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Experimental and
Computational Study on Sonic
Boom Reduction
Jury
 Prof 1 : Mohammed Khalil IBRAHIM
 Prof 2 : Ali Mohammed Omar ASHRAF
 Prof 3 : El Hachmi ESSADIQI
Students
 Anas LAAMIRI
 Ayoub BOUDLAL
Université Internationale de Rabat 2018/2019
Preface
This report is written as a thesis for the Aerospace Engineering degree at the
International University of Rabat. It is a reflection of the work we performed on
sonic boom minimization. We tried to reduce the sonic boom of a 2D Non-
lifting and lifting object by analyzing the relation of the shape of the object and
the asymptotic shock strength it produces on the ground in a supersonic flow.
At this point we would like to write some words of gratitude. We would like to
thank everybody who helped us realizing this report. First of all, we would like
to thank Prof. Mohammed Khalil IBRAHIM for guiding us through the
graduation project. He pointed us in the right direction by giving us advice and
comments on the work. Furthermore, we would like to thank the technical staff
for the adequate help they provided when the computational hardware was not
quite working along.
Ayoub BOUDLAL and Anas LAAMIRI.
Abstract
Sonic boom reduction has been a major obstacle in the aviation industry for the
last 20 years, scientists from all over the world strive to find a solution for
reduction of the impact sonic boom on the ground, hence bring back Supersonic
travel back to life after the retirement of the first supersonic civil transport
airplane, concord, in 2011. To do so, the emphasis in latest research has been on
supersonic plane shape optimization to decrease the sound signature on the floor
resulting from a supersonic aircraft's Sonic boom in cruise flight at elevated
altitude. CFD technology offers an appealing option to help in the design and
optimization of supersonic cars due to the constraints of in-flight testing and
laboratory scale testing costs. Due to the significant rise in computing power, the
predictive capacity of CFD technology has considerably enhanced over the past
decade, enabling the treatment of more complicated geometries with bigger
meshes, better numerical algorithms and enhanced turbulence models for
Reynolds-averaged Navier-Stokes (RANS). As computing energy continues to
rise, numerical optimization techniques were coupled with CFD to further assist
in the design phase. But first we must understand the phenomena. This thesis
provides a careful study of the sonic boom and its signature on the ground. The
study is conducted following three approaches of analysis: Analytical,
computational and experimental. Once the understanding of the phenomena is
all done, we move into finding the flight conditions and shape that minimize the
sonic boom and provide the required lift.
Table of content
PREFACE............................................................................................................ 3
ABSTRACT.......................................................................................................... 4
CHAPTER 1: INTRODUCTION .......................................................................... 8
1. What is Sonic Boom?...................................................................................................8
1.1 How Sonic Boom is generated ..............................................................................8
1.2 How large can a sonic boom be?.........................................................................10
2. Impact of Sonic Boom in community.........................................................................10
2.1 Can it cause damage?..........................................................................................10
2.2 Effect of sonic boom in human health.................................................................11
3. Historical Background ...............................................................................................12
3.1 First Sonic Boom ever created ............................................................................12
3.2 Supersonic Transport (SST)................................................................................13
4. Prevision attempt to reduce Sonic Boom....................................................................13
4.1 In search of a quieter Boom ................................................................................13
4.2 Current and future Research Studies ...................................................................14
4.3 Commercial Prospects.........................................................................................14
5. Organization of report................................................................................................15
CHAPTER 2: METHODOLOGY ...................................................................... 16
1. Introduction ...............................................................................................................16
2. Experimental..............................................................................................................16
2.1 Wind Tunnel.......................................................................................................16
2.1.1 Working section...........................................................................................17
2.1.2 Instruments frame and instruments...............................................................20
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2.1. 3 Model..........................................................................................................20
2.1.4 Versatile Data Acquisition System (VDAS).................................................20
2.1.5 Schlieren Appartus (AF302A)......................................................................21
2.1.6 Technical Details .........................................................................................21
2.1.7 Layout and Location....................................................................................22
2.1.8 Wind Tunnel assembly ................................................................................23
2.1.9 Experimental procedures..............................................................................26
2.2 Field Testing.......................................................................................................28
2.2.1 Measuring Sonic Boom................................................................................29
2.2.2 Measurement Systems .................................................................................29
3. Whitham’s Theory (Analytical)..................................................................................37
3.1 2D shape method method (2D diamond wedge) ..................................................39
3.2 Limitations of Whitham theory ...........................................................................41
4. BASS Theory (Analytical).........................................................................................42
5. CFD (Computational) ................................................................................................50
CHAPTER 3: SONIC BOOM RESULTS ............................................................ 52
1. Introduction ...............................................................................................................52
2. Experimental Results .................................................................................................52
3. Computational Results...............................................................................................53
3.1 No lifting case (0° angle of attack).....................................................................53
3.2 Lifting case ( with an angle of attack 5°).............................................................80
4. Analytical Results......................................................................................................86
5. Conclusion.................................................................................................................87
5.1 0° angle of attack ................................................................................................87
5.2 5° angle of attack ................................................................................................89
CHAPTER 4: MINIMIZATION TO REDUCE SONIC BOOM ............................... 83
1. Introduction ...............................................................................................................83
1.1 Diamond wedge..................................................................................................83
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2. Minimization techniques to reduce Sonic Boom.........................................................85
2.1 Sonic boom reduction technique using Matlab contour for diamond wedge.........85
2.2 Quiet spike Sonic boom reduction technique.......................................................85
2.2.1 Introduction of the idea................................................................................85
3. Results of minimalization for 2D shape......................................................................86
3.1 Diamond wedge results.......................................................................................86
3.2 Minimization technique inspired form F-15b NASA’S modified supersonic
aircraft...........................................................................................................................86
CHAPTER 5: CONCLUSION ........................................................................... 90
REFERENCES .............................................................................................. 91
APPENDIX .................................................................................................... 92
LIST OF FIGURES ....................................................................................... 95
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CHAPTER 1 : INTRODUCTION
1. What is Sonic Boom
People have been fixated on speed for a very long time. They are discovering approaches to
travel quicker which have prompted numerous developments that we see today including the
rapid airplane.
It was this interest for speed for people which set off an American military pilot, Chuck
Yeager to speed test a flying machine where he figured out how to travel 428 m/s, breaking
the sound wall for the absolute first time and travel quicker than the speed of sound.
1.1. How Sonic Boom is generated
When the object travels faster than the velocity of the sound, the produced sound waves can
not migrate from each other as the velocity is beyond that of the sound — thus colliding with
each other. That's the wave-emitting object that travels quicker than the waves themselves.
This causes the waves to force themselves or combine to travel in a single shock wave at a
critical speed known as ' Mach 1 ' and has an estimated value of 1,235 km/h. So, because of
this compression of the sound waves, a "boom" is heard. These are known as Sonic booms.
Figure 1.1 Illustration of the shock wave
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This produces a large quantity of sound energy, making our ears a sound comparable to that
of thunderclap.
According to NASA, when the air reacts like a liquid to supersonic objects and the force
produced by objects pushing aside air molecules as they travel through the air forming a
shock wave that is like a ship hitting the water, a sonic boom occurs. The booms can continue
as far as the object is moving in supersonic speed. The waves are formed in a conical shape
behind the object.
The boom is continually produced as long as the plane is supersonic. A tight surface track is
created along the aircraft's flight route called the "boom carpet."
Figure 1.2 Shock impact on the ground
The pressure signature on the ground tends to offer an N-Shape wave, the objective of this
thesis is to reduce it.
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1.2. How large can a sonic boom be?
A sonic boom's size relies on the aircraft's size and weight. The sonic boom intensity is based
on the length of the aircraft and its cross-sectional region, whereas its shape depends on the
near-ground local air turbulence.
Wind, velocity, direction, and also air temperature and pressure influence the direction in
which the sonic boom travels and the strength of shock waves produced by sound wave
compression.
Figure 1.3 Sonic Boom carpet
2. Impact of Sonic Boom in community
2.1. Can It Cause Damage?
The boom intensity can be measured in pounds of air pressure per square foot (PSF). It is the
amount of pressure that the normal pressure around us increases (2,116 psf/14.7 psi).
And there is no anticipated harm to any constructions when measuring one pound of
overpressure. Supersonic aircraft at ordinary working altitude have overpressures of 1 to 2
psf.
The booms triggered by big supersonic aircraft can be noisy, capturing the attention of people,
and the sound of livestock can be upset. Strong booms can also cause the construction
systems to suffer minor harm.
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Without causing any harm, buildings in good condition can resist shockwaves of up to 11 psf.
A shockwave of less than 2 psf, however, will have a small opportunity of having an impact
on historical structures and poor condition buildings.
The chances of structural harm and greater government response are also improved if the
overpressure rises. Tests showed that buildings in good condition were undamaged by
overpressures of up to 11 psf, which means that whether or not it gets impacted depends on
the condition of the construction systems.
Figure 1.4 Spread of the distribution for actual pressure
2.2. Effect of sonic boom on human health
The effects of sonic boom on physical and mental health are presented. Sonic booms have
marked effects on behavior and subjective experience as exemplified by startle reactions and
attendant feelings of fear. Such intrusions disrupt sleep, rest and relaxation, and also interfere
with communications. These forms of sonic boom interruption generate annoyance which is
perceived greater when indoors, and which is judged equal to that experienced by residents
living around busy airports. In this regard, indications are that sonic boom disturbances
produced by commercial SST aircraft now being designed will not be deemed acceptable by
at least 25 percent of the population regardless of habituation.
From the psychological viewpoint, greater public acceptance of SST booms will be largely
contingent on determining and prescribing overpressure limits below which startle reactions
are minimal, posing no problems to performance or risk of personal injury.
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3. Historical Background
3.1 First Sonic Boom ever created
Aviation evolved at an incredible speed after the Wright Brothers made their first flight in
Kitty Hawk, North Carolina, on December 17, 1903. WWI took war to the skies within two
decades, and commercial airlines ferried customers all over the world. Aviation made another
big leap forward on October 14, 1947; test pilot Chuck Yeager became the first human to
break the sound barrier, achieving Mach 1 in the BellX-1 rocket-powered aircraft, a
collaborative U.S. project. Air Force and National Aeronautics Consultative Committee
(NACA), NASA's precursor.
Figure 1.5 First pilot to reach the sound barrier
But the X-1 itself was mainly intended for study purposes, not for business travelers. Soon
supersonic military jets were on the rise, but like the X-1, they were sprinters: they could only
fly for a few seconds at Mach 1, maybe a few minutes at most, before running out of fuel.
While this worked for tiny planes carrying out sharp maneuvers, big business airliners –often
traveling in straight lines or smooth curves–would have to cruise at supersonic velocity for a
much longer period of time. However, the progression inspired the commercial aviation sector
to investigate the development of supersonic transportation (SSTs) or civilian supersonic
aircraft.
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While the X-1 demonstrated that we had the correct instruments to fly at supersonic speeds,
some significant details required to be ironed out, such as the ability to cruise above Mach 1
for a comparatively lengthy flight duration, as well as the financial viability of such a project.
Multiple countries, including the U.S., began studies in the 1950s, but a slew of
developmental challenges faced by SSTs meant that only three nations would continue to
construct and fly such aircrafts: The United Kingdom, France, and the Soviet Union.
3.2. Supersonic Transport (SST)
To make SST possible, Concorde technicians from the British Aircraft Corporation of the
United Kingdom, France Aerospatiale, and the other businesses contracted to work on parts of
the aviation (like Rolls-Royce who built the motors) had to create fresh techniques or refine
ancient ones, from fly-by-wire controls in the cockpit (digital interfaces versus analog ones)
to heat-resistant tyres
4. Prevision attempt to reduce Sonic Boom
NASA and private firms are pushing for studies to restore supersonic flight to the aerospace
industry. The Concorde in 2003 was the last commercial supersonic flight. Beginning in 1976,
the Concorde flew commercially, seating up to 128 passengers. The cruising speed was 1,354
mph (2,179 km/h) at 2,04 Mach. The jet flew from Singapore to London, from New York to
London and from New York to Mexico on a regular basis before that. But on its way to
Mexico, it would have to fly at subsonic speeds while crossing Florida because in several
nations, including the United States, supersonic flight over land was, and still is, either
prohibited or extremely controlled. Universities, private businesses, and NASA are working
to fix the issue of sonic booms to make supersonic flight legal for overland paths.
