percent difference

is calculated at Y/D = -0.310 with a value of 181% and the minimum value of 17.7% at Y = 0.

This comparison has a consistently poor correlation to the CFD results for the entire distribution.

The average percent difference is 22.7%, with the large outliers removed from the calculation,

this diffuser geometry shows the worst correlation. As for the high difference for the entire

distribution many factors could have affected both sets of data.

0

50

100

150

200

250

300

350

400

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Per

cent

Dif

fere

nce

Y/D

72

Lastly it is shown, for the ‘7.5 Base’ geometry that at the top of the distribution at Y/D =

0.543 and Y/D = 0.465 the largest difference in the experimental and CFD results exists. Moving

closer to the center of the distribution the trends show very similar curves. The non-

dimensionalized experimental results show a larger magnitude then the CFD results, for most of

the distribution. From the plots it seems that at Y/D = 0.310 shows the best correlation across

the whole distribution. To quantify the comparison for this model a percentage difference

calculation was completed to analyze the comparison. Figure 50 complies the percent difference

for the “7.5 Base” geometry comparison.

Figure 50 – Percent Difference of Experimental and CFD results - 7.5 Base - Small Scale

The largest percent difference was at Y/D = 0.543 where is was calculated to 267%. The lowest

percent difference was at Y/D = -0.155 with a value of 4.85%. There is a continuous trend that

towards the edges of the distribution a higher difference is present. When the outliers are

discarded from the percent difference calculation along the edges the average percent difference

is 13.6%. This diffuser geometry show the second best correlation. Finally, the results for both

the experimental and CFD calculations indicated that a separated flow exists in this model.

0

50

100

150

200

250

300

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Per

cent

Dif

fere

nce

Y/D

73

Overall the comparison of the experimental and CFD results has concluded in a poor correlation

resulting in disproval of the CFD results.

74

CHATPER 4

CONCLUSION

4.1 Conclusion

The main focus for this research was to experimentally identify a diffuser geometry that

would result in the largest reduction in total pressure losses. Total pressure values measured 1/8”

downstream of the tunnel exit were utilized in determining the most efficient diffuser geometry.

Based on the previous research evaluating diffusers with different shapes and sizes four

geometry shapes were identified and used within the current experiments (Olcmen, 2011).

Selected four geometries consist of the base model diffuser currently being utilized in the SARL

tunnel, 8ᵒ half-apex angle labeled as “7.5 Base”, 3.5ᵒ half-apex angle labeled as “3.5 Base”, a

modified version of the “3.5 Base” with the addition of a constant area flat diffuser labeled as

“3.5 Base + Flat”, and a modification of the 35F with the addition of an annular conical

attachment labeled as “3.5 Base Flat + Conical”. A “3.5 Base” model with both the flat and

conical attachments was previously analyzed and evaluated to be resulting in the greatest

reduction in total pressure losses for the SARL tunnel. ANSYS FLUENT and SolidWorks Flow

simulations were made to evaluate the efficiency of each diffuser in comparison the original

SARL tunnel. CFD results concluded that the “3.5 Base + Flat + Conical” geometry showed the

largest reduction in total pressure across the pressure distribution. The models that were used in

the CFD calculations were fabricated using a 3-D printer at the WPAFB-AFRL. An experimental

set up was designed to supply a fully developed flow with an inlet uniform pipe velocity of 60

75

m/s with a diffuser center inlet velocity of 72.5 m/s. A Kiel probe and a NetScanner pressure

scanner was used to record the total pressure values of the “3.5 Base”, “3.5 Base + Flat”, “3.5

Base + Flat + Conical” and, “7.5 Base” diffuser geometries. The total pressure readings for each

geometry were evaluated and compared against the CFD results. Average total pressure losses

were calculated to quantify the reduction in losses and improved efficiency for the SARL tunnel.

Experimental research on the small scale diffusers has shown that large reduction in

pressure losses can be achieved at the exit of the SARL tunnel. Experimental results show that

the “3.5 Base + Flat + Conical diffuser” model is the best diffuser in reducing the losses at the

exit of the tunnel in reference to the original “7.5 Base” model. The “3.5 Base + Flat + Conical”

model shows a 37.1% reduction in total pressure losses for the small scale model, with an overall

tunnel efficiency improvement of 11.1%. In addition, the full scale approximation for this model

shows a 39.9% improvement in total pressure losses and an overall tunnel efficiency

improvement of 11.9%. This was as expected as indicated by the preliminary diffuser designs

(Olcmen, 2011). The “3.5 Base + Flat” model showed an experimental reduction of pressure

losses of 14.6% and overall tunnel efficiency improvement of 4.38%. Due to the error in the

CFD fully developed small scale results for the ‘3.5 Base + Flat’ model, the approximation to the

full scale SARL tunnel has been omitted. Experimental results show that the “3.5 Base” model

reduced total pressure losses by 2.97% and improved the overall efficiency of the tunnel by

0.891%. The approximated full scale results for the “3.5 Base” model shows a lower reduction

of total pressure losses of 0.893% and a 0.268% improvement in overall efficiency for tunnel.

In comparison the CFD results for the “3.5 Base + Flat + Conical” model shows the

largest reduction in total pressure losses of 45%. The “3.5 Base + Flat” also showed

improvement in total pressure losses from the “7.5 Base” model. CFD results showed a

76

reduction of total pressure losses for the “3.5 Base + Flat” model of 27.7%. King (2011) stated

that the “3.5 Base” model shows minimal improvements to the efficiency of the SARL tunnel.

CFD results show a decrease in reduction of total pressure losses of 8.1%. The large difference

between the experimental and CFD results were the experimental results showed an

improvement in total pressure loss reduction, where the CFD results showed a decrease in total

pressure loss reduction.

The comparison of the CFD and experimental results show a good correlation in

geometric trends but the magnitude is where the results differ. The CFD and experimental results

were compared in depth to show the percent difference between the two results for each diffuser

model. These analysis shows that there are large differences between the CFD results and the

experimental data at the shear layer near the jet’s edge. The large percent difference for each

diffuser geometry at the shear layer was omitted during the average percent difference

calculations. The average percent difference for the “7.5 Base” model was calculated as13.7%,

which showed the best correlation of all the models. Results showed that the “3.5 Base + Flat”

diffuser had a slightly higher difference by 16.9%. The “3.5 Base” model showed the third best

correlation of a 17.5% difference. Lastly, though the “3.5 Base + Flat + Conical” model showed

the largest reduction in total pressure losses it showed the least agreeable data with a percent

difference of 22.7%.

In conclusion, improvements in total pressure loss reduction can be achieved through

diffuser attachments. The experimental results have proven that the “3.5 Base + Flat + Conical”

model shows the largest improvement in total pressure loss reduction in the diffuser. In addition,

the CFD showed a similar result that the “3.5 Base + Flat + Conical” geometry gives the most

improvement to the SARL tunnel. Previous SARL analysis by Britcher (2011) states that large

77

improvements can be made in efficiency of the SARL tunnel by refining the current diffuser

geometry. These experimental results agree with Britcher’s (2011) analysis that with the use of

diffusers the efficiency and cost of operation can be positively impacted with the installation of

the “3.5 Base + Flat +Conical” diffuser geometry.

4.2 Future Work

The experimental procedure could show increased accuracy with improvements to the

experimental setup. An automated traverse could increase the accuracy when acquiring the

pressure readings. In addition, pressure distributions could be measured at both the inlet and exit

of the diffuser to show a better analysis of head losses through the entire diffuser. Improvements

could be made to acquire a more accurate velocity and pressure distribution with a laser based

technique. Considering such a fluctuating flow field downstream of the exit of the diffuser,

Particle Image Velocimetry (PIV) could be utilized to acquire the distributions. The use of PIV

would allow better understanding of the unsteady flow and would enable spatially resolved

measurements in much more timely manner (Raffel, 1998). As stated in King (2012), the Air

Force is interested in reducing the jet noise associated with the SARL tunnel. Experimental

acoustic measurements could be made to determine the noise generated by each of the diffuser

nozzles. Acoustic measurements could be analyzed for each diffuser model to show which

nozzle decreased noise. With both an investigation of the flow effects and noise measurements a

combined report would be very useful to determine the benefits gained by using each diffuser

geometry. In addition to the experimental results, the CFD results in this thesis show a

significant difference from the expected results. Comparison of a more accurate higher fidelity

CFD calculations could be completed. This will lend to a better comparison from the small scale

78

experimental results versus CFD results and aid in relating these results to the full scale SARL

tunnel.

