EFFECT OF SINGLE LIGHT ORIENTATION ON LANDING GEAR WAKE · Figure 2.9: Two cylinders in the tandem arrangement [41]. L is the distance between the centers of the two cylinders (same

EFFECT OF SINGLE LIGHT ORIENTATION ON

LANDING GEAR WAKE

EFFECT OF SINGLE LIGHT ORIENTATION ON

LANDING GEAR WAKE

By

MARKO AREŽINA, B. ENG. MGT.

A Thesis Submitted to the School of Graduate Studies

In Partial Fulfillment of the Requirements for the Degree

Master of Applied Science

McMaster University

© Copyright Marko Arežina, July 2017

iii

Master of Applied Science (2017) McMaster University

Mechanical Engineering Hamilton, Ontario, Canada

TITLE: Effect of Single Light Orientation on Landing Gear Wake

AUTHOR: Marko Arežina, B. Eng. Mgt. (McMaster University)

SUPERVISOR: Professor Samir Ziada

NUMBER OF PAGES: xxiv, 149

iv

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ABSTRACT Within the overarching area of airplane noise, landing gear noise has been proven to be a

major contributor to airframe noise. Despite a large focus given to it by past research

work, landing gear noise investigations have continuously failed to include landing lights,

completely disregarding their potential for seriously altering the landing gear wake

structure and overall noise signature. This thesis is one of the first studies to focus on the

effect of landing light orientation on landing gear wake and landing gear noise. Pressure

fluctuations in the wake of a simplified single light landing gear model are investigated

experimentally for several freestream velocities and at various elevations of measurement

plane. The effect of the distance between the light and the landing gear strut is also

investigated. Three-dimensional flow is found in the wake at the center, or zero elevation,

plane. This three-dimensionality is found to be much weaker at the highest elevation from

the light, where the wake is found to be primarily two-dimensional. The nature of the

transition region between the three-dimensional flow and two-dimensional flow is not

investigated, but it is acknowledged that a transition region exists. Complex flow

behaviour leading to a wake width larger than twice the size of the light-strut assembly

width is found to be present at the zero elevation, and phase-locked PIV imaging is

unable to capture any periodic motion within the wake at this elevation. In contrast, the

wake at the highest elevation is found to resemble the flow in the wake of circular

cylinders, and phase-locked PIV imaging at this elevation clearly captures an alternate

vortex shedding scheme. Due to this difference in wake structures, the periodicity at the

highest elevation is found to be stronger than that observed at the zero elevation. Changes

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in light-strut spacing are found to inversely affect the strength of the periodicity in the

wake, as larger spacing is linked to greater influence of three-dimensionality, and

therefore a weaker periodicity. Changes in light-strut spacing are also found to be

inversely related to the oscillation frequency of the periodicity, with the cause for this

relationship possibly explained by the wider wake at increased spacing. It is found that

the oscillation frequency of periodicity in the single light landing gear wake is

consistently in the Strouhal number range of St=0.16-0.18 for all light-strut spacing

distances, freestream velocities, and elevations. The flow around the light-strut assembly

is therefore characterized as modulated flow around a cylindrical strut because alternate

vortex shedding is dominant except for a slight region where the light acts to generate

three-dimensionality, and because the oscillation frequency is near that of vortex

shedding from a circular cylinder, St=0.19. The wakes of the single light landing gear and

two-light landing gear models are compared, but neither design can be supported as

quieter than the other at this time due to the unknown amount of vertical radiation from

the landing gear wakes.

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ACKNOWLEDGEMENTS I thank my parents and siblings for their love and support over the last few of years. They

have been patiently waiting for years for me to begin a career so I can buy them nice

things, and I keep extending my schooling, to their visible dismay each time I announce

an extension. To be completely serious, without the encouragement and support of my

family, I would still not be done writing. This thesis was a team effort.

I thank the machine shop team: John Colenbrander, Michael Lee, Mark MacKenzie, Dan

Wright, and Ron Lodewyks. Additionally, I thank the administrative team: Florence

Rosato, Lily Sazz-Fayter, and Leslie Kocsis, and former member Vania Loyzer. These

two groups really should merge under a ‘Graduate Support Group’ or similar designation;

they have assisted me in one facet or another countless times.

A few years ago, Dr. Samir Ziada, maybe out of kindness, or perhaps out of an inability

to say, “No”, or maybe due to a momentary lack of judgement, agreed to accept me as a

student. Since that time, he has provided calm and unwavering support, guidance, and

patience throughout the ups and downs of graduate student work. I am proud of my work,

and without him I never would have arrived at this point. I will forever be grateful.

Finally, I must thank my colleagues in the aeroacoustics research group, who each

contributed in one way or another to this thesis. They were such a pleasant group that we

developed friendships by accident. I even almost stayed for a Ph.D. Almost. Wherever we

end up, I will always remember them.

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CONTENTS 1 Introduction .................................................................................................................. 1

Problem and Motivation ........................................................................................ 1 1.1

Scope ..................................................................................................................... 5 1.2

2 Literature Review ......................................................................................................... 6

A Brief History of Airplane Noise Regulation ...................................................... 6 2.1

Regulatory Pressure on the Air Transport Industry .............................................. 8 2.2

Prior Scientific Work .......................................................................................... 10 2.3

Flow Around Bluff Bodies ........................................................................... 11 2.3.1

Landing Gear Noise ..................................................................................... 26 2.3.2

Summary ............................................................................................................. 32 2.4

3 Experimental Apparatus and Methodology ............................................................... 33

Wind Tunnel ........................................................................................................ 33 3.1

Wind Tunnel Test Section ........................................................................... 34 3.1.1

Landing Gear Model ........................................................................................... 34 3.2

Landing Gear Model Components ............................................................... 37 3.2.1

Strut Vortex Shedding Frequency ................................................................ 40 3.2.2

Landing Light Vortex Shedding Frequency................................................. 41 3.2.3

x

Experimental Test Cases .................................................................................... 43 3.3

Experimental Investigation by Means of Microphone Recordings .................... 46 3.4

Experimental Investigation by Means of Hot-wire Anemometry ...................... 51 3.5

Traverse System ................................................................................................. 54 3.6

Experimental Investigation by Means of PIV .................................................... 55 3.7

Description of PIV System used for Experimental Investigation ............... 55 3.7.1

General PIV Theory .................................................................................... 57 3.7.2

Phase-locked PIV Theory and Triggering System ...................................... 58 3.7.3

MATLAB ........................................................................................................... 60 3.8

Microphone and Hot-wire Results .............................................................. 60 3.8.1

Time-Averaged Images for PIV of Light-Strut Wake ................................ 62 3.8.2

Phase-locked Image Mirroring for PIV of Light-Strut Wake ..................... 64 3.8.3

Time-Averaged PIV Images of Flow Around Light-Strut Assembly ......... 68 3.8.4

Summary ............................................................................................................. 71 3.9

4 Microphone and Hot-wire Results ............................................................................ 72

Microphone Results ............................................................................................ 72 4.1

Hot-wire Results ................................................................................................. 74 4.2

Inconsequential Spectral Characteristics of Microphone and Hot-wire Results 76 4.3

Lack of Wind Tunnel Blower Frequency Peak in Hot-wire Data ............... 76 4.3.1

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Signal from Flow Activity in Wake Region ................................................ 77 4.3.2

Wind Tunnel Signature ................................................................................ 80 4.3.3

Peak near St=0.35 ........................................................................................ 84 4.3.4

Main Feature: Single Peak in the St=0.16-0.18 Region ...................................... 90 4.4

Trend #1: Decrease in St=0.16-0.18 Peak Magnitude with Increase in Light-4.4.1

Strut Spacing .............................................................................................................. 92

Trend #2: Decrease in St=0.16-0.18 Peak Frequency with Increase in Light-4.4.2

Strut Spacing .............................................................................................................. 92

Trend #3: Increase in St=0.16-0.18 Peak Magnitude with Increase in 4.4.3

Elevation .................................................................................................................... 93

5 PIV Results ................................................................................................................ 97

Introduction ......................................................................................................... 97 5.1

Negligible Effect of Velocity and Light-Strut Spacing Parameters on Wake ..... 98 5.2

No Change in Wake with Change in Velocity ............................................. 98 5.2.1

No Change in Wake with Change in Light-Strut Spacing ......................... 100 5.2.2

Significant Effect of Measurement Plane Elevation on Wake Structure .......... 102 5.3

Only Wake Activity at the Highest Elevation Showed Vortex Propagation 5.3.1

and Shedding ............................................................................................................ 104

Complex Flow Behaviour between Light and Strut for Z=0D Case ................. 113 5.4

Spatial Origin of St=0.16-0.18 Signal ............................................................... 116 5.5

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6 Discussion ............................................................................................................... 122

Three-Dimensional Flow Activity and Vortex Shedding Process .................... 122 6.1

Wake Structure at Various Elevations .............................................................. 124 6.2

Signal Strength at Various Elevations .............................................................. 128 6.3

Signal Strength at Various Light-Strut Spacing Ratios .................................... 128 6.4

Effect of Light-Strut Spacing on Oscillation Frequency .................................. 129 6.5

Effect of Innermost Shear Layers at Highest Elevation ................................... 130 6.6

Acoustic and Flow Oscillations at St=0.16-0.18 .............................................. 130 6.7

7 Summary and Conclusions ...................................................................................... 134

Conclusions ...................................................................................................... 134 7.1

Industry Applications ....................................................................................... 137 7.2

Recommendations for Future Work ................................................................. 138 7.3

References ....................................................................................................................... 141

Appendix A: Trigger Circuit Diagram ............................................................................ 145

Appendix B: Uncertainty Analysis ................................................................................. 146

B.1 Direct Measurements ........................................................................................ 146

B.2 Non-dimensional Numbers ............................................................................... 147

B.2.1 Non-dimensional Pressure, P* .................................................................. 147

B.2.2 Strouhal Number, St .................................................................................. 148

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B.3 Flow Visualization Uncertainty ........................................................................ 149

xiv

LIST OF FIGURES

Figure 1.1: Relative EPNL for various aircraft noise sources for long range aircraft (left)

and short range aircraft (right). Long range aircraft are defined as those with

flights equal to or more than 4000 kilometres while short range aircraft are

defined as those with flights of less than 1500 kilometres. Adapted from [2].

........................................................................................................................ 2

Figure 1.2: Schematic of (a) ONERA-Airbus LAGOON landing gear model [4] and (b)

NASA-Gulfstream ¼-scale G550 partially dressed landing gear model with

all smaller components and landing gear lights removed (left) and fully

dressed landing gear model, with all components included (right) [5].

Landing gear lights are present only for the case of the fully dressed NASA-

Gulfstream landing gear model. ..................................................................... 3

Figure 1.3: Photo of an aircraft landing gear titled: HN-441 F-A-18C Hornet Finnish Air

Force ILA 2012 nose landing gear, by Julian Herzog, available under a

Creative Commons Attribution 4.0 International license. .............................. 4

Figure 2.1: Illustration of evolving ICAO noise standards, reproduced from [9]. .............. 8

Figure 2.2: Regions of disturbed flow around a cylinder [17]. ......................................... 11

Figure 2.3: Flow regimes for flow around a circular cylinder. Reproduced from [18]. ... 15

Figure 2.4: Strouhal-Reynolds number relationship for flow across a circular cylinder

[19]. .............................................................................................................. 16

Figure 2.5: Disk wake structure shows three different modes present in the wake [21]. . 18

Figure 2.6: Planar cut of wake shows numerically simulated vorticity contours at various

downstream sections of the wake: (a) x/D=0.5, (b) x/D=3.5, (c)x/D=7, where

x represents the downstream distance away from the disk and D represents

the disk diameter [25]. .................................................................................. 18

Figure 2.7: Numerically simulated flow behind a circular disk, highlights wake structure

[25]. .............................................................................................................. 19

Figure 2.8: Classification of interference regions for various cylinder arrangements [41].

T is the transverse spacing between axes of cylinders, D is the cylinder

diameter, and L is the streamwise spacing between axes of cylinders. The

diagonal hashed lines represent regions where bistable flow is prevalent. .. 21

xv

Figure 2.9: Two cylinders in the tandem arrangement [41]. L is the distance between the

centers of the two cylinders (same as in the above figure), y and x denote the

vertical and horizontal Cartesian coordinate axes, V is the flow velocity

incident at an angle α=0 degrees relative to an imaginary vector connecting

the centers of the cylinders. ........................................................................... 22

Figure 2.10: Observable flow patterns when two cylinders are placed in the tandem

arrangement, (a) flow pattern regions with different Reynolds numbers and

L/D ratios, (b) visual description of each flow pattern [42]. ......................... 23

Figure 2.11: Observable flow patterns for different configurations of two cylinders

immersed in a flow [40]. Flow characteristics are shown for various

locations of the downstream cylinder at different T/D and L/D values

relative to the initial cylinder found at the origin. ......................................... 24

Figure 2.12: Strouhal number recorded behind the downstream cylinder for the two

cylinders in tandem arrangement as a function of Reynolds number and for

different streamwise spacing values between the two cylinders [42]. .......... 26

Figure 2.13: Reproduced isometric view of model used in experimental study of Salt et al.

[47], representing a landing gear strut with one landing light on either side.

....................................................................................................................... 28

Figure 2.14: Mean two-dimensional vorticity field for center plane, including primary

locations of pressure fluctuations for each frequency; f1=St=0.11 and

f2=St=0.33. As shown in [47]. ....................................................................... 29

Figure 2.15: Phase-locked vorticity images of the wake behind the two-light landing gear

configuration at: (a) 0˚, (b) 90˚, (c) 180˚, (d) 270˚, for the largest light

spacing and at the zero elevation [47]. .......................................................... 31

Figure 3.1: General diagram of wind tunnel used for experimental investigation, with

legend. Adapted from [48]. ........................................................................... 33

Figure 3.2: Front view diagram of empty wind tunnel test section with dashed lines

illustrating location of Pitot tube measurements that were used for

calibration of the wind tunnel. ...................................................................... 34

Figure 3.3: Landing gear model views: (left) actual landing gear model and (right)

rendered CAD isometric view of landing gear model. ................................. 35

Figure 3.4: Inventor isometric CAD rendering of light-strut assembly installed within the

wind tunnel test section, with SR=0.5. .......................................................... 36

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Figure 3.5: Photo by James Lepore and Eric Salt [49]. Reproduced with permission.

Photo depicts two-light model installed in wind tunnel test section. A similar

setup was used for the single light model testing. ........................................ 36

Figure 3.6: Dimensioned landing light views. All dimensions in mm. ............................. 38

Figure 3.7: Dimensioned views of all three aluminum bars. All bars were of the same

thickness. All dimensions in mm.................................................................. 38

Figure 3.8: Inventor CAD-rendered rear view of the assembled light and aluminum bar. 39

Figure 3.9: Dimensioned views of strut. All dimensions in mm. ...................................... 39

Figure 3.10: Top view of light-strut assembly without clamping mechanism, showing

light, strut, and bar that was used to hold the assembly together. ................ 40

Figure 3.11: Setup for testing of lone landing light vortex shedding frequency: (left)

close-up of upstream facing side, (right) view of light installed in the wind

tunnel test section. ........................................................................................ 42

Figure 3.12: Vortex shedding from model landing light, showing two separate best-fit

lines through two separate sets of data and the corresponding slope of each

line. ............................................................................................................... 43


Image displays microphone initial setup, with nosecone. ............................ 46


Photo depicts microphone, pipe, mount, and traverse system, as used during

microphone measurements. .......................................................................... 47

Figure 3.15: Inventor CAD-rendered images of microphone placed in position for

measurements while secured to pipe. Top shows isometric close-up view,

bottom shows top view with wooden panels removed for model visibility.

Model is set up for SR=0.5 configuration, microphone is at Z=0D elevation.

...................................................................................................................... 49

Figure 3.16: Depictions of 3-D printed piece. Top left: technical drawing without

dimensions depicting top view, front view, and assembled isometric view.

Reproduced with permission from [49]. Top right: piece installed on end of

pipe. Bottom: piece assembled with microphone enclosed. ......................... 50

Figure 3.17: Illustration of microphone measurement locations, depicted by open circles,

and path of traversed microphone, depicted by arrows, during the

measurements. Light-strut assembly setup is in the SR=0.5 configuration.

xvii

The arrows in front of the light-strut assembly represent the direction of the

flow. .............................................................................................................. 50

Figure 3.18: Top: Stand with hot-wire assembly installed; Bottom Left: close-up of hot-

wire assembly showing clamping mechanism that holds the hot-wire probe

in place; Bottom Right: Inventor CAD rendering of hot-wire assembly that

will be used to illustrate its use. .................................................................... 52

Figure 3.19: Inventor CAD-rendered images of hot-wire placed in position for

measurements while secured to pipe. Top shows a close-up of the isometric

view, bottom shows top view with wooden panels removed for model

visibility. Model is set up for SR=0.5 configuration, hot-wire is at Z=0D

elevation. ....................................................................................................... 53

Figure 3.20: Illustration of hot-wire measurement locations, depicted by open circles, and

path of traversed hot-wire, depicted by arrows, during the measurements.

Light-strut assembly setup is in the SR=0.5 configuration. The arrows in

front of the light-strut assembly represent the direction of the flow. ............ 54

Figure 3.21: Isometric depiction of three-dimensional traversing system used for moving

the microphone and hot-wire to each observation point. Reproduced from

TSI website [50]. ........................................................................................... 55

Figure 3.22: Isometric (top) and slightly tilted front view (bottom) of experimental setup

during PIV. The bottom view is slightly tilted to ensure the thin laser sheet is

not invisible in the image. The plane of interest is the Z=0D elevation, while

the model is set up for the SR=0.5 configuration. ......................................... 57

Figure 3.23: Photo of trigger box taped to wooden blocks. ............................................... 60

Figure 3.24: PIV results showing the velocity plot for the SR=0.5, Vt=10 m/s, Z=0D case.