4.1. In Search of a Quieter Boom
Many complained about the property damage caused by sonic booms during the Concorde
days, let alone the noise pollution that many found intolerable. More than 38,000 claims were
lodged against the U.S. between 1956 and 1968. Air Force harm caused by sonic booms. As a
consequence, supersonic flight over territory has been forbidden by the Federal Aviation
Administration (FAA) since 1971. Concerns about the environmental impacts, including
ozone depletion and climate change, were also influencing this ban.
To evaluate sonic booms, NASA launched the Shaped Sonic Boom Experiment in 2001. In an
attempt to reduce the effects of sonic booms during test flights, they modified the fuselage of
a Northrop F-5E Tiger II. The F-5E's nose was removed and a bigger, longer version was
substituted. The fairing was also lengthened and deepened under the fuselage. The modified
F-5E or Shaped Sonic Boom Demonstrator flew in 2003, and NASA took 1,300
measurements of sonic boom from different ground sensors from that stage. NASA
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technicians verified that the changes resulted in an 18 percent decrease in the original pressure
impulse and booms were 4.7 decibels quieter on average compared to an unmodified F-5E.
Figure 1.6 Spike technique
As a technique of reducing the original shock wave produced during supersonic flight, Quiet
Spike was tested. The spike in front of the airplane produces three tiny shockwaves before
reaching the aircraft's primary body when breaking the sound barrier. The next phase of
NASA was to hold its first Fundamental Aeronautics Conference in 2007, planning its next
phases of supersonic studies.
4.2. Current and Future Research Studies
Researchers have shown that it is possible to build supersonic airfoils to induce passive
laminar flow control (LFC). These decreases or eliminates the turbulent wing crossflow
producing shock waves. Consequently, the objective of this study is to produce LFC on the
wing, meaning that the leading edge of the wing during supersonic flight would stay subsonic.
The lack of a supersonic leading edge would decrease shock waves and minimize flow
disturbances, resulting in flight that is more stable and effective. Research conducted at MIT's
Aviation and Environment Laboratory, with NASA's assistance, analyzes the environmental
impacts of sonic booms. The aim is to know how the atmosphere is affected by high altitude
emissions from supersonic aircraft. In stratospheric circumstances, they will monitor biofuel
emissions, study their effect on ozone depletion, and attempt to determine how they can cause
greater concentrations of UV in the atmosphere and on the floor.
4.3. Commercial Prospects
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Since 2002, when it launched its Supersonic Natural Laminar Flow technology, Aerion Corp.
has been working to reduce sonic booms. Aerion has intended a supersonic LFC wing that
decreases drag over the wing by 50 percent. Laminar flow wings are thin and soft so that the
boundary layer is not traversed and the flow is turbulent. The wing structure of Aerion is
unbroken but tapered with a comparatively sharp leading edge, featuring a modified bi-
convex airfoil with slightly curved upper and lower surfaces. On its Supersonic Aerion AS2,
Aerion will use this wing. The wing carries high-lift flaps that are similar to big subsonic
business jets to offer the aircraft low approach and landing speeds.
The flaps also let the aircraft land where visibility is great at comparatively small angles of
attack. The wing cuts drag the complete airframe by 20 percent to increase effectiveness.
Figure 1.7 Aerion Aircraft
5. Organization of report
In this thesis, we start by defining the methodology used, we then proceed to the
understanding of the sonic boom by studying the effect of shockwave in different cases, on
the ground and on the body, the analysis will be conducted using Computational fluid
dynamics (FLUENT) and comparing it with the results of Wind Tunnel and finally with the
results obtained from the theory. Once all done with the comparison and understanding we
move on to finding a solution to minimize the pressure signature on the ground and hopefully
contribute into making the supersonic travel possible again.
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CHAPTER 2 : METHODOLOGY
1. Introduction
In this thesis, we aim to get various results from the theory, CFD and wind tunnel. Each
Method will provide us with results, hopefully the results match. The main aim is to
understand sonic boom effects on the ground and on the body. This chapter will end with a
better understanding of the sonic boom effect which will lead us into coming up with
adequate solution(s) for minimization of the pressure signature of shock wave on the ground.
2. Experimental
2.1. Wind tunnel
Many engineers work with air flow at supersonic speeds. It is important for them to know the
characteristic effects of supersonic flow around different shapes at different Mach numbers.
This allows engineers to predict and produce designs that will perform well under supersonic
conditions.
Supersonic air speed test equipment is usually very expensive, so it is normally found at
national aero engineering companies and institutions. The equipment Continuous Supersonic
Wind Tunnel (AF302) is a cost-effective laboratory scale unit. It includes a selection of
shapes (models) for experiments at air speeds from subsonic up to Mach 1.8. The results of
tests from this apparatus can be easily scaled up to produce predictions of performance of
much larger wind tunnel tests.
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Figure 2.1 The continuous Supersonic Wind Tunnel
The Continuous Supersonic Wind Tunnel includes several parts:
• The Diffuser Duct (in three sections).
• The Working Section and stand.
• Three different Working Section Liners.
• A set of Aerodynamic Models that fit in the Working Section.
• The Instrument Frame.
• The Flexible Tube and Support Stand.
• The Vacuum Pump.
2.1.1. Working Section
The Working Section is a precision engineered convergent-divergent rectangle-section nozzle
with pressure tappings along the bottom. The bottom of the nozzle is flat and fixed, but you
have a choice of three different shaped top pieces (liners).
This is so you can change the shape of the nozzle, to set the approximate air speed that passes
through it (subsonic, Mach 1.4 or 1.8).
In our project we will work on 1.8 Nozzle.
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Figure 2.2 The liner that fit in the top of the working section
Figure 2.3 The working selection
Models fit into the Working Section. The Working Section has two circular glass windows
('portals'), each window is inside a gear ring. The models fit into the space between the
windows. Slots in the windows hold the model in place. The user can turn a small angle
control that turns the gear ring. This turns the angle of the portals and the model. An angle
encoder on one side of the Working Section connects to TecQuipment's optional VDAS@.
The angle encoder connects to a special interface board (supplied with the Wind Tunnel) that
fits into the VDAS@ hardware. The VDAS@ displays and records the angle of the model.
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2.1.2 Instrument frame and instruments
Figure 2.4 The instrument frame
The separate Instrument Frame stands on a suitable bench or table (not supplied). It
connects to the electrical supply and gives power to any of the electronic instruments
used with the Wind Tunnel. The instruñlents fit onto the frame and connect to the
pressure tappings and other parts of the Wind Tunnel.
Supplied with the Instrument Frame is a 'mimic' of the pressure tappings along the
Working Section. The tappings from the Working Section connect to the mimic, then
you can easily connect your pressure measurement instruments to the mimic.
Also supplied with the Instrument Frame is the 32 Way Pressure Display. This
instrument has a multiline display that shows the pressures connected to its inputs.
When you press its scroll button, the display scrolls through all 32 pressure readings.
The display has a 'zero readings' button so that you can zero the pressure readings
before you do a test. The back of the 32-Way Pressure Display has a connection for
TecQuipment's VDAS@.
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2.1.3 Model
Figure 2.5 The Two-dimensional Model
Figure 2.5 shows the model used in our project with the Wind Tunnel. The airflow around the
model is two dimensional. This is because it fits exactly between each glass window, so the
airflow is only above and below the model, not around its ends. The model has a pressure
tappings so that you can measure the pressure distribution around the double wedge airfoil in
supersonic flow.
Note: You do not use the model with pressure tappings with the Schlieren
apparatus,as the pressure pipes block the view. Use the identical model without the
pressure pipes for Schlieren imaging.
2.1.4 Versatile Data Acquisition System (VDAS)
Figure 2.6 The VDAS Software and hardware
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TecQuipment's VDAS@ is an essential ancillary for use with the Wind Tunnel. It is a two-
part product (Hardware and Software) that will:
 automatically log data from your experiments
 automatically calculate data for you
 save you time
 reduce errors
 create charts and tables of your data
 export your data for processing in other software
2.1.5 Schlieren Appartus (AF302A)
The Schlieren Apparatus (AF302A) is for use with the Continuous Supersonic Wind Tunnel.
It uses refracted light and mirrors to show the pressure waves around the models in the
Working Section of the Wind Tunnel.
2.1.6 Technical Details
Item Details
Wind Tunnel
Dimensions
and weights
Dimensions (Wind Tunnel Only): 1600 mm high x 4000 mm long x
900 mm wide
Main part (with working section and one
liner): 115 kg Bypass pipe: 5 kg
Diffuser (four sections): 20 kg
Support stand: 69 kg
Total Weight: 209 kg
Instrument
Frame
1260 mm long x 840 mm high x 510 mm wide
Weight: 22 kg (without instruments)
Electrical Supply: 220 VAC
to 240 VAC 50 Fuse: 20
mm 10 A Type T
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Vacuum Pump Nominal Dimensions (fitted with noise damping hood): 1800 mm high
x 1800 mm long x 1500 mm wide, plus an exhaust silencer of
approximately 2600 mm high.
Weights:
Noise damping hood: 250 kg
Pump units together: 1000 kg
Silencer: 325 kg
Control Box: 80 kg
Flexible Pipe: 55 kg
Total Weight: 1710 kg
Electrical Supply: 400 VAC Three
phase, neutral and earth 250 A starting
current and 90 A running current User-
accessible circuit protection:
6 A type C MCB (miniature circuit breaker) - for overall protection of
the low current control circuits.
2 A I-IRC fuse - protects the 24 V control circuits.
4 A type D MCB - protects the three-phase fan in
the vacuum pump. 1 A 20 mm - protects the
auxiliary supply circuit to the drive.
Working
Section
Nominal Maximum Dimensions : 100 mm x 25 mm
Rotating Portal with Angle Encoder
25 pressure tappings plus two for the model with tappings
Interchangeable
Liners
Three: Subsonic, Mach I .4 and
Mach 1.8 Nominal Weights: 7
kg each
Table 2.1 Details of the wind tunnel.
2.1.7 Layout and Location
Figure 2.7 shows one suggested layout of the Wind Tunnel and its optional parts. Even
though it sits in a noise reducing hood, the Vacuum Pump creates the highest noise levels, so
TecQuipment recommend that you fit it in a separate sound-proof room next to the Wind
Tunnel.
As the air passes through the Working Section it becomes very cold, so any moisture in the air
can freeze, causing poor images and streaks in the Working Section portal. For this reason,
make sure the air in your laboratory has a normal to low moisture content.
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2.1.8 Wind Tunnel Assembly
If you are to use the Wind Tunnel with the optional Schlieren Apparatus, you must NOTE
assemble the Wind Tunnel so that its bypass valve duct passes through the lower middle
part of the Schlieren Apparatus. Therefore, you must put the Schlieren Apparatus in
position first.
1. Use a suitable lifting machine and assistance to put the Vacuum Pump into
position as shown in the layout of Figure 2.7.
2. Move the main part of the Wind Tunnel into Position. Figure 2.7 shows the main
parts you need to assemble.
3. Put the Schlieren Apparatus its table into position next to the main part of the
Wind Tunnel. Assemble its delicate optical instruments after you install the
Wind Tunnel.
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Figure 2.7 Layout of the Wind Tunnel
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The wind tunnel and Schlieren Apparatus The model
The instrument frame and VDAS system
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2.1.9 Experimental procedures
Two-dimensional Flow Around an Object
Object
Use the optional Schlieren Apparatus to demonstrate the air flow around the models.
Procedures
1. Fit the Mach 1.8 liner to the Working Section.
2. Fit the model into the Working Section, so that the model is held in place between the
two portal windows.
3. Set up the optional Schlieren Apparatus as described in its User Guide.
4. Fully open the bypass valve.
5. Start the vacuum pump and wait for it to reach full speed.
6. Shut the bypass valve.
7. Use VDAS@ to record all pressure readings.
8. Use the Schlieren Apparatus to visualize the flow patterns around the model. Use the
control under the Portal to rotate the model and change the incidence angle. Use the
Schlieren Apparatus to record the images.