79

REFERENCES

Britcher, Colin P., “Analysis of the AFRL SARL facility drive system”, Old Dominion

University, Department of Mechanical and Aerospace Engineering, Norfolk, VA, 2011.

Colemen, H. W., Steele, W. G., “Experimentation and Uncertainty Analysis for

Engineers – 2nd Edition” John Wiley & Sons, New York, NY, 1999.

Eckert, W.T., Mort, K.W., Jope, J., “Aerodynamic Design Guidelines and Computer

Program for Estimation of Subsonic Wind Tunnel Performance”, Ames Research Center and

U.S. Army Air Mobility R&D Laboratory, NASA TN D-8243, Moffett Field, CA, 1976.

Farokhi, S., Aircraft Propulsion, John Wiley & Sons, Hoboken, NJ, 2009, pp. 227-235.

Fox, R.W., McDonald, A.T., Pritchard, P.J., (2010). Introduction to Fluid Mechanics. 8th

Edition, John Wiley & Sons Inc.

Hoffman, K.A., Chiang, S. T., Computational Fluid Dynamics for Engineers – Volume I,

The Wichita State University, Wichita, Kansas, 1993.

Holman, J.P., “Experimental Methods for Engineers – 7th Edition”, McGraw-Hill

Companies, Inc., New York, NY, 2001, pp. 52-55; 98–101.

King, Christopher D. (2011), Computational Analysis of Diffuser Performance for

Subsonic Aerodynamic Research Laboratory Wind Tunnel, Thesis, The University of Alabama.

King, Christopher D., Ölçmen, Semih M., Sharif, Muhammad A. R., Presdorf, Tom

Computational Analysis of Diffuser Performance for Subsonic Aerodynamic Research Laboratory

Wind Tunnel. The University of Alabama, Aerospace Engineering and Mechanics Department,

Tuscaloosa, Al, 2013

Kline, S. J. and F.A. McClintock. “Describing Uncertainties in Single-Sample

Experiments,” Mechanical Engineering, January 1953.

Mehta RD, Bradshaw P (1979). Design rules for small low speed wind tunnels.

Aeronautical Journal 73:443-449.

Munson, B. R., Young, D. F., “Fundamentals of Fluid Mechanics – 3rd Edition”, John

Wiley & Sons, Inc., Canada, 1990.

Norris G., Dominy R.G. and Smith A.D.. Strut Influences Within a Diffusing Annular S-

Shaped Duct. Proceedings of ASME Turbo Expo 1998, Stockholm, Sweden, 98-GT-425, pp 1-9,

1998.

80

Ölçmen, S. M., “SARL Efficiency Improvement and Noise Reduction”, Final Report as Summer

Research Faculty supplied to WPAFB in Dayton, OH, 2011.

Presdorf TA (1992). Subsonic Aerodynamic Research Laboratory. Wright-Patterson Air

Force Base, WL-TR-3053, Wright-Patterson AFB, OH 45431, USA.

Raffel, Markus, Willert, Christian. E., Kompenhans, Jurgen., Particle Image Velocimetry,

Springer, New York, NY, 1998, pp. 1-10.

Schmidt, J., (May 19, 1989 data appended to) Analysis of the Langley Eight-Foot

Transonic Wind Tunnel Fan to be Used as the Drive Fan in the SARL Wind Tunnel, 1986.

Shuja SZ, Habib MA (1996). Fluid flow and heat transfer characteristics in axisymmetric

annular diffusers. Computers and Fluids 25(2):133-150.

Ubertini, Stefano, Desideri, Umberto, “Experimental performance analysis of an annular

diffuser with and without struts”, University of Perugia, Department of Industrial Engineering,

Perugia, Italy, 2000

White, Frank M., “Fluid Mechanics – 2nd Edition”, McGraw- Hill Companies, Inc., New

York, NY, 1986, pp. 337; 345 - 351

81

APPENDIX A

Normalized CFD Simulation Line Plot Velocity Distributions at 1/8 downstream of the drive

shaft

U = 60 m/s, D = 1.61 inches

Figure 51 – ANSYS FLUENT flow simulation Normalized Velocity of Section 1 at Exit for


82



83



84


3.5 Base + Flat Geometry – Small Scale – Fully Developed Flow

85



86



87



88



89





90



91



92

APPENDIX B

Data Reduction

Figure 63 – NetScanner United Software Startup screenshot for extracting raw data to

Excel

When the NUSS program is open the run button was clicked to open the playback

window. With the playback window open under the “playback controls” the raw data file was

93

selected to the right of the of “play” button. With the raw data selected the “options” were

selected to open the “Choose Window”. Under the “Playback Options” to convert the data

properly the “Skip Pausing on Events” and the “Skip Updating Run Form” had to be selected.

Continuing on below under the “Secondary File Format” the “Spreadsheet A” and “Stream 1”

was selected. With all the options in place the “Play” was run and the raw data was converted to

an excel file. This process was repeated for each data point for all the diffuser geometries. The

pressure readings for each location on the grid were averaged over the 15 seconds. Once the

average pressure readings was obtained, the velocity for each location was calculated using

Bernoulli’s equation. The data was taken each day for the atmospheric pressure and temperature

to calculate the velocity for each location. With the velocity data the velocity profile was graphed

in both excel and MatLab.

94

APPENDIX C

Uncertainty Distributions of Diffuser Geometries

Figure 64 - Experimental contour plot of uncertainty for velocity results of no diffuser –

small scale – fully developed flow – Vc = 72.5 m/s, D = 1.61 inches

0.543

0.310

0.077

-0.155

-0.388

0

0.02

0.04

0.06

0.08

0.1

0.12

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.02 0.02-0.04 0.04-0.06 0.06-0.08 0.08-0.1 0.1-0.12

95

Figure 65 - Experimental contour plot of uncertainty for velocity results of 3.5 Base – small

scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches

0.543

0.310

0.077

-0.155

-0.388

0

0.05

0.1

0.15

0.2

0.25

0.3

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3

96

Figure 66 - Experimental contour plot of uncertainty for velocity results of 3.5 Base + Flat

– small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches

0.543

0.310

0.077

-0.155

-0.388

0

0.1

0.2

0.3

0.4

0.5

0.6

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6

97

Figure 67 - Experimental contour plot of uncertainty for velocity results of 3.5 Base + Flat

+ Conical – small scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches

0.543

0.310

0.077

-0.155

-0.388

0

0.02

0.04

0.06

0.08

0.1

0.12

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.02 0.02-0.04 0.04-0.06 0.06-0.08 0.08-0.1 0.1-0.12

98

Figure 68 - Experimental contour plot of uncertainty for velocity results of 7.5 Base – small

scale – fully developed flow - Vc = 72.5 m/s, D = 1.61 inches

0.543

0.310

0.077

-0.155

-0.388

0

0.05

0.1

0.15

0.2

0.25

0.3

Y/D

Norm

aliz

ed V

eloci

ty

X/D

0-0.05 0.05-0.1 0.1-0.15 0.15-0.2 0.2-0.25 0.25-0.3

99

APPENDIX D

Normalized Experimental Measurements Line Plot Velocity Distribution 1/8” downstream of the

drive shaft

U = 72.5 m/s, D = 1.61 inches


Small Scale – Fully Developed Flow

100



101



102

Figure 72 – Experimental Normalized Velocity of Section 1 at Exit for 3.5 Base + Flat