....................................................................................................................... 63

Figure 3.25: PIV results showing the velocity plot for the SR=1.25, Vt=10 m/s, Z=0D

case. ............................................................................................................... 63

Figure 3.26: PIV results showing the velocity plot for the SR=0.5, Vt=10 m/s, Z=0D case,

identical case as in Figure 3.24 but acquired in later PIV rounds and showing

the microphone interfering with the camera view of the wake. The

microphone is observed approximately in the X/D=1.0 to X/D=2.0 range and

it resembles closely the outline of the microphone-pipe assembly shown in

Figure 3.15. ................................................................................................... 64

xviii

Figure 3.27: PIV results showing the velocity plot for the SR=0.5, Vt=10 m/s, Z=0D case;

identical case as in Figure 3.24 and Figure 3.26 but with cropping of

microphone half and flipping of the top half applied. .................................. 65

Figure 3.28: Initial version of a pair of phase-locked vorticity images half a cycle apart,

for the SR=0.5, Vt=10 m/s, Z=1D case. ....................................................... 67

Figure 3.29: Mirrored version of the images shown in Figure 3.28. ................................. 68

Figure 3.30: Figure 3.29 with swapped bottom halves and with d2 parameter outlines

added............................................................................................................. 68

Figure 3.31: PIV results showing vorticity plot around light-strut assembly for SR=0.5,

Vt=10 m/s, Z=0D case. This is the original image prior to flipping the top

half. ............................................................................................................... 69

Figure 3.32: PIV results showing mirrored vorticity plot around light-strut assembly for

SR=0.5, Vt=10 m/s, Z=0D case. ................................................................... 69


Vt=10 m/s, Z=0D case, with light and strut graphic visible. ........................ 71

Figure 4.1: Positions at which microphone readings were recorded for the SR=0.5, Vt=10

m/s. Z=0D case shown relative to the position of the light-strut assembly;

arrows denote the flow direction. ................................................................. 72

Figure 4.2: Frequency spectra showing microphone results for case of SR=0.5, Vt=10

m/s, Z=0D. .................................................................................................... 73

Figure 4.3: Frequency spectra showing microphone results for case of SR=0.5, Vt=10

m/s, Z=0D in non-dimensional form with reduced domain. ........................ 73

Figure 4.4: Positions at which hot-wire readings were recorded for the SR=0.5, Vt=10

m/s. Z=0D case shown relative to the position of the light-strut assembly;

arrows denote the flow direction. ................................................................. 75

Figure 4.5: Frequency spectra showing hot-wire results for case of SR=0.5, Vt=10 m/s,

Z=0D. ........................................................................................................... 75

Figure 4.6: Frequency spectra showing hot-wire results for case of SR=0.5, Vt=10 m/s,

Z=0D in non-dimensional form with reduced domain. ................................ 76

Figure 4.7: SR=0.5, Vt=10 m/s, Z=0D case without measurements in the wake- top panel:

microphone measurement positions relative to the location of the light-strut

assembly, bottom panel: aggregated non-dimensional microphone frequency

spectra of the measurements in the top panel. .............................................. 78

xix

Figure 4.8: Microphone frequency spectra for the arrangement described by Figure 4.1

showing all experimental cases for various freestream velocities - top panel:

10 m/s, middle panel: 20 m/s, bottom panel: 30 m/s .................................... 79

Figure 4.9: Microphone (top) and hot-wire (bottom) non-dimensional frequency results

for empty wind tunnel configuration at 10 m/s. ............................................ 81

Figure 4.10: Frequency spectra showing microphone results for the case of SR=0.5,

Vt=10 m/s, Z=0D (solid lines), as well as the average wind tunnel

microphone signal at Vt=10 m/s (dashed line), in non-dimensional form. ... 83

Figure 4.11: Frequency spectra showing hot-wire results for the case of SR=0.5, Vt=10

m/s, Z=0D (solid lines), as well as the average wind tunnel hot-wire signal at

Vt=10 m/s (dashed line), in non-dimensional form. ...................................... 83

Figure 4.12: Hot-wire results for the SR=1.25, Vt=10 m/s, Z=0D case. ........................... 84

Figure 4.13: Microphone signal for all cases – all spacing settings, all velocities, all

elevations – on the same non-dimensionalized domain. ............................... 85

Figure 4.14: Hot-wire signal for all cases – all spacing settings, all velocities, all

elevations – shown on the same non-dimensionalized domain. ................... 85


elevations – shown on the same non-dimensionalized domain, with SR=0.5,

Z=1D, cases removed for all velocities. ........................................................ 87


elevations – shown on the same non-dimensionalized domain, with SR=0.5,

Z=1D and Z=0.5D, cases removed for all velocities. ................................... 87

Figure 4.17: Non-dimensional microphone signal for all cases – all spacing settings, all

velocities, all elevations – shown on the same non-dimensionalized domain,

with SR=0.5, Z=1D, cases removed for all velocities. .................................. 88

Figure 4.18: Non-dimensional microphone signal for all cases – all spacing settings, all

velocities, all elevations – shown on the same non-dimensionalized domain,

with SR=0.5, Z=1D and Z=0.5D, cases removed for all velocities. ............. 88

Figure 4.19: Hot-wire signal showing spectra for all SR=0.5 cases, including all velocities

and elevations, along with the average peak Strouhal number. .................... 91

Figure 4.20: Hot-wire signal showing spectra for all SR=0.85 cases, including all

velocities and elevations, along with the average peak Strouhal number. .... 91

xx

Figure 4.21: Hot-wire signal showing spectra for all SR=1.25 cases, including all

velocities and elevations, along with the average peak Strouhal number. ... 92

Figure 4.22: Hot-wire results for all Z=0D cases. ............................................................. 94

Figure 4.23: Hot-wire results for all Z=0.5D cases. .......................................................... 95

Figure 4.24: Hot-wire results for all Z=1D cases. ............................................................. 95


...................................................................................................................... 99


...................................................................................................................... 99


.................................................................................................................... 100


.................................................................................................................... 101


.................................................................................................................... 101


.................................................................................................................... 102

Figure 5.7: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z=0D case. . 103

Figure 5.8: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z=0.5D case.

.................................................................................................................... 103

Figure 5.9: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z =1D case. 104

Figure 5.10: PIV results showing vorticity plot with outlined vortical structures for points

1-4 in the acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0D case. Top left

corner depicts the point in the acoustic cycle for which each image was

captured, bottom left image illustrates the height setting. .......................... 107


1-4 in the acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0.5D case. Top left




1-4 in the acoustic cycle for the SR=0.5, Vt=10 m/s, Z=1D case. Top left

xxi




Vt=10 m/s, Z=0D case, with light and strut visible. Bottom left image

illustrates the height setting. ........................................................................ 114

Figure 5.14: PIV results showing velocity plot around light-strut assembly for SR=0.5,

Vt=10 m/s, Z=0D case, with light and strut visible. Bottom left image


Figure 5.15: Velocity vectors from PIV of SR=0.5, Vt=10 m/s, Z=0D case, focused on

specific region between light and strut in Figure 5.14. ............................... 116

Figure 5.16: PIV results showing the vorticity plot for the SR=0.5, Vt=10 m/s, Z=0D

case, overlaid with hot-wire measurement locations. Bottom left image


Figure 5.17: PIV results showing the vorticity plot for the SR=0.5, Vt =10 m/s, Z=0D

case, overlaid with hot-wire measurement locations, and illustrating 12

spectra associated with 12 selected measurement points. Lines connect each

measurement point to its spectrum. All spectra have the same scale. ......... 119

Figure 5.18: PIV results showing the vorticity plot for the SR=0.5, Vt=10 m/s, Z=0.5D

case, overlaid with hot-wire measurement locations, and illustrating eight

spectra associated with eight selected measurement points. Lines connect

each measurement point to its spectrum. All spectra have the same scale. 120

Figure 5.19: PIV results showing the vorticity plot for the SR=0.5, Vt=10 m/s, Z=1D

case, overlaid with hot-wire measurement locations, and illustrating eight

spectra associated with eight selected measurement points. Lines connect

each measurement point to its spectrum. All spectra have the same scale. 121

Figure 6.1: Figure 5.14 with arrows providing artistic representation of streamlines for

each of the three hypothesized flow patterns. Arrows are labelled according

to which flow pattern each represents: 1 – flow reattachment to the strut and

subsequent shedding, forming the wake directly behind the strut; 2 –

avoidance of reattachment, flow around pattern #1, formation of high

velocity region in overall wake; 3 – flow in cross-stream direction away

from light-strut assembly, creation of wide wake. ...................................... 126

Figure 6.2: Artistic representation of possible flow movement around light-strut assembly

for SR=0.5 case; top: top view, bottom: side view. Arrows represent

streamlines. The three flow options depicted here are the same as those

shown in Figure 6.1. .................................................................................... 127

xxii

Figure 6.3: Proposed flow behaviour for light-strut problem. Region 1 represents the

complex three-dimensional flow behaviour, Region 3 represents the

approximately two-dimensional cylinder vortex shedding regime, and

Region 2 represents the transition from Region 1 to Region 3. ................. 132

Figure 0.1: Circuit diagram for trigger system used in conjunction with TSI PIV system to

obtain phase-locked images, as produced by Arthurs [53]......................... 145

xxiii

LIST OF TABLES

Table 2-1: Various reported values for the Strouhal number of the vortex shedding helical

mode found in the wake of a circular disk. Strouhal and Reynolds numbers

were based on the tunnel velocity and disk diameter. ................................... 20

Table 3-1: Experimental matrix shows test cases with accurate artistic representations of

side and top views of the assembly to illustrate different experimental cases.

The diameters, D, of the strut and light, are equivalent. ............................... 45

Table 4-1: Average hot-wire Strouhal number of the single peak in the 0.16-0.18 range

for each case. ................................................................................................. 93

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NOMENCLATURE EPNL Effective Perceived Noise Level [EPNdB]

MTOM Maximum Takeoff Mass [t]

Re Non-dimensional velocity, Reynolds number (based on

freestream wind tunnel velocity and light or strut diameter)

[]

St Non-dimensional frequency, Strouhal number (based on

freestream wind tunnel velocity and characteristic length of

bluff body, usually diameter)

[]

f Frequency of periodicity in the flow [Hz]

D Diameter of light or strut [m]

Z Elevation [m]

S Spacing between light and strut [m]

SR Spacing Ratio []

X/D Non-dimensional distance in the cross-stream direction

within the landing gear wake, relative to strut center

[]

Y/D Non-dimensional distance in streamwise direction within

the landing gear wake, relative to strut center

[]

V Local velocity in wake [m/s]

Vt Freestream Wind Tunnel Velocity [m/s]

ω Local vorticity in wake [1/s]

ρ Density of air [kg/m3]

Pmax Maximum RMS acoustic pressure amplitude [Pa]

P* Non-dimensional pressure amplitude []

1

1 INTRODUCTION

Increasing global population has resulted in an increasing amount of both air traffic and

civilian exposure to aircraft noise. Perhaps in response to this trend, increasingly strict

aircraft noise regulations have led to a push for airplane noise reduction. These

regulations, alongside the practice of airplane noise fees levied at each airport, have

greatly incentivized manufacturers to pursue technologies for reducing airplane noise.

Problem and Motivation 1.1Airplane noise can mainly be divided into two categories: engine noise and aerodynamic

noise. The engine noise sources are the fan or propeller, compressors, combustor,

turbines, jet or nozzle, and auxiliary power unit. Aerodynamic noise consists of the sound

generated from the physical movement of the plane through the air. Main sources are the

wings, H-tail or V-tail, flaps, slats, landing gear, and fuselage. Transmission of these

sounds through the air is affected by atmospheric conditions via reflection, scattering, and

absorption [1].

The landing phase of an aircraft flight commonly involves the engine thrust level at the

lowest setting and results in a significantly reduced quantity of engine noise in

comparison to previous portions of the flight. Accordingly, it is during the landing phase

that the aerodynamic noise, relative to the engine noise, is at its greatest. Of the total

aerodynamic noise, the most significant is landing gear noise. This is depicted in the

2

figure below adapted from a presentation by Dobrzynski at the 14th

AIAA/CEAS

Aeroacoustics Conference [2]. Evidently, for long range aircraft, those with flight paths

of 4000 or more kilometres, landing gear noise alone is higher upon landing than the

engine noise; for short range aircraft, those that fly less than 1500 kilometres, landing

gear noise is among the most significant aerodynamic noise sources, although about two

EPNdB lesser in magnitude than the engine noise.

Figure 1.1: Relative EPNL for various aircraft noise sources for long range aircraft (left) and short range

aircraft (right). Long range aircraft are defined as those with flights equal to or more than 4000 kilometres while

short range aircraft are defined as those with flights of less than 1500 kilometres. Adapted from [2].

Ensuing from its significance among other aerodynamic sources has been a great world-

wide effort to gain a greater understanding of landing gear noise. A number of

international projects have covered the subject to varying degrees within the overarching

umbrella of aerodynamic noise; a general overview of these was provided by Bouvy et al.

[3]. Additionally, inter-company partnerships attempting to encourage research in the area

of landing gear noise have created and released to the scientific community landing gear

configurations for use as a baseline for experimental work. Two such examples are the

LAGOON landing gear by ONERA and Airbus and the ¼-scale Gulfstream G550 landing

3

gear provided through NASA-Gulfstream collaboration. Each example landing gear is

pictured below in Figure 1.2.

(a) (b) Figure 1.2: Schematic of (a) ONERA-Airbus LAGOON landing gear model [4] and (b) NASA-Gulfstream ¼-

scale G550 partially dressed landing gear model with all smaller components and landing gear lights removed

(left) and fully dressed landing gear model, with all components included (right) [5]. Landing gear lights are

present only for the case of the fully dressed NASA-Gulfstream landing gear model.

Research regarding landing gear noise has focused mainly on far-field acoustics, that is

measurements were mainly performed at distances far enough away from the landing gear

that the entire structure could be classified as a single source. Studies that focused more

closely on the landing gear near-wake rarely included the landing gear lights in their

investigations. Only the largest features, the main strut and wheels, were consistently

included across all studies. Smaller landing gear features such as the landing gear lights,

smaller linkages, bolts, cables, and straps were ignored. As seen in Figure 1.2, the

LAGOON landing gear model and the partially dressed ¼-scale G550 model do not

include any smaller features. Unfortunately, the majority of existing literature based off of

the G550 model focused on the partially dressed option and not the fully dressed case, in

effect ignoring smaller features and lights. This is somewhat understandable as the

4

landing gear structure is complex and it is intuitive to initially focus only on the largest

physical components when faced with a complicated physical noise source. However,

there are arguments to be made for the inclusion of the landing gear lights in modelling of

landing gear noise. For the NASA-Gulfstream model itself the light cluster in the fully

dressed model has been identified as a dominant noise source [6]. More importantly, the

landing light is not always smaller than the largest landing gear features.

Figure 1.3: Photo of an aircraft landing gear titled: HN-441 F-A-18C Hornet Finnish Air Force ILA 2012 nose

landing gear, by Julian Herzog, available under a Creative Commons Attribution 4.0 International license.

A real-world picture of a nose landing gear is provided in Figure 1.3 above, showing that

landing gear lights do exist at characteristic lengths as large as the main strut. Therefore,

their effect on the wake and acoustics of the overall landing gear will not be negligible in

all, if any, cases. Considering this statement and recalling the previously described,

increasingly strict state of the regulatory environment, it is clear that scientific work

5

accounting for the effect of landing gear lights is needed. Thus, the motivation for this

thesis is explained.

Scope 1.2Thesis work was completed utilizing a simplified model of the landing gear consisting of

a single light and a lone strut only. This could be seen as an interesting choice considering

the lack of landing gear light research was a direct result of the over-simplification of the

landing gear models in the first place. However, Guo [7] showed that the frequencies of

landing gear components can be grouped based on their size, allowing for the exclusion

of most of the smaller features, such as linkages, bolts, cables, and straps. Guo’s findings

allowed for the drawing of conclusions regarding the frequency output of the model, even

if the model was a simplified one. Guo’s findings will be further explored in the literature

review.

Of course, precisely because the model was not fully representative of a fully dressed

landing gear the thesis work could not be too ambitious, and was limited in its focus to

broad trends in the wake and frequency spectra rather than attempts to define any features

quantitatively, or to attempt to set definite guidelines for industry. The thesis purpose was

simply to observe the general effect of varying orientation of the landing light on the

landing gear wake, and subsequently on the landing gear noise. A variation in landing

light orientation was achieved by changing the spacing between the model landing light

and the model strut while they were situated in a tandem arrangement.

6

2 LITERATURE REVIEW

This literature review will first introduce the reader to the regulatory environment within

the current air transport industry, and will then discuss relevant scientific work. Section

2.1 and Section 2.2 may be omitted by those wishing to begin at the discussion of prior

scientific work.

A Brief History of Airplane Noise Regulation 2.1

The beginning of the 1960s saw the commercial airliner industry in its younger stages.

Companies searching to transform themselves from military suppliers during World War

II to civilian airliner manufacturers in the post-war period had developed the first

generation of commercial jet airliners during the previous decade, the 1950s. The industry

climate in the 60s was far from what it is today – commercial flight distance and duration

records were broken at a regular pace and the modern commercial aircraft manufacturing

duopoly, Boeing and Airbus, were still in their infancy. Boeing would not release its

signature airliner, the 737, until 1968, while Airbus was only officially founded in 1970.

It was against this backdrop of change and growth of the industry that complaints of

excessive noise produced by commercial aircraft were first examined. The International

Civil Aviation Organization (ICAO), the main international civil air transportation

governing body, took notice of complaints and recommended a set of noise regulations

limiting total noise emissions from all future, newly-manufactured civil aircraft models.

These regulations were adopted, passed into law by each member state, and became

7

applicable worldwide in 1972 under Chapter 2 of Annex 16 of Volume I to the

Convention on International Civil Aviation [8]. The initial standards were continuously

revisited throughout the years and were made more stringent in 1977 through Chapter 3

and again in 2006 through Chapter 4. The recent Chapter 14 standard is not yet in effect

but has been approved, and will likely be applicable by 2020 [9], [10]. Figure 2.1 below,

offered at a 2013 ICAO presentation, illustrates the increasingly limiting nature of the

ICAO standards. The lines plotted are the upper limits, in EPNdB, of permitted aircraft

noise.

EPNdB is a measure of effective perceived noise level (EPNL), which is a representation

of the pressure amplitude of a sound that accounts for the potential annoyance the sound

may cause due to its spectral nature, duration, and the time of day during which it is

emitted. These factors are important because human hearing is more sensitive to sounds

composed of tones or narrow rather than broadband peaks, is more sensitive to longer

rather than shorter sounds, and is more sensitive to nighttime sound when background

noises are at a minimum rather than daytime sound. ICAO explains the specific

procedures and calculations to be used in measuring the sound emitted by various types of

aircraft in the appendices to [8]. The cumulative EPNL shown in Figure 2.1 is the total

EPNL from three different locations summed together: aircraft approaching the runway

during landing, point of maximum sound emission while the aircraft is taxiing, and

aircraft away from the runway during takeoff. The specific distances and orientations for

8

these measurement locations are defined by the ICAO each time a noise standard is

updated [8].

Noise standards limit the sound emission of an aircraft based on the weight of the

airplane; this allows for placement of smaller airports that service smaller, quieter planes

closer to residential areas than major international airports. For this reason Figure 2.1

shows cumulative EPNL graphed as a function of maximum takeoff mass (MTOM), a

measure of the weight of an aircraft fully loaded with passengers and luggage. For

reference, the newest Boeing 747 has a MTOM of approximately 450 tonnes [11] while

the newest, largest Boeing 737 has a MTOM of approximately 90 tonnes [12].

Figure 2.1: Illustration of evolving ICAO noise standards, reproduced from [9].

Regulatory Pressure on the Air Transport Industry 2.2With the applicability of Chapter 4 noise standards in 2006 also began the phase out of

any aircraft that did not pass the Chapter 3 certification process. The Chapter 14 noise

9

standards will similarly start a phase out of all aircraft that are not able to pass the

Chapter 4 certification process. ICAO’s long term 2030 vision reveals the hope of a

further 10 EPNdB reduction relative to the Chapter 14 standards [10]. It seems inevitable

that a phase out will occur by the year 2030 of those aircraft that are not able to pass

Chapter 14 certification. Therefore, ICAO’s standards act to set up a pattern of

discontinuation that effectively renders inoperative those commercial aircraft which are

uncompliant with at least the previous generation of noise limits. This pattern forces

manufacturers to remain in a state of constant innovation, as they must design for their

proposed aircraft to meet all regulations, including future increases in stringency,

throughout the entire duration of the aircraft’s lifespan. Failure to ensure this could result

in early retirement of the aircraft and many years of lost profit for the aircraft operator.

Logically, operators will avoid this risk and seek to only purchase aircraft tailored with

noise-reducing technologies that will allow for compliance with standards for as long as

the aircraft is mechanically fit to fly. Therefore, ICAO standards equate to serious

regulatory pressure on manufacturers as they must design for compliance with future

noise standards one or two generations ahead of the active regulation if they wish to

remain relevant to potential customers.

A second pressure on manufacturers is related to airport noise fees. The majority of

airports use a combination of noise level and MTOM to calculate noise charges [13] that

they levy on every departing and arriving aircraft, and some also apply additional

nighttime penalties or impose curfews. The ICAO does not regulate airport application of

10

noise penalties so each individual airport is likely to enforce a unique payment scheme

adapted to its region’s regulatory and physical environment. A summary of current noise

fee strategies was published by Girvin in 2009 [14]. Regardless of the specifics, a noisier

aircraft will therefore generally be more financially punitive to the operator than a quieter

aircraft, at any airport in the world. Thus, this is an added incentive for manufacturers to

focus on advancement in noise-reducing technologies.

The enormous pressure on the industry to advance in technology has generated great

quantities of both private and public research relating to numerous aircraft noise topics.

However, some topics have been left relatively unexamined, an example being the

landing lights and their effect on the overall landing gear noise. The rare existing work in

this area is discussed next.