9. Fully open the bypass valve and press the stop button.
Note:
Each time you adjust the model angle, open the bypass valve to reduce the
vacuum pressure in the wind tunnel, so you can turn the model angle more easily. Then shut
the bypass valve.
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Figure 2.8 Typical Schlieren Image - Mach 1.8 Liner with a 50
Double Wedge Model.
At low incidence (less than half the total leading-edge-angle) you should see shock waves
from the leading and trailing edges and Prandtl-Meyer expansion from the corners. At higher
incidences expansion appears above the leading edge and below the trailing edges. The
patterns should confirm theoretical predictions quite well, allowing for the boundary layers
around the tunnel and models. These will cause somes light effects, listed here:
a) Shock waves may appear as a narrow 'fan'. This may seem odd to the
student who has learnt that under these conditions a shock wave is very
thin (approximately 0.0025 mm). It is because the shock waves are not
plane. Boundary layers form on the side walls of the tunnel. The Mach
Number decreases near to the boundary layers, so the leading-edge
shock waves are at a greater angle to the flow. The shock wave 'fan' is a
side elevation of a surface that bends upstream, near the tunnel walls.
The downstream edge 'fan' is a relevant part of the shock.
b) When the model incidence angle is half the total leading-edge angle, the
flow passes over the upper front surface without deflection. The leading
edge should only produce a very small disturbance in this flow, showing
a Mach line. In practice, a small "fan" tends to appear, for the reasons
explained in paragraph (a). Also, the flow very close to the leading-edge
is complicated by the growth of the boundary-layer over the upper
surface of the model. If the leading edge is thin (up to 0.05 mm) the
disturbance near the surface is a weak shock wave graph followed by a
region of expansion. If you study your images, you will see this
phenomenon, which tends to cancel out near the surface.
c) Again, due to the boundary layers on the sidewalls of the working
section, the leading edge of a Prandtl-Meyer expansion appears to lie at
too great an angle to the flow.
d) Shock waves from the trailing edge of a model appear more diffuse than
those from the leading edge. This is due to the shocks producing rapid
thickening of the model boundary-layer towards the trailing edge, so that
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the changes in flow direction become less abrupt. At a fairly small
incidence, the boundary-layer separates from the upper surface in front
of the trailing edge, producing quite a complicated shock pattern.
e) It is important to distinguish between genuine phenomena in the flow
such as those mentioned above and spurious optical effects. For example,
if the orientation of the Schlieren apparatus is such that a Prandtl-Meyer
expansion appears lighter than the background, a small dark region may
appear near the corner from which the expansion starts. This is due to
"overloading" of the Schlieren apparatus: the density gradient near the
corner may be so great that the light rays passing through this region are
deflected so far that they miss the final lens altogether.
2.2 Field Testing
In this section we will see field testing techniques used to measure the Sonic boom.
2.2.1. Measuring Sonic Booms
Sonic booms cover a broad variety of frequencies with a total infrasonic component of less
than 1 Hz and a fast pressure of more than 10 kHz. They also give a broad variety of
dynamics of more than 200 Pa (140 dB SPL) and a low pressure-ss than 0.1 Pa (74 dB SPL).
Initial and final abrupt pressure increases cause impulse noise.
Figure 2.9 Acoustic content of a sonic boom
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Figure 2.10 Sonic boom signature
2.2.2. Measurement Systems
The goals are to check the measuring scheme and identify suitable transducers and
installations during five flyovers and three flight conditions. Indoor and outdoor sonic booms
were evaluated along with vibration along gates and walls in a site construction. Measures
were also produced from a 1000 m suspended weather balloon.
Figure 2.11 Test site measurement.
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A. Indoor measurement system
To satisfy their demands, the Japan Aerospace Exploration Agency (JAXA) chose a NI PXI
system with a range of modules. Due to its elevated resolution and wide dynamic range, low
cut-off frequency (0.5 Hz for AC coupling), and software-configurable AC / DC coupling and
embedded piezoelectric (IEPE) conditioning, the NI PXI-4472B dynamic signal acquisition
(DSA) module was used to obtain vibro-acoustic information from microphones and
accelerometers. Synchronization via GPS was given by the NI PXI-6682 timing and
synchronization module. An NI 8353 controller offers high-speed information streaming via a
RAID 0 as well as the high capability required for up to one hour recording of 16 channels.
Figure 2.12 Instruments system used for indoor measurements
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Figure 2.13 Instrumentation graphical user interface of outdoor recorded Sonic boom
The aircraft flew at a peak altitude of 14 km (about 46,000 ft) and at least 6 km (about
20,000ft) for the trials. The sonic boom's overpressure heard inside the test building was about
a quarter of what was heard outside. Recent study demonstrates that due to the rattling noise
and building vibration, the sonic boom of the present aircraft heard inside a building can
cause important annoyance.
Figure 2.14 Indoor measurements
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The sonic boom will also be heard indoors with overland supersonic flight. Inside a
construction, the noise of a sonic boom should be smaller than outside. Looking at the
outcomes of JAXA's 2009 sonic boom measurement experiment, the acoustic pressure
indoors compared to outdoors is considerably decreased. Also, as seen in the outdoor N-wave,
the waveform observed indoors does not have a fast rise in acoustic pressure and has a smooth
slope. Secondary noises, such as window rattling owing to the abrupt rise in acoustic pressure
and low frequency element of sonic booms, influence human noise perception. Indoors may
be bigger the psychological impacts induced by a sonic boom.
It is thought that it is essential to explore how to also evaluate these indoor impacts as metrics
to be used in global norms for sonic boom noise. JAXA has created a sonic boom simulator
and uses its measurement system to perform evaluation tests on test topics using file
recording.
B. Outdoor measurement system
In order to avoid the influence of the turbulence near the ground, a blimp or weather balloon
equipped with infrasonic microphones was held at an altitude of 1 km and some other
infrasonic microphones are also installed at several points between the blimp and the ground
to measure the effect of the turbulence on the sonic boom signature.
Using the tethered blimp to prevent the impacts of atmospheric turbulence, a lightweight
model was used for aerial readings distributed to 1,000 m. This system is based on stand-
alone, wireless LAN-controlled aloft computers with a 4-channel dynamic signal acquisition
module NI-9234 for high-precision audio frequency readings.
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Figure 2.15 Outdoor measurement systems
C. Infrasonic microphones
Modern measurement microphones have vent holes to equalize changes in atmospheric
pressure. This functions as a filter with a high pass that cuts below 3-5 Hz. A condenser
microphone's reduced limiting frequency is acoustically regulated by the microphone's inner
volume and air equalization vent, which guarantees that tiny atmospheric differences are
equalized while rapid differences in sound pressure are not equalized as we want to assess
them. A good measuring microphone should equalize to cut off unwanted pressure
fluctuations that surround us in many respects as quickly as possible.
Wind turbulence-door slam-movement of the ground etc. For many high-quality measuring
microphones, the normal cut-off is 3-5 Hz. It should be 0.1-0.5 Hz for infrasound.
Pre-polarized microphones deliver important benefits over polarized price, weight and energy
usage, making them helpful as used here for mobile field measurements. A microphone
system's low-frequency reaction is provided by the preamplifier's electrical cut-off and the
microphone capsule's acoustic cut-off.
These newer microphones have stiffer diaphragms that decrease the mechanical cut-off A-
field Microphone System, Infrasound Type 40AZ-S1 is provided with a unique adaptor that
reduces the preamplifier's reduced cut-off frequency and has been used in these trials. It also
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has the thermal noise that increases. The elevated input-frequency 3-dB limit f L= 0.2 Hz for
the GRAS Type 40AZ microphone capsule capability (20 pF).
Figure 2.16 Infrasonic microphone used
D. Drop Test Measurements
The D-SEND project consists of drop trials for D-SEND #1 and D-SEND #2. Two distinct
axisymmetric bodies were placed in the D-SEND #1 drop experiment and the sound booms
were analyzed and compared. An experimental supersonic aircraft model (unmanned aircraft
with no engine and low sonic boom design technology will be dropped and the sonic boom
will be measured in the D-SEND #2 drop test. This is planned for the summer of 2013. The
sonic booms will be measured and recorded by the microphone system which is linked to a
line between the ground and the blimp (altitude=1 km).
Two sample bodies were dropped from an altitude of 30 km at a 20-second interval in D-
SEND #1. The test bodies were the NWM (N-Wave Model) generating a N wave's pressure
signature, and the LBM (Low-Boom Model) generating a low boom wave's pressure
signature.
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Figure 2.17 drop test Diagram
Both men trace nearly the same history of Mach numbers and produce forward and
perpendicular sonic booms to the angle of the Mach cone. The sound booms are evaluated 1
km from the floor by a boom measuring scheme (BMS). The telemetry scheme transmits
information such as velocity (speed) and position information of the drop test designs to the
floor.
Figure 2.18 N-WAVE and Low-Boom models being prepared for drop
Through this experiment, JAXA proved its axisymmetric design concept technology with low
sonic boom that halved the sonic boom.
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Figure 2.19 constracting Sonic Boom signatures recorded with NWM and LBM test bodies
The information from the experiment is useful as a reference for validating the technique of
assessment of sonic boom propagation and is anticipated to contribute in the future to low-
sonic boom research. JAXA has also developed a fresh technique for showing the notion of
low sonic boom design in the form of a balloon drop test for the first time.
For D-SEND #2, using J-boom design technology, an experimental supersonic airplane
(S3CM: S-cube Concept Model) will be used. On the front and bottom of the fuselage, the
aircraft has a shaped boom mark.
Figure 2.20 Experimental Supersonic airplane model to be used in D-SEND #2
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The aircraft will be dropped from a 30 km altitude and gliding at Mach 1.3 over one of four
boom measuring devices and a 50° flight path angle. The formed boom signature produced by
the aircraft is projected vertically towards the sonic boom scheme at this angle of flight path.
The objective is to set values for low-sonic boom design technology and to develop the so far
advanced low-boom wave procurement technology.
Figure 2.21 Diagram of D-SEND #2 test planned for 2013
JAXA experiments in Sweden have validated that the measuring system can measure sonic
booms and work well with a variety of microphones optimized for measuring infrasound. In
order to decrease the impacts of atmospheric turbulence, the ground-based measuring scheme
was extended to include an aerial measuring system distributed at altitudes up to 1,000 m. In
the next scheduled drop test, JAXA hopes to speed up the growth of civil supersonic aircraft
by showing low-boom design technology.
3. Whitham Theory (Analytical)
Known people attempted to create theories after the origin of sonic boom to predict the
propagation of the sonic boom through the atmosphere and to minimize the power of the
sonic boom. The Whitham's theory is the most relevant theory that is still used today from
theoretical components to wind tunnel experiments and CFD methods. According to this
theory, the wavefront from the aircraft to the ground can be divided into three regions; near-
field, midfield and far-field flow, see the Figure below, the Figure is a schematic of the
coalescence of near-field shock waves, leading to a so-called far-field N-wave. From this
figure it is possible to draw some significant points of attention:
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A pressure disruption in the footprint characterizes the sonic boom described by the
Whitham's theory, which has an original rapid pressure increase and a second instantaneous
increase back to the local pressure. There is also a linear reduction in pressure to below local
pressure between these two abrupt pressures. The observer on the floor actually perceives the
bow shock and the tail shock as the effects of the two abrupt jumps of stress described above.
It is now apparent that the amplitude and duration of this N-wave shape sonic boom is linked
to the airplane's geometry. The loudness of the booms to be heard can be determined by the
pressure disturbance rate as well as by the pressure disturbance rate. In addition, when the
time between these two shocks is very short, only one boom will be heard by the ground
observer. As stated above, the following figure basically demonstrates three distinct wave
fronts and the respective signatures at three distances away from the aircraft. There are
usually two waves for an axisymmetric body as a well-known airfoil, the bow shock
connected to the nose and the tail shock connected to the tail. However, as we understand that
an aircraft is not a smooth and axisymmetric body, what happens in the near-field is that the
shock wave pattern includes many shock waves, corresponding to the different compressions
induced by the aircraft's geometry.