103



104



105

Figure 75 – Experimental Normalized Velocity of Section 1 at Exit for 3.5 Base + Flat +

Conical Geometry – Small Scale – Fully Developed Flow

106





107



108



109



110

APPENDIX E

Comparison of Experimental versus CFD diffuser model results 1/8 downstream of the drive

shaft

U = 72.5 m/s, D = 1.61 inches (Experimental)

U = 60 m/s, D = 1.61 inches (CFD)

3.5 BASE

111

112

Figure 81 – Scatter plots of Experimental and CFD comparison for 3.5 Base Diffuser model

3.5 BASE + FLAT

113

114

115

Figure 82 – Scatter plots of Experimental and CFD comparison for 3.5 Base + Flat Diffuser

model

116

3.5 BASE + FLAT + CONICAL

117

118

Figure 83 - Scatter plots of Experimental and CFD comparison for 3.5 Base + Flat +

Conical Diffuser model

119

7.5 BASE

120

121

Figure 84 - - Scatter plots of Experimental and CFD comparison for 7.5 Base Diffuser

model

122

APPENDIX F

SolidWorks Diffuser model drawings

123

124

125

126

127

128

APPENDIX G

Experimental Raw Velocity Results 1/8” downstream of the drive shaft

NO DIFFUSER

(X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s]

(-0.875, 0.875) 0 (-0.75, 0.875) 0 (-0.625, 0.875) 0 (-0.5, 0.875) 0

(-0.875, 0.75) 0 (-0.75, 0.75) 0 (-0.625, 0.75) 0 (-0.5, 0.75) 0

(-0.875, 0.625) 0 (-0.75, 0.625) 0 (-0.625, 0.625) 2.358127 (-0.5, 0.625) 32.32866

(-0.875, 0.5) 0 (-0.75, 0.5) 2.060062 (-0.625, 0.5) 40.22937 (-0.5, 0.5) 54.66994

(-0.875, 0.375) 1.524901 (-0.75, 0.375) 13.01528 (-0.625, 0.375) 55.12887 (-0.5, 0.375) 61.44282

(-0.875, 0.25) 2.114597 (-0.75, 0.25) 50.13105 (-0.625, 0.25) 59.42683 (-0.5, 0.25) 64.63394

(-0.875, 0.125) 2.358352 (-0.75, 0.125) 54.07017 (-0.625, 0.125) 61.90174 (-0.5, 0.125) 65.9237

(-0.875, 0) 0.928691 (-0.75, 0) 54.93036 (-0.625, 0) 62.60178 (-0.5, 0) 66.29763

(-0.875, -0.125) 2.400664 (-0.75, -0.125) 54.14272 (-0.625, -0.125) 62.5823 (-0.5, -0.125) 66.47514

(-0.875, -0.25) 2.257022 (-0.75, -0.25) 50.16296 (-0.625, -0.25) 60.057 (-0.5, -0.25) 64.85133

(-0.875, -0.375) 1.494094 (-0.75, -0.375) 22.93465 (-0.625, -0.375) 53.76854 (-0.5, -0.375) 60.98752

(-0.875, -0.5) 0 (-0.75, -0.5) 2.38843 (-0.625, -0.5) 46.51178 (-0.5, -0.5) 56.26708

(-0.875, -0.625) 0 (-0.75, -0.625) 0 (-0.625, -0.625) 2.742467 (-0.5, -0.625) 42.49734

(-0.875, -0.75) 0 (-0.75, -0.75) 0 (-0.625, -0.75) 0 (-0.5, -0.75) 0

(-0.875, -0.875) 0 (-0.75, -0.875) 0 (-0.625, -0.875) 0 (-0.5, -0.875) 0


(-0.375, 0.875) 0 (-0.25, 0.875) 0 (-0.125, 0.875) 0 (0, 0.875) 1.595264

(-0.375, 0.75) 1.795689 (-0.25, 0.75) 33.91509 (-0.125, 0.75) 47.2556 (0, 0.75) 48.06227

129

(-0.375, 0.625) 52.66904 (-0.25, 0.625) 56.49376 (-0.125, 0.625) 57.57699 (0, 0.625) 58.47519

(-0.375, 0.5) 59.40782 (-0.25, 0.5) 61.98952 (-0.125, 0.5) 62.53213 (0, 0.5) 63.18508

(-0.375, 0.375) 64.50073 (-0.25, 0.375) 66.76351 (-0.125, 0.375) 67.42985 (0, 0.375) 66.84765

(-0.375, 0.25) 67.33433 (-0.25, 0.25) 68.94872 (-0.125, 0.25) 69.36265 (0, 0.25) 69.35879

(-0.375, 0.125) 68.85284 (-0.25, 0.125) 69.52912 (-0.125, 0.125) 70.51079 (0, 0.125) 70.42838

(-0.375, 0) 69.86719 (-0.25, 0) 70.62566 (-0.125, 0) 70.94721 (0, 0) 70.38136

(-0.375, -0.125) 68.88944 (-0.25, -0.125) 69.55604 (-0.125, -0.125) 70.20915 (0, -0.125) 70.56333

(-0.375, -0.25) 66.76184 (-0.25, -0.25) 67.57698 (-0.125, -0.25) 68.48042 (0, -0.25) 68.72554

(-0.375, -0.375) 64.5875 (-0.25, -0.375) 65.86134 (-0.125, -0.375) 66.27042 (0, -0.375) 66.33185

(-0.375, -0.5) 59.62594 (-0.25, -0.5) 62.33553 (-0.125, -0.5) 62.89471 (0, -0.5) 65.18554

(-0.375, -0.625) 53.2547 (-0.25, -0.625) 55.81979 (-0.125, -0.625) 57.65346 (0, -0.625) 58.96292

(-0.375, -0.75) 18.4919 (-0.25, -0.75) 47.8975 (-0.125, -0.75) 50.52681 (0, -0.75) 51.82608

(-0.375, -0.875) 0 (-0.25, -0.875) 0 (-0.125, -0.875) 0 (0, -0.875) 3.14975


(0.125, 0.875) 0 (0.25, 0.875) 0 (0.375, 0.875) 0 (0.5, 0.875) 0

(0.125, 0.75) 48.30038 (0.25, 0.75) 44.71521 (0.375, 0.75) 6.032019 (0.5, 0.75) 0

(0.125, 0.625) 58.04273 (0.25, 0.625) 56.24385 (0.375, 0.625) 53.05178 (0.5, 0.625) 46.52327

(0.125, 0.5) 62.54471 (0.25, 0.5) 61.83771 (0.375, 0.5) 59.34097 (0.5, 0.5) 55.95029

(0.125, 0.375) 65.84768 (0.25, 0.375) 65.8382 (0.375, 0.375) 63.94698 (0.5, 0.375) 60.5142

(0.125, 0.25) 69.0241 (0.25, 0.25) 67.72956 (0.375, 0.25) 65.68692 (0.5, 0.25) 63.34622

(0.125, 0.125) 69.94254 (0.25, 0.125) 68.87385 (0.375, 0.125) 67.68039 (0.5, 0.125) 66.14206

(0.125, 0) 70.14324 (0.25, 0) 69.76518 (0.375, 0) 68.1163 (0.5, 0) 66.09838

(0.125, -0.125) 69.29837 (0.25, -0.125) 69.29748 (0.375, -0.125) 68.22435 (0.5, -0.125) 66.15091

(0.125, -0.25) 68.47438 (0.25, -0.25) 68.22878 (0.375, -0.25) 66.87652 (0.5, -0.25) 64.91314

(0.125, -0.375) 67.17439 (0.25, -0.375) 66.61286 (0.375, -0.375) 64.55959 (0.5, -0.375) 62.59664

(0.125, -0.5) 62.95395 (0.25, -0.5) 61.6038 (0.375, -0.5) 61.11663 (0.5, -0.5) 56.69836