Prior Scientific Work 2.3For centuries humans have understood that flow-structure interaction has the potential to

generate sound. Leonardo da Vinci famously coined the term “Aeolian” tone to describe

the sound generated by vortex shedding from a cylinder. More recently, Lighthill [15]

developed the acoustic analogy whereby the compressible Navier-Stokes equations were

rearranged into a form of the wave equation, thus creating a mathematical basis for sound

generation from fluid flow. Lighthill highlighted the link between fluid flow and acoustic

generation, consequently showing that an object in a flow can generate sound which can

then be assessed and predicted not only through direct acoustic recording but also

indirectly by observing the movement of the fluid around the object. As a result, this

11

literature review will first cover experimental work related to flow around landing gear

bluff bodies, and then will focus on landing gear noise research.

Flow Around Bluff Bodies 2.3.1Any object placed in a flow will have an effect on the movement of the fluid in its

vicinity. When this object is non-streamlined, a so-called bluff body, the affected flow

will organize into regions similar to those shown in Figure 2.2 below [16], which is a

slightly adapted reproduction of an image by Zdravkovich [16] provided by Demartino

and Ricciardelli [17] and shows the regions of disturbed flow around a cylinder, a well-

known bluff body. Zdravkovich describes the different regions in the following manner:

I. One narrow region of retarded flow

II. Two boundary layers attached to the surface of the cylinder

III. Two sidewise regions of displaced and accelerated flow for

which UIII>U

IV. One wide downstream region of separated flow called the

wake for which UIV<U (Pages 3 and 4 of [16])

Figure 2.2: Regions of disturbed flow around a cylinder [17].

An important feature not mentioned above is the shear layer, which is the separated

boundary layer in Figure 2.2 that divides region III from region IV. Shear layers are

present whenever two fluids with differing velocities share a border, and are important

12

due to their role as the source of periodicity – they generate vortices in the wake of

cylinders and disks. Shear layers, along with all regions shown in Figure 2.2, are common

in all flows around bluff bodies.

An aircraft landing gear assembly can be considered a single bluff body, albeit one that is

very physically complex. The flow disturbed by a landing gear can therefore be

categorized into those regions seen in Figure 2.2 relatively easily, just as any other bluff

body. However, problems arise when more specific analyses of the landing gear wake are

attempted, due to local interaction of the many individual wakes generated by the many

individual landing gear components. The landing gear model was thus simplified to avoid

these issues as much as possible.

Unfortunately, the simplified form of the landing gear consisting of only the light and the

strut, to the knowledge of the author, has not been previously investigated in literature.

However, it was deemed possible to model the light as a disk – the basis for this

simpification is discussed in the experimental apparatus and methodology section – and

the strut as a cylinder, and to proceed with a search within literature for a study of flow

around a disk-cylinder assembly. Again, it was discovered that this setup had not been

investigated in literature. Again, a simplification was required; the flow over a disk, the

flow over a cylinder, and the flow around two cylinders were separately considered, as

these subjects were research areas for which a reasonable amount of scientific work had

been published. The knowledge of wake behaviour from all three of these independent

13

research areas was then combined to form a single, more complete understanding of the

wake observed during the investigation. In the following sections, the existing work in

each area is presented; the flow over a lone cylinder is presented first and followed by

flow over a disk, with the flow around two cylinders discussed last.

2.3.1.1 Flow across a Circular Cylinder

With many industrial applications, flow across a circular cylinder is a subject that has

been studied intensively now for over a century. The focus in this section will rest

primarily on general characteristics of the wake with increasing Reynolds number,

characteristics that are unanimously agreed upon by the scientific community. For an in-

depth look at the experimental history of the field, the reader is encouraged to consult the

book by Zdravkovich [16].

Figure 2.3 below displays the general patterns observed in the wake of a right circular

cylinder in a cross flow. The image was published in 1966 by Lienhard [18]. Since this

time the Reynolds number limits for each mode have been under dispute but there has

been universal agreement regarding the general behaviour of each mode and progression

from one mode to the next. At first, flow around a cylinder is completely laminar and the

downstream half of the flow is entirely symmetric relative to the upstream half. This is

pictured in Figure 2.3 in the first regime shown. The second regime shows Föppl vortices:

with an increase in Reynolds number, separation of the flow is initiated and a closed near-

wake develops that consists of a set of weak recirculating regions. Further increase in the

Reynolds number encourages growth of the Föppl vortices until they become unstable

14

and the separated shear layers begin to oscillate with increasing amplitude, eventually

leading to the establishment of an alternating vortex pattern – known as the von Kármán

vortex street – in the wake. This vortex street is depicted in the third regime in Figure 2.3.

Eventually, as observed in the fourth regime, the increasing Reynolds number triggers a

transition to turbulence beginning in the far wake and moving upstream until the near-

wake, separated shear layers, and vortices all transition to turbulence. A still further

increase in Reynolds number brings about the fifth regime, where the transition to

turbulence has reached the separation points on the cylinder and there is a breakdown of

the alternating vortex street pattern. The final regime shown in Figure 2.3, and the final

regime known in literature, is the sixth regime, for which the alternating vortex street has

reappeared and in which the boundary layer attached to the cylinder is turbulent in

conjunction with the turbulent wake and shear layers.

15

Figure 2.3: Flow regimes for flow around a circular cylinder. Reproduced from [18].

The frequency of shedding of the vortices in the various regimes varied with Reynolds

number. Figure 2.4 displays the non-dimensionalized frequency, Strouhal number, of

cylinder vortex shedding as a function of Reynolds number, as presented by Blevins [19].

Prior to further examination, the concept of the Strouhal number should be introduced.

The Strouhal number, abbreviated St, is a common non-dimensionalized quantity in

aeroacoustics used to describe the frequency of periodic vortex shedding from a bluff

16

body. It is calculated by dividing the frequency by the flow velocity and multiplying by a

characteristic length. For circular objects the characteristic length is almost always the

diameter. In Figure 2.4, for the values in the range of approximately 3*102≤Re≤10

5 the

Strouhal number is relatively consistent at roughly St=0.2. Due to the lack of consistency

of Strouhal values at any other Reynolds numbers and the large amount of real-world

practical examples in the aforementioned Reynolds number range, the St=0.2 value is

often cited as the circular cylinder vortex shedding frequency.

Figure 2.4: Strouhal-Reynolds number relationship for flow across a circular cylinder [19].

2.3.1.2 Flow around a Disk

Flow around a disk is a three-dimensional problem that is a more complex case than that

of flow around a single cylinder, due mainly to the disk’s axisymmetric geometry.

Experimental investigation by a number of different authors has over the years slowly

shone some light on the activity in the wake of the disk, as can be deduced from [20]–

[23]. However, this has not yet resulted in a complete consensus on the features that are

present. A review of the early work in the field is provided by Kiya et al. [24], while the

17

literature review by Yang et al. [25] shows effectively the current state of knowledge.

Most experimental and numerical work has focused on defining critical Reynolds

numbers at mode transitions and frequencies of oscillation of each mode for low

Reynolds numbers, generally for values less than 500 [22], [26]–[32]. For high Reynolds

numbers between 104

and 105, the general consensus seems to be that there are three

different instabilities resulting in three different flow patterns: a recirculation bubble,

antisymmetric fluctuations due to a helical vortex, and Kelvin-Helmholtz oscillations of

the shear layer [21], [24], [25], [33], with the helical mode dominant in most cases [23],

[33]–[39]. This helical mode is depicted below in Figure 2.5, Figure 2.6, and Figure 2.7,

which aid in understanding the complexity of the disk wake. Figure 2.5 presents all three

previously discussed modes, while Figure 2.6 and Figure 2.7 attempt to describe the

three-dimensionality present in the wake. It should be noted that Figure 2.6 and Figure

2.7 utilize the same axis naming convention so that Figure 2.6 can be thought of as

showing downstream planar slices of the wake in Figure 2.7. While Figure 2.7 drives

home the notion that the cylinder wake is complex along its entire downstream length,

Figure 2.6 excellently highlights the rotating nature of this wake by showing three

different planes at three different distances from the disk presenting three vorticity

pairings all apparently rotated at some angle relative to each other.

18

Figure 2.5: Disk wake structure shows three different modes present in the wake [21].

Figure 2.6: Planar cut of wake shows numerically simulated vorticity contours at various downstream sections of

the wake: (a) x/D=0.5, (b) x/D=3.5, (c)x/D=7, where x represents the downstream distance away from the disk

and D represents the disk diameter [25].

19

Figure 2.7: Numerically simulated flow behind a circular disk, highlights wake structure [25].

As a result of its overwhelming presence in the flow, there is a relatively large amount of

data reporting the frequency of the helical mode; a selected number of studies reporting a

Strouhal number for the helical vortex shedding mode are summarized below in Table

2-1. It is clear from the results displayed in the table that the helical mode can be found to

oscillate in the region of St=0.13-0.15, with St=0.135 seemingly the most accurate value,

especially for larger Reynolds numbers.

20

Table 2-1: Various reported values for the Strouhal number of the vortex shedding helical mode found in the

wake of a circular disk. Strouhal and Reynolds numbers were based on the tunnel velocity and disk diameter.

Author Year of

Publication

Reported

Strouhal Number

Details

Yang et al. [25] 2014 0.136-0.142

numerical study using

large eddy simulation

Re=104

Bobinski et al.

[22]

2014 0.15 experimental study

50≤Re≤500

Johansson and

George [23]


Re=26400

Miau et al. [35] 1997 0.135 experimental study

104≤Re≤10

5

Cannon et al. [34] 1993 0.15 experimental study

Re=1.32*104

Lee and Bearman

[38]


Re=1.4*105

Berger et al. [21] 1990 0.135 experimental study

104≤Re≤10

5

Fuchs et al. [33] 1979 0.135 experimental study

Re=5*104

Roberts [37] 1973 0.135 experimental study

Re=7.8*104

Calvert [36] 1967 0.135 experimental study

Re=5*104

2.3.1.3 Flow Around Two Cylinders

Zdravkovich studied flow around two cylinders in various arrangements and defined two

interference regions [40],[41] depending on the relative orientation of the two cylinders,

as shown in Figure 2.8 below. The figure displays the first cylinder at the origin with the

position of the second cylinder determined by the transverse (vertical axis) and

downstream (horizontal axis) spacing.

21

Figure 2.8: Classification of interference regions for various cylinder arrangements [41]. T is the transverse

spacing between axes of cylinders, D is the cylinder diameter, and L is the streamwise spacing between axes of

cylinders. The diagonal hashed lines represent regions where bistable flow is prevalent.

In the proximity interference region the presence of an additional cylinder nearby affects

the flow around both, but neither cylinder is within the wake of the other. In the wake

interference region one cylinder is located in the wake of the other and flow around both

cylinders is affected. Zdravkovich also describes a third region that is a combination of

the proximity and wake regions, as well as a region of no interference where flow around

each cylinder is unaffected by the presence of the other cylinder. The main conclusion for

cylinders positioned in a zone of interaction is that attempting to extrapolate those trends

present in the flow around a single cylinder to the case of two cylinders cannot be

achieved successfully – the two cylinder case is too complex. For the purposes of the

investigation discussed in this thesis only the wake interference region is of interest, and

only for the case of one cylinder directly behind the other, as shown in Figure 2.9 below.

The setup shown, with one cylinder directly behind the other, is known as the tandem

arrangement of two cylinders in a cross flow.

22

Figure 2.9: Two cylinders in the tandem arrangement [41]. L is the distance between the centers of the two

cylinders (same as in the above figure), y and x denote the vertical and horizontal Cartesian coordinate axes, V is

the flow velocity incident at an angle α=0 degrees relative to an imaginary vector connecting the centers of the

cylinders.

It should be recalled again, as will be presented in the Experimental Apparatus section,

that the light used during experimental work displayed vortex shedding at frequencies

very similar to that of a disk, thereby allowing for the assumption that the wake behaviour

of the lone light used in the thesis model was similar to the wake of a lone disk in

crossflow. This assumption was significant because it allowed for the light and strut to be

approximated as a disk and cylinder in tandem. It cannot be expected for a disk and

cylinder in tandem to present similar wake structures as that of two cylinders in tandem.

However, the nature in which the flow patterns of the two cylinders in tandem transform

as the spacing between the two is varied was used as a basis for some limited conclusions

concerning the light-strut model as the spacing between the light and the strut was varied.

Therefore, in this sense, it was beneficial to have some understanding of the behaviour of

the flow for the case of two tandem cylinders in crossflow.

23

(a)

(b)

Figure 2.10: Observable flow patterns when two cylinders are placed in the tandem arrangement, (a) flow

pattern regions with different Reynolds numbers and L/D ratios, (b) visual description of each flow pattern [42].

Igarashi defined different flow patterns that correspond to different values of streamwise

cylinder spacing, as well as presented sketches of each flow regime [42]. Figure 2.10

above depicts the different flow pattern regions on the left and describes visually the

behaviour of each region on the right. Zdravkovich [40], [41], [43] reported similar flow

patterns as Igarashi, as shown in Figure 2.11 below, and Xu and Zhou echoed his

qualitative findings [8].

24

Figure 2.11: Observable flow patterns for different configurations of two cylinders immersed in a flow [40]. Flow

characteristics are shown for various locations of the downstream cylinder at different T/D and L/D values

relative to the initial cylinder found at the origin.

There is some disagreement by different authors on the exact number of various flow

patterns and the specific L/D locations of each transition to a new pattern. However, the

general progression of flow patterns presented here has not been debated and is validated

in the most recent review on the subject by Sumner [45]. With reference to Figure 2.10,

for small L/D ratios, represented by Case A, the shear layer that separates from the

leading cylinder does not reattach on the downstream cylinder, instead curling up,

forming vortices behind the downstream cylinder, and resulting in flow behaviour that

resembles vortex shedding from a single bluff body. As the streamwise spacing between

the cylinders is increased, Case B – Case D, the shear layer from the leading cylinder

begins to reattach to the second cylinder and vortices that are shed now originate from a

separation point on the downstream cylinder instead of the leading cylinder. With further

25

increases in streamwise spacing the reattachment point moves further upstream along the

face of the downstream cylinder until the shear layer no longer reattaches and instead

curls up and forms a vortex prior to contact with the downstream cylinder. This change

reverses and reoccurs intermittently in the bistable Case E, and, after an additional

increase in streamwise spacing, becomes permanent in Case F. At this point, and for

subsequent increases in spacing, there are two vortex streets present, one behind the first

cylinder and one behind the second cylinder. Interestingly, regardless of the streamwise

spacing ratio there is only one vortex shedding frequency present at any one time; even

when two vortex streets are visible their vortex shedding is synchronized.

This is not to say that the frequencies remain constant with changes in streamwise

spacing. On the contrary, there is significant fluctuation in Strouhal number with changes

in the spacing between two tandem cylinders [44]–[46]. Igarashi used Figure 2.12 below

to show the effects of Reynolds number on the vortex shedding Strouhal number found

behind the downstream cylinder in the tandem arrangement. However, Figure 2.12 can

also be used to highlight the decrease in Strouhal number with increasing L/D ratios.

Ratios of L/D greater than 3.09 can be ignored as the effect of the additional cylinder,

upstream or downstream, is greatly diminished – the wake pattern is largely unaffected –

for these values of cylinder spacing. This leaves the ratios 1.03≤L/D≤3.09 for which the

data show a sizeable decrease in Strouhal number for each increase in inter-cylinder

spacing.

26

Figure 2.12: Strouhal number recorded behind the downstream cylinder for the two cylinders in tandem

arrangement as a function of Reynolds number and for different streamwise spacing values between the two

cylinders [42].

Landing Gear Noise 2.3.2There exist two scientific works relevant to the present investigation: Guo and Salt et al.

They are discussed next.

2.3.2.1 Guo [7]

Guo [7] showed that landing gear components can be broken down into three different

groups depending on their frequency response when immersed in a flow. The three

groups were separated as such: low-frequency, mid-frequency, and high-frequency. In

general, the size of the components determined their grouping; large objects such as the

strut and wheels were placed in the low frequency domain while the smallest components

27

such as bolts and cables were positioned in the high frequency domain. The consequence

of this conclusion is that a study of the general spectral characteristics of landing gear

components in the low frequency domain can be performed without including

components in the mid-frequency and low-frequency domains, as they will not add any

significant spectral features to the low-frequency results. Under Guo’s classification

system, landing gear lights in industry would likely fall in the mid-frequency or low-

frequency domain due to their varying sizes relative to the main landing gear struts. The

design used in this thesis was of similar diameter to the strut so was classified in the low-

frequency domain group. As a result of their classification in the high-frequency domain,

smaller features such as bolts, cables, and straps were not incorporated into the simplified

model used in the thesis experimental work. Additionally, despite the wheels classified as

producing sound in the low-frequency domain, the main interaction of the landing light

wake occurred with the structure and wake of the strut, not the landing gear wheels, so

they were not included in the experimental model. Thus, the model comprised only the

landing light and the main strut.

There was a downside to using such a simplified model. Guo also showed that high-

frequency components were an important contributor to the overall EPNL produced by

the landing gear, predicting that a ‘fully dressed’ version of the landing gear with all

components installed produced an EPNL 7.8 decibels greater than the ‘clean’

configuration featuring only the strut and wheel. Clearly, Guo’s work calls for inclusion

of the greatest number of features possible in the landing gear model during landing gear

28

noise level prediction. Otherwise, the prediction will not be accurate. As a result, the

simplified model used in this thesis could not be used for predicting noise levels, but only

for predicting general spectral features and wake patterns.

2.3.2.2 Salt et al. [47]

Salt et al. [47] completed a study with a very similar experimental apparatus as the setup

used within this thesis work, the difference being their study investigated the effect of

orientation of two lights and a strut, with one light on either side of the strut. The setup

was likewise simplified, consisting of only the strut and the lights with no wheels, cables,

bolts, or other small features. An isometric view is shown below in Figure 2.13.

Figure 2.13: Reproduced isometric view of model used in experimental study of Salt et al. [47], representing a

landing gear strut with one landing light on either side.

Salt et al. reported the existence of three separate frequencies generated by the flow

around their model. Within the wake of the two lights and strut there were prominent

peaks at St=0.11 and St=0.33. Further away, above and below the lights in the z direction

there existed a third frequency, St=0.2. The frequencies were located in different areas of

29

the wake, and therefore were not harmonics of one another. The St=0.2 frequency was

deduced to be the lone cylinder vortex shedding frequency, while it was concluded that

the St=0.11 and St=0.33 tones were generated as a result of the interaction of the flow

with the assembly of the two lights and strut. These two latter frequencies were found

primarily in the wake directly behind the landing lights, as shown in Figure 2.14 below.

Furthermore, the St=0.11 tone was found to propagate generally in the x-y plane, while

the St=0.33 tone displayed three-dimensional behaviour. Therefore, Salt et al. argued that

despite the prevalence of three distinct frequencies in the wake it was possible that the

St=0.33 tone was dominant in the downward z direction, which in practical scenarios

would equate to the direction of the ground, at some far distance away from the landing

gear assembly.

Figure 2.14: Mean two-dimensional vorticity field for center plane, including primary locations of pressure

fluctuations for each frequency; f1=St=0.11 and f2=St=0.33. As shown in [47].

30

Due to the greatly two-dimensional nature of the oscillation at St=0.11, propagation

through the wake was captured in the x-y plane and is shown below in Figure 2.15. The

figure displays the generation, propagation, and dissipation of vortices for the largest light

spacing investigated by Salt et al. [47] at the zero elevation, the configuration for which

the strongest wake pulsations were observed to occur at a Strouhal frequency of St=0.11.

Alternately shedding periodic structures are clearly noticeable within the wake, features

that were expected to be replicated within the single light experiments that were

performed in this thesis. As will be shown in the results, this was not the case.

31

Figure 2.15: Phase-locked vorticity images of the wake behind the two-light landing gear configuration at: (a) 0˚,

(b) 90˚, (c) 180˚, (d) 270˚, for the largest light spacing and at the zero elevation [47].

32

Summary 2.4It has been established that the regulatory pressure on aircraft manufacturers is the driver

behind modern aircraft noise research. Yet, despite this significant pressure there has been

relatively little work concerning an important part of the overall landing gear assembly –

the landing light. Focusing on the flow around a cylinder, a disk, and two tandem

cylinders allowed for the establishment of a familiarity with the flow patterns present in

the wakes of those bluff bodies that are similar in structure to the light and strut.