However, the shock wave patterns will develop away from the aircraft due to nonlinear effects
such as atmospheric turbulence and gradients of air temperature. The shock wave patterns
combine in the far-field and essentially form two primary waves, the shock wave of the bow
and tail. Whitham created this operation to determine the shock formation and calculate the
associated distortion and is known as the theory of sonic boom by the Whitham. From earlier
research,
Figure 2.22 Pressure signature diagram
It can be concluded that there are many variables affecting the power of the sonic boom,
namely airplane weight, size and shape, as well as altitude, attitude and flight route and
climate or atmospheric conditions. A heavier aircraft causes a greater sonic boom than a light
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aircraft due to the former displacing more air and creating more lift. One of the most efficient
strategies to reducing the intensity of the sonic boom is altitude, as it determines the distance
the sonic boom travels before it reaches the floor.
Wind, airplane velocity and direction, air temperature and pressure influence the direction and
strength of shock waves. The point has been reached in all these classical studies on the sonic
boom that any enhancement in the parameters that regulate the effectiveness of the output of
the aircraft will result in a decrease in the weight of the aircraft. As a result, this weight
decrease results in a decrease of the sonic boom. In the (proportion) not just weight but also
improvements weight thrust, drag lift (ratio), structural effectiveness and specific fuel
consumption lead to minimization of sonic boom. Going to this topic is beyond the scope of
this thesis, minimizing the sonic boom and achieving better aerodynamic efficiency.
A brief summary of the theoretical part of the theory of Whitham will be given in the
following and its implementation and limitations will be discussed in addition. The theory of
Whitham is selected to be explained in this thesis because it is an analytical predictive
technique on which almost all of today's continuing research is based. Furthermore, the theory
of the Whitham can be used to explore the trait of sonic boom induced by a straightforward
2D body with a certain thickness.
3.1. 2D shape method (2D Diamond wedge)
The first step to apply the theory of Whitham to the optimum contours (diamond wedge) is to
discover the respective feature of Whitham's F-function. This feature actually reflects the
body's flow disruption. In other words, the geometry of the contour is the primary
consideration for the Whitham F-function magnitude. The potentially troubled speeds are
provided as follows:
(2.1)
According to the Whitham theory, the variable can determine any distinctive curve that
originates from the body surface. This variable is a function of x and y perpendicular to the
boundary wall y= y(x) respectively. In 2D continuous supersonic flows, F(j) is equivalent to
the border curve at the stage where the characteristic line crosses it, i.e. F(j)=y'(X). The
distance to this characteristic line X(a) from the tip of the nose can be determined by X-
βy(X)=al. Figure 2.23 is a sketch of the distinctive line that emanates from the body at point b
and passes through point p in the field of flow.
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Figure 2.23 Sketch of a characteristic line, Whitham’s theory
Knowing the Whitham’s F-function enables us to approximate the pressure jump or pressure
signature for the occurred shock wave as follows:
(2.2)
Figure 2.23 represents the Whitham’s F-function with the corresponding overpressure for a
first variant contour with a volume of approximately V≈ 0.0571 at M0= 2.0. The top plot
demonstrates that the F -function resulting from the inclination of the surface reduces from
the nose to the level of the shoulder. The lower plot 2.23 represents the values for the near-
field overpressure
∆
by considering a distance of r=1.0 away from the x-axis. From lower
plot 2.23 that the first value for
∆
indicates in fact the leading shock power for this body at
M0= 2.0. From this, by using the Whitham theory for distinct contours, we can now acquire
the leading shock power.
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Figure 2.24 Upper plot: F-function, Lower plot: Pressure Jump

3.2. Limitations of Whitham’s Theory
Complete application of conventional sonic boom theory is very complicated, so a computer
program evaluation is preferred. Up to now, a few computer programs have been created to
implement the theory of Whitham. All of these programs treat the F-function as an input and
execute the calculation of ray tracing and signature aging. The input of the F-function can be
obtained from a distinct linear flow calculation acquired from wind tunnel or computing
systems. Between the years 1969 and 1972, two computer programs were created from which
both of them are currently being used or at least they have become the main component of all
other programs up to our moment.
The first program was Hayes ' ARAP model that regarded all the information from the
conventional theory in a horizontal, non-uniform and windy environment for a particular
maneuvering aircraft. Thomas created the second program in a manner that could be input
straight from wind tunnel experiments. Noting that each of these programs has its own
capacities and constraints is of great significance.
More recently, as an option to wind tunnel testing, CFD techniques have become considered.
These CFD schemes were needed to calculate the near-field F-function. But getting a full
near-field signature from CFD needs a very big spatial grid that was used for aerodynamic
design reasons as never before. Men expect to be able to calculate the entire flow field of any
aircraft even to very big distances with the rise in computing energy in the future. While the
theory of the Whitham is the most applicable 3D flow theory, it can not yet be used to find an
precise relationship between the aircraft's geometry and the near-field signature. That's
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because the near-field pressure disturbances are heavily non-linear that the theory neglects.
Scientists have lately created higher-order alternatives of the governing differential equations
by maintaining higher-order terms in the equations in order to take these non-linear effects
into account. But these techniques are not yet used sufficiently advanced to allow practical
issues to be predicted using such techniques. And also, because their results are based on
improved linearized theory, these greater order approximation methods like the Whitham's
theory can not be used at higher Mach numbers.
There are also phenomena such as hypersonic flight speeds, concentrated booms, shock wave
rise times, and atmospheric turbulence impacts beyond the Whitham theory's capabilities.
The theory of the Whitham neglects the non-linear effects in the near-field as they decrease
quickly moving away from the aircraft, allowing the linear flow area rule theory to be
implemented in the far-field. The forecast of the Whitham has been validated at mild
supersonic Mach numbers for slim bodies. It implies that the flow field must be analyzed in
one way or another for the hypersonic speed car.
When an aircraft accelerates, turns, or other maneuvers, it appears that the focus of the shock
waves leads to the amplification of the intensity of the sonic boom. The observed
overpressure on the floor is about 2-5 times greater than those in a typical N-wave when
boom concentrating happens. This phenomenon allows the region of the ray tube to disappear
at certain points so that the ray tracing technique used by the Whitham theory can no longer
be used.
Furthermore, the theory of the Whitham does not take into consideration the structure of the
shock waves and therefore utilizes the concept of soft shock that actually means thin waves.
However, recent flight experiments indicate that shocks from the sonic boom are significantly
thicker than anticipated.
Some issues stay open about turbulence propagation in the reduced air, ab-sorption and
dispersion owing to the impacts of non-equilibrium and viscosity. The impacts of atmospheric
turbulence are also beyond the ability of the Whitham theory to trace rays because the
Whitham theory neglects the existence of turbulence in the atmosphere.
4. BASS Theory (Analytical)
First, a summary will be provided in this section for the BASS principle, which is a measure
of the asymptotic shock intensity of an item in a supersonic flow field with a very tiny
density. Subsequently, the geometry of a 2D diamond wedge body will be implemented with
a certain thickness for which this report will determine the asymptotic shock power.
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The characteristic lines indicate a convergent trend in a compression flow domain, according
to the characteristic theory of features. And a shock wave will be created when the features
tend to cross each other.
(2.3)
This equation represents the slope of a shock wave as the average of the slopes of the
characteristic lines υ0 and υ1 merging into the shock. The practical problem with this
equation is when the orientation is rotated the characteristic slopes will be changed w.r.t each
other. So, in order to analyze the asymptotic shock strength later on in this report a rotational
invariant jump equation is required as follows:
(2.4)
This equation demonstrates that the shock route angle is equal to the character angle bisector
before and after the shock. Using the relationships of trigonometry, this equation can be
written as follows:
(2.5)
The power of such a shock wave can be determined by the following expression once the
shock route can be modeled by the invariant jump equation (2.4).
(2.6)
As stated, the distinctive angles behind and before the shock wave, respectively, are range 1
and range 0. Throughout this dissertation this expression will be used to evaluate the shock's
asymptotic power.
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An object moving at a supersonic speed leads both the shock wave and the expansion waves
to occur. The waves of expansion communicate with the wave of shock as they migrate into
space. The shock force will be reduced as a result of this interaction and eventually becomes
zero when the range gets to infinity. An expression extracted from P.G describes a metric for
the decline of shock intensity to zero when the range gets to infinity. Bakker and BASS is
referred to. BASS stands for the asymptotic shock resistance of the Bakker and represents the
shock resistance asymptotic decline conduct of a body with infinitesimally small density.
Below is a brief description of the BASS theory:
In order to attain the BASS measure, the features must be projected onto the x-axis and this is
only feasible if we are aware of the distribution along the x-axis. According to the simple
wave theory all curved Γ − characteristics originate from the undisturbed flow field and
therefore the invariant of the isentropic flow V0
− remains constant everywhere in the flow
domain. The Γ + characteristics are straight lines and have a slope of υ = tan θ = tan (μ + φ).
The profile and the value υ for this point is the following:
(2.7)
Where ζ is the x-coordinate of point Q(x, y) which itself is the intersection point of the Γ+
characteristic with the object surface. This equation indicates in fact the gradient of the line PQ
which equals to υP . The task is now to express ζ as function of x and y. According to the simple wave
theory we know already νP = νQ and νQ + φQ = V0
−
. This gives us νQ as follows:
(2.8)
In this equation f−(ζ) is the gradient of the object in point Q which also indicates the flow
direction. We can express υ as follows:
(2.9)
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Figure 2.25 An object in a supersonic flow field
Using this equation and knowing the slope of characteristic Mach lines along the
x-axis tan (μ) =

we can express the flow direction as follows:
(2.10)
This equation shows the flow direction φ as a function of υ along the x-axis with the known
Prandtl-Glauert factor β which can be defined as follows:
(2.11)
With knowing the following expression for Prandtl-Meyer angle;
(2.12)
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It is impossible to express υ in terms of x so we do other way around namely x=x(υ). This
means we can express x coordinates as a function of the local flow direction x=x(tanϕ). So,
equation 2.10 becomes:
(2.13)
This equation is called F(υ) function which indicates the x-coordinates in terms of υ along the
surface. The x-coordinate of point Q can be defined with ζ= F(υQ) which gives υQ = F−1
(ζ). So,
there are now two expressions for υ(x,y) at point Q as follows:
(2.14)
υ(x, y) = F−1
(ζ) (2.15)
From these two equations we are able to write ζas a function of x and y, ζ= ζ(x, y). This result
together with equations (2.14) and (2.15) enable us to describe the location of υ(x ,y) along the
surface. For the analytical simplicity, the υ-distribution will be projected into the x-axis which
means the characteristic lines will continue until they intersect the x-axis. This means that y-
coordinate of point Q becomes zero for which the corresponding υ becomes:
( , ) = = ( ) (2.16)
From this we know that which results in . And this gives us the
corresponding y-coordinates of the characteristic lines as follows:
y = υ (x, y) [x – F (υ (x, y))] (2.17)
Once the υ-distribution is known along the surface, the next step to make the BASS theory
complete is to define an expression for the shock path. The jump equation will be as follows:
(2.18)
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It should be noted that υin this equation indicates υ1. And the differential equation
represents the υ-distribution along the shock wave. Integration of with the known
boundary conditions at the leading x=F(υl) =0 results in desired coordinates for the shock path
as follows:
(2.19)
(2.20)
The parameter x given in expression (2.19) represents the shock path location which can be
determined by integration of the characteristics along the shock wave. As it was earlier
explained, the asymptotic shock strength can be defined as a measure that the shock strength
decays to zero when the shock wave goes to infinity. This definition is obviously to observe
from equation (2.19) which shows when θ→ θo, the shock wave goes to an infinite distance
from the object, Υ(θ) → ∞.
Earlier it was mentioned the asymptotic shock strength can be determined by equation (2.15).
And we know that substitution of equation (2.19) in (2.20) gives us the behavior of the shock
strength when y → ∞. So, in order to calculate the asymptotic shock strength, we must express
Σ(y) explicitly. For this reason, firstly Υ(θ) must be developed in terms of (tanθ− tanθ0) by
using Taylor series expansions. Putting the new Υ(θ) into equation (2.20) gives us a new
definition of the vertical path of the shock as follows:
(2.21)
This result gives us the following expression for Σ.