(0.125, -0.625) 57.94313 (0.25, -0.625) 57.05481 (0.375, -0.625) 53.79719 (0.5, -0.625) 48.43036

130

(0.125, -0.75) 52.3623 (0.25, -0.75) 49.45024 (0.375, -0.75) 25.53086 (0.5, -0.75) 0

(0.125, -0.875) 0 (0.25, -0.875) 0 (0.375, -0.875) 0 (0.5, -0.875) 0

(X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s]

(0.625, 0.875) 0 (0.75, 0.875) 0 (0.875, 0.875) 0

(0.625, 0.75) 0 (0.75, 0.75) 0 (0.875, 0.75) 0

(0.625, 0.625) 1.143097 (0.75, 0.625) 0 (0.875, 0.625) 0

(0.625, 0.5) 48.61482 (0.75, 0.5) 0.744533 (0.875, 0.5) 0

(0.625, 0.375) 55.66579 (0.75, 0.375) 45.19456 (0.875, 0.375) 1.052677

(0.625, 0.25) 59.64195 (0.75, 0.25) 53.49459 (0.875, 0.25) 1.070877

(0.625, 0.125) 61.67583 (0.75, 0.125) 56.35399 (0.875, 0.125) 7.637423

(0.625, 0) 62.28715 (0.75, 0) 56.25292 (0.875, 0) 7.488169

(0.625, -0.125) 62.57787 (0.75, -0.125) 56.26418 (0.875, -0.125) 7.334676

(0.625, -0.25) 61.06587 (0.75, -0.25) 53.97434 (0.875, -0.25) 1.181661

(0.625, -0.375) 58.01627 (0.75, -0.375) 46.41698 (0.875, -0.375) 1.24458

(0.625, -0.5) 51.60859 (0.75, -0.5) 2.458593 (0.875, -0.5) 0

(0.625, -0.625) 4.153083 (0.75, -0.625) 0 (0.875, -0.625) 0

(0.625, -0.75) 0 (0.75, -0.75) 0 (0.875, -0.75) 0

(0.625, -0.875) 0 (0.75, -0.875) 0 (0.875, -0.875) 0

3.5 BASE


(-0.875, 0.875) 4.8274 (-0.75, 0.875) 6.6371 (-0.625, 0.875) 10.3837 (-0.5, 0.875) 14.4888

(-0.875, 0.75) 11.3508 (-0.75, 0.75) 14.9597 (-0.625, 0.75) 18.1175 (-0.5, 0.75) 23.6793

131

(-0.875, 0.625) 20.0412 (-0.75, 0.625) 24.3363 (-0.625, 0.625) 28.2117 (-0.5, 0.625) 32.7958

(-0.875, 0.5) 26.6348 (-0.75, 0.5) 36.1333 (-0.625, 0.5) 40.5299 (-0.5, 0.5) 43.6103

(-0.875, 0.375) 32.5919 (-0.75, 0.375) 46.2009 (-0.625, 0.375) 53.3985 (-0.5, 0.375) 56.1113

(-0.875, 0.25) 36.8044 (-0.75, 0.25) 52.9624 (-0.625, 0.25) 60.4061 (-0.5, 0.25) 62.1597

(-0.875, 0.125) 44.9658 (-0.75, 0.125) 57.9659 (-0.625, 0.125) 60.6298 (-0.5, 0.125) 61.7120

(-0.875, 0) 45.4515 (-0.75, 0) 59.3170 (-0.625, 0) 62.8728 (-0.5, 0) 58.6769

(-0.875, -0.125) 45.9996 (-0.75, -0.125) 59.5557 (-0.625, -0.125) 64.1751 (-0.5, -0.125) 62.6517

(-0.875, -0.25) 42.1082 (-0.75, -0.25) 54.6077 (-0.625, -0.25) 61.4494 (-0.5, -0.25) 64.7137

(-0.875, -0.375) 38.6620 (-0.75, -0.375) 50.7439 (-0.625, -0.375) 58.8991 (-0.5, -0.375) 63.1134

(-0.875, -0.5) 32.3953 (-0.75, -0.5) 43.9097 (-0.625, -0.5) 53.4516 (-0.5, -0.5) 60.0620

(-0.875, -0.625) 23.2216 (-0.75, -0.625) 34.5304 (-0.625, -0.625) 44.7957 (-0.5, -0.625) 52.4921

(-0.875, -0.75) 15.5995 (-0.75, -0.75) 23.5892 (-0.625, -0.75) 29.3741 (-0.5, -0.75) 36.3466

(-0.875, -0.875) 7.6994 (-0.75, -0.875) 12.1300 (-0.625, -0.875) 17.4338 (-0.5, -0.875) 21.4659


(-0.375, 0.875) 21.4489 (-0.25, 0.875) 26.4157 (-0.125, 0.875) 31.7497 (0, 0.875) 32.5325

(-0.375, 0.75) 31.1084 (-0.25, 0.75) 38.5436 (-0.125, 0.75) 43.6828 (0, 0.75) 45.2900

(-0.375, 0.625) 42.8451 (-0.25, 0.625) 50.2413 (-0.125, 0.625) 54.4447 (0, 0.625) 55.8480

(-0.375, 0.5) 53.3515 (-0.25, 0.5) 60.5232 (-0.125, 0.5) 61.7125 (0, 0.5) 62.2149

(-0.375, 0.375) 62.0986 (-0.25, 0.375) 64.4503 (-0.125, 0.375) 64.5170 (0, 0.375) 65.2042

(-0.375, 0.25) 62.8149 (-0.25, 0.25) 57.5989 (-0.125, 0.25) 58.7189 (0, 0.25) 63.4184

(-0.375, 0.125) 58.1325 (-0.25, 0.125) 49.8282 (-0.125, 0.125) 46.4992 (0, 0.125) 49.6344

(-0.375, 0) 55.7341 (-0.25, 0) 47.1849 (-0.125, 0) 35.9335 (0, 0) 21.5655

(-0.375, -0.125) 59.8926 (-0.25, -0.125) 49.9040 (-0.125, -0.125) 36.0149 (0, -0.125) 34.1127

(-0.375, -0.25) 61.7957 (-0.25, -0.25) 53.5400 (-0.125, -0.25) 43.0121 (0, -0.25) 41.2037

(-0.375, -0.375) 58.7237 (-0.25, -0.375) 53.2210 (-0.125, -0.375) 51.4184 (0, -0.375) 51.3538

(-0.375, -0.5) 58.9011 (-0.25, -0.5) 54.9406 (-0.125, -0.5) 56.4723 (0, -0.5) 59.5401

(-0.375, -0.625) 54.5377 (-0.25, -0.625) 55.3799 (-0.125, -0.625) 57.7240 (0, -0.625) 59.7744

132

(-0.375, -0.75) 41.1942 (-0.25, -0.75) 45.3152 (-0.125, -0.75) 48.7259 (0, -0.75) 50.9106

(-0.375, -0.875) 24.8641 (-0.25, -0.875) 30.4241 (-0.125, -0.875) 34.6005 (0, -0.875) 35.2959


(0.125, 0.875) 30.2032 (0.25, 0.875) 24.1314 (0.375, 0.875) 18.9744 (0.5, 0.875) 12.7538

(0.125, 0.75) 41.6426 (0.25, 0.75) 37.0821 (0.375, 0.75) 27.9768 (0.5, 0.75) 20.3063

(0.125, 0.625) 54.2763 (0.25, 0.625) 50.2572 (0.375, 0.625) 41.0704 (0.5, 0.625) 30.1577

(0.125, 0.5) 62.8568 (0.25, 0.5) 60.2627 (0.375, 0.5) 51.9160 (0.5, 0.5) 41.1612

(0.125, 0.375) 65.0396 (0.25, 0.375) 63.7705 (0.375, 0.375) 61.2472 (0.5, 0.375) 54.0811

(0.125, 0.25) 61.7394 (0.25, 0.25) 58.4447 (0.375, 0.25) 62.9459 (0.5, 0.25) 61.8774