Furthermore, addressing relevant landing gear noise literature in Guo [7] and Salt et al.

[47] allowed for the conclusions, respectively, that the landing light possessed the

potential to significantly contribute to overall landing gear noise and that light-strut

assemblies were capable of generating unique frequencies with significant three-

dimensional components. The work of Salt et al. [47] also provided a potential preview of

the structure of the wake for the single light landing gear case studied here. The

experimental methodology and apparatus used to investigate this single light case is

explained in the following section.

33

3 EXPERIMENTAL APPARATUS AND

METHODOLOGY

This section presents all instrumentation and procedures used during experimental

investigation. First, the test facility and landing gear model are described. Next, a

summary of the test cases is provided. Following this, a description is presented of

different investigative methods – microphone recordings, hot-wire anemometry, and

time-averaged and phase-locked PIV. Finally, certain MATLAB solutions to processing

issues are explained.

Wind Tunnel 3.1

An open loop wind tunnel powered by a 50 HP motor was used for all experimental

testing. The tunnel is displayed in the schematic shown in Figure 3.1 below. All

experimental investigation occurred at position “6”, which corresponded to the outlet of

the wind tunnel.

1 Inlet

2 Blower

3 Variable Frequency Controller

4 Electric Motor

5 Settling Chamber

6 Outlet and Test Section

Figure 3.1: General diagram of wind tunnel used for experimental investigation, with legend. Adapted from [48].

34

Wind Tunnel Test Section 3.1.1

Experimental investigation was performed with the landing gear model installed in the

test section of the wind tunnel. The inner dimensions of the test section were 708 mm

(27.875 in) by 216 mm (8.5 in). The depth of the test section alone was 508 mm (20 in),

and with added acrylic panes, which are discussed later, was doubled to 1016 mm (40 in).

The wind tunnel was calibrated using a Pitot tube connected to a Fluke 922 Airflow

Meter with an accuracy of 2.5% at 10.00 m/s and a resolution of 0.001 m/s. The

calibration was performed on both sides of the test section centerline, as shown in the

image below where the dashed lines represent the Pitot tube locations during calibration.

Figure 3.2: Front view diagram of empty wind tunnel test section with dashed lines illustrating location of Pitot

tube measurements that were used for calibration of the wind tunnel.

Landing Gear Model 3.2

As mentioned in the introductory section to this thesis, the landing gear model used

during experiments was greatly simplified relative to a modern landing gear assembly. Of

the major components only the light and strut were included – a picture is shown below in

Figure 3.3, presenting both the actual model and a CAD-rendered view. The strut was a

simple hollow cylinder fashioned from a PVC pipe with a diameter of 42.4 mm (1.67 in)

and a wall thickness of 4.1 mm (0.16 in). The model landing light was 3-D printed using

VisiJet EX200 plastic with a design based on existing landing lights observed in industry.

Its specific dimensions are detailed in the technical information provided by Figure 3.6

273 mm 273 mm

708 mm

35

below. Of importance is its diameter, which was the same as that of the cylinder: 42.4

mm (1.67 in). As a result, when the model was correctly installed in the wind tunnel test

section, the light faced into the flow, the frontal area of the model was consequently

equivalent to the frontal area of the lone cylinder, and the blockage ratio was only 4.6%.

Figure 3.3: Landing gear model views: (left) actual landing gear model and (right) rendered CAD isometric view

of landing gear model.

The landing gear model is displayed in an isometric CAD rendering in Figure 3.4 below,

installed in the wind tunnel test section. Additionally, a photo of the two-light landing

gear model installed in the same test section is presented in Figure 3.5. Both figures also

show two acrylic panes extending from the top and bottom of the wooden wind tunnel

test section. The panes were added to allow for effective PIV, as the camera was required

to be positioned such that it was viewing the planes of interest in a perpendicular manner,

and not at an angle. The specifics of PIV will be introduced in a later section; for now, it

is important to note that the transparent acrylic provided a solution which physically

36

secured the assembly while also allowing for the camera to be positioned normal to the

plane of interest, with clear sight lines to the model.

Figure 3.4: Inventor isometric CAD rendering of light-strut assembly installed within the wind tunnel test

section, with SR=0.5.

Figure 3.5: Photo by James Lepore and Eric Salt [49]. Reproduced with permission. Photo depicts two-light

model installed in wind tunnel test section. A similar setup was used for the single light model testing.

Thus far a general look at the landing gear model has been provided. A more detailed

look at the model components is discussed next. This includes technical drawings of the

Acrylic

Panes Two-Light Model

37

three most important model components, the light, bars, and strut, in Figure 3.6, Figure

3.7, and Figure 3.9, respectively.

Landing Gear Model Components 3.2.1

Dimensions of the landing light are shown in Figure 3.6 below. The rectangular slot in the

rear face of the light was used to connect the light to the strut via a small aluminum bar.

The bar was kept in place by RTV 102 high performance adhesive that was applied each

time the bar was inserted into the light. Dimensioned views of the aluminum bars are

provided in Figure 3.7 below. The figure displays three different bar lengths – longer bars

were used for experiments with greater light-strut spacing and shorter bars were used for

lesser light-strut spacing. Figure 3.7 also shows holes in the aluminum bars. Originally,

the bars were to be held in place within the light through a pin-locking mechanism but

this idea was abandoned in favour of the adhesive option. Consequently, the holes were

present but were not a functional feature during experimental investigation.

38

Figure 3.6: Dimensioned landing light views. All dimensions in mm.

Figure 3.7: Dimensioned views of all three aluminum bars. All bars were of the same thickness. All dimensions in

mm.

39

The light and bar assembled together are shown in Figure 3.8. To complete the light-strut

assembly the free end of the bar was inserted into a slot machined into the cylinder

surface halfway along the cylinder length. The slot is visible in the dimensioned drawings

of the strut presented in Figure 3.9.

Figure 3.8: Inventor CAD-rendered rear view of the assembled light and aluminum bar.

Figure 3.9: Dimensioned views of strut. All dimensions in mm.

40

The bar was inserted past the cylinder wall until it reached well into the hollow strut,

almost to the rear inner wall. It was secured inside of the strut by a clamping mechanism

strong enough to prevent any movement during experimental testing. A CAD-rendered

top view is presented in Figure 3.10, showing the fully assembled model minus the

clamping mechanism. As mentioned above, different bars were selected depending on the

required spacing between the light and the strut. However, the length of bar remaining

within the strut consistently matched that shown in the figure below, regardless of light-

strut spacing.

Figure 3.10: Top view of light-strut assembly without clamping mechanism, showing light, strut, and bar that

was used to hold the assembly together.

Strut Vortex Shedding Frequency 3.2.2

The literature review showed that the vortex shedding frequency behind a cylinder is

generally present at approximately St=0.2. Microphone measurements in the wake of the

cylindrical strut resulted in measured periodicity at St=0.19, which aligns well with the

reported literature value. The strut was thus confirmed to behave as a cylinder in cross-

flow with a shedding frequency of St=0.19.

41

Landing Light Vortex Shedding Frequency 3.2.3

Successful understanding of the behaviour of the light-strut wake was thought to depend

largely on the degree to which the knowledge of flow behaviour around a circular disk

could be applied to the flow around the light. If the two flow behaviours were similar,

existing literature regarding the circular disk could serve as a starting point from which to

develop a cognizance of the light-strut wake. However, if the flow around the disk was

unrelated to flow around the landing light, the base upon which to build an understanding

of the behaviour present during experimental testing would have been close to negligible

as there was a lack of significant literature regarding flow around a lone landing gear

light. Therefore, verifying that the link between the two fields existed was important; this

section provides evidence of that link.

To demonstrate the similarity in the wake patterns for flow over a disk and flow over a

light, the vortex shedding frequency of the two was compared. As discussed in the

literature review, the vortex shedding frequency of a circular disk is situated in the

St=0.135-0.15 range, with most research work reporting a St=0.135 value. The vortex

shedding frequency of the light was obtained through experimental testing of the lone

light in the wind tunnel in the manner shown in Figure 3.11.

42

Figure 3.11: Setup for testing of lone landing light vortex shedding frequency: (left) close-up of upstream facing

side, (right) view of light installed in the wind tunnel test section.

The frequency was recorded with a microphone for various speeds at two different

locations around the perimeter of the light, resulting in two runs. Figure 3.12 below

displays the results of the measurements: two sets of data points for the different

velocities tested as well as a linear regression with the associated slope presented for each

line. The two best fit lines resulted in frequency-to-velocity ratios of 3.2911 and 3.1854.

Multiplying these ratios by the diameter of the light resulted in calculated Strouhal

numbers based on the light diameter and wind tunnel velocity of approximately 0.135 and

0.140, respectively. Thus, it can be concluded that the landing light interacted with the air

flow in a fashion very much comparable to that of a circular disk, and consequently, it

was correct to initially assume that a resemblance between the two flow patterns existed.

43

Figure 3.12: Vortex shedding from model landing light, showing two separate best-fit lines through two separate

sets of data and the corresponding slope of each line.

Experimental Test Cases 3.3

The light-strut assembly was tested at three different elevations in an effort to locate the

plane where the pressure fluctuations were strongest and to gain an understanding of the

flow behaviour behind the light-strut assembly. Three different wind tunnel velocities

were used to test for the presence of different modes within a range of velocities, and

three different light-strut spacing settings were used to investigate the effect of changing

light orientation on the light-strut wake. Table 3-1 below illustrates the experimental

matrix and provides accurate artistic representations of the side and top views to aid in

visualization of the difference between various test cases.

Frequency/Velocity = 3.1854

Frequency/Velocity = 3.2911

0

20

40

60

80

100

120

0 5 10 15 20 25 30 35

Vo

rte

x Sh

ed

din

g Fr

eq

ue

ncy

(H

z)

Wind Tunnel Velocity (m/s)

Run #1 Run #2

44

The first row in Table 3-1, describing the changes in elevation, shows a side view of the

light-strut assembly with a dashed line representing the elevation at which measurements

were recorded. The three elevations used were those corresponding to the center of the

light, the top edge of the light, and one diametric length away from the center of the light.

The center of the light was chosen as the zero elevation, such that the three test elevations

corresponded to Z=0D, Z=0.5D, and Z=1D numerical values, where D represents the

diameter of the light and strut.

The three velocity settings used were 10 m/s, 20 m/s, and 30 m/s. Assuming an air

temperature of 25 ̊C, these values corresponded to Reynolds numbers of 2.70*104,

5.40*104, and 8.10*10

4, respectively, based on the light or strut diameter and freestream

wind tunnel velocity.

The three spacing settings, 0.5D, 0.85D, and 1.25D, were based on the distance between

the center of the strut and the rear face of the light. These were again numerically

represented as multiples of the diameter of the light and strut. The top views in the table

below depict these settings as the light is moved away from the strut. The spacing values

were chosen based on observation of real landing gear setups – the smallest spacing

corresponded to the rear of the light in physical contact with the front of the strut, the

largest spacing represented a distance slightly larger than the largest spacing observed in

practice, and the intermediate value corresponded to a spacing approximately midway

between these two extremes. It is notable for the reader that all later references to spacing

45

are expressed in terms of dimensionless spacing presented as the spacing ratio, SR, which

represents the spacing divided by the diameter.

Table 3-1: Experimental matrix shows test cases with accurate artistic representations of side and top views of

the assembly to illustrate different experimental cases. The diameters, D, of the strut and light, are equivalent.

Experimental

Parameter

Experimental Parameter Values

Elevation, Z 0D 0.5D 1D

Freestream

Wind Tunnel

Velocity, Vt

10 m/s 20 m/s 30 m/s

Spacing, S 0.5D 0.85D 1.25D

The three different elevations combined with three different velocities and three different

spacing settings produced 27 different experimental cases. Each of these cases was

investigated using microphone testing, hot-wire testing, and time-averaged PIV, while a

select few cases were further investigated using phase-locked PIV. All cases mentioned in

the previous sentence involved measurement of the near-wake region, the area directly

46

behind the light-strut assembly. Prior to conclusion of experimental work, additional

examination of the flow around the assembly was conducted for a select few

configurations using time-averaged PIV. The ensuing sections explain the instrumentation

and methodology used during the different stages of testing, and will describe the role of

MATLAB software in generation of the figures presented in the results section.

Experimental Investigation by Means of Microphone 3.4

Recordings

The initial investigation of the light-strut wake was performed using a microphone. The

G.R.A.S. microphone system consisted of a 1/4 inch Type 40BP microphone, Type 26AC

preamplifier, and Type 12AA amplifier. The microphone response was linear in the range

of 4 Hz to 70 kHz with a 3% maximum distortion at 170 dB. The system was calibrated

using a G.R.A.S. Type 42AB pistonphone, while a National Instruments 9215 with BNC

data acquisition device was used to record the microphone signal. A G.R.A.S. Type

RA0022 Nose Cone was mounted over the microphone diaphragm to reduce unwanted

pressure fluctuations arising from the interaction of the microphone with the flow. A

photo of initial setup is shown below in Figure 3.13.

Figure 3.13: Photo by James Lepore and Eric Salt [49]. Reproduced with permission. Image displays

microphone initial setup, with nosecone.

Due to the nature of experimental investigation, any bluff bodies present within the test

section were potentially capable of causing noise pollution and invalidating the results, so

all objects other than the model were to be removed from the test section. Simultaneously,

47

examination of the near-wake required microphone readings in close proximity to the

strut. The solution to these two conflicting requirements was a long hollow 9.5 mm (3/8

in) diameter metal pipe, one end of which was affixed to the traverse system, presented

later, and the other securing the microphone in place. The pipe was pointed directly into

the flow with all wiring running lengthwise within its hollow body, allowing for minimal

agitation of the flow. The pipe was secured to the traverse via a wooden mount. The

microphone, pipe, mount, and traverse are presented in a photo below in Figure 3.14. The

microphone at a position in the wake of the model is shown in the rendered images in

Figure 3.15.

Figure 3.14: Photo by James Lepore and Eric Salt [49]. Reproduced with permission. Photo depicts microphone,

pipe, mount, and traverse system, as used during microphone measurements.

Discrepancy in diameters between the pipe and microphone necessitated the use of a 3-D

printed plastic piece that allowed for smooth transition from the pipe to the microphone

and also functioned to physically secure and constrain the microphone to the pipe. The

Microphone Pipe Mount

Traverse

48

printed piece, the nature in which it was held by the pipe, and the nature in which it

secured the microphone are shown in Figure 3.16 below. The piece is also vaguely visible

in Figure 3.15.

During the measurements, the microphone and hotwire experienced small amplitude

vibrations due to the vibration of their long holder which was exposed to the pressure

fluctuations in the model wake. However, for all the measurements performed at 10 m/s,

the velocity for which most of the cases in the results are shown, these vibrations were

very small. In addition, the frequency of these vibrations was much lower than the flow

fluctuation frequencies that were observed in the model wake, and therefore, these small

amplitude vibrations did not interfere with measurement of the main periodic trends

found in the wake.

49

Figure 3.15: Inventor CAD-rendered images of microphone placed in position for measurements while secured

to pipe. Top shows isometric close-up view, bottom shows top view with wooden panels removed for model

visibility. Model is set up for SR=0.5 configuration, microphone is at Z=0D elevation.

Once fully assembled, the microphone system was used in conjunction with the traverse

to gather data. Each test case involved 50 measurement points obtained by traversing the

microphone through a grid spacing of one centimetre. The path of the microphone to each

measurement point is presented below in Figure 3.17. Beginning at the point closest to

“Start”, the traverse moved the microphone along the path shown by the arrows, stopping

at each circle to record a measurement, and finished at the circle at the conclusion of the

path, marked as “End”.

50

Figure 3.16: Depictions of 3-D printed piece. Top left: technical drawing without dimensions depicting top view,

front view, and assembled isometric view. Reproduced with permission from [49]. Top right: piece installed on

end of pipe. Bottom: piece assembled with microphone enclosed.

Figure 3.17: Illustration of microphone measurement locations, depicted by open circles, and path of traversed

microphone, depicted by arrows, during the measurements. Light-strut assembly setup is in the SR=0.5

configuration. The arrows in front of the light-strut assembly represent the direction of the flow.

End

Start

51

Experimental Investigation by Means of Hot-wire 3.5

Anemometry

Hot-wire anemometry was used to investigate the light-strut problem after microphone

measurements were completed. A constant-temperature, single-wire, 55P16 Dantec hot-

wire probe with 5 μm thickness was employed, and was connected to a mini-CTA bridge.

The hot-wire assembly, consisting of a rod attached to a clamping mechanism holding the

probe in position, is shown in Figure 3.18 fixed to a generic stand. This same assembly

was used during hot-wire experiments, where it was fastened to the pipe instead. A close-

up and CAD rendering of the hot-wire assembly are also provided in Figure 3.18.

52

Figure 3.18: Top: Stand with hot-wire assembly installed; Bottom Left: close-up of hot-wire assembly showing

clamping mechanism that holds the hot-wire probe in place; Bottom Right: Inventor CAD rendering of hot-wire

assembly that will be used to illustrate its use.

The traverse system was used similarly to acquire hot-wire measurements as in the case

of the microphone. However, there was a minor dissimilarity: the pipe was again used,

but the hot-wire was affixed to it differently than the microphone. The cause of the

differing fastening procedure was the decreased concern with bluff bodies in the flow.

Hot-wire measurements were not directly affected by acoustics, so noise pollution was

not a factor and the need for a streamlined system was not as great. As a result, the hot-

53

wire assembly was fixed to the top surface of the hollow pipe as opposed to inserted

within the pipe, as the former was the more time-efficient option. The assembly was fixed

to the pipe with adhesive tape strong enough to obstruct all movement relative to the pipe,

even at the highest wind tunnel velocities. Rendered images of the hot-wire assembly

fastened to the pipe are shown in Figure 3.19, presenting both an isometric and top view

of its positioning within the wind tunnel test section during experimental testing.

Figure 3.19: Inventor CAD-rendered images of hot-wire placed in position for measurements while secured to

pipe. Top shows a close-up of the isometric view, bottom shows top view with wooden panels removed for model

visibility. Model is set up for SR=0.5 configuration, hot-wire is at Z=0D elevation.

54

After successful assembly of the hot-wire components and installation on the hollow pipe,

hot-wire measurements were obtained by traversing the probe through a grid spacing of

two centimetres. For these readings, each test involved 20 measurement points. A fewer

number of measurements were recorded for the hot-wire in comparison to the microphone

because the purpose of the measurements was slightly different; microphone

measurements provided an initial sense of the problem while hot-wire measurements

served mainly to confirm the trends already observed in the microphone results. The path

of the hot-wire probe to each measurement point is depicted below in Figure 3.20. Again,

beginning at the point closest to “Start”, the traverse moved the hot-wire along the path

shown by the arrows, stopping at each circle to record a measurement, and finished at the

circle at the conclusion of the path, marked as “End”.

Figure 3.20: Illustration of hot-wire measurement locations, depicted by open circles, and path of traversed hot-

wire, depicted by arrows, during the measurements. Light-strut assembly setup is in the SR=0.5 configuration.

The arrows in front of the light-strut assembly represent the direction of the flow.

Traverse System 3.6

The traverse system that was used to collect measurements at each of the locations of

interest is described here. The traverse was an isel model 234411 three axis traverse, with

an isel C142-4 controller, a step resolution of 6.25 μm, and an accuracy of +/- 300 μm. It

Start

End

55

is pictured below as an isometric CAD graphic in Figure 3.21. Additionally, the majority

of the traverse is visible in the photo in Figure 3.14. A serial-to-USB cable was used to

connect the traverse to a computer, and MATLAB was used to communicate commands

to the machine.

Figure 3.21: Isometric depiction of three-dimensional traversing system used for moving the microphone and

hot-wire to each observation point. Reproduced from TSI website [50].

Experimental Investigation by Means of PIV 3.7

Hot-wire and microphone results provided frequency content information and allowed for

a rough idea of the location of the largest wake fluctuations. PIV was needed to obtain a

picture of the wake, not for quantitative purposes, but to gain a sense of understanding of

the origin and path of major flow structures present within the wake.