+ Higher Order Terms (2.22)
As it can be observed, the asymptotic shock strength will decay to zero with the factor kl,
where the simplified form of the dominant coefficient l˜
0 is the following:
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(2.23)
The influence of higher order terms is very small; therefore, it is decided to neglect the effect
of these higher order terms in the asymptotic shock strength Σ. It means the dominant term for
the asymptotic shock strength when y → ∞ becomes:
(2.24)
The term is constant and does not depend on body geometry. As it only gives the
Mach number of the undisturbed flow, it is considered as the Mfactor. We already know the
characteristic angle of the undisturbed flow θ0 is the sum of the undisturbed Mach angle and
undisturbed flow angle θ0=µ0+ϕ0. So, this help us to express Mfactor only in free flow Mach
number as follows:
(2.25)
Thus, Al can be addressed as the only measure for the asymptotic shock strength of the
leading-edge shock which depends on the shock wave-expansion interaction:
(2.26)
This integral shows the asymptotic shock power for an item in a constant and invisible
supersonic flow, according to the BASS theory. Al is an integration of the cosθ distribution
along the body surface in a domain which is defined from 0 at the nose to x0 at the shoulder
point of the body where the θ0 characteristic intersects. At the shoulder point a Prandtl-Meyer
expansion wave will occur where the flow expands to the free flow condition. And x0 is in fact
the x-coordinate of the intersection of the Γ0-characteristic through the shoulder point for
which the slope is zero with the x-axis. So, in this way the x-coordinates which are involved in
this integral are actually the x-locations of the projected characteristic lines onto the x-axis.
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We have:
(2.27)
And with the trigonometric identity:
(2.28)
We can write this:
(2.29)
In the final and we after we did some calculations this results in:
(2.30)
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With =
5. CFD (ANSYS Fluent)
Fluent software includes the wide, physical modeling capacities required for industrial apps to
model flow, turbulence, heat transfer and responses. These vary from air flow through an
aircraft wing to furnace combustion, from bubble columns to oil platforms, from blood flow
to production of semiconductors, and from clean room design to wastewater treatment plants.
Fluent covers a wide variety, including unique designs, capable of modeling combustion in-
cylinder, aero-acoustics, turbo machinery, and multi-phase systems.
Fluent also provides extremely scalable, high-performance computing (HPC) to assist rapidly
and cost-effectively solve complicated, large-model CFD simulations. By scaling to 172,000
cores, Fluent set a world record for supercomputing.
The setup of any Fluent study is divided to 5 steps:
1. Geometry: Input of the geometry that you would like to study, and setting the
computational domain
2. Meshing: Setting up a dynamic mesh is needed for any coupled analysis where a
system receives displacements
3. Configuration: Setting up boundary conditions and restrictions
4. Solution: Mainly this part of the analysis is reserved to plotting the variables, such
as the pressure distribution along a surface or the body.
5. Results: Visual representation of the flow and variable variation, for example
pressure.
Figure 2.26 Fluent CFD
For comparison, this work will be conducted on 2D and 3D with different solver models such
as Inviscid and laminar. Once all done, we will apply an angle of attack of 5 degrees which is
the lifting case and redo the entire study in the different solver models.
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CHAPTER 3 : SONIC BOOM RESULTS
1. Introduction
In this chapter we will see all the results found by the three approaches of analysis:
theoretical, computational and experimental. And a comparison between them.
2. Experimental Results (Wind Tunnel)
After conducting the experiment, we were finally able to get schlieren photos and take
pressure measurements, the following is the pressure plot for 0° of attack:
And the schlieren photo is as follows:
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The shock wave shows clearly, these results will be later on compared with the fluent and
theory
3. Computational Results
3.1. No Lifting case for diamond shape airfoil (0° angle of attack)
The model that will be used as discussed before is the 10° double wedge diamond airfoil, this
model is perfect for preliminary studies for sonic boom production and reduction. the model
is shown in Chapter 2
There are many models in the CFD that can be used and compute the lift and pressure
distribution along the body (the 10° double wedge airfoil in our case). In this research we will
only use three models which are: INVISCID, LAMINAR and TURBULENT, and then
compare them to get a good idea on which model is best fit for our research. first of all, let's
start by modeling the flow only in 2D. once the three models are compared, we will then redo
the computation all over again, but this time in 3D.
After finishing the 3D modeling and computations, we will then proceed to comparing the 3D
results to the 2D. And choose which case gives the more accurate results.
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2D MODELING AND COMPUTATION:
As discussed before the fluent study will be conducted in three cases: INVISCID, LAMINAR
and TURBULENT. Let us start with the first case, which is INVISCID.
a. INVISCID FLUENT COMPUTATION
First of all, we need to select an analysis system for CFD: it will be "FLUENT" in our case as
shown below:
Figure 3.1 Fluent CFD
a1. Geometry:
To get matching results with the wind tunnel, we will take a rectangular computational
domain that put the airfoil model in the middle section. the dimensions will be
(200mm;100mm) in (x;y) coordinates. In 2D we can cut roots by only plotting half plane, and
later use symmetry giving the fact that our body (double wedge is a symmetrical airfoil) as
shown in the figure below:
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Figure 3.2 Computational domain
As a first step in FLUENT, we have to draw the geometry and the computational domain. In
2D CFD, it is as easy as drawing a few lines, setting angles and distances and finally generate
A surface from all of it combined as shown below:
Figure 3.3 Geometry layout
Figure 3.4 Body before symmetry
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Next, we need to cut the computational domain into parts, four in our case. So that the
program will be made aware each time there is a change in surface. In our case the domain
splitting will be made at the level of the start of the double wedge as shown below:
Figure 3.5 Face split
As we can see the domain is split into four parts and we are all done for the geometry part.
a2. Meshing:
First up, we need to name the borders of the computational domain, so that we can input
boundary conditions in the setup part that will be discussed later. we have three named
selections:
 Fairfield: is a simulation of the ground, where we will take pressure measurements.
 Symmetry: the two lines coming out from the edges parallel to x axis, will be used to
create a symmetry and get a view for the entire computational domain
 Wall: which is the upper part of our diamond airfoil.
As shown below these are the named selections:
Figure 3.6 Farfield after named selection
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Figure 3.7 Symmetry
Figure 3.8 Symmetry
Next up, is the meshing configuration. To start with we will assign a face meshing to each
computational domain
Figure 3.9 Face meshing
And afterwards we will assign an edge sizing to each line that split the domains and also the
lines that define the wall as shown below and increase the mesh accuracy for the boundary
layer:
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Figure 3.10 Sizing
Once all that is done and checked we will configure the mesh setup by setting function of
meshing into "proximity and curvature”, relevance center into "fin", setting the maximum
face size and max size and, smoothing to high and then finally generating a grid.
The grid generated had a max element of "17200" elements and quality ratio of "0.60409"
which good considering the fact that the quality ratio should be below "0.98"As a result of
this work we got an accurate grid as shown below:
Figure 3.11 Grid/Meshing
a3. Setup:
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Figure 3.12 Setup Configuration
Next up is the setup part, where we will input boundary conditions and select solver model
and general settings. These settings and conditions should match the wind tunnel setting,
giving the fact that we will compare the results later on.
As a general setting we are going to set the solver setting into "density based" and time as
"steady”. going into models we are going to set the energy equations into "on" and the
calculation model into inviscid. Next is setting the air into ideal gas. in the boundary
condition setting: the farfield will be set as a "pressure Farfield and the mach number set to
"1.8 mach" to match the wind tunnel speed. the inlet pressure P∞ will be set to "0.23bar"
again, as a matching to the wind tunnel conditions. Next the named selection "symmetry
"should be set as a symmetry .and the double wedge as "wall".
As a reference value, we going to ask the program to start computing from the farfield and
select it as a reference domain.
As a solution model we going to make it all into second order solving, because it is alot more
accurate than first order.
In the monitors part we are going to set the residuals into something very low, at least ten to
the power mince five.
Before starting the calculations, we have to do standard initialization also from the Farfield
settings.
Next up is the calculations part. But before doing so we hit the check case , to see if we have
any problems with the grid or any recommendation from the software, if not we proceed into
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the calculations, and start the iterations .Once the program has finished the calculation we
move on into the next step which is the solution.
In this part we will mainly take the pressure distribution along the airfoil and on the ground to
compare it later with the other results.
As predicted the pressure distribution on the ground gave us an N-wave shape as shown
below
Figure 3.13 Pressure plot on the Farfield
And the distribution along the airfoil:
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Figure 3.14 Pressure plot along the body
These results will be later compared with the other results obtained from other models in 2D
and finally compared with 3D results to decide which gives the best computation and
analysis.
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a4. Results plot:
Figure 3.15 Pressure Contour
As excepted the results are symmetrical and the shockwave shown clearly along with
expansion and after shock, once the flow passes the airfoil it returns to its normal value which
is the input value.
b. LAMINAR AND TURBULENT:
The same procedure will be followed in our next computation except one slight detail.
inputting the solver model as Laminar and redoing the calculations all over again. Once all
done, we will save the results and again redo the calculations but only this time we will use
the turbulent model which is "k-epsilon-realizable" and save the results. After plotting and
comparing the results we had matching plot as shown below:
As a small reminder, the input pressure is "0.23bar" matching the wind tunnel settings-
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Figure 3.16 Comparison between Inviscid, laminar and turbulent
From this comparison, we can conclude that in 2D computations, it does not make any
difference whether we choose INVISCID or LAMINAR or TURBULENT.
There for from now on, if we are to do any computation in 2D, we will input INVISCID as a
solver model.
CATIA conception of the double wedge airfoil:
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Figure 3.17 Catia layouts
1. COMPUTATION USING INVISCID SOLVER:
a1. Geometry:
Same as 2D, in 3D we will use the fluent to do our calculations and conception. After
building the double wedge in CATIA, we import it as ".stp” file into geometry and generate
the file inside "Design modeler". In the non-lifting case the angle of attack is set to zero,
therefore we don't need to input rotation .Next step is Enclosure ,which is the computational
domain ,the dimensions of this domain are (100mm;25mm;50mm) in the (x;y;z) coordinates
.the figure of the enclosure is shown below:
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Figure 3.18 Computation domain for the 3D analysis
Next up we need to create a Boolean to subtract the body from the enclosure, this is a very
important step that will help us produce a more accurate meshing and accurate simulation of
fluid flow over the body (double wedge airfoil).
a2. Meshing:
Basically, the meshing process is a lot like similar to the 2D, except in 3D there is no domain
splitting. We begin with by creating named selection, four to be exact:
 INLET: The flow inlet, the setting will be configured in the setup part.
 OUTLET: a pressure outlet that defines the exit of airflow.
 SURROUNDING: The side and above surroundings of the airfoil.
 FARFIELD: the part that represents the ground in our case.
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Figure 3.19 Named selections
Figure 3.20 Surroundings
After defining the named selections, we move on to setting up the meshing. To begin with, we
set function of meshing into "proximity and curvature”, relevance center into "fin", setting the
maximum face size and max size and, smoothing to high and then finally generating a grid.
The grid generated had a max element of "265000" elements and quality ratio of "0.7856"
which good considering the fact that the quality ratio should be below "0.98".
The generated mesh look like the following:
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Figure 3.21 Grid generated
This sums up the meshing process.
a3. Setup:
Figure 3.22 Setup configuration
To begin with we select the type of our process as a density-based analysis and time as steady.
Next up the energy equation set "on" and solver model as "INVISCID”. Next is the boundary
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conditions, just like the 2D, we need to give similar boundary conditions for us to be able to
compare results afterwards. As a reminder, the inlet pressure is "0.23" bar and a speed of
Mach 1.8.
The Farfield and the surroundings, in our case will be selected as "wall", and the outlet as
"pressure outlet". Then we will ask the software to take the inlet as a "reference value". Next
up is the solution methods, we select second order instead of first order, giving that second
order will give more accurate results. Select the residuals to something less than ten to the
power mince five and as a final step before is initialization, we choose to initialize from the
inlet. Finally, we enter the number of iterations as 1000 and ask the software to compute.
This sums up the setup part.
a4. Solution:
In this part we ask the program to plot the pressure signature on the ground, which is the
Farfield in our case showed in the figure below:
Figure 3.23 Pressure plot on the farfield
As excepted, the N-wave shows on the ground and leaves a pretty significant signature on the
ground, later on it will be compared with other results (laminar and turbulent).