(0.125, 0.125) 51.9129 (0.25, 0.125) 56.1015 (0.375, 0.125) 63.3989 (0.5, 0.125) 63.6323

(0.125, 0) 35.4999 (0.25, 0) 55.7430 (0.375, 0) 60.6663 (0.5, 0) 64.9200

(0.125, -0.125) 46.5900 (0.25, -0.125) 54.7837 (0.375, -0.125) 61.1446 (0.5, -0.125) 63.9779

(0.125, -0.25) 53.4718 (0.25, -0.25) 61.2483 (0.375, -0.25) 62.7439 (0.5, -0.25) 60.5947

(0.125, -0.375) 56.4407 (0.25, -0.375) 61.1624 (0.375, -0.375) 60.3496 (0.5, -0.375) 54.6174

(0.125, -0.5) 59.9784 (0.25, -0.5) 59.9564 (0.375, -0.5) 55.6864 (0.5, -0.5) 45.1102

(0.125, -0.625) 57.4033 (0.25, -0.625) 53.9592 (0.375, -0.625) 46.6197 (0.5, -0.625) 36.1692

(0.125, -0.75) 46.1792 (0.25, -0.75) 38.4466 (0.375, -0.75) 32.7613 (0.5, -0.75) 26.9126

(0.125, -0.875) 32.4896 (0.25, -0.875) 25.4625 (0.375, -0.875) 20.7319 (0.5, -0.875) 16.0694


(0.625, 0.875) 6.0040 (0.75, 0.875) 2.8015 (0.875, 0.875) 0.7408

(0.625, 0.75) 13.2865 (0.75, 0.75) 8.4549 (0.875, 0.75) 4.9914

(0.625, 0.625) 22.1658 (0.75, 0.625) 16.4558 (0.875, 0.625) 11.3143

(0.625, 0.5) 33.1053 (0.75, 0.5) 25.9779 (0.875, 0.5) 18.0418

(0.625, 0.375) 45.7139 (0.75, 0.375) 34.7755 (0.875, 0.375) 23.0652

(0.625, 0.25) 51.6398 (0.75, 0.25) 38.4987 (0.875, 0.25) 24.3293

(0.625, 0.125) 53.3560 (0.75, 0.125) 40.9376 (0.875, 0.125) 29.4020

133

(0.625, 0) 60.1884 (0.75, 0) 46.7081 (0.875, 0) 33.0404

(0.625, -0.125) 60.7280 (0.75, -0.125) 50.2281 (0.875, -0.125) 34.8839

(0.625, -0.25) 54.3095 (0.75, -0.25) 46.1181 (0.875, -0.25) 33.0610

(0.625, -0.375) 46.2005 (0.75, -0.375) 38.5345 (0.875, -0.375) 28.7046

(0.625, -0.5) 37.8633 (0.75, -0.5) 29.9255 (0.875, -0.5) 22.5825

(0.625, -0.625) 27.3372 (0.75, -0.625) 19.4823 (0.875, -0.625) 12.8884

(0.625, -0.75) 17.9358 (0.75, -0.75) 12.4209 (0.875, -0.75) 7.4422

(0.625, -0.875) 11.4705 (0.75, -0.875) 6.5647 (0.875, -0.875) 2.3000

134

3.5 BASE + FLAT


(-0.875, 0.875) 1.630 (-0.75, 0.875) 5.331 (-0.625, 0.875) 9.278 (-0.5, 0.875) 14.528

(-0.875, 0.75) 7.442 (-0.75, 0.75) 14.221 (-0.625, 0.75) 18.500 (-0.5, 0.75) 24.418

(-0.875, 0.625) 15.443 (-0.75, 0.625) 25.305 (-0.625, 0.625) 34.053 (-0.5, 0.625) 37.356

(-0.875, 0.5) 25.116 (-0.75, 0.5) 39.707 (-0.625, 0.5) 44.384 (-0.5, 0.5) 46.814

(-0.875, 0.375) 33.380 (-0.75, 0.375) 48.994 (-0.625, 0.375) 53.315 (-0.5, 0.375) 55.404

(-0.875, 0.25) 42.222 (-0.75, 0.25) 56.119 (-0.625, 0.25) 57.307 (-0.5, 0.25) 58.221

(-0.875, 0.125) 46.467 (-0.75, 0.125) 57.277 (-0.625, 0.125) 56.690 (-0.5, 0.125) 54.507

(-0.875, 0) 46.529 (-0.75, 0) 58.050 (-0.625, 0) 56.791 (-0.5, 0) 52.360

(-0.875, -0.125) 40.956 (-0.75, -0.125) 53.098 (-0.625, -0.125) 58.217 (-0.5, -0.125) 57.034

(-0.875, -0.25) 38.075 (-0.75, -0.25) 49.825 (-0.625, -0.25) 55.753 (-0.5, -0.25) 58.246

(-0.875, -0.375) 35.981 (-0.75, -0.375) 47.429 (-0.625, -0.375) 54.499 (-0.5, -0.375) 56.308

(-0.875, -0.5) 25.666 (-0.75, -0.5) 38.708 (-0.625, -0.5) 50.188 (-0.5, -0.5) 54.899

(-0.875, -0.625) 17.129 (-0.75, -0.625) 31.342 (-0.625, -0.625) 44.685 (-0.5, -0.625) 54.229

(-0.875, -0.75) 8.886 (-0.75, -0.75) 20.295 (-0.625, -0.75) 32.658 (-0.5, -0.75) 43.495

(-0.875, -0.875) 2.749 (-0.75, -0.875) 0.141 (-0.625, -0.875) 17.234 (-0.5, -0.875) 26.195


(-0.375, 0.875) 19.205 (-0.25, 0.875) 22.539 (-0.125, 0.875) 24.806 (0, 0.875) 29.189

(-0.375, 0.75) 31.801 (-0.25, 0.75) 34.792 (-0.125, 0.75) 38.225 (0, 0.75) 41.628

(-0.375, 0.625) 46.006 (-0.25, 0.625) 50.045 (-0.125, 0.625) 50.189 (0, 0.625) 53.205

(-0.375, 0.5) 55.845 (-0.25, 0.5) 58.138 (-0.125, 0.5) 57.766 (0, 0.5) 58.233

(-0.375, 0.375) 58.382 (-0.25, 0.375) 57.145 (-0.125, 0.375) 58.220 (0, 0.375) 60.151

(-0.375, 0.25) 53.630 (-0.25, 0.25) 48.148 (-0.125, 0.25) 52.956 (0, 0.25) 57.112

(-0.375, 0.125) 48.541 (-0.25, 0.125) 42.367 (-0.125, 0.125) 39.638 (0, 0.125) 44.362

(-0.375, 0) 48.634 (-0.25, 0) 42.197 (-0.125, 0) 31.296 (0, 0) 0.625

(-0.375, -0.125) 55.449 (-0.25, -0.125) 47.724 (-0.125, -0.125) 33.154 (0, -0.125) 26.149

135

(-0.375, -0.25) 55.685 (-0.25, -0.25) 47.046 (-0.125, -0.25) 35.836 (0, -0.25) 33.334

(-0.375, -0.375) 50.289 (-0.25, -0.375) 43.673 (-0.125, -0.375) 37.653 (0, -0.375) 38.483

(-0.375, -0.5) 50.073 (-0.25, -0.5) 46.857 (-0.125, -0.5) 46.446 (0, -0.5) 45.639

(-0.375, -0.625) 53.146 (-0.25, -0.625) 50.390 (-0.125, -0.625) 52.335 (0, -0.625) 54.002

(-0.375, -0.75) 49.929 (-0.25, -0.75) 50.940 (-0.125, -0.75) 51.384 (0, -0.75) 52.945

(-0.375, -0.875) 34.868 (-0.25, -0.875) 36.490 (-0.125, -0.875) 37.511 (0, -0.875) 40.505