Description of PIV System used for Experimental Investigation 3.7.1

A CAD-rendered display of the PIV system during experimental investigation, alongside

the test section with the model installed, is presented in Figure 3.22. Two different views

are shown, an isometric view and a front view that was slightly tilted to allow for

visibility of the laser light sheet. The camera and laser are presented in their general

56

undetailed form at their approximate locations during experimental testing. The green

sheet seen emitting from the laser is the light sheet. The relatively large separation

distances of the camera and the laser from the landing gear assembly were necessitated to

achieve optimal camera field of view versus focus, and optimal laser intensity versus

width.

The PIV laser system used for this experimental study was provided by TSI. The laser

was a New-Wave Solo 120 XT pulsed Nd:YAG laser outputting light at a frequency of

532 nm, with a maximum energy of 120 mJ per pulse. The light sheet thickness was 2

mm. The camera used was a 12-bit Power View 4 MegaPixel CCD camera with a 2048

by 2048 pixel resolution used alongside a Nikon AF Nikkor 50 mm lens with a maximum

aperture of f/1.8. The camera was positioned normal to the plane of interest and the

camera lens was fitted with a bandpass filter centered at 532 nm with a bandwidth of 10

nm, with the purpose of filtering all external non-laser light. Due to the pulsed nature of

the laser emission, the camera image capture and laser firing processes needed to be

synchronized. This was achieved using a TSI LaserPulse Model 610035 synchronizer. A

Laskin aerosol generator was used to introduce seeding to the air prior to its passage

through the wind tunnel. The seeding material used was bis (2-ethylhexyl) sebacate, with

a mean particle diameter of 1 µm.

Insight 4G software, again provided by TSI, was used to capture, store, and process PIV

images. Each image was processed using the Classical PIV algorithm over an initial

57

window size of 32 by 32 pixels with a Gaussian interpolation scheme, leading to a final

window size, after refinements, of 16 by 16 pixels. The velocity vector validation rates

placed consistently in the 90%-95% range.

Figure 3.22: Isometric (top) and slightly tilted front view (bottom) of experimental setup during PIV. The bottom

view is slightly tilted to ensure the thin laser sheet is not invisible in the image. The plane of interest is the Z=0D

elevation, while the model is set up for the SR=0.5 configuration.

General PIV Theory 3.7.2

Particle Image Velocimetry (PIV) systems in general function by first filling the flow

with a seeding particle that is easily illuminated but not large enough to interfere with

path of the flow. A pulsed laser sheet is then used to illuminate the plane of interest at

58

constant time intervals, with a camera system recording images each time the laser is

pulsed. For example, the PIV system used in this thesis captured images in pairs. The

laser pulsed twice, with each pulse separated by a pre-set time interval, and the camera

captured an image for each pulse. The process was then repeated until 200 image pairs

had been captured for each test case. When these images were processed a correlation

algorithm matched particle groupings in each image pair to obtain localized flow

displacement from one pulse to the next. Knowledge of the time interval between pulses

allowed for a calculation of the localized flow velocities using the now-known

displacement values. Thus, the final product was a set of 200 maps of velocity vectors,

which were then averaged to create one final velocity map per test case that effectively

illustrated the behaviour of the flow in the illuminated plane. Final images resulting from

this process were considered time-averaged images because the 200 image pairs were

captured independent of the microphone signal, such that the first of two in each pair of

laser pulses was initiated at a randomly selected instance in time. The large number of

images captured randomly ensured that the final averaged image presented a wake

depicting the mean location over time of any periodic structures – hence the “time-

averaged” moniker. Phase-locked images, for which the laser pulse was not fired at

random, are discussed next.

Phase-locked PIV Theory and Triggering System 3.7.3

The microphone placed in the light-strut wake experienced heightened pressure

fluctuations as a vortex or vorticity blob impinged upon it. The impingements occurred

with a regular frequency and were visible in the time signal captured by MATLAB in the

59

form of a sine wave. Thus, it was possible to correlate the position within the acoustic

signal with the position of the periodic structure behind the light-strut assembly. In

essence, images captured at different locations in the acoustic signal showed the vorticity

or vortices at different stages of propagation through the wake. During phase-locked

experimental investigation, images were captured at 𝜋/4 radian increments in the 2𝜋

radian acoustic cycle, yielding eight separate points in the cycle and eight separate sets of

images for each experimental case. Compiling the set of images from subsequent points

in the acoustic cycle yielded a crude, eight-frame “animation” of the formation,

propagation, and dissipation of periodic vorticity or vortices in the wake of the light-strut

assembly. This animation was used to aid in the understanding of observed experimental

trends.

Phase-locked images were acquired after initial time-averaged PIV had been completed.

As alluded to in the previous paragraph, this process involved using the microphone

signal to coordinate the laser fire sequence and subsequent image capture such that the

camera acted to capture pictures only at a certain point in the acoustic cycle. The

coordination was achieved using a triggering system, or more simply, a trigger.

Therefore, for phase-locked images the synchronized laser and camera needed to be

prompted, or triggered, to work at specific points in time. The existing PIV system did not

provide a means of doing this, so a previously designed in-house trigger was used. The

trigger received the microphone signal and sent out a pulse at a specified point in the

acoustic cycle to the synchronizer, which then ensured that the first of two laser pulses for

60

each image pair was consistently initiated at the desired time, leading to a valid phase-

locked image at the chosen acoustic cycle point. An image of the trigger is provided

below in Figure 3.23 and the circuit diagram is shown in Figure 0.1 in Appendix A.

Figure 3.23: Photo of trigger box taped to wooden blocks.

MATLAB 3.8

MATLAB 2014b software was used extensively throughout the experimental

investigative process to command and coordinate equipment, to process the collected

data, and to organize the data for presentation to the reader. This latter function,

presentation of the data, is the focus of this section.

Microphone and Hot-wire Results 3.8.1

Spectral analysis and averaging of the pressure signal was performed at the time of

acquisition using MATLAB software. Time signals were converted to the frequency

domain through MATLAB’s built-in FFT function, using Hanning windowing. The

61

software was also used to control the traverse during microphone and hot-wire

measurements when the traverse needed to be moved from one measurement location to

the next. These measurements are presented in the results section in spectral plots in the

form of non-dimensional pressure and non-dimensional frequency, or Strouhal number:

𝑁𝑜𝑛 − 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙 𝑃𝑟𝑒𝑠𝑢𝑟𝑒, 𝑃∗ =𝑃𝑚𝑎𝑥

12

∗ 𝜌 ∗ 𝑉𝑡2 (1)

𝑆𝑡𝑟𝑜𝑢ℎ𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟, 𝑆𝑡 =𝑓 ∗ 𝐷

𝑉𝑡 (2)

where Pmax is the maximum RMS acoustic pressure amplitude, ρ is the density of air, Vt is

the freestream wind tunnel velocity, f is the frequency, and D is the diameter of both the

strut and light, since they are equal.

The PIV system outputted a square matrix of velocity vectors. MATLAB was used to

generate the images presented in the results by creating contour plots of the data with

smoothing subsequently applied. The contour plots depicted either non-dimensional

velocity or non-dimensional vorticity:

𝑁𝑜𝑛 − 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =𝑉

𝑉𝑡 (3)

𝑁𝑜𝑛 − 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙 𝑉𝑜𝑟𝑡𝑖𝑐𝑖𝑡𝑦 =𝜔 ∗ 𝐷

𝑉𝑡 (4)

where V is the local velocity, Vt is again the freestream wind tunnel velocity, ω is the

local vorticity, and D is again the diameter of both the strut and light.

62

Time-Averaged Images for PIV of Light-Strut Wake 3.8.2

PIV images shown in the results section that are not phase-locked to a certain point in the

acoustic cycle were expected to exemplify a symmetric top and bottom half of the image.

This was confirmed early on with microphone measurements. A lack of symmetry in

some images can be attributed to the incorrect positioning of the landing light into the

flow and slight rotation toward one or the other side. For cases where this was true,

asymmetry was not discovered until after the initial round of PIV results were processed

and therefore it could not be corrected prior to ending the round of experiments. After

initial detection of this problem, extra care was employed to ensure precise positioning of

the light. As a result, the issue was nonexistent for all later rounds of PIV. Figure 3.24

and Figure 3.25 below illustrate the PIV velocity plot results for two different cases, with

Figure 3.24 showing an asymmetric image from the first round of PIV and Figure 3.25

showing an almost perfectly symmetric image acquired in later PIV rounds. Additionally,

the same case as depicted in Figure 3.24 was investigated during later phase-locked PIV

testing, for which the velocity plot results are shown in Figure 3.26. Part of the wake was

blocked due to the presence of the microphone yet still the improvement in symmetry was

evident, confirming the idea that correct positioning of the strut-light assembly within the

test section consistently gave rise to a symmetric wake.

63



64

Figure 3.26: PIV results showing the velocity plot for the SR=0.5, Vt=10 m/s, Z=0D case, identical case as in

Figure 3.24 but acquired in later PIV rounds and showing the microphone interfering with the camera view of

the wake. The microphone is observed approximately in the X/D=1.0 to X/D=2.0 range and it resembles closely

the outline of the microphone-pipe assembly shown in Figure 3.15.

Phase-locked Image Mirroring for PIV of Light-Strut Wake 3.8.3

A negative element of phase-locked PIV was the need for the microphone to be placed

directly in the shear layer to obtain a strong signal of periodic wake oscillation. This, in

turn, meant that the microphone was situated within the field of view and interfered with

PIV images, as depicted previously in Figure 3.26. To avoid this situation when

presenting results, the bottom half of the near-wake, the half which included the

microphone, was cropped out of all images similar to Figure 3.26, and the top half was

then flipped to provide a final image illustrating the appearance of the wake without the

visual pollution of the microphone assembly included. This process applied to Figure 3.26

resulted in Figure 3.27 below. Visually, the two figures are very similar except for the

added region in the X/D< -1.5 area in Figure 3.27, an area which does not exist in Figure

3.26 because the camera field of view was not large enough to accommodate it. However,

65

this area was not removed from images such as Figure 3.27 because the symmetry

existing in other parts of the wake was assumed to exist here as well – it seemed intuitive

that the top and bottom halves of the image would be symmetric completely and no

evidence was found to suggest otherwise. Regardless, this extra area was used merely to

invoke a sense of symmetry in the images and never as a basis for discussions or

conclusions, so the issue of its validity within the results is a secondary matter. It should

also be noted that y-axis of Figure 3.27, corresponding to the cross-stream direction, was

now centered on X/D=0.0 running through the center of the light-strut assembly, whereas

in Figure 3.26 X/D=0.0 was outside of the axis range. For this reason, some images in the

results section are centered on X/D=0.0 while others are centered on various other

positive values between X/D=1.5 and X/D=2.0.

Figure 3.27: PIV results showing the velocity plot for the SR=0.5, Vt=10 m/s, Z=0D case; identical case as in

Figure 3.24 and Figure 3.26 but with cropping of microphone half and flipping of the top half applied.

Alternating shedding patterns are defined in literature by the periodic components in the

wake propagating downstream 𝜋 radians out of phase with one another, but with an

66

equivalent shedding frequency. If one was to observe only one half of the alternate

shedding wake, the movement of the vorticity would seem identical to the observed

vorticity in the opposite half – the two halves of the wake could be flipped and there

would exist zero identifying features to verify a swap had occurred. However, the wake

viewed as a whole would continue to be asymmetric due to the out-of-phase nature of the

periodic components in either wake half. Therefore, after cropping and flipping to

generate images without the microphone assembly, as was done to generate Figure 3.27,

phase-locked images required further processing because the periodic components in each

half of the wake were not presented as out of phase with each other. To correct for this,

the bottom half of each image was interchanged with the bottom half of the image that

was acquired 𝜋 radians later in the acoustic cycle. It should be recalled that phase-locked

PIV of each case produced eight images; as a result, there existed four pairs of images for

each case that were acquired 𝜋 radians apart in the acoustic cycle and for which the

bottom halves were swapped.

To demonstrate the process described above, a pair of images 𝜋 radians out of phase with

one another for the SR=0.5, Vt=10 m/s, Z=1D phase-locked case is displayed in Figure

3.28, Figure 3.29, and Figure 3.30 below. These figures illustrate the process of arriving

at a completed phase-locked image through non-dimensional vorticity plots, which

displayed the wake structures more clearly than the velocity plots. Circular black outlines,

calculated based on the d2 parameter by Vollmers [51], seen in the vorticity plots were

used to define the locations of vortex structures or vorticity blobs within the wake. The d2

67

parameter outlines were used in Figure 3.28 which, similar to Figure 3.26 above,

provided the initial image with the microphone assembly included. Figure 3.29 shows the

microphone removed through mirroring of the image top half, and does not include the d2

parameter. It is also obvious in this figure that each half of the wake is not out of phase

with the other side, and further processing is required to finalize the image. This

processing is achieved in the following figure, Figure 3.30, where finally a complete

image is presented, with both bottom halves from Figure 3.29 swapped and the d2

parameter outline included. Although the microphone assembly greatly embellished the

view in Figure 3.28, it certainly appeared, especially when the d2 parameter outlines were

compared, that Figure 3.30 showed all the same flow characteristics as Figure 3.28. Thus,

this process of mirroring and swapping was deemed appropriate and used to effectively

provide phase-locked images with the microphone assembly excluded.

Figure 3.28: Initial version of a pair of phase-locked vorticity images half a cycle apart, for the SR=0.5, Vt=10

m/s, Z=1D case.

68

Figure 3.29: Mirrored version of the images shown in Figure 3.28.

Figure 3.30: Figure 3.29 with swapped bottom halves and with d2 parameter outlines added.

Time-Averaged PIV Images of Flow Around Light-Strut Assembly 3.8.4

After PIV images in the wake of the light-strut assembly were finalized, analysis of the

dynamics of fluid flow in between the light and the strut began via the method of time-

averaged PIV. A typical image from this investigation is shown below in Figure 3.31. The

laser light impinged on the light-strut assembly from one side so that the other side was

dark, producing the large white area at approximately X/D<2.5 and between

approximately Y/D=2.0 and Y/D=3.5 in Figure 3.31. To remove this section a flipping

69

process similar to that used to generate Figure 3.27 was employed, resulting in Figure

3.32.

Figure 3.31: PIV results showing vorticity plot around light-strut assembly for SR=0.5, Vt=10 m/s, Z=0D case.

This is the original image prior to flipping the top half.

Figure 3.32: PIV results showing mirrored vorticity plot around light-strut assembly for SR=0.5, Vt=10 m/s,

Z=0D case.

It is worth noting that the overlaid image of the light-strut assembly in Figure 3.33 depicts

the assembly’s actual size and position relative to the illustrated flow. Figure 3.32

70

displays Figure 3.33 without the overlaid image, allowing for a comparison of the two

figures and highlighting the discrepancy between the actual size of the light and strut and

that of the apparent outline of the light-strut assembly that is observed in Figure 3.32.

This outline was not an accurate illustration of size and position of the light and strut for

two reasons: perspective distortion and laser light reflection. The camera was not directly

underneath the light and strut during testing; instead, it was slightly in front and to the

side of the assembly. This, along with the camera position causing it to look up along the

length of the strut, and introduced perspective distortion so that light and strut dimensions

were skewed in such a way that their sizes were misrepresented. Laser light reflection

contributed to the inaccuracy of the outline in Figure 3.32 by oversaturating any areas

close to the strut or light and obscuring the seeding particles that were present in these

regions. These two factors collectively made the light-strut outline larger than it really

was in comparison with the rest of the PIV image, thus necessitating a correction in the

form of the overlaid plan view used in Figure 3.33.

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Figure 3.33: PIV results showing vorticity plot around light-strut assembly for SR=0.5, Vt=10 m/s, Z=0D case,

with light and strut graphic visible.

Summary 3.9

Overall, this section provided a thorough review of experimental equipment and

procedure to ensure a complete understanding of the results. A description of the setup

and usage of the microphone, hot-wire, and PIV systems was provided. The different

experimental cases, consisting of variation in elevation, wind tunnel velocity, and light-

strut spacing, were introduced. The distinction between time-averaged and phase-locked

PIV images was discussed. Finally, certain processes applied to the PIV images, most

significantly the mirroring of images, were explained. The detailed examination of the

microphone, hot-wire, and PIV procedures presented in this section will allow the reader

to fully appreciate the results acquired through the usage of these systems. These results

are presented next.

72

4 MICROPHONE AND HOT-WIRE

RESULTS

Microphone and hot-wire measurements were performed to gain an initial understanding

of the nature of the landing-gear-immersed-in-flow problem. In the interest of brevity, the

results will be presented utilizing the spacing ratio, SR=0.5, freestream wind tunnel

velocity, Vt=10 m/s, and elevation, Z=0D example case.

Microphone Results 4.1

The locations at which microphone data were acquired for the example case are shown in

Figure 4.1 in the form of an aerial view of the measurement plane. This arrangement,

consisting of 50 measurement points, was also used in all other experimental cases during

microphone data collection.

Figure 4.1: Positions at which microphone readings were recorded for the SR=0.5, Vt=10 m/s. Z=0D case shown

relative to the position of the light-strut assembly; arrows denote the flow direction.

The frequency spectrum from each measurement location in Figure 4.1 is displayed in a

combined graph in Figure 4.2 below. The spectra aggregated in this manner were unable

to convey any positional trends but did confirm the presence of two dominant frequencies

73

and the definite lack of any substantial sound signature higher than 500 Hz. Figure 4.2

was further investigated by carefully examining the relevant portions of the spectra. There

was a clear lack of distinct peaks at any frequency greater than approximately 100 Hz,

indicating the set of significant frequencies of interest to be 0 to 100 Hz. This relevant

domain was presented in non-dimensional form in Figure 4.3 below.

Figure 4.2: Frequency spectra showing microphone results for case of SR=0.5, Vt=10 m/s, Z=0D.

Figure 4.3: Frequency spectra showing microphone results for case of SR=0.5, Vt=10 m/s, Z=0D in non-

dimensional form with reduced domain.

74

Figure 4.3 plainly displays the two aforementioned dominant frequencies, the first at

St~0.025 and the second at St~0.175, as well as a smaller third peak at St~0.29. The first

peak was less organized than it appeared to be in Figure 4.2 and did not present itself in

all spectra, hinting at the existence of a local phenomenon. The third peak was attributed

to the wind tunnel blower blade passing frequency (BPF) as its value coincided with the

calculated blower frequency, St=0.287. The first and second peaks were also visible in

Figure 4.5 and Figure 4.6, which are hot-wire analogues to the microphone results shown

in Figure 4.2 and Figure 4.3. The third peak was not seen in Figure 4.5 and Figure 4.6 for

reasons that will be addressed in a subsequent section.

Hot-wire Results 4.2

The locations at which the hot-wire measurements were recorded were different than the

locations at which the microphone measurements were acquired. However, the same area

in the wake was measured by the hot-wire as was done for the microphone. The

arrangement for the hot-wire measurements is depicted in the form of an aerial view of

the measurement plane in Figure 4.4 below, and consists of 20 recorded points instead of

the 50 measurement points for microphone data. Figure 4.5 displays the extended

frequency spectra and Figure 4.6 highlights the important spectral range within Figure

4.5.

75

Figure 4.4: Positions at which hot-wire readings were recorded for the SR=0.5, Vt=10 m/s. Z=0D case shown

relative to the position of the light-strut assembly; arrows denote the flow direction.

Figure 4.5: Frequency spectra showing hot-wire results for case of SR=0.5, Vt=10 m/s, Z=0D.

76

Figure 4.6: Frequency spectra showing hot-wire results for case of SR=0.5, Vt=10 m/s, Z=0D in non-dimensional

form with reduced domain.

Inconsequential Spectral Characteristics of Microphone 4.3

and Hot-wire Results

There existed a number of features or trends within the results that were not of interest in

the study and will not be acknowledged in later sections. These include: the third peak in

Figure 4.3, the first peak in Figure 4.3, and the peak near St=0.35, which was not seen in

Figure 4.3 but found in a limited number of cases. The spectral characteristics that are

addressed in this section are those that were not directly caused by flow interaction with

the light-strut assembly, and although they may appear prominent, did not contribute to

the overall discussion of the changing flow behaviour between different experimental

cases.