Next, we ask the program to plot the pressure distribution over the body (double wedge
airfoil) and we get the following
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Figure 3.24 Pressure plot along the body
This figure will be later on compared with the turbulent, and laminar results from 3D.
a5. Results:
Next up, we insert an isosurface, that can move along the y axis, and set variable as "pressure"
we get the following results:
Figure 3.25 pressure contour
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As excepted the results are symmetrical and the shockwave shown clearly along with
expansion and after shock, once the flow passes the airfoil it returns to its normal value which
is the input value "0.23bar".
2. COMPUTATION USING LAMINAR SOLVER:
We start all over again and redo the entire steps done in INVISCID, except this time we will
use a laminar solvent. this time viscosity will be taken into consideration and many other
factors.
We input the settings just like before but with slight differences, like considering the viscosity
and density in this case. we proceed into initialization of the software from the inlet and we
start the computation.
After finish the calculations we get the following pressure signature on the ground:
Figure 3.26 pressure plot on the Farfield
We can notice the pressure fluctuating frequently, and this due the disturbance in the flow and
the consideration of viscosity different than zero. this figure will be later on compared to the
TURBULENT and INVISCID results.
Next up we plot the pressure distribution along the body (double wedge airfoil):
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Figure 3.27 Pressure plot along the body
Same as the plot on the Farfield, we notice the fluctuation due to disturbance in the airflow
above the body.
Next up, in the figure below we plot the pressure contour and get an idea on the shape of
shock wave:
Figure 3.28 Pressure contour
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The shockwave and the expansion wave are clearly shown, but we do notice a slight
disturbance on the wall, and this is due to boundary layer generated on wall. this is normal
considering the fact that viscosity is different than zero. also, we notice a parallel lines
coming up from the wall, these lines are called characteristic lines also known as Mach lines,
these lines will be explained in the optimization part (final part of the thesis).
3. COMPUTATION USING TURBULENT SOLVER:
As we understand, the distinction between laminar and turbulent is that the fluid follows a
smooth route in laminar, routes that never interfere with each other, rather in chaotic uneven
flow defined by small areas of whirlpool. This fluid's velocity is certainly not continuous at all
points.
Same as before, we will do the input the geometry and do the meshing, and proceed to the
setup. The only difference is, we are going to use a different solver model which is "spalart-
allmaras”. we will input the wind tunnel settings as before and start the calculations.
Once the calculations are over, we proceed into plotting the pressure distribution on the
ground and we get the following:
Figure 3.29 Pressure plot on the Farfield
The pressure is allot less fluctuating than the laminar, the result will be later compared to the
remaining figures.
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Next up the plot over the body:
Figure 3.30 Pressure plot along the body
As a final result we are going to plot the pressure contour around the airfoil:
Figure 3.31 Pressure contour
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The pressure plot is similar the results obtained before, the shockwave and the expansion
clearly shown
4. COMPARISON BETWEEN INVISCID, LAMINAR AND TURBULENT:
Next up we need to compare the results of the three models used in 3D computation.
Let us start by comparing the pressure signature on the ground:
Figure 3.32 Comparison between Laminar, turbulent and inviscid results
We can notice that both the LAMINAR and TURBULENT models fluctuate allot, whereas
the INVISCID plot is smoother and more accurate.
Let us plot the pressure distribution over the airfoil for each model and compare
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Figure 3.33 Comparison on pressure plots along the body on Turbulent, Laminar and inviscid
Again, we notice the INVISCID model is the smoothest and more accurate model. Therefore,
the most logical and accurate solver model to use is INVISCID. From now on, the 3Dresults
will be given using INVISCID solver model.
5. COMPARISON BETWEEN THE 2D AND 3D:
As a final checkup, we need to choose between the 2D and 3D, let us compare the pressure
plots for both:
Figure 3.34 Comparison between 3D Inviscid and 2D inviscid
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The 3D modeling is known to give more accurate results, giving the fact that it considers all
variables and also consider the thickness of the model, whereas the 2D model is based on only
2 axes.
For the time being we will compare both results and compare them to the wind tunnel results.
Figure 3.35 Comparison between 2D and 3D inviscid and windtunnel results
In 2D the flow is moving in one direction, whereas in 3D the kinetic energy in the flow is
higher (along with the mass flow) this explains why the 3D results are slightly higher than the
2D. We can see that the ind tunnel limited results giving the fact that it only takes
measurements in several points (25 points). Also, from now on the Fluent study will be
conducted in 2D solver models for simplicity reasons, and also giving the fact the windtunnel
is 2D measurement equipment.
3.2. Lifting case for diamond shape airfoil (5° angle of attack)
The second part of this chapter is to study the lifting case, which is applying an angle of
attack to our body, first of all we will start with a 5 degree angle of attack ,after conducting
the wind tunnel experiment we have a general idea on the pressure signature on the ground
and on the body, also we managed to get a clear view of the shock wave and expansion wave.
FLUENT MODELING AND COMPUATION:
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We will use the same model there for we will not need to rebuild the model in CATIA all
over again, all we need to do import the "doublewedge.stp" and apply a rotation, the
remaining steps are the same as the steps taken before in the 3D computation for non-lifting
case. Only this time we will use only the INVISCID solver model, giving the results and
analysis obtained before.
Let us start by setting up the angle of attack
Figure 3.36 Rotation along ZX axis (5 degrees)
The angle of attack is set to 5 degrees with a rotation around the ZX Plane as shown in the
figure above.
Following the same steps as before we get a mesh of roughly 100 thousand elements and
quality of 0,897 which is acceptable considering the fact it should be lower than 0.9.
Figure 3.37 Grid generated
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We can notice the grid is more concentrated around the body, which is a good thing, that will
give is a more accurate reading on the pressure distribution along the body and on the farfield
(the ground).
Next up is the setup, just like before, inputting the settings that match the wind tunnel, we
initiate the calculation and plot the pressure distribution on the ground and get the following
result:
Figure 3.38 Pressure plot on the farfield Lifting case
Next up is plotting the pressure distribution along the body:
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Figure 3.39 Pressure plot along the body (lifting case)
Now, we need to compare these results with the wind tunnel, let us start by comparing the
farfield results:
Figure 3.40 Comparison Fluent vs wind tunnel results (Lifting case)
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The results of the wind tunnel compare to Fluent, the distance between readings in the wind
tunnel between measurement point inside the test section, there is a 25 mm distance between
each point.
The results are correct and match. we can now increase the angle of attack a little bit.
As a final result, we will plot the pressure contour:
Figure 3.41 Pressure contour (lifting case)
From this pressure contour we can see that when applying angle of attack the N-shape wave
tend to disappear.
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4. Analytical Results of Whitham’s theory
Figure 3.42 Pressure signature in the ground along the length of the working section in the wind tunnel
5. Conclusion
5.1. 0° angle of attack
Pressure angle measurement:
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Figure 3.43 Shock wave angle measurement for 0° angle of attack
Figure 3.44 Schlieren photo for 0° angle of attack
We can come to the conclusion that the wind tunnel and fluent results (angle measurement)
tend to match. therefore, the Fluent results are confirmed.
5.1. 5° angle of attack
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Figure 3.45 Theta-beta-mach curve
In theory the angle of attack for 5°, beta should be equal to 38.56444, we will compare them
with the results obtained from the fluent and wind tunnel experiment.
Figure 3.46 Fluent angle measurement at 5° angle of attack
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Figure 3.47 Schlieren Photo at 5° angle of attack
We can come to the conclusion, that the results match!
CHAPTER 4 : MINIMIZATION OF SONIC BOOM
1. Introduction
The idea behind the technique that we will use is adding a spike to the body, this way we can
direct the shock in a different direction or at least minimize it. First of all, we came up with a
Matlab code that predicts the and pressure variation, this way we can come up with a shape
that produces minimum pressure signature and acceptable lift. the Matlab code result is shown
in the following section.
1.1. Diamond Wedge
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Figure 4.1 Lift coefficient versus Pressure signature (flight conditions)
The red line represents the angle of attack, and the blue line represents the Mach number.
Now, for diamond wedge we are able to predicts the and pressure variation for different
input Mach number and angle of attack. this way if we are to modify the shape, we can do the
same analysis and predict the and pressure variation.
Let us plot the following conditions:
 Mach 1.8 and angle of attack 0°
 Mach 1.8 and angle of attack 5°
The following is a plot of the previously mentioned flight conditions:
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Figure 4.2 flight conditions in theory
From the previous figure we got the following results for specified flight (Mach 1.8)
conditions:
Mach 1.8 DPmax
Alpha = 0° 0 1.7
Alpha = 5° 0.24 2.7
Let us now compare these results with the results obtained from CFD Fluent.
Mach 1.8 DPmax
Alpha = 0° -0.0005 1.8
Alpha = 5° 0.214 2.5
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2. Minimization techniques to reduce Sonic Boom
2.1. Sonic boom reduction technique using Matlab Contour for
diamond wedge
2.1.1. Sketch of the Diamond wedge (Lambda and t)
“t” Modification
λ Modification
 Optimized Shape
2.1.2. Lift Coefficient
Flight conditions:
Mach 1.8
5° Angle of attack
P∞= 0.23 bar
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2.1.3. Drag Coefficient
Flight conditions:
Mach 1.8
5° Angle of attack
P∞= 0.23 bar
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2.1.4. Pressure signature and Lift Coefficient
Flight conditions:
Mach 1.8
5° Angle of attack
P∞= 0.23 bar
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2.1.5. The Minimized Pressure Signature
= 0.05
= 0.72
2.2. Scheme of the new optimized shape
Shape corresponding to:
t = 0.05c
λ = 0.72c
= 0.025c
λ = 0.72c
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3. Results of minimization for 2D shape
3.1. Diamond wedge results
3.1.1. Geometry of the new shape
3.1.2. Grid generated
Number of elements: 50 k roughly
Quality ratio: 0.6 < 0.9
Run time: less than 10 minutes
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3.1.3. Results pressure plot on ground
3.2. Minimization technique inspired from F-15b NASA's
modified supersonic aircraft
Introduction to the idea
The following proposed solution is inspired from the modified F-15b supersonic aircraft, this
modification was geometry based, a spike was added at the nose of the aircraft to help reduce
and spread the sonic boom and pressure signature on the ground. the following figure is a
picture of the modified supersonic aircraft.
3.1.4. Pressure contour
P (bar)
15% reduction
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3.2. Quiet spike sonic boom reduction technique
3.2.1. Introduction of the idea
After understanding the sonic boom and the way it spreads, we can illustrate the sonic boom
propagation in the following figure:
Figure 4.3 Sonic boom Illustration
The idea behind the technique that we will use is adding a spike to the body, this way we can
direct the shock in a different direction or at least minimize it. First of all, we came up with a
Matlab code that predicts the and pressure variation, this way we can come up with a shape
that produces minimum pressure signature and acceptable lift. the Matlab code result is shown
in the following section.
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Figure 4.4 F-15b Spike
As you can see, the spike added is divided into several parts. We will apply the same analysis
to our diamond wedge. the following is an illustration of the modifications we will add to the
airfoil.
Adaptation of the idea to our problem
Figure 4.5 Modified diamond double-wedge airfoil
Our added spike consists of two parts, with a main objective: reduce the sonic boom impact
on the ground. Let us plot this geometry in ANSYS and follow the same steps as in the
chapters before. Note that the analysis will be conducted in 2D for simplicity reasons.
a1. Setup:
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As done before we will only plot half of the wing in the geometry and use symmetry later,
due to the fact that our body is symmetrical. Moving on to the meshing we generate a precise
grid by following the same steps as in the chapters before. The generated mesh had a number
of elements of 50 thousand elements with a quality element of 0.85 which is less than 0.9 an
acceptable rate. The grid generated is as follows:
Next up is the setup part, we will use the same flight conditions as used before, A mach 1.8 as
an inlet velocity and density-based analysis. once the setup is all done, we move on into the
pressure plot and pressure contour illustration.
a2. Results:
The following figure is a pressure distribution plot on the farfield, we can see that the N-wave
signature on the ground is disturbed
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90
Let us compare this signature with the double wedge airfoil on the same conditions:
Figure 4.6 comparison between normal shape and optimized
We can see that delta P max is significantly reduced (from 0.41bar to 0.36 bar) We conclude
that the technique works and is a promising solution for our problem.