(0.125, 0.875) 26.803 (0.25, 0.875) 20.221 (0.375, 0.875) 15.846 (0.5, 0.875) 10.901

(0.125, 0.75) 38.262 (0.25, 0.75) 32.705 (0.375, 0.75) 29.161 (0.5, 0.75) 20.879

(0.125, 0.625) 50.804 (0.25, 0.625) 50.417 (0.375, 0.625) 45.069 (0.5, 0.625) 35.980

(0.125, 0.5) 58.177 (0.25, 0.5) 58.458 (0.375, 0.5) 54.162 (0.5, 0.5) 45.962

(0.125, 0.375) 59.922 (0.25, 0.375) 59.026 (0.375, 0.375) 58.975 (0.5, 0.375) 54.416

(0.125, 0.25) 55.716 (0.25, 0.25) 51.522 (0.375, 0.25) 57.865 (0.5, 0.25) 58.707

(0.125, 0.125) 45.337 (0.25, 0.125) 49.446 (0.375, 0.125) 57.473 (0.5, 0.125) 59.901

(0.125, 0) 34.053 (0.25, 0) 47.913 (0.375, 0) 53.773 (0.5, 0) 60.943

(0.125, -0.125) 38.105 (0.25, -0.125) 46.195 (0.375, -0.125) 52.252 (0.5, -0.125) 59.074

(0.125, -0.25) 45.457 (0.25, -0.25) 53.221 (0.375, -0.25) 56.516 (0.5, -0.25) 57.478

(0.125, -0.375) 46.857 (0.25, -0.375) 56.164 (0.375, -0.375) 55.399 (0.5, -0.375) 51.714

(0.125, -0.5) 48.719 (0.25, -0.5) 54.660 (0.375, -0.5) 54.689 (0.5, -0.5) 46.595

(0.125, -0.625) 54.666 (0.25, -0.625) 54.737 (0.375, -0.625) 49.961 (0.5, -0.625) 40.358

(0.125, -0.75) 48.468 (0.25, -0.75) 43.295 (0.375, -0.75) 37.694 (0.5, -0.75) 28.654

(0.125, -0.875) 37.578 (0.25, -0.875) 28.556 (0.375, -0.875) 22.987 (0.5, -0.875) 15.977


(0.625, 0.875) 5.655 (0.75, 0.875) 1.627 (0.875, 0.875) 1.176

(0.625, 0.75) 13.401 (0.75, 0.75) 6.684 (0.875, 0.75) 2.474

(0.625, 0.625) 26.264 (0.75, 0.625) 21.258 (0.875, 0.625) 11.492

136

(0.625, 0.5) 39.448 (0.75, 0.5) 30.322 (0.875, 0.5) 19.133

(0.625, 0.375) 48.549 (0.75, 0.375) 37.925 (0.875, 0.375) 29.567

(0.625, 0.25) 51.948 (0.75, 0.25) 37.986 (0.875, 0.25) 23.991

(0.625, 0.125) 54.815 (0.75, 0.125) 40.211 (0.875, 0.125) 25.547

(0.625, 0) 58.564 (0.75, 0) 48.082 (0.875, 0) 32.307

(0.625, -0.125) 55.922 (0.75, -0.125) 44.569 (0.875, -0.125) 30.936

(0.625, -0.25) 52.464 (0.75, -0.25) 42.016 (0.875, -0.25) 27.946

(0.625, -0.375) 46.055 (0.75, -0.375) 38.924 (0.875, -0.375) 25.169

(0.625, -0.5) 37.635 (0.75, -0.5) 27.672 (0.875, -0.5) 18.594

(0.625, -0.625) 27.957 (0.75, -0.625) 19.226 (0.875, -0.625) 10.071

(0.625, -0.75) 18.228 (0.75, -0.75) 9.756 (0.875, -0.75) 2.324

(0.625, -0.875) 9.251 (0.75, -0.875) 2.398 (0.875, -0.875) 1.585

137

7.5 BASE


(-0.875, 0.875) 2.998 (-0.75, 0.875) 5.567 (-0.625, 0.875) 8.383 (-0.5, 0.875) 11.213

(-0.875, 0.75) 9.529 (-0.75, 0.75) 12.570 (-0.625, 0.75) 16.987 (-0.5, 0.75) 18.770

(-0.875, 0.625) 14.950 (-0.75, 0.625) 20.856 (-0.625, 0.625) 25.733 (-0.5, 0.625) 30.117

(-0.875, 0.5) 22.778 (-0.75, 0.5) 30.919 (-0.625, 0.5) 38.004 (-0.5, 0.5) 42.954

(-0.875, 0.375) 28.394 (-0.75, 0.375) 39.542 (-0.625, 0.375) 48.569 (-0.5, 0.375) 54.719

(-0.875, 0.25) 32.736 (-0.75, 0.25) 45.075 (-0.625, 0.25) 56.516 (-0.5, 0.25) 61.648

(-0.875, 0.125) 36.345 (-0.75, 0.125) 48.836 (-0.625, 0.125) 58.612 (-0.5, 0.125) 62.904

(-0.875, 0) 40.685 (-0.75, 0) 53.591 (-0.625, 0) 63.659 (-0.5, 0) 63.084

(-0.875, -0.125) 42.803 (-0.75, -0.125) 57.037 (-0.625, -0.125) 63.714 (-0.5, -0.125) 63.998

(-0.875, -0.25) 49.634 (-0.75, -0.25) 56.165 (-0.625, -0.25) 63.159 (-0.5, -0.25) 64.648

(-0.875, -0.375) 41.592 (-0.75, -0.375) 51.723 (-0.625, -0.375) 56.586 (-0.5, -0.375) 61.183

(-0.875, -0.5) 31.917 (-0.75, -0.5) 37.705 (-0.625, -0.5) 44.905 (-0.5, -0.5) 51.297

(-0.875, -0.625) 25.059 (-0.75, -0.625) 31.300 (-0.625, -0.625) 35.722 (-0.5, -0.625) 42.174

(-0.875, -0.75) 16.926 (-0.75, -0.75) 21.500 (-0.625, -0.75) 25.878 (-0.5, -0.75) 31.387

(-0.875, -0.875) 8.712 (-0.75, -0.875) 13.257 (-0.625, -0.875) 17.403 (-0.5, -0.875) 20.483


(-0.375, 0.875) 12.678 (-0.25, 0.875) 13.718 (-0.125, 0.875) 13.990 (0, 0.875) 15.306

(-0.375, 0.75) 20.845 (-0.25, 0.75) 22.653 (-0.125, 0.75) 23.931 (0, 0.75) 22.587

(-0.375, 0.625) 32.389 (-0.25, 0.625) 33.359 (-0.125, 0.625) 34.101 (0, 0.625) 33.286

(-0.375, 0.5) 46.558 (-0.25, 0.5) 47.175 (-0.125, 0.5) 44.321 (0, 0.5) 44.102

(-0.375, 0.375) 56.593 (-0.25, 0.375) 56.111 (-0.125, 0.375) 53.162 (0, 0.375) 52.729

(-0.375, 0.25) 62.038 (-0.25, 0.25) 58.692 (-0.125, 0.25) 55.938 (0, 0.25) 56.484

(-0.375, 0.125) 60.540 (-0.25, 0.125) 55.932 (-0.125, 0.125) 51.575 (0, 0.125) 47.115

(-0.375, 0) 58.359 (-0.25, 0) 53.580 (-0.125, 0) 46.911 (0, 0) 35.327

(-0.375, -0.125) 60.902 (-0.25, -0.125) 58.315 (-0.125, -0.125) 48.641 (0, -0.125) 38.416

138

(-0.375, -0.25) 62.681 (-0.25, -0.25) 58.456 (-0.125, -0.25) 46.996 (0, -0.25) 42.919

(-0.375, -0.375) 63.836 (-0.25, -0.375) 59.763 (-0.125, -0.375) 52.975 (0, -0.375) 52.569