Lack of Wind Tunnel Blower Frequency Peak in Hot-wire Data 4.3.1

The hot-wire signals shown in Figure 4.5 and Figure 4.6 were similar in frequency

content to the microphone signals presented in Figure 4.2 and Figure 4.3 with the sole

77

difference found in the wind tunnel blower frequency peak, occurring at St=0.29, which

was seen in all microphone data but not in the hot-wire data. Therefore, the blower

frequency peak observed in the microphone results was caused by a purely acoustic

phenomenon, did not exist due to any recurring flow phenomena, had no effect on flow

around the light-strut assembly, and therefore could be ignored. Conversely, the first and

second peaks were found in the hot-wire data as well as in the microphone results,

confirming that they were caused by the behaviour of the flow, were not exclusively

acoustic in nature, and could not be so easily ignored.

Signal from Flow Activity in Wake Region 4.3.2

The large first peak in Figure 4.3 between St=0 and St=0.05 prevailed only in a limited

area of the wake – it was not present in all spectra. This notion was verified in Figure 4.7,

which displays the results in Figure 4.3 but with the measurements directly behind the

light-strut assembly removed from the pool of aggregated spectra. In comparing Figure

4.3 and Figure 4.7, it was clear that eliminating measurements recorded in the wake

directly behind the light-strut assembly also eliminated the large first peak. Therefore,

unsteady activity in the wake region behind the light-strut assembly was concluded to be

the likely cause of the first peak in Figure 4.3.

78

Figure 4.7: SR=0.5, Vt=10 m/s, Z=0D case without measurements in the wake- top panel: microphone

measurement positions relative to the location of the light-strut assembly, bottom panel: aggregated non-

dimensional microphone frequency spectra of the measurements in the top panel.

Figure 4.8 below is presented as supplementary proof for the above conclusion. It depicts

the unchanging nature of the first peak frequency with any combination of changes in

spacing, velocity, or measurement plane height – behaviour that contrasts the second peak

which shifted to successively higher frequencies with increasing flow velocity. Therefore,

the first peak was evidently unrelated to the light-strut problem and for this reason,

although visibly present, it will be largely ignored for the remainder of the discussion.

79

Figure 4.8: Microphone frequency spectra for the arrangement described by Figure 4.1 showing all experimental

cases for various freestream velocities - top panel: 10 m/s, middle panel: 20 m/s, bottom panel: 30 m/s

80

Wind Tunnel Signature 4.3.3

Figure 4.9 below displays the microphone and hot-wire wind tunnel signatures collected

at various points corresponding to those shown in Figure 4.1 and Figure 4.4, but with the

light-strut assembly removed. The similarity in domain range to previous figures was

purposefully pursued to ensure ease of comparison. The amplitudes found in Figure 4.9

were, for the most part, an order of magnitude smaller than those found in Figure 4.3 and

Figure 4.6, demonstrating that predominant frequencies observed in microphone and hot-

wire results were generated by flow interaction with the light-strut assembly and did not

originate from the background wind tunnel signature. The one exception was the wind

tunnel blower frequency at St=0.29, whose microphone amplitude in Figure 4.9 matched

the amplitude of the blower frequency in Figure 4.3.

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Figure 4.9: Microphone (top) and hot-wire (bottom) non-dimensional frequency results for empty wind tunnel

configuration at 10 m/s.

Figure 4.10 and Figure 4.11 below are replicas of Figure 4.3 and Figure 4.6, respectively,

with the average wind tunnel signal from Figure 4.9 added as a dashed line. Figure 4.10

shows that the wind tunnel acoustic characteristics were not similar to those generated by

the light-strut assembly interacting with the flow, as the first two peaks were completely

independent of the wind tunnel spectrum. The final third peak was the wind tunnel blower

82

frequency and was equally present in both the experimental cases and the wind tunnel

signal, as expected. Figure 4.11 indicates that the wind tunnel hot-wire signal bore no

similarity to the hot-wire spectra originating from light-strut assembly whatsoever. The

amplitude of the wind tunnel signal was at most frequencies so low that it did not even

appear in the figure. The microphone and hot-wire comparison therefore allowed for the

conclusion that only the BPF at St=0.29 had originated from operation of the wind tunnel

alone – any other prominent peaks were caused by the flow around the light-strut

assembly.

Not all tested cases resulted in a clear and obvious peak, an example being the SR=1.25,

Vt=10 m/s, Z=0D case, for which hot-wire results are displayed in Figure 4.12 below. In

this figure there was no distinguishable peak and the signal appeared as broadband noise,

suggesting that for this case and all similar cases the periodicity in the wake was very

weak or nonexistent. For some of these indistinct cases, the microphone results showed

spectra of some resemblance to the wind tunnel signal but this was never replicated in the

hot-wire results. Thus, even when the wind tunnel background signal magnitude was not

completely insignificant it remained purely acoustic, and had no effect on the light-strut

wake.

83

Figure 4.10: Frequency spectra showing microphone results for the case of SR=0.5, Vt=10 m/s, Z=0D (solid

lines), as well as the average wind tunnel microphone signal at Vt=10 m/s (dashed line), in non-dimensional form.

Figure 4.11: Frequency spectra showing hot-wire results for the case of SR=0.5, Vt=10 m/s, Z=0D (solid lines), as

well as the average wind tunnel hot-wire signal at Vt=10 m/s (dashed line), in non-dimensional form.

84

Figure 4.12: Hot-wire results for the SR=1.25, Vt=10 m/s, Z=0D case.

Peak near St=0.35 4.3.4

Figure 4.13 and Figure 4.14 below are the microphone and hot-wire signals, respectively,

for the entire range of 27 experimental cases – all three light-strut spacing variations, each

investigated at all three different velocities, and at all three elevations. As mentioned in

previous sections, the first peak in Figure 4.13 at St=0-0.05 and the barely visible St=0.29

BPF were deemed irrelevant as they were not related to organized flow oscillations within

the wake. The middle peak occurring at St=0.16-0.18 represented periodicity caused by

the flow interacting with the light-strut assembly. A fourth peak was also present near

St=0.35, and is discussed in this section.

85

Figure 4.13: Microphone signal for all cases – all spacing settings, all velocities, all elevations – on the same non-

dimensionalized domain.

Figure 4.14: Hot-wire signal for all cases – all spacing settings, all velocities, all elevations – shown on the same

non-dimensionalized domain.

The slight peak near St=0.35 in Figure 4.13 and Figure 4.14 was observed only in SR=0.5

cases and only for the two higher elevations, and was most prominent for the highest

elevation. This was confirmed by observing Figure 4.14, Figure 4.15, and Figure 4.16 in

succession, which are figures that display the hot-wire signal for all cases, the hot-wire

86

signal for all cases without the SR=0.5, Z=1D cases, and the hot-wire signal for all cases

without the SR=0.5, Z=0.5D and Z=1D cases, respectively. The majority of the St~0.35

peak disappeared as the SR=0.5, Z=1D cases were removed, and it completely vanished

when the SR=0.5, Z=0.5D cases were also removed. Therefore, the peak near St=0.35 in

Figure 4.14 originated from the specific experimental cases NOT displayed in Figure

4.16, namely the SR=0.5, Z=0.5D and Z=1D cases, spanning all velocities. Furthermore,

most of the St~0.35 peak was eliminated by removal of the SR=0.5, Z=1D cases, proving

that it was the SR=0.5, Z=1D cases that were primarily responsible for the peak near

St=0.35. As shown in Figure 4.17 and Figure 4.18, which present the microphone signals

for the conditions analogous to those in Figure 4.15 and Figure 4.16, the microphone

signals also showed a slight peak near St=0.35, and again, when Figure 4.13, Figure 4.17,

and Figure 4.18 were compared, it was obvious that the SR=0.5, Z=0.5D and Z=1D cases

produced the St~0.35 peak and, further, that the highest elevation cases were chiefly

responsible for it.

87


non-dimensionalized domain, with SR=0.5, Z=1D, cases removed for all velocities.


non-dimensionalized domain, with SR=0.5, Z=1D and Z=0.5D, cases removed for all velocities.

88

Figure 4.17: Non-dimensional microphone signal for all cases – all spacing settings, all velocities, all elevations –

shown on the same non-dimensionalized domain, with SR=0.5, Z=1D, cases removed for all velocities.

Figure 4.18: Non-dimensional microphone signal for all cases – all spacing settings, all velocities, all elevations –

shown on the same non-dimensionalized domain, with SR=0.5, Z=1D and Z=0.5D, cases removed for all

velocities.

The frequency of the peak near St=0.35 was always twice that of the St=0.16-0.18 peak, a

relationship explained through examination of the origins of the St~0.35 peak. In cases

where the peak was visible, its amplitude was greatest towards the centerline of the light-

89

strut assembly, or the line X/D=0.0 in Figure 4.1. Due to the symmetry of the geometry,

measurements recorded along the centerline experienced flow periodicity from both sides

of the light-strut assembly. The effect of the doubled periodicity was a doubling of the

frequency, which is precisely what is seen in the results displayed above. Additionally, as

will be shown in the PIV results, the regions of strongest periodicity in the flow were

located away from the centerline, so the pressure or flow oscillations near the wake

centerline were expected to be relatively weaker than the overall strongest pulsations

observed in each case. For this reason, the magnitude of the St~0.35 peak was

proportional to, but always of much lesser magnitude, than the peak at St=0.16-0.18.

Therefore, a reasonable explanation for why the St~0.35 peak was visible in merely a

select few experimental cases was that these specific cases corresponded to the strongest

amplitude St=0.16-0.18 peaks among all experiments – indeed, the discrepancy in

St=0.16-0.18 peak magnitudes between Figure 4.14 and Figure 4.15 appears to support

the notion that the SR=0.5, Z=1D cases generated the highest St=0.16-0.18 peak

magnitudes. For these cases, the St~0.35 peak, always being lesser in magnitude by some

factor when compared the St=0.16-0.18 peak, was distinguishable above the noise floor

of the signal. In contrast, cases with smaller amplitude St=0.16-0.18 peaks produced

St~0.35 peaks that were not strong enough to be visible above the signal noise threshold.

Ultimately, regardless of the cause of the peak near St=0.35, it was not present in the

majority of experimental cases investigated. It was thus not considered to be a feature

90

universally present in the landing gear – landing light problem and will not be further

considered for the remainder of the discussion.

Main Feature: Single Peak in the St=0.16-0.18 Region 4.4

Examination of the landing gear – landing light problem hitherto has focused on

eliminating the spectral features which were deemed to be irrelevant to the main

discussion. Having achieved that the focus now falls on the one feature of significance,

namely the St=0.16-0.18 peak. Figure 4.19, Figure 4.20, and Figure 4.21 below, which

show hot-wire results for all SR=0.5, SR=0.85, and SR=1.25 cases, respectively,

including all velocities and elevations, confirm that the light-strut assembly produced one

tone, and it was consistently located in the St=0.16-0.18 domain. This was easily gleaned

from the figures when the features discounted in previous sections were ignored. Trends

associated with the St=0.16-0.18 peak will be discussed in this section using only hot-

wire results, as microphone results did not provide any additional information.

91

. Figure 4.19: Hot-wire signal showing spectra for all SR=0.5 cases, including all velocities and elevations, along

with the average peak Strouhal number.

Figure 4.20: Hot-wire signal showing spectra for all SR=0.85 cases, including all velocities and elevations, along


92

Figure 4.21: Hot-wire signal showing spectra for all SR=1.25 cases, including all velocities and elevations, along


Trend #1: Decrease in St=0.16-0.18 Peak Magnitude with Increase in 4.4.1

Light-Strut Spacing

As depicted in Figure 4.19, Figure 4.20, and Figure 4.21, the SR=0.5 tests generated the

largest magnitudes, the SR=0.85 cases produced weaker peaks by approximately a factor

of two compared to those of the SR=0.5 cases, and the SR=1.25 cases generated almost

negligible peaks.

Trend #2: Decrease in St=0.16-0.18 Peak Frequency with Increase in 4.4.2

Light-Strut Spacing

Table 4-1 below presents the average peak Strouhal number for each case for the peak

found in the 0.16-0.18 region. For the example case displayed previously in Figure 4.1

through Figure 4.7 the existence of a solitary peak at St~0.175 was clear. Furthermore, all

spectra for SR=0.5 cases showed a peak at approximately a St=0.176 value, as depicted in

Figure 4.19 and reflected in Table 4-1 values. The empty entries for various cases

93

represent experiments for which a clear and obvious peak was not present, a situation

exemplified in Figure 4.12.

Table 4-1, along with Figure 4.19, Figure 4.20, and Figure 4.21, clearly shows the

Strouhal number of the main peak decreasing with increasing spacing between the strut

and the light. At a spacing ratio, SR, of 0.5, the average Strouhal number of the peak was

0.176. This value decreased to an average Strouhal number of 0.168 at a spacing ratio of

0.85 and decreased further to an average Strouhal number of 0.163 for the largest spacing

ratio of 1.25.

Table 4-1: Average hot-wire Strouhal number of the single peak in the 0.16-0.18 range for each case.

Spacing

Ratio, SR

(S/D)

Elevation,

(Z/D)

Freestream Wind Tunnel

Velocity, Vt (m/s)

10 20 30

0.5 0 0.175 0.177 0.176

0.5 0.175 0.177 0.176

1 0.176 0.176 0.177

0.85 0 - - -

0.5 0.167 0.169 0.168

1 0.168 0.169 0.169

1.25 0 - - -

0.5 - - -

1 0.162 0.164 0.163

Trend #3: Increase in St=0.16-0.18 Peak Magnitude with Increase in 4.4.3

Elevation

A final trend was present when observing the magnitude of the St=0.16-0.18 peak with

increasing elevation from the center plane. For all three spacing settings and all three

velocities the magnitude universally increased as the elevation was increased. Figure

4.22, Figure 4.23, and Figure 4.24 represent the Z=0D, Z=0.5D, and Z=1D cases,

respectively. The change in peak magnitude from the lowest elevation to the intermediate

94

height was negligible, but the increase from the intermediate setting to the top elevation

was unmistakeable. The peak magnitude in Figure 4.22 and Figure 4.23 was equal to

slightly less than 1.0 while in Figure 4.24 it was equal to almost 3.0. Therefore, the

highest elevation clearly provided the peak with the largest magnitude, a 200%+ increase

when compared to the intermediate and zero height settings.

Figure 4.22: Hot-wire results for all Z=0D cases.

95

Figure 4.23: Hot-wire results for all Z=0.5D cases.

Figure 4.24: Hot-wire results for all Z=1D cases.

4.4.3.1 Elevations Greater than 1D Showed No Change in Frequency or Magnitude

A traverse up and down the length of the strut to within half a diameter of the top and

bottom acrylic panels showed that the peak frequency and magnitude remained virtually

constant even for elevations greater than one diameter. A frequency shift to the previously

measured St=0.19 vortex shedding frequency of the lone strut was never observed.

96

Furthermore, the amplitude of the signal was always larger than that found at the

intermediate and zero heights. Thus, signal frequency along the entire length of the light-

strut assembly and signal magnitude for elevations at 1D+ was found to be constant.

97

5 PIV RESULTS

Introduction 5.1

In an attempt to understand the trends discussed in the previous section, PIV was used to

obtain further information from the flow. Velocity and vorticity contour plots are used

here to present the results of this testing.

There are a number of items in the following PIV images that are worth listing

beforehand:

Air flow globally moved from left to right.

Positive vorticity, in red, rotated in the counter-clockwise direction, while

negative vorticity, in blue, rotated in the clockwise direction.

The light-strut assembly plan views that are shown in the images are positioned

exactly as they were during experimental testing, i.e. the distances between the

wake and the light-strut image are to scale, as is the assembly image size.

The light-strut assembly side views were placed into the top left or bottom left

corners of the images along with a dashed line and a label describing the plane at

which images were acquired. These views are not part of the overall contour plots,

they are there merely to remind the reader of the experimental settings for each

specific image.

In these images V represents the local velocity, Vt represents the freestream wind

tunnel velocity, and 𝜔 represents the local vorticity.

98

Negligible Effect of Velocity and Light-Strut Spacing 5.2

Parameters on Wake

The freestream wind tunnel velocity and light-strut spacing parameter did not have any

substantial effect on the structure of the wake. This topic is examined here.

No Change in Wake with Change in Velocity 5.2.1

The spacing ratio, SR=0.5, elevation, Z=0D case is used as an example to illustrate the

lack of change in the wake for different velocities. For this case, Figure 5.1, Figure 5.2,

and Figure 5.3 below represent the 10 m/s, 20 m/s, and 30 m/s results, respectively. While

not completely similar, the wakes in these figures exhibited like characteristics which did

not vary with changes in flow velocity. All three figures display a large overall wake

roughly three diameters wide in the X/D direction and centerd on the light-strut assembly

spanning from slightly less than X/D=0.5 to slightly above X/D=3.0. Within this wake, a

region of low velocity exists directly behind the strut, spanning until approximately

Y/D=3.0, flanked on either side by a region of high velocity spanning until approximately

Y/D=2.0. Outside of these regions of higher and lower velocity the wake itself was of

lower velocity than the higher velocity regions but of higher velocity than the lower

velocity region. If one moved along Y/D=1.0 from outside of the wake at X/D~3.5 to the

low velocity region directly behind the strut at X/D~1.75, one would have experienced

the following relative velocities: high – low – high – low – lowest. This overall pattern

was true for all tests done at this elevation, regardless of velocity. At higher elevations, as

will be seen in subsequent sections, the wake behaved differently but the trend with

respect to velocity was the same. Therefore, changes in velocity did not significantly

affect the wake.

99



100


No Change in Wake with Change in Light-Strut Spacing 5.2.2

The example case used here to demonstrate the negligible effect of the light-strut spacing

on the overall wake is the Vt=10 m/s, Z=0D case. Figure 5.4, Figure 5.5, and Figure 5.6

represent this case at a spacing of SR=0.5, SR=0.85, and SR=1.25, respectively. The

same wake features described in the previous section appeared again in all three of the

figures. Figure 5.5 and Figure 5.6 exhibited a less defined transition from high velocity

regions to the outer boundary of the wake than what was seen for the SR=0.5 case in

Figure 5.4. However, the high – low – high – low – lowest pattern remained, as well as

the presence of regions of low and high velocity within the wake. Hence, changes in

light-strut spacing did not have a significant effect on the structure of the wake.

101



102


Significant Effect of Measurement Plane Elevation on 5.3

Wake Structure

The measurement plane elevation proved to be the one experimental parameter that when

altered resulted in a significant change in the composition of the wake of the light-strut

assembly. To demonstrate this the SR=0.5, Vt=10 m/s case was used, with Figure 5.7,

Figure 5.8, and Figure 5.9 representing the Z=0D, Z=0.5D, and Z=1D cases, respectively.

The wake in Figure 5.7 has already been discussed in the two previous sections, but the

wake structures seen in Figure 5.8 and Figure 5.9 are considerably different from that

seen in Figure 5.7. Figure 5.9 displayed a smaller-sized wake, relative to Figure 5.7, that

closely resembled a cylinder wake; only one low-velocity region was present. The wake

in Figure 5.8 appeared to be a distorted version of the Figure 5.9 wake, somewhat

resembling a combination of the cylinder wake in Figure 5.9 and the low velocity region

in Figure 5.7. The complete change of wake structure when moving from Z=0D in Figure

5.7 to Z=0.5D in Figure 5.8 and then the slight wake difference when moving to Z=1D in

103

Figure 5.9 was a pattern seen across all sets of Z=0D – Z=0.5D – Z=1D cases, regardless

of velocity or spacing. Therefore, it was obvious that the structure of the observed wake

depended on the elevation at which testing was conducted.

Figure 5.7: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z=0D case.

Figure 5.8: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z=0.5D case.

104

Figure 5.9: PIV results showing the velocity plot for SR=0.5, Vt=10 m/s, Z =1D case.