The following is an illustration of the pressure contour:
Experimental and Computational Study on Sonic Boom Reduction
UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019
91
Figure 1.7 Pressure contour of optimized airfoil
A close up on the modifications added and their effects:
We can see that the spike added helped spread the shock wave into several ones, which helped
to reduce the pressure signature on the ground. An adequate solution for a complicated
problem.
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction
Experimental and Computational Study on Sonic Boom Reduction

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Experimental and Computational Study on Sonic Boom Reduction

  • 1. Experimental and Computational Study on Sonic Boom Reduction Jury  Prof 1 : Mohammed Khalil IBRAHIM  Prof 2 : Ali Mohammed Omar ASHRAF  Prof 3 : El Hachmi ESSADIQI Students  Anas LAAMIRI  Ayoub BOUDLAL Université Internationale de Rabat 2018/2019
  • 2.
  • 3. Preface This report is written as a thesis for the Aerospace Engineering degree at the International University of Rabat. It is a reflection of the work we performed on sonic boom minimization. We tried to reduce the sonic boom of a 2D Non- lifting and lifting object by analyzing the relation of the shape of the object and the asymptotic shock strength it produces on the ground in a supersonic flow. At this point we would like to write some words of gratitude. We would like to thank everybody who helped us realizing this report. First of all, we would like to thank Prof. Mohammed Khalil IBRAHIM for guiding us through the graduation project. He pointed us in the right direction by giving us advice and comments on the work. Furthermore, we would like to thank the technical staff for the adequate help they provided when the computational hardware was not quite working along. Ayoub BOUDLAL and Anas LAAMIRI.
  • 4. Abstract Sonic boom reduction has been a major obstacle in the aviation industry for the last 20 years, scientists from all over the world strive to find a solution for reduction of the impact sonic boom on the ground, hence bring back Supersonic travel back to life after the retirement of the first supersonic civil transport airplane, concord, in 2011. To do so, the emphasis in latest research has been on supersonic plane shape optimization to decrease the sound signature on the floor resulting from a supersonic aircraft's Sonic boom in cruise flight at elevated altitude. CFD technology offers an appealing option to help in the design and optimization of supersonic cars due to the constraints of in-flight testing and laboratory scale testing costs. Due to the significant rise in computing power, the predictive capacity of CFD technology has considerably enhanced over the past decade, enabling the treatment of more complicated geometries with bigger meshes, better numerical algorithms and enhanced turbulence models for Reynolds-averaged Navier-Stokes (RANS). As computing energy continues to rise, numerical optimization techniques were coupled with CFD to further assist in the design phase. But first we must understand the phenomena. This thesis provides a careful study of the sonic boom and its signature on the ground. The study is conducted following three approaches of analysis: Analytical, computational and experimental. Once the understanding of the phenomena is all done, we move into finding the flight conditions and shape that minimize the sonic boom and provide the required lift.
  • 5. Table of content PREFACE............................................................................................................ 3 ABSTRACT.......................................................................................................... 4 CHAPTER 1: INTRODUCTION .......................................................................... 8 1. What is Sonic Boom?...................................................................................................8 1.1 How Sonic Boom is generated ..............................................................................8 1.2 How large can a sonic boom be?.........................................................................10 2. Impact of Sonic Boom in community.........................................................................10 2.1 Can it cause damage?..........................................................................................10 2.2 Effect of sonic boom in human health.................................................................11 3. Historical Background ...............................................................................................12 3.1 First Sonic Boom ever created ............................................................................12 3.2 Supersonic Transport (SST)................................................................................13 4. Prevision attempt to reduce Sonic Boom....................................................................13 4.1 In search of a quieter Boom ................................................................................13 4.2 Current and future Research Studies ...................................................................14 4.3 Commercial Prospects.........................................................................................14 5. Organization of report................................................................................................15 CHAPTER 2: METHODOLOGY ...................................................................... 16 1. Introduction ...............................................................................................................16 2. Experimental..............................................................................................................16 2.1 Wind Tunnel.......................................................................................................16 2.1.1 Working section...........................................................................................17 2.1.2 Instruments frame and instruments...............................................................20
  • 6. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 1 2.1. 3 Model..........................................................................................................20 2.1.4 Versatile Data Acquisition System (VDAS).................................................20 2.1.5 Schlieren Appartus (AF302A)......................................................................21 2.1.6 Technical Details .........................................................................................21 2.1.7 Layout and Location....................................................................................22 2.1.8 Wind Tunnel assembly ................................................................................23 2.1.9 Experimental procedures..............................................................................26 2.2 Field Testing.......................................................................................................28 2.2.1 Measuring Sonic Boom................................................................................29 2.2.2 Measurement Systems .................................................................................29 3. Whitham’s Theory (Analytical)..................................................................................37 3.1 2D shape method method (2D diamond wedge) ..................................................39 3.2 Limitations of Whitham theory ...........................................................................41 4. BASS Theory (Analytical).........................................................................................42 5. CFD (Computational) ................................................................................................50 CHAPTER 3: SONIC BOOM RESULTS ............................................................ 52 1. Introduction ...............................................................................................................52 2. Experimental Results .................................................................................................52 3. Computational Results...............................................................................................53 3.1 No lifting case (0° angle of attack).....................................................................53 3.2 Lifting case ( with an angle of attack 5°).............................................................80 4. Analytical Results......................................................................................................86 5. Conclusion.................................................................................................................87 5.1 0° angle of attack ................................................................................................87 5.2 5° angle of attack ................................................................................................89 CHAPTER 4: MINIMIZATION TO REDUCE SONIC BOOM ............................... 83 1. Introduction ...............................................................................................................83 1.1 Diamond wedge..................................................................................................83
  • 7. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 2 2. Minimization techniques to reduce Sonic Boom.........................................................85 2.1 Sonic boom reduction technique using Matlab contour for diamond wedge.........85 2.2 Quiet spike Sonic boom reduction technique.......................................................85 2.2.1 Introduction of the idea................................................................................85 3. Results of minimalization for 2D shape......................................................................86 3.1 Diamond wedge results.......................................................................................86 3.2 Minimization technique inspired form F-15b NASA’S modified supersonic aircraft...........................................................................................................................86 CHAPTER 5: CONCLUSION ........................................................................... 90 REFERENCES .............................................................................................. 91 APPENDIX .................................................................................................... 92 LIST OF FIGURES ....................................................................................... 95
  • 8. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 3 CHAPTER 1 : INTRODUCTION 1. What is Sonic Boom People have been fixated on speed for a very long time. They are discovering approaches to travel quicker which have prompted numerous developments that we see today including the rapid airplane. It was this interest for speed for people which set off an American military pilot, Chuck Yeager to speed test a flying machine where he figured out how to travel 428 m/s, breaking the sound wall for the absolute first time and travel quicker than the speed of sound. 1.1. How Sonic Boom is generated When the object travels faster than the velocity of the sound, the produced sound waves can not migrate from each other as the velocity is beyond that of the sound — thus colliding with each other. That's the wave-emitting object that travels quicker than the waves themselves. This causes the waves to force themselves or combine to travel in a single shock wave at a critical speed known as ' Mach 1 ' and has an estimated value of 1,235 km/h. So, because of this compression of the sound waves, a "boom" is heard. These are known as Sonic booms. Figure 1.1 Illustration of the shock wave
  • 9. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 4 This produces a large quantity of sound energy, making our ears a sound comparable to that of thunderclap. According to NASA, when the air reacts like a liquid to supersonic objects and the force produced by objects pushing aside air molecules as they travel through the air forming a shock wave that is like a ship hitting the water, a sonic boom occurs. The booms can continue as far as the object is moving in supersonic speed. The waves are formed in a conical shape behind the object. The boom is continually produced as long as the plane is supersonic. A tight surface track is created along the aircraft's flight route called the "boom carpet." Figure 1.2 Shock impact on the ground The pressure signature on the ground tends to offer an N-Shape wave, the objective of this thesis is to reduce it.
  • 10. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 5 1.2. How large can a sonic boom be? A sonic boom's size relies on the aircraft's size and weight. The sonic boom intensity is based on the length of the aircraft and its cross-sectional region, whereas its shape depends on the near-ground local air turbulence. Wind, velocity, direction, and also air temperature and pressure influence the direction in which the sonic boom travels and the strength of shock waves produced by sound wave compression. Figure 1.3 Sonic Boom carpet 2. Impact of Sonic Boom in community 2.1. Can It Cause Damage? The boom intensity can be measured in pounds of air pressure per square foot (PSF). It is the amount of pressure that the normal pressure around us increases (2,116 psf/14.7 psi). And there is no anticipated harm to any constructions when measuring one pound of overpressure. Supersonic aircraft at ordinary working altitude have overpressures of 1 to 2 psf. The booms triggered by big supersonic aircraft can be noisy, capturing the attention of people, and the sound of livestock can be upset. Strong booms can also cause the construction systems to suffer minor harm.
  • 11. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 6 Without causing any harm, buildings in good condition can resist shockwaves of up to 11 psf. A shockwave of less than 2 psf, however, will have a small opportunity of having an impact on historical structures and poor condition buildings. The chances of structural harm and greater government response are also improved if the overpressure rises. Tests showed that buildings in good condition were undamaged by overpressures of up to 11 psf, which means that whether or not it gets impacted depends on the condition of the construction systems. Figure 1.4 Spread of the distribution for actual pressure 2.2. Effect of sonic boom on human health The effects of sonic boom on physical and mental health are presented. Sonic booms have marked effects on behavior and subjective experience as exemplified by startle reactions and attendant feelings of fear. Such intrusions disrupt sleep, rest and relaxation, and also interfere with communications. These forms of sonic boom interruption generate annoyance which is perceived greater when indoors, and which is judged equal to that experienced by residents living around busy airports. In this regard, indications are that sonic boom disturbances produced by commercial SST aircraft now being designed will not be deemed acceptable by at least 25 percent of the population regardless of habituation. From the psychological viewpoint, greater public acceptance of SST booms will be largely contingent on determining and prescribing overpressure limits below which startle reactions are minimal, posing no problems to performance or risk of personal injury.
  • 12. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 7 3. Historical Background 3.1 First Sonic Boom ever created Aviation evolved at an incredible speed after the Wright Brothers made their first flight in Kitty Hawk, North Carolina, on December 17, 1903. WWI took war to the skies within two decades, and commercial airlines ferried customers all over the world. Aviation made another big leap forward on October 14, 1947; test pilot Chuck Yeager became the first human to break the sound barrier, achieving Mach 1 in the BellX-1 rocket-powered aircraft, a collaborative U.S. project. Air Force and National Aeronautics Consultative Committee (NACA), NASA's precursor. Figure 1.5 First pilot to reach the sound barrier But the X-1 itself was mainly intended for study purposes, not for business travelers. Soon supersonic military jets were on the rise, but like the X-1, they were sprinters: they could only fly for a few seconds at Mach 1, maybe a few minutes at most, before running out of fuel. While this worked for tiny planes carrying out sharp maneuvers, big business airliners –often traveling in straight lines or smooth curves–would have to cruise at supersonic velocity for a much longer period of time. However, the progression inspired the commercial aviation sector to investigate the development of supersonic transportation (SSTs) or civilian supersonic aircraft.