(-0.375, -0.5) 56.135 (-0.25, -0.5) 58.451 (-0.125, -0.5) 57.634 (0, -0.5) 58.384

(-0.375, -0.625) 47.534 (-0.25, -0.625) 50.717 (-0.125, -0.625) 54.112 (0, -0.625) 57.857

(-0.375, -0.75) 34.864 (-0.25, -0.75) 39.681 (-0.125, -0.75) 45.079 (0, -0.75) 50.398

(-0.375, -0.875) 25.808 (-0.25, -0.875) 28.798 (-0.125, -0.875) 34.720 (0, -0.875) 38.475


(0.125, 0.875) 17.400 (0.25, 0.875) 19.098 (0.375, 0.875) 19.288 (0.5, 0.875) 18.067

(0.125, 0.75) 24.748 (0.25, 0.75) 28.465 (0.375, 0.75) 29.033 (0.5, 0.75) 27.496

(0.125, 0.625) 34.601 (0.25, 0.625) 38.368 (0.375, 0.625) 38.979 (0.5, 0.625) 37.458

(0.125, 0.5) 44.824 (0.25, 0.5) 48.324 (0.375, 0.5) 49.389 (0.5, 0.5) 46.838

(0.125, 0.375) 52.848 (0.25, 0.375) 56.347 (0.375, 0.375) 58.381 (0.5, 0.375) 55.890

(0.125, 0.25) 57.506 (0.25, 0.25) 61.174 (0.375, 0.25) 64.766 (0.5, 0.25) 63.550

(0.125, 0.125) 38.353 (0.25, 0.125) 55.039 (0.375, 0.125) 59.198 (0.5, 0.125) 63.944

(0.125, 0) 18.609 (0.25, 0) 46.546 (0.375, 0) 55.127 (0.5, 0) 60.741

(0.125, -0.125) 35.539 (0.25, -0.125) 43.736 (0.375, -0.125) 54.840 (0.5, -0.125) 62.054

(0.125, -0.25) 45.682 (0.25, -0.25) 54.185 (0.375, -0.25) 63.291 (0.5, -0.25) 65.086

(0.125, -0.375) 54.875 (0.25, -0.375) 57.203 (0.375, -0.375) 62.436 (0.5, -0.375) 60.818

(0.125, -0.5) 61.127 (0.25, -0.5) 60.829 (0.375, -0.5) 60.299 (0.5, -0.5) 56.565

(0.125, -0.625) 61.015 (0.25, -0.625) 60.482 (0.375, -0.625) 55.431 (0.5, -0.625) 48.443

(0.125, -0.75) 51.868 (0.25, -0.75) 50.992 (0.375, -0.75) 46.154 (0.5, -0.75) 36.159

(0.125, -0.875) 37.818 (0.25, -0.875) 35.033 (0.375, -0.875) 32.252 (0.5, -0.875) 25.458


(0.625, 0.875) 16.452 (0.75, 0.875) 13.604 (0.875, 0.875) 10.843

(0.625, 0.75) 24.026 (0.75, 0.75) 19.923 (0.875, 0.75) 16.704

(0.625, 0.625) 33.180 (0.75, 0.625) 29.806 (0.875, 0.625) 24.305

139

(0.625, 0.5) 43.181 (0.75, 0.5) 38.600 (0.875, 0.5) 32.007

(0.625, 0.375) 53.247 (0.75, 0.375) 50.343 (0.875, 0.375) 39.748

(0.625, 0.25) 60.051 (0.75, 0.25) 58.789 (0.875, 0.25) 50.270

(0.625, 0.125) 64.702 (0.75, 0.125) 64.708 (0.875, 0.125) 58.415

(0.625, 0) 64.809 (0.75, 0) 67.072 (0.875, 0) 62.403

(0.625, -0.125) 65.540 (0.75, -0.125) 66.222 (0.875, -0.125) 60.639

(0.625, -0.25) 62.952 (0.75, -0.25) 56.532 (0.875, -0.25) 47.092

(0.625, -0.375) 56.136 (0.75, -0.375) 46.536 (0.875, -0.375) 40.431

(0.625, -0.5) 48.409 (0.75, -0.5) 36.550 (0.875, -0.5) 28.037

(0.625, -0.625) 39.507 (0.75, -0.625) 28.999 (0.875, -0.625) 21.915

(0.625, -0.75) 28.451 (0.75, -0.75) 21.292 (0.875, -0.75) 14.666

(0.625, -0.875) 18.787 (0.75, -0.875) 13.561 (0.875, -0.875) 7.428

140

3.5 BASE + FLAT + CONICAL

(X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s] (X,Y) V [m/s]

(-1.0, 1.0) 5.203 (-0.875, 1.0) 13.502 (0.75, -1.0) 22.142 (0.625, -1.0) 31.356 (0.5, -1.0) 32.052

(-1.0, 0.875) 23.198 (-0.875, 0.875) 32.498 (-0.75, 0.875) 28.783 (-0.625, 0.875) 34.572 (-0.5, 0.875) 35.126

(-1.0, 0.75) 30.786 (-0.875, 0.75) 25.388 (-0.75, 0.75) 40.117 (-0.625, 0.75) 50.926 (-0.5, 0.75) 49.148

(-1.0, 0.625) 24.627 (-0.875, 0.625) 34.330 (-0.75, 0.625) 50.348 (-0.625, 0.625) 49.955 (-0.5, 0.625) 24.758

(-1.0, 0.5) 26.605 (-0.875, 0.5) 44.198 (-0.75, 0.5) 52.414 (-0.625, 0.5) 23.767 (-0.5, 0.5) 36.929

(-1.0, 0.375) 36.135 (-0.875, 0.375) 52.037 (-0.75, 0.375) 43.378 (-0.625, 0.375) 31.106 (-0.5, 0.375) 39.693

(-1.0, 0.25) 24.861 (-0.875, 0.25) 40.013 (-0.75, 0.25) 53.547 (-0.625, 0.25) 25.165 (-0.5, 0.25) 37.390

(-1.0, 0.125) 24.520 (-0.875, 0.125) 42.322 (-0.75, 0.125) 52.483 (-0.625, 0.125) 24.542 (-0.5, 0.125) 39.109

(-1.0, 0) 21.160 (-0.875, 0) 35.698 (-0.75, 0) 42.849 (-0.625, 0) 26.709 (-0.5, 0) 41.075

(-1.0, -0.125) 19.156 (-0.875, -0.125) 15.924 (-0.75, -0.125) 24.733 (-0.625, -0.125) 16.284 (-0.5, -0.125) 34.502

(-1.0, -0.25) 15.280 (-0.875, -0.25) 11.819 (-0.75, -0.25) 9.029 (-0.625, -0.25) 24.194 (-0.5, -0.25) 42.052

(-1.0, -0.375) 14.658 (-0.875, -0.375) 16.191 (-0.75, -0.375) 13.228 (-0.625, -0.375) 8.122 (-0.5, -0.375) 29.437

(-1.0, -0.5) 12.546 (-0.875, -0.5) 14.950 (-0.75, -0.5) 4.564 (-0.625, -0.5) 21.239 (-0.5, -0.5) 25.707

(-1.0, -0.625) 12.358 (-0.875, -0.625) 14.639 (-0.75, -0.625) 8.622 (-0.625, -0.625) 32.151 (-0.5, -0.625) 45.632

(-1.0, -0.75) 16.995 (-0.875, -0.75) 25.469 (-0.75, -0.75) 23.145 (-0.625, -0.75) 22.276 (-0.5, -0.75) 37.946

(-1.0, -0.875) 10.653 (-0.875, -0.875) 17.718 (-0.75, -0.875) 22.938 (-0.625, -0.875) 26.908 (-0.5, -0.875) 23.689

(-1.0, -1.0) 1.433 (-0.875, -1.0) 6.190 (-0.75, -1.0) 11.562 (-0.625, -1.0) 17.927 (-0.5, -1.0) 24.458