Only Wake Activity at the Highest Elevation Showed Vortex Propagation 5.3.1

and Shedding

Figure 5.10 to Figure 5.12 below showcases the phase-locked vorticity plots for the cases

presented in Figure 5.7, Figure 5.8, and Figure 5.9 over eight points in the acoustic cycle.

For each case, an image was included for the corresponding point in the acoustic cycle,

resulting in eight images representing points in the cycle that are 𝝅/4 radians apart. Each

figure is composed of eight sub-figures which were labelled with a number corresponding

to the position they represent within the acoustic cycle. A sine wave and corresponding

circular marker denoting the phase is located in the top left corner of each PIV sub-figure.

The 0 and 2𝝅 radian phases were interchangeable with respect to PIV so the sine wave in

the top right corner of any 0 radian phase image shows two markers: a marker at 0 radians

and a marker at 2𝝅 radians. Figure 5.10 presents the vorticity for each point in the

acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0D case. Figure 5.11 depicts the vorticity for

each point in the acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0.5D case. Figure 5.12

105

shows the vorticity for each point in the acoustic cycle for the SR=0.5, Vt=10 m/s, Z=1D

case. The vorticity is a non-dimensional vorticity that was non-dimensionalized based on

the freestream wind tunnel velocity and strut diameter, and the colour scale was

unchanged across all three figures. As introduced in the apparatus and methodology

section, circular black outlines seen in the vorticity plots were used to define the locations

of vortex structures or vorticity blobs within the wake. The rightward movement of these

outlines through consecutive sub-figures, which signify consecutive points in the acoustic

cycle, represented the propagation of vortex-like structures through the wake during one

period of oscillation.

Through comparison of Figure 5.10, Figure 5.11, and Figure 5.12, it was deduced that

only the Z=1D elevation displayed clear vortex development and propagation, while the

Z=0D and Z=0.5D cases showed partial development or propagation at times but lacked

consistency throughout the entire cycle. For example, for the Z=0D case, the clockwise-

rotating shear layer closest to X/D=0.0 appeared to include a growing vortex in the sub-

figures corresponding to acoustic cycle points 5-6-7 in Figure 5.10. Contrary to what was

expected, in the image for point 8 the vorticity was not further grown or released and

decreased to a minor size as would be expected if a vortex had been forming or had been

shed; instead, the outline returned to a smaller, but intermediate size. Similarly, for the

Z=0.5D case, the counter-clockwise rotating shear layer depicted a decreasing –

increasing – decreasing vorticity blob trend for the 1-2-3-4 points in the acoustic cycle in

Figure 5.11. At least three of the images on the counter-clockwise rotating side should

106

have included outlines increasing in size with respect to the previous point in the cycle if

vortex shedding was present. These two examples show that Figure 5.10, representing the

Z=0D case, and Figure 5.11, representing the Z=0.5D case, represent wakes where

persistent vortex shedding did not appear to be present. In comparison, focusing on the

clockwise rotating vorticity in Figure 5.12, points 1-8 in the acoustic cycle displayed an

increasingly large vorticity blob throughout that was steadily moving to the right,

signifying a vortex that started formation at point 1, was grown and propagated during

intermediate points, and was to be shed immediately after point 8. Additionally, the

vorticity blob within the counter-clockwise vorticity region appeared to be consistently 𝜋

radians out of phase when compared to the vorticity blob in the clockwise rotating

vorticity region. For example, at point 1 and point 8, where the clockwise vorticity blob

was at its minimum and maximum sizes, the counter-clockwise vorticity blob was at its

medium sizes. On the other hand, at point 4 and point 5, where the clockwise vorticity

blob was at its medium sizes, the counter-clockwise vorticity blob was at its maximum

and minimum sizes, respectively. Like the clockwise vorticity blob, the counter-

clockwise vorticity blob also moved to the right from point to point in the acoustic cycle

until it was apparently shed from the shear layer, evidence not only that vortex shedding

was occurring in the Z=1D measurement plane, but also that it was occurring in an

alternate shedding manner.

107

Figure 5.10: PIV results showing vorticity plot with outlined vortical structures for points 1-4 in the acoustic

cycle for the SR=0.5, Vt=10 m/s, Z=0D case. Top left corner depicts the point in the acoustic cycle for which each

image was captured, bottom left image illustrates the height setting.

Fig

ure

5.1

0:

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108

Figure 5.10 (continued): PIV results showing vorticity plot with outlined vortical structures for points 5-8 in the

acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0D case. Top left corner depicts the point in the acoustic cycle for

which each image was captured, bottom left image illustrates the height setting.

Fig

ure

5.1

0 (

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): P

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109


cycle for the SR=0.5, Vt=10 m/s, Z=0.5D case. Top left corner depicts the point in the acoustic cycle for which

each image was captured, bottom left image illustrates the height setting.

1)

2)

3)

4)

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ure

5.1

1:

PIV

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110


acoustic cycle for the SR=0.5, Vt=10 m/s, Z=0.5D case. Top left corner depicts the point in the acoustic cycle for


5)

6)

7)

8)

Fig

ure

5.1

1 (

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): P

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111


cycle for the SR=0.5, Vt=10 m/s, Z=1D case. Top left corner depicts the point in the acoustic cycle for which each

image was captured, bottom left image illustrates the height setting.

1)

2)

4)

3) F

igu

re 5

.12

: P

IV r

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112


acoustic cycle for the SR=0.5, Vt=10 m/s, Z=1D case. Top left corner depicts the point in the acoustic cycle for


5)

6)

8)

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igu

re 5

.12

(co

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113

Complex Flow Behaviour between Light and Strut for 5.4

Z=0D Case

A PIV investigation of the flow between the light and the strut was performed in an

attempt to understand the origins of the structures observed in the wake for the Z=0D

case. The results are shown below in Figure 5.13 and Figure 5.14. There was difficulty in

imagining a scenario in which the flow behaviour seen in these figures was mainly two-

dimensional. There were too many inconsistencies present. The wake behind the strut

behaved as if flow were separating from the strut, but separation had very clearly

occurred from the front of the light and did not reattach at any point at this elevation. The

flow separating from the strut must have originated somewhere, but it did not appear as if

the origin was in the zero elevation plane shown in Figure 5.13 and Figure 5.14. Another

inconsistency with a two-dimensional explanation was the origin of the outer-most shear

layers in the zero elevation wake. For example, in Figure 5.13 at Y/D=3.5, there were two

outer shear layers on either side of X/D=0.0 and one inner shear layer. The inner shear

layer was just discussed to have originated from flow separation from the strut. Without

viewing Figure 5.13 and Figure 5.14, one would have assumed that the outer shear layers

originated from flow separation from the light. However, both of these shear layers curled

out from the region between the strut and the light and did not appear to be an extension

of the flow that separated from the front of the light. Instead, the shear layers seemed to

originate somewhere within the wake of the light, and again, from some other elevation.

A final discrepancy was found in Figure 5.14 in the region between the light and the strut.

There was a sizeable region directly behind the light which was composed of a high

velocity flow. If this were a two-dimensional problem, the wake behind the light would

114

have been consistently at a lower velocity than flow outside of it. Therefore, it was not

only difficult to imagine a mainly two-dimensional explanation for Figure 5.13 and

Figure 5.14, but also difficult to imagine anything other than a three-dimensional

explanation for the flow behaviours shown.

Figure 5.13: PIV results showing vorticity plot around light-strut assembly for SR=0.5, Vt=10 m/s, Z=0D case,

with light and strut visible. Bottom left image illustrates the height setting.

115

Figure 5.14: PIV results showing velocity plot around light-strut assembly for SR=0.5, Vt=10 m/s, Z=0D case,

with light and strut visible. Bottom left image illustrates the height setting.

Figure 5.15 below displays a portion of the velocity vectors used to form the contour plot

in Figure 5.14. The region depicted is the area between the light and the strut, within the

X/D=0.3-0.8, Y/D=1.9-2.3 bounds in Figure 5.14. It was interesting that flow in this area

was moving mainly in the cross-flow direction and not toward the light, as might have

been expected for flow in the wake of a bluff body. This was yet another clue that the

flow behaviour observed in Figure 5.13 and Figure 5.14 was three-dimensional in nature

and could not be explained adequately using a two-dimensional flow description.

116

Figure 5.15: Velocity vectors from PIV of SR=0.5, Vt=10 m/s, Z=0D case, focused on specific region between light

and strut in Figure 5.14.

Spatial Origin of St=0.16-0.18 Signal 5.5

Microphone and hot-wire measurements showed the presence of the St=0.16-0.18 peak in

the wake of the light-strut assembly. A closer look at the PIV tests yielded information

about the specific locations in the wake where the periodicity originated. Figure 5.16

displays the PIV vorticity contour plot for the SR=0.5, Vt=10 m/s, Z=0D case with

overlaid hot-wire measurement locations. Figure 5.17 is a replica of Figure 5.16, except

hot-wire spectra at 12 different measurement locations are visualized. In the figure, all

spectra have the same scale and are linked by a line to the measurement point they

represent.

117

Figure 5.16: PIV results showing the vorticity plot for the SR=0.5, Vt=10 m/s, Z=0D case, overlaid with hot-wire

measurement locations. Bottom left image illustrates the height setting.

The spectra in Figure 5.17 depict an increase in peak strength with increased proximity to

the X/D=0.0 centerline. In general, in the cross-stream direction the two points closest to

the centerline showed peaks that were much greater in amplitude than the peaks of the

two points further away. Therefore, the vorticity closer to the light-strut assembly

appeared to be the source of the St=0.16-0.18 peak.

What was somewhat interesting was when the measurements at X/D~0.25 and X/D~0.70

were compared it appeared that the peaks found at X/D~0.70 locations were greater in

magnitude even though the regions of strong vorticity in Figure 5.17 appeared much

closer to the X/D~0.25 measurement locations. One would assume that oscillations would

be greatest at regions of greatest vorticity, which did not appear to be the case. Figure

5.18 and Figure 5.19 can be used to explain away this seemingly perplexing feature in

Figure 5.17. They are the Z=0.5D and Z=1D analogues to Figure 5.17, respectively,

except they showed the spectra of the closest 8 hot-wire measurements relative to the

118

light-strut assembly, and not the closest 12. For these figures the X/D~0.70 measurements

also yielded greater peaks when compared to those at X/D~0.25, but in these images, the

strongest vorticity matched up well with the locations of the strongest peaks. Relative to

Figure 5.17, the regions of greatest vorticity had shifted away from X/D=0.25 and toward

X/D=0.70, and this was most pronounced at the highest elevation. In addition, the

locations of the strongest peaks most closely matched with the areas of strong vorticity at

the highest elevation. Therefore, vorticity shown in Figure 5.19, at the greatest height,

appeared to be highly influential on the signal measured in the zero elevation plane

illustrated in Figure 5.17, providing further evidence that there was significant three-

dimensional activity present in the light-strut wake.

M.A.Sc. Thesis – Marko Arežina McMaster University – Mechanical Engineering

119

Figure 5.17: PIV results showing the vorticity plot for the

SR=0.5, Vt =10 m/s, Z=0D case, overlaid with hot-wire

measurement locations, and illustrating 12 spectra

associated with 12 selected measurement points. Lines

connect each measurement point to its spectrum. All

spectra have the same scale.

Fig

ure

5.1

7:

PIV

res

ult

s sh

ow

ing

th

e vort

icit

y p

lot

for

the

SR

=0

.5,

Vt

=10

m/s

,

Z=

0D

case

, o

verl

aid

wit

h h

ot-

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120


SR=0.5, Vt=10 m/s, Z=0.5D case, overlaid with hot-wire

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121


SR=0.5, Vt=10 m/s, Z=1D case, overlaid with hot-wire

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122

6 DISCUSSION

A summary of the observed characteristics and trends associated with the light-strut

problem is as follows (listed in order of discussion):

Signs of three-dimensional flow activity were present

Clear vortex shedding observed solely at highest elevation

Drastic change in wake structure with increasing elevation

Increase in magnitude of signal with increasing elevation

Decrease in magnitude of signal with increasing light-strut spacing

Decrease in frequency of signal with increasing light-strut spacing

Strong signal originated from innermost shear layers at highest elevation

Acoustic and flow oscillations were present at one frequency, St=0.16-0.18

This section provides a discussion of these characteristics and trends and their implication

in the understanding of the flow behaviour in the near-wake. It is important to recall that

the trends discussed here were global and not exclusive to the spacing ratio, SR=0.5, and

freestream wind tunnel velocity, Vt=10 m/s setup despite predominant use of this setting

in figures and descriptions.

Three-Dimensional Flow Activity and Vortex Shedding 6.1

Process

The possibility of significant three-dimensional behaviour in Figure 5.13 and Figure 5.14

has been discussed in the results section for the region between the light and strut. There


123

were no signs in these figures or in other data collected suggesting that the complex three-

dimensional activity was confined only to the region between the light and the strut. In all

likelihood the three-dimensionality generated there was transported downstream into the

wake, as this would explain the lack of organized vortex shedding occurring at zero

elevation. In contrast, at the highest elevation, flow impinging on the light-strut assembly

interacted mainly with the strut alone and was more two-dimensional in nature; because

of this, the two-dimensional PIV images at the Z=1D elevation showed vortex shedding.

At some distance between these two regimes, the two-dimensional strut wake and the

three-dimensional light-strut wake met and there was a shift from a two-dimensional

wake to a three-dimensional wake. It is not known whether this occurred through a sort of

gradual change or sudden jump in flow pattern. This is an interesting question which

should be addressed in future work using stereoscopic PIV techniques.

The present results show that the wake at the intermediate elevation was still three-

dimensional in nature. In observing Figure 5.11, it was deduced that vortex shedding in

the two-dimensional intermediate plane was very weak or did not exist, similar to the

situation in the zero elevation plane. This could be explained if, similar to the zero

elevation case, the flow at the intermediate height was still largely influenced by the

three-dimensional light-strut wake. Additionally, a look at hot-wire results for different

elevations in Figure 4.22, Figure 4.23, and Figure 4.24, which represent Z=0D, Z=0.5D,

and Z=1D, respectively, showed that the signal peak grew in magnitude with higher

elevation. The zero and intermediate heights provided spectral peaks of similar amplitude


124

to each other, while in comparison, the measurements at the highest elevation were much

greater. Again, this could be explained if the flow at the intermediate height was still

largely three-dimensional, as the hot-wire measurements at this plane were similar to

those taken at the zero elevation plane. These clues seem to suggest that the wake at the

intermediate height behaved similarly to the zero elevation flow. However, PIV images of

the intermediate region showed a greater similarity with the images of the highest plane

than with that of the zero plane. Therefore, the wake at the intermediate region was likely

in the zone of transition from the three-dimensional light-strut wake to the two-

dimensional strut wake as it displayed features found in both wakes. Future research

would do well to document the gradual change of influence of one wake versus the other

as the height is varied, or to pinpoint the location of the previously mentioned jump if the

shift from one wake to the other is found to be sudden rather than gradual.

Wake Structure at Various Elevations 6.2

The intermediate and highest elevation wakes showed mean flow patterns similar to each

other and a lone cylinder wake. However, although the intermediate elevation and the

zero elevation wakes were both strongly influenced by three-dimensionality, they greatly

differed in structure. A more specific analysis of the wake at zero height was deemed

necessary as its structure was complex.

Based on the zero elevation PIV images there appeared to be three different flow pattern

options for the flow after it had moved around the top, bottom, or sides of the light. The

three flow pattern options are illustrated below in Figure 6.1, with arrows representing


125

streamlines for each option. The arrows are not meant to be understood as precise

representations of streamlines, they are artistic representations of the general paths of the

hypothesized flow patterns. The first option involved the flow reattaching to the strut and

then forming the innermost shear layers in Figure 5.13. The second option was the flow

moving around the shear layers formed due to the first option and forming a high velocity

region on either side of the strut. This high velocity region is seen in Figure 5.14 on either

side of the wake directly behind the strut. The final option was the main reason behind the

wide zero-elevation wake. The flow initially progressed directly outward in the cross-

stream direction away from the light-strut assembly, as displayed in Figure 5.15. The

velocities were large enough to create the small diamond-shaped region of high velocity

magnitude flow located between the light and the strut in Figure 5.14. As this flow

reached the boundary between the light wake and the higher velocity freestream flow, it

was directed downstream, creating the unique wide wake observed in the zero elevation

PIV images.


126

Figure 6.1: Figure 5.14 with arrows providing artistic representation of streamlines for each of the three

hypothesized flow patterns. Arrows are labelled according to which flow pattern each represents: 1 – flow

reattachment to the strut and subsequent shedding, forming the wake directly behind the strut; 2 – avoidance of

reattachment, flow around pattern #1, formation of high velocity region in overall wake; 3 – flow in cross-stream

direction away from light-strut assembly, creation of wide wake.

Figure 6.1 illustrates the three hypothesized flow patterns in a two-dimensional sense. It

is difficult to understand the three-dimensional activity, but the likely path of the

streamlines in Figure 6.1 is shown in Figure 6.2. A top and side view for each pattern is

displayed, and each option is labelled with the same number as in Figure 6.1. Again,

arrows are artistic versions of streamlines for each option and are not meant to be

understood as precise representations. The streamlines in the side views are only shown

for the top half of each assembly; in reality they exhibit symmetry about the light axis.

When comparing the arrows in the top views with the path of the flow in the side views, it

was clear how two-dimensional PIV images may not convey the three-dimensional

features of the flow.

2

2

3

1

3


127

1) 2) 3) Figure 6.2: Artistic representation of possible flow movement around light-strut assembly for SR=0.5 case; top:

top view, bottom: side view. Arrows represent streamlines. The three flow options depicted here are the same as

those shown in Figure 6.1.

The hypothesized flow patterns can be used to explain why there was such a radical

change in wake structure moving from zero to intermediate elevation. All three flow

patterns were initiated by movement around the light. At the intermediate height, which

coincided with the top edge of the light, the flow faced a reduced light width and thus was

not forced to move around the light to the same extent as was required at the zero height.

The influence of the light on the flow and the resulting three-dimensional effects were

thus reduced, allowing the wake behind the assembly to form into a narrower shape

resembling a lone cylinder wake.


128

Signal Strength at Various Elevations 6.3

The increase of the magnitude of the signal with elevation was likely related to the three-

dimensionality discussed previously. Three-dimensional flow behaviour generated

between the light and strut and impinging on the strut likely lost much of its organized

structure, if any existed, by being forced to flow around the strut, a two-dimensional bluff

body. However, this three-dimensionality was not completely destroyed and thus there

was a periodicity present that was weaker than that found at the highest elevation, where

no object existed to break up the vortex shedding from the strut. As a result,

measurements at the zero and intermediate elevation planes, regions highly influenced by

the combined light-strut wake, showed weaker signal peaks than at the highest elevation,

which was predominantly influenced by the lone strut wake.

Signal Strength at Various Light-Strut Spacing Ratios 6.4

The decrease in signal magnitude with increasing light-strut spacing seemed to have been

caused by the increase in light wake size prior to impingement upon the strut. The light

wake at zero elevation, just prior to impingement on the strut, was much larger than the

diameter of the light itself, as can be observed in Figure 5.13 and Figure 5.14. In these

figures, the light contacted the strut at about Y/D=2.2, at which point the overall wake

had developed to be almost two diameters wide. Based on this, one could reasonably

assume that the light wake upon meeting the strut at Y/D=2.2 in the vertical plane, the y-z

plane in Figure 5.13 and Figure 5.14, may also have been substantially larger than the

diameter of the light. Furthermore, the complete light-strut wake did not reach its

maximum width until almost Y/D=3.5 in Figure 5.13 and Figure 5.14; the wake


129

continued to expand in width for more than a diameter length away from the point where

the light ended. Intuitively, as the spacing between the light and the strut increased, the

wake width at the point where it met the strut also increased, as the wake was allowed

more room to expand prior to impingement on the strut. Instead of a width of two

diameters as for the SR=0.5 case, the wake width was likely greater for the SR=0.85

setting and still greater for the SR=1.25 spacing. Again, one might reasonably assume that

a similar behaviour existed in the vertical plane. Thus, as the spacing between the light

and the strut was increased, the light-strut wake was evermore present at higher

elevations, leading to the existence of a weaker and more three-dimensional wake in

comparison to the smallest light spacing case. This weaker wake presented in the hot-wire

and microphone measurements as decreasing peak magnitude with increasing spacing.