(-0.375, 1.0) 23.358 (-0.25, 1.0) 10.367 (-0.125, 1.0) 16.294 (0, 1.0) 17.759

(-0.375, 0.875) 19.912 (-0.25, 0.875) 14.158 (-0.125, 0.875) 18.186 (0, 0.875) 15.362

(-0.375, 0.75) 28.551 (-0.25, 0.75) 12.902 (-0.125, 0.75) 8.317 (0, 0.75) 1.753

(-0.375, 0.625) 34.271 (-0.25, 0.625) 39.430 (-0.125, 0.625) 33.075 (0, 0.625) 31.259

(-0.375, 0.5) 42.501 (-0.25, 0.5) 47.225 (-0.125, 0.5) 48.109 (0, 0.5) 46.736

(-0.375, 0.375) 39.736 (-0.25, 0.375) 44.260 (-0.125, 0.375) 50.740 (0, 0.375) 50.977

(-0.375, 0.25) 38.627 (-0.25, 0.25) 32.981 (-0.125, 0.25) 34.233 (0, 0.25) 41.652

(-0.375, 0.125) 40.926 (-0.25, 0.125) 33.332 (-0.125, 0.125) 25.737 (0, 0.125) 27.138

141

(-0.375, 0) 46.232 (-0.25, 0) 37.737 (-0.125, 0) 27.901 (0, 0) 22.980

(-0.375, -0.125) 43.385 (-0.25, -0.125) 42.218 (-0.125, -0.125) 36.417 (0, -0.125) 33.451

(-0.375, -0.25) 46.686 (-0.25, -0.25) 45.635 (-0.125, -0.25) 43.458 (0, -0.25) 47.119

(-0.375, -0.375) 42.596 (-0.25, -0.375) 46.065 (-0.125, -0.375) 45.867 (0, -0.375) 45.276

(-0.375, -0.5) 27.679 (-0.25, -0.5) 34.772 (-0.125, -0.5) 35.905 (0, -0.5) 35.203

(-0.375, -0.625) 51.766 (-0.25, -0.625) 49.341 (-0.125, -0.625) 44.356 (0, -0.625) 45.979

(-0.375, -0.75) 41.758 (-0.25, -0.75) 43.754 (-0.125, -0.75) 42.632 (0, -0.75) 41.118

(-0.375, -0.875) 25.020 (-0.25, -0.875) 28.209 (-0.125, -0.875) 26.896 (0, -0.875) 25.716

(-0.375, -1.0) 27.297 (-0.25, -1.0) 29.259 (-0.125, -1.0) 29.239 (0, -1.0) 30.693


(0.125, 1.0) 17.053 (0.25, 1.0) 1.837 (0.375, 1.0) 21.839 (0.5, 1.0) 33.683

(0.125, 0.875) 18.036 (0.25, 0.875) 32.235 (0.375, 0.875) 35.075 (0.5, 0.875) 30.442

(0.125, 0.75) 26.729 (0.25, 0.75) 48.630 (0.375, 0.75) 51.672 (0.5, 0.75) 44.170

(0.125, 0.625) 33.296 (0.25, 0.625) 27.062 (0.375, 0.625) 54.132 (0.5, 0.625) 52.555

(0.125, 0.5) 46.643 (0.25, 0.5) 40.632 (0.375, 0.5) 31.222 (0.5, 0.5) 54.573

(0.125, 0.375) 47.796 (0.25, 0.375) 48.166 (0.375, 0.375) 48.871 (0.5, 0.375) 39.049

(0.125, 0.25) 42.465 (0.25, 0.25) 40.446 (0.375, 0.25) 46.141 (0.5, 0.25) 44.837

(0.125, 0.125) 28.128 (0.25, 0.125) 31.425 (0.375, 0.125) 41.076 (0.5, 0.125) 46.329

(0.125, 0) 27.929 (0.25, 0) 38.514 (0.375, 0) 46.469 (0.5, 0) 46.896

(0.125, -0.125) 40.792 (0.25, -0.125) 48.146 (0.375, -0.125) 47.827 (0.5, -0.125) 39.978

(0.125, -0.25) 50.420 (0.25, -0.25) 42.642 (0.375, -0.25) 23.215 (0.5, -0.25) 12.232

(0.125, -0.375) 44.055 (0.25, -0.375) 31.859 (0.375, -0.375) 8.491 (0.5, -0.375) 12.422

(0.125, -0.5) 28.279 (0.25, -0.5) 24.359 (0.375, -0.5) 29.997 (0.5, -0.5) 10.329

(0.125, -0.625) 49.992 (0.25, -0.625) 51.065 (0.375, -0.625) 41.485 (0.5, -0.625) 22.703

(0.125, -0.75) 37.569 (0.25, -0.75) 36.065 (0.375, -0.75) 30.701 (0.5, -0.75) 24.503

(0.125, -0.875) 23.488 (0.25, -0.875) 23.587 (0.375, -0.875) 28.510 (0.5, -0.875) 26.690

(0.125, -1.0) 29.265 (0.25, -1.0) 25.305 (0.375, -1.0) 21.944 (0.5, -1.0) 14.860

142


(-0.625, 1.0) 34.016 (-0.75, 1.0) 23.729 (-0.875, 1.0) 12.787 (-1.0, 1.0) 2.736

(0.625, 0.875) 38.172 (0.75, 0.875) 26.898 (0.875, 0.875) 13.018 (-1.0, 0.875) 3.161

(0.625, 0.75) 30.740 (0.75, 0.75) 36.608 (0.875, 0.75) 20.214 (-1.0, 0.75) 7.434

(0.625, 0.625) 37.083 (0.75, 0.625) 28.119 (0.875, 0.625) 34.542 (-1.0, 0.625) 19.778

(0.625, 0.5) 42.756 (0.75, 0.5) 26.720 (0.875, 0.5) 37.100 (-1.0, 0.5) 25.136

(0.625, 0.375) 45.946 (0.75, 0.375) 49.443 (0.875, 0.375) 31.876 (-1.0, 0.375) 29.742

(0.625, 0.25) 30.067 (0.75, 0.25) 52.590 (0.875, 0.25) 39.448 (-1.0, 0.25) 26.643

(0.625, 0.125) 34.292 (0.75, 0.125) 52.105 (0.875, 0.125) 44.178 (-1.0, 0.125) 27.076

(0.625, 0) 32.332 (0.75, 0) 38.887 (0.875, 0) 34.711 (-1.0, 0) 22.241

(0.625, -0.125) 20.569 (0.75, -0.125) 16.028 (0.875, -0.125) 9.043 (-1.0, -0.125) 20.943

(0.625, -0.25) 17.585 (0.75, -0.25) 17.630 (0.875, -0.25) 20.014 (-1.0, -0.25) 21.532

(0.625, -0.375) 18.244 (0.75, -0.375) 17.004 (0.875, -0.375) 6.973 (-1.0, -0.375) 12.696

(0.625, -0.5) 16.594 (0.75, -0.5) 4.421 (0.875, -0.5) 5.468 (-1.0, -0.5) 6.882

(0.625, -0.625) 19.109 (0.75, -0.625) 22.130 (0.875, -0.625) 12.378 (-1.0, -0.625) 4.889

(0.625, -0.75) 27.150 (0.75, -0.75) 20.891 (0.875, -0.75) 11.095 (-1.0, -0.75) 2.597

(0.625, -0.875) 20.420 (0.75, -0.875) 10.894 (0.875, -0.875) 3.760 (-1.0, -0.875) 2.442

(0.625, -1.0) 7.954 (0.75, -1.0) 1.621 (0.875, -1.0) 1.958 (1.0, -1.0) 1.584

Air Force Public Release Case Number 88ABW-2015-2920

Documents

EXPERIMENTAL ANALYSIS OF DIFFUSER PERFORMANCE …acumen.lib.ua.edu/content/u0015/0000001/0002183/u0015_0000001_0002183.pdfFigure 16 – ANSYS FLUENT flow simulation 2-D contour non–dimensionalized