Effect of Light-Strut Spacing on Oscillation Frequency 6.5

As for the decrease in frequency with increasing light-strut spacing, it was difficult to

offer a hypothesis without more thorough analysis of the complicated three-dimensional

flow behaviour between the light and the strut. This was something that has been left for

future work. However, as described in the literature review, it was interesting to note that

studies of two cylinders in tandem also reported a decreasing vortex shedding frequency

with an increase in spacing. One explanation for this behaviour by Alam and Zhou [52]

proposed that the upstream cylinder wake became wider as the spacing was increased,

generating a lower overall flow velocity at the upstream side of the downstream cylinder,

and thus resulting in a lower shedding frequency. This theory has not been verified but

nonetheless is intriguing considering its applicability to the light-strut problem, especially


130

as it has already been argued that the downstream strut sees a wider wake as the

separation between itself and the light is increased.

Effect of Innermost Shear Layers at Highest Elevation 6.6

Together, Figure 5.17, Figure 5.18, and Figure 5.19 showed that the peak at St=0.16-0.18

captured by hot-wire and microphone measurements at the zero and intermediate

elevation matched better with the shear layers found at the highest elevation than the

shear layers in the zero or intermediate elevation plane. This was evidence that the flow

periodicity at the highest elevation dominated the entire light-strut wake. The flow

patterns described previously in the discussion related to Figure 6.2 did not help explain

how the dominant periodicity at the highest height affected the periodicity in the Z=0.5D

and Z=0D planes. This is something that will need to be addressed in future work, as it

was difficult to theorize on the specific mechanisms at play when the flow was so

obviously three-dimensional. However, the fact that the periodicity at the highest

elevation dominated the periodicity of the entire light-strut wake and that this periodicity

originated in the innermost shear layers suggested the light-strut problem could be viewed

simply as a cylinder wake modulated by the presence of a light, a light which had

profound three-dimensional influence on certain portions of the wake.

Acoustic and Flow Oscillations at St=0.16-0.18 6.7

The light-strut assembly generated one main frequency for all conditions tested other than

those for which no spectral peak was observed. This frequency was always found to be in

the range of St=0.16-0.18, which was above the lone light shedding frequency, St=0.135,

but below the shedding frequency for the strut, St=0.19. Furthermore, the light-strut


131

shedding frequency was significantly stronger when measurements were performed at the

Z=1D height, outside of the combined light-strut wake and within only the strut wake. At

this same elevation, phase-locked PIV images showed that the wake greatly resembled a

cylinder wake. Additionally, due to observations that the frequency and magnitude at

elevations higher than one diameter were similar to those at one diameter it was likely

that flow for all Z=1D+ behaved similarly to that of the Z=1D flow. Therefore, flow

behaviour at all areas of the wake unaffected by the combined light-strut wake likely

resembled vortex shedding from a cylinder, although with the slightly modified St=0.16-

0.18 frequency. Flow behaviour within the light-strut wake was a complicated three-

dimensional phenomenon, with the periodic frequency matching that of the vortex

shedding from the strut alone. Ranges of activity of each of the flow behaviours are

depicted in Figure 6.3 below. The conclusion, then, for the light-strut problem was that it

tended to generate a wake that was best described as a modified cylinder wake: two-

dimensional, regular cylinder vortex shedding at a modified frequency in all areas outside

of the light-strut wake, shown as Region 3 in Figure 6.3, and a complex three-

dimensional behaviour within it, shown as Region 1 in Figure 6.3. Separating these two

zones was a transition region of unknown size, shown as Region 2 in Figure 6.3, which

may or may not have also housed periodic components.


132

Figure 6.3: Proposed flow behaviour for light-strut problem. Region 1 represents the complex three-dimensional

flow behaviour, Region 3 represents the approximately two-dimensional cylinder vortex shedding regime, and

Region 2 represents the transition from Region 1 to Region 3.

Figure 6.3 illustrates the flow behaviour for the light-strut problem using the smallest

light-strut spacing, but the same behaviour was observed for the intermediate and largest

spacing settings. This was contrary to the case of two tandem cylinders where the flow

regime changed as the spacing was increased. For example, as the cylinder spacing was

increased the flow began to reattach on the upstream surface of the downstream cylinder

such that the downstream cylinder now generated its own wake and was no longer

immersed in the wake of the upstream cylinder. For the light-strut problem, there was not

enough evidence – the difference in PIV images for the various light spacing settings was

not substantial – to suggest that a new flow regime was present as spacing was increased.

This may have been due to three-dimensionality of the flow behind the light and its

unchanging nature regardless of spacing, or it may have been that the spacing between the

light and the strut, even at the largest setting, was not large enough to trigger the onset of

a new flow regime. Perhaps an even larger spacing would have caused reattachment of

the flow; however, the spacing ranges were chosen such that upper limit of SR=1.25

1

2

2

3

3


133

would be the maximum advisable setup for which the light-strut assembly was still

structurally sound.

Figure 6.3 and the accompanying discussion of flow behaviour implied that Region 3, the

region of the two-dimensional cylinder vortex shedding regime, would persist regardless

of strut length. This was somewhat misleading because it was true that the flow regime

was expected to be the same throughout all of Region 3, but the frequency was expected

to shift back to a more standard cylinder vortex shedding frequency at some distance far

enough from the light. However, this critical distance at which the influence of the light

became negligible was unknown, allowing for the possibility that for all practical landing

gear strut sizes the frequency would remain unchanged along the length of the strut.

Discovery of the value of the critical strut length should be one of the targets of future

work on this topic in order to establish an expectation of real-world frequencies in the

landing gear wake.


134

7 SUMMARY AND CONCLUSIONS

Conclusions 7.1

The wake of a single light landing gear model was investigated using microphone, hot-

wire, and PIV systems – including both time-averaged and phase-locked PIV.

Additionally, flow directly around the model was observed using time-averaged PIV. The

experimental investigation included testing of three light-strut spacing distances,

combined with three different velocities, and combined with three different elevations.

Only the final PIV, time-averaged testing of the flow directly around the light-strut

model, did not include testing of all 27 experimental cases – instead it focused on a select

few cases chosen after observation of previous experimental results. Collectively, the

experimental results showed a number of features that led to the following conclusions

regarding the single light landing gear problem:

1. Three-dimensionality in the flow around the single light landing gear existed at

the zero elevation. It was present in the region between the light and the strut and

subsequently transported downstream to the wake. Some distance above and

below the light, the flow passed around the strut cross-section largely unaffected

by the three-dimensionality present at the zero elevation, and went on to generate

a primarily two-dimensional wake. A transition region between the highly two-

dimensional wake at higher elevations and the three-dimensional wake at the zero

elevation existed at a certain elevation or range of elevations, but its size and

resident flow features were not identified.


135

2. Complex flow behaviour existed at the zero elevation plane. This flow generated a

wake of a width that was greater than twice the physical width of the light-strut

assembly. Phase-locked images at this elevation were not able to capture any

vortex shedding or other periodic propagation through the wake. From the zero

elevation, the wake width decreased as the elevation was increased, eventually

leading to a flow resembling a cylinder wake. At the highest elevation, periodicity

in the form of alternate vortex shedding was clearly visible in phase-locked PIV

images.

3. Regions highly influenced by the combined light-strut wake contained weaker

periodicity than at the higher elevations, where the strut alone was the main

influence. This was related to the difference in wake structure in the different

regimes – the light-strut structure allowed for the mostly two-dimensional wake at

the highest elevation to develop unimpeded, while, in contrast, the strut interfered

with the three-dimensional light wake development, leading to the generation of a

relatively weaker three-dimensional wake at heights close to the zero elevation.

4. Increasing the light-strut spacing was found to decrease the strength of the

periodicity in the wake. Increased distance between the light and the strut resulted

in a more developed light wake, i.e., wider and higher, prior to impingement upon

the strut. Consequently, the wake at higher elevations was influenced by the three-

dimensional regime generated by the light-strut combination more greatly at larger

spacing than at lower spacing, resulting in a weakened periodicity over a larger


136

spanwise portion of the wake for the largest spacing than was the case for smallest

spacing.

5. Increasing the light-strut spacing also had the effect of slightly reducing the

oscillation frequency of the periodicity found within the wake. This effect was not

well understood but similar behaviour has been observed in literature for the case

of two tandem cylinders, with one theory linking the decrease in frequency to the

wider wake seen by the downstream strut at larger separation distances. As

mentioned in Item #4, a wider wake was present at increased light-strut spacing,

so this theory, if verified, is equally applicable for the light-strut assembly.

6. Periodicity in the wake of the light-strut assembly was present at a single

frequency. In general, this frequency was located in the range of St=0.16-0.18,

with the specific value dependent on light-strut spacing, and was constant along

the entire length of the assembly and for all tested velocities. This constant value

was always greater than the lone light shedding frequency, St=0.135, but smaller

than the vortex shedding frequency for the strut, St=0.19.

7. The flow pattern and single shedding frequency along the strut length allowed the

flow around the light-strut assembly to be classified as flow around a cylindrical

strut modulated by a light. At the highest tested elevations, the periodicity in the

wake resembled the alternating vortex shedding pattern observed in flows around

lone cylinders, while at the zero elevation, there was very little to no observed

periodic propagation through the wake. Thus, the simplest description of the light-

strut wake was that of a modulated cylindrical strut with mainly an alternate


137

vortex shedding wake, but with a wake region of complex three-dimensional flow

due to interaction of the flow with the light, and a periodic frequency marginally

different from that of the classical cylinder vortex shedding frequency, again due

to the presence of the light.

Industry Applications 7.2

Prior work in literature for the case of two lights with strut concluded that there were

three different frequencies present in the near-wake, two from the interactions of the

light-strut assembly with the flow and one at elevations far away from the light which

corresponded to the cylinder shedding frequency [47]. In contrast to that work, the results

here have shown only one frequency at all elevations for the case of single light with

strut. It may be valid to assume that this will not hold for all aspect ratios. At some critical

strut length the frequency present will likely shift to that of vortex shedding from a lone

cylinder. However, with this critical length unknown it is difficult to predict whether one

frequency or two should be expected from modern landing gear designs that are fitted

with a single light. Regardless of the number, two or one, this will be less than the three

that were present for the case of two lights. The conclusion must then be that modern

aircraft manufacturers would need to expend more resources to mitigate the extra

frequency present and would thus prefer the single light case.

Nonetheless, it is difficult to endorse one configuration over the other without considering

directivity of the sound sources. Salt et al. [47] showed that just one of the three

frequencies present in the two-light configuration case had a strong downward radiating


138

component, which is important practically because downward radiating sound will be

more disturbing to residents on the ground when compared to other components that are

emitted sideways into the air. If the single light case studied in this thesis consisted of a

strong downward component, something that certainly seems possible considering the

apparent three-dimensional activity in the wake, a direct comparison of sound

magnitudes, not number of frequencies, will decide which configuration is most ideal.

Unfortunately, only two-dimensional work was performed for this thesis so confirmation

or rejection of this possibility will remain a task for future work, and by extension a

definite recommendation for industry best practices will not be possible at this time.

Recommendations for Future Work 7.3

As discussed in the literature review section, landing lights have been largely ignored in

literature, with this thesis being one of a few experimental investigations focusing on

landing light orientation. As a result, there exists a potential for a large amount of

research to be completed on the subject. Some of the potential research work related to

this thesis is as follows:

1. A basic stereoscopic PIV (SPIV) study conducted on wake of the light-strut

assembly is needed. Stereoscopic PIV captures out of plane movement of the

flow, thus providing results that would clarify the question of the existence of

downward radiation of the St=0.16-0.18 frequency, which, as discussed, is

directly related to the applicability of this thesis work in industry. This study could

successfully be completed using the same cases tested in this thesis.


139

2. For questions concerning more fundamental physics of the flow, a detailed and

comprehensive SPIV study, perhaps even a volumetric SPIV study, is required.

Volumetric SPIV involves SPIV tests at successive parallel planes offset by only

small distances. The end result is a velocity data set for an entire volume of fluid

in all three directions. The process is quite intensive, but if performed for the

range of elevations – 0D-1D – used in this thesis and performed in the wake as

well as directly around the light-strut assembly, it has the potential to: describe the

nature of the transition region between the higher, mostly two-dimensional flow

and the lower three-dimensional regime; lead to an understanding of the entire

wake region, including a description of the complex three-dimensional regime and

a look into the influence of the higher regime on the zero elevation regime and

vice versa; and provide clues relating to how the modification of the vortex

shedding frequency occurs, clarifying why the flow at zero elevation organizes

itself in the manner that has been observed.

3. To locate the critical strut length away from the light at which the vortex shedding

frequency reverts back to a classical vortex shedding frequency, a basic

experimental investigation is necessary. A simple study based on actual landing

gear strut lengths will be practical; however, if the critical length is not found at

practical sizes and scientific curiosity is to be appeased, a more exhaustive study

may be required.

4. The light-strut problem shares many similarities with the disk-cylinder problem,

not least of which is the lack of existing literature on the topic. Assuming most of


140

the conclusions of this thesis are valid for the disk-cylinder problem, an

interesting study would be a look at the results of flow around other axisymmetric

bodies in tandem with a cylinder, such as spheres or square prisms. Results of

these studies could be used to engineer a quieter landing light design.

5. A set of experiments recreating the work completed in this thesis, and also in Salt

et al. [47], but using lights of various smaller diameters would be beneficial to

industry, as it would reproduce the existing situation in which lights exist at

various diameters, even among aircraft of similar size.


141

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145

APPENDIX A: TRIGGER CIRCUIT

DIAGRAM

Figure 0.1: Circuit diagram for trigger system used in conjunction with TSI PIV system to obtain phase-locked

images, as produced by Arthurs [53].


146

APPENDIX B: UNCERTAINTY ANALYSIS

B.1 Direct Measurements

Periodicity in the wake of the single light landing gear problem showed little variation in

frequency during experimentation. Spectral averaging further reduced this variation, as

almost no frequency change was observed after 5-10 averages. This was equally true for

the hot-wire measurements. For both the microphone and hot-wire frequency

measurements, systematic uncertainty, br, was found to be ±0.38 Hz due to the analog-to-

digital data acquisition system and random uncertainty, sr, was found to be ±0.16 Hz at

10 m/s, ±0.56 Hz at 20 m/s, and ±0.65 Hz at 30 m/s. Using Equation (1) from Coleman

and Steele [54], the overall uncertainty, Ur, in the frequency measurements was ±0.8 Hz

at 10 m/s, ±1.35 Hz at 20 m/s, and ±1.5 Hz at 30 m/s, corresponding to relative

uncertainties of approximately 2.0%, 1.7%, and 1.3%, respectively.

𝑈𝑟 = 2(𝑏𝑟

2 + 𝑠𝑟2)

12 (1)

Microphone and hot-wire measurements were recorded using a 50 kHz sampling rate, 50

averaged one second long samples for the microphone, and 60 averaged one second long

samples for the hot-wire. The result was a repeatability uncertainty of 3% for both.

Coupled with the ±0.08 mV resolution error for both the microphone and hot-wire, and

with an approximate calibration error of 5% for the microphone, the uncertainties

according to Equation (1) were 12% in the microphone pressure measurements and 6% in

the hot-wire amplitude measurements.


147

B.2 Non-dimensional Numbers

Non-dimensional numbers reported within this thesis inherently carried more uncertainty

than the direct measurements considered above due their amalgamation of different

values. The overall effect of individual uncertainties was calculated using the Taylor

Series Method (TSM) from Coleman and Steele [54], which is shown below in Equation

(2):

𝑈𝑟2 = (

𝜕𝑟

𝜕𝑋1)

2

(𝑈𝑋1)

2+ (

𝜕𝑟

𝜕𝑋2)

2

(𝑈𝑋2)

2+ (

𝜕𝑟

𝜕𝑋3)

2

(𝑈𝑋3)

2+ ⋯ + (

𝜕𝑟

𝜕𝑋𝐽)

2

(𝑈𝑋𝐽)

2 (2)

where Ur, as before, is the overall uncertainty of the non-dimensional number in question,

r, Xi-J are the measured values that are part of the non-dimensional number, and UXi-J are

their associated uncertainties.

Equation (2) modified for relative uncertainties is shown below as Equation (3), where

Ur/r is the relative overall relative uncertainty of the non-dimensional number, and UXi/Xi

are the overall relative uncertainties of each term within the non-dimensional number.

𝑈𝑟2

𝑟2= (

𝑋1

𝑟

𝜕𝑟

𝜕𝑋1

)2

(𝑈𝑋1

𝑋1)

2

+ (𝑋2

𝑟

𝜕𝑟

𝜕𝑋2

)2

(𝑈𝑋2

𝑋2)

2

+ (𝑋3

𝑟

𝜕𝑟

𝜕𝑋3

)2

(𝑈𝑋3

𝑋3)

2

+ ⋯

+ (𝑋𝐽

𝑟

𝜕𝑟

𝜕𝑋𝐽

)

2

(𝑈𝑋𝐽

𝑋𝐽)

2

(3)

B.2.1 Non-dimensional Pressure, P*

The uncertainty in the non-dimensional pressure, P*, which is given by Equation (4), was

calculated using the Taylor Series Method introduced above.


148

𝑃∗ =

𝑃𝑚𝑎𝑥

12

∗ 𝜌 ∗ 𝑉𝑡2

(4)

𝑈𝑃∗2

𝑃∗2 = (𝑃

𝑃∗

𝜕𝑃∗

𝜕𝑃)

2

(𝑈𝑃

𝑃)

2

+ (𝜌

𝑃∗

𝜕𝑃∗

𝜕𝜌)

2

(𝑈𝜌

𝜌)

2

+ (𝑉𝑡

𝑃∗

𝜕𝑃∗

𝜕𝑉𝑡)

2

(𝑈𝑉𝑡

𝑉𝑡)

2

(5)

which simplifies to:

𝑈𝑃∗2

𝑃∗2 = (𝑈𝑃

𝑃)

2

+ (𝑈𝜌

𝜌)

2

+ 4 (𝑈𝑉𝑡

𝑉𝑡)

2

(6)

where the relative error in pressure was, as calculated above, 12%, the relative error in

density was assumed to be negligible as a tabulated value was used, and the relative error

in the freestream wind tunnel velocity was 0.4%. Substituting these values into Equation

(6) and solving for the overall relative error in the non-dimensional pressure results in:

𝑈𝑃∗

𝑃∗= √(12)2 + 4(0.4)2 ≈ 12% (7)

Thus, the relative uncertainty in the non-dimensional pressure was approximately 12%.

B.2.2 Strouhal Number, St

TSM was not used for the Strouhal number to calculate the overall uncertainty in the

Strouhal number because the collapse of the data at different velocities to the same

Strouhal numbers resulted in a lower random uncertainty than would have been calculated

via the TSM approach. Analyzing the Strouhal number results directly led to a calculated

uncertainty, at maximum, of ±0.002.


149

B.3 Flow Visualization Uncertainty

Flow visualization through PIV was meant mainly as a qualitative tool to understand

overall behaviour of the flow in the wake of the single light landing gear. Nevertheless,

one of the techniques used to achieve this was phase-locked PIV, which required an

image capture at a specific point in the acoustic cycle to be successful. Due to the finite

resolution of the data acquisition system, the images were not always captured at the

specified point. The sampling rate of 50 kHz, at one second intervals, and with zero-

padding included resulted in frequency bins of approximately 0.76 Hz width. The

maximum error associated with this processing system was approximately 1%, which

corresponded to ±3.6˚. By observation of the PIV results, it was understood that this error

was not great enough to have a significant effect on the final averaged images. Each

investigated case included the averaging of at least 200 images, and yet convergence

generally occurred after just 10-20 images were averaged.

Documents

EFFECT OF SINGLE LIGHT ORIENTATION ON LANDING GEAR WAKE · Figure 2.9: Two cylinders in the tandem arrangement [41]. L is the distance between the centers of the two cylinders (same