  • 13. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 8 While the X-1 demonstrated that we had the correct instruments to fly at supersonic speeds, some significant details required to be ironed out, such as the ability to cruise above Mach 1 for a comparatively lengthy flight duration, as well as the financial viability of such a project. Multiple countries, including the U.S., began studies in the 1950s, but a slew of developmental challenges faced by SSTs meant that only three nations would continue to construct and fly such aircrafts: The United Kingdom, France, and the Soviet Union. 3.2. Supersonic Transport (SST) To make SST possible, Concorde technicians from the British Aircraft Corporation of the United Kingdom, France Aerospatiale, and the other businesses contracted to work on parts of the aviation (like Rolls-Royce who built the motors) had to create fresh techniques or refine ancient ones, from fly-by-wire controls in the cockpit (digital interfaces versus analog ones) to heat-resistant tyres 4. Prevision attempt to reduce Sonic Boom NASA and private firms are pushing for studies to restore supersonic flight to the aerospace industry. The Concorde in 2003 was the last commercial supersonic flight. Beginning in 1976, the Concorde flew commercially, seating up to 128 passengers. The cruising speed was 1,354 mph (2,179 km/h) at 2,04 Mach. The jet flew from Singapore to London, from New York to London and from New York to Mexico on a regular basis before that. But on its way to Mexico, it would have to fly at subsonic speeds while crossing Florida because in several nations, including the United States, supersonic flight over land was, and still is, either prohibited or extremely controlled. Universities, private businesses, and NASA are working to fix the issue of sonic booms to make supersonic flight legal for overland paths. 4.1. In Search of a Quieter Boom Many complained about the property damage caused by sonic booms during the Concorde days, let alone the noise pollution that many found intolerable. More than 38,000 claims were lodged against the U.S. between 1956 and 1968. Air Force harm caused by sonic booms. As a consequence, supersonic flight over territory has been forbidden by the Federal Aviation Administration (FAA) since 1971. Concerns about the environmental impacts, including ozone depletion and climate change, were also influencing this ban. To evaluate sonic booms, NASA launched the Shaped Sonic Boom Experiment in 2001. In an attempt to reduce the effects of sonic booms during test flights, they modified the fuselage of a Northrop F-5E Tiger II. The F-5E's nose was removed and a bigger, longer version was substituted. The fairing was also lengthened and deepened under the fuselage. The modified F-5E or Shaped Sonic Boom Demonstrator flew in 2003, and NASA took 1,300 measurements of sonic boom from different ground sensors from that stage. NASA
  • 14. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 9 technicians verified that the changes resulted in an 18 percent decrease in the original pressure impulse and booms were 4.7 decibels quieter on average compared to an unmodified F-5E. Figure 1.6 Spike technique As a technique of reducing the original shock wave produced during supersonic flight, Quiet Spike was tested. The spike in front of the airplane produces three tiny shockwaves before reaching the aircraft's primary body when breaking the sound barrier. The next phase of NASA was to hold its first Fundamental Aeronautics Conference in 2007, planning its next phases of supersonic studies. 4.2. Current and Future Research Studies Researchers have shown that it is possible to build supersonic airfoils to induce passive laminar flow control (LFC). These decreases or eliminates the turbulent wing crossflow producing shock waves. Consequently, the objective of this study is to produce LFC on the wing, meaning that the leading edge of the wing during supersonic flight would stay subsonic. The lack of a supersonic leading edge would decrease shock waves and minimize flow disturbances, resulting in flight that is more stable and effective. Research conducted at MIT's Aviation and Environment Laboratory, with NASA's assistance, analyzes the environmental impacts of sonic booms. The aim is to know how the atmosphere is affected by high altitude emissions from supersonic aircraft. In stratospheric circumstances, they will monitor biofuel emissions, study their effect on ozone depletion, and attempt to determine how they can cause greater concentrations of UV in the atmosphere and on the floor. 4.3. Commercial Prospects
  • 15. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 10 Since 2002, when it launched its Supersonic Natural Laminar Flow technology, Aerion Corp. has been working to reduce sonic booms. Aerion has intended a supersonic LFC wing that decreases drag over the wing by 50 percent. Laminar flow wings are thin and soft so that the boundary layer is not traversed and the flow is turbulent. The wing structure of Aerion is unbroken but tapered with a comparatively sharp leading edge, featuring a modified bi- convex airfoil with slightly curved upper and lower surfaces. On its Supersonic Aerion AS2, Aerion will use this wing. The wing carries high-lift flaps that are similar to big subsonic business jets to offer the aircraft low approach and landing speeds. The flaps also let the aircraft land where visibility is great at comparatively small angles of attack. The wing cuts drag the complete airframe by 20 percent to increase effectiveness. Figure 1.7 Aerion Aircraft 5. Organization of report In this thesis, we start by defining the methodology used, we then proceed to the understanding of the sonic boom by studying the effect of shockwave in different cases, on the ground and on the body, the analysis will be conducted using Computational fluid dynamics (FLUENT) and comparing it with the results of Wind Tunnel and finally with the results obtained from the theory. Once all done with the comparison and understanding we move on to finding a solution to minimize the pressure signature on the ground and hopefully contribute into making the supersonic travel possible again.
  • 16. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 11 CHAPTER 2 : METHODOLOGY 1. Introduction In this thesis, we aim to get various results from the theory, CFD and wind tunnel. Each Method will provide us with results, hopefully the results match. The main aim is to understand sonic boom effects on the ground and on the body. This chapter will end with a better understanding of the sonic boom effect which will lead us into coming up with adequate solution(s) for minimization of the pressure signature of shock wave on the ground. 2. Experimental 2.1. Wind tunnel Many engineers work with air flow at supersonic speeds. It is important for them to know the characteristic effects of supersonic flow around different shapes at different Mach numbers. This allows engineers to predict and produce designs that will perform well under supersonic conditions. Supersonic air speed test equipment is usually very expensive, so it is normally found at national aero engineering companies and institutions. The equipment Continuous Supersonic Wind Tunnel (AF302) is a cost-effective laboratory scale unit. It includes a selection of shapes (models) for experiments at air speeds from subsonic up to Mach 1.8. The results of tests from this apparatus can be easily scaled up to produce predictions of performance of much larger wind tunnel tests.
  • 17. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 12 Figure 2.1 The continuous Supersonic Wind Tunnel The Continuous Supersonic Wind Tunnel includes several parts: • The Diffuser Duct (in three sections). • The Working Section and stand. • Three different Working Section Liners. • A set of Aerodynamic Models that fit in the Working Section. • The Instrument Frame. • The Flexible Tube and Support Stand. • The Vacuum Pump. 2.1.1. Working Section The Working Section is a precision engineered convergent-divergent rectangle-section nozzle with pressure tappings along the bottom. The bottom of the nozzle is flat and fixed, but you have a choice of three different shaped top pieces (liners). This is so you can change the shape of the nozzle, to set the approximate air speed that passes through it (subsonic, Mach 1.4 or 1.8). In our project we will work on 1.8 Nozzle.
  • 18. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 13 Figure 2.2 The liner that fit in the top of the working section Figure 2.3 The working selection Models fit into the Working Section. The Working Section has two circular glass windows ('portals'), each window is inside a gear ring. The models fit into the space between the windows. Slots in the windows hold the model in place. The user can turn a small angle control that turns the gear ring. This turns the angle of the portals and the model. An angle encoder on one side of the Working Section connects to TecQuipment's optional VDAS@. The angle encoder connects to a special interface board (supplied with the Wind Tunnel) that fits into the VDAS@ hardware. The VDAS@ displays and records the angle of the model.
  • 19. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 14 2.1.2 Instrument frame and instruments Figure 2.4 The instrument frame The separate Instrument Frame stands on a suitable bench or table (not supplied). It connects to the electrical supply and gives power to any of the electronic instruments used with the Wind Tunnel. The instruñlents fit onto the frame and connect to the pressure tappings and other parts of the Wind Tunnel. Supplied with the Instrument Frame is a 'mimic' of the pressure tappings along the Working Section. The tappings from the Working Section connect to the mimic, then you can easily connect your pressure measurement instruments to the mimic. Also supplied with the Instrument Frame is the 32 Way Pressure Display. This instrument has a multiline display that shows the pressures connected to its inputs. When you press its scroll button, the display scrolls through all 32 pressure readings. The display has a 'zero readings' button so that you can zero the pressure readings before you do a test. The back of the 32-Way Pressure Display has a connection for TecQuipment's VDAS@.
  • 20. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 15 2.1.3 Model Figure 2.5 The Two-dimensional Model Figure 2.5 shows the model used in our project with the Wind Tunnel. The airflow around the model is two dimensional. This is because it fits exactly between each glass window, so the airflow is only above and below the model, not around its ends. The model has a pressure tappings so that you can measure the pressure distribution around the double wedge airfoil in supersonic flow. Note: You do not use the model with pressure tappings with the Schlieren apparatus,as the pressure pipes block the view. Use the identical model without the pressure pipes for Schlieren imaging. 2.1.4 Versatile Data Acquisition System (VDAS) Figure 2.6 The VDAS Software and hardware
  • 21. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 16 TecQuipment's VDAS@ is an essential ancillary for use with the Wind Tunnel. It is a two- part product (Hardware and Software) that will:  automatically log data from your experiments  automatically calculate data for you  save you time  reduce errors  create charts and tables of your data  export your data for processing in other software 2.1.5 Schlieren Appartus (AF302A) The Schlieren Apparatus (AF302A) is for use with the Continuous Supersonic Wind Tunnel. It uses refracted light and mirrors to show the pressure waves around the models in the Working Section of the Wind Tunnel. 2.1.6 Technical Details Item Details Wind Tunnel Dimensions and weights Dimensions (Wind Tunnel Only): 1600 mm high x 4000 mm long x 900 mm wide Main part (with working section and one liner): 115 kg Bypass pipe: 5 kg Diffuser (four sections): 20 kg Support stand: 69 kg Total Weight: 209 kg Instrument Frame 1260 mm long x 840 mm high x 510 mm wide Weight: 22 kg (without instruments) Electrical Supply: 220 VAC to 240 VAC 50 Fuse: 20 mm 10 A Type T
  • 22. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 17 Vacuum Pump Nominal Dimensions (fitted with noise damping hood): 1800 mm high x 1800 mm long x 1500 mm wide, plus an exhaust silencer of approximately 2600 mm high. Weights: Noise damping hood: 250 kg Pump units together: 1000 kg Silencer: 325 kg Control Box: 80 kg Flexible Pipe: 55 kg Total Weight: 1710 kg Electrical Supply: 400 VAC Three phase, neutral and earth 250 A starting current and 90 A running current User- accessible circuit protection: 6 A type C MCB (miniature circuit breaker) - for overall protection of the low current control circuits. 2 A I-IRC fuse - protects the 24 V control circuits. 4 A type D MCB - protects the three-phase fan in the vacuum pump. 1 A 20 mm - protects the auxiliary supply circuit to the drive. Working Section Nominal Maximum Dimensions : 100 mm x 25 mm Rotating Portal with Angle Encoder 25 pressure tappings plus two for the model with tappings Interchangeable Liners Three: Subsonic, Mach I .4 and Mach 1.8 Nominal Weights: 7 kg each Table 2.1 Details of the wind tunnel. 2.1.7 Layout and Location Figure 2.7 shows one suggested layout of the Wind Tunnel and its optional parts. Even though it sits in a noise reducing hood, the Vacuum Pump creates the highest noise levels, so TecQuipment recommend that you fit it in a separate sound-proof room next to the Wind Tunnel. As the air passes through the Working Section it becomes very cold, so any moisture in the air can freeze, causing poor images and streaks in the Working Section portal. For this reason, make sure the air in your laboratory has a normal to low moisture content.
  • 23. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 18 2.1.8 Wind Tunnel Assembly If you are to use the Wind Tunnel with the optional Schlieren Apparatus, you must NOTE assemble the Wind Tunnel so that its bypass valve duct passes through the lower middle part of the Schlieren Apparatus. Therefore, you must put the Schlieren Apparatus in position first. 1. Use a suitable lifting machine and assistance to put the Vacuum Pump into position as shown in the layout of Figure 2.7. 2. Move the main part of the Wind Tunnel into Position. Figure 2.7 shows the main parts you need to assemble. 3. Put the Schlieren Apparatus its table into position next to the main part of the Wind Tunnel. Assemble its delicate optical instruments after you install the Wind Tunnel.
  • 24. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 19 Figure 2.7 Layout of the Wind Tunnel
  • 25. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 20 The wind tunnel and Schlieren Apparatus The model The instrument frame and VDAS system
  • 26. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 21 2.1.9 Experimental procedures Two-dimensional Flow Around an Object Object Use the optional Schlieren Apparatus to demonstrate the air flow around the models. Procedures 1. Fit the Mach 1.8 liner to the Working Section. 2. Fit the model into the Working Section, so that the model is held in place between the two portal windows. 3. Set up the optional Schlieren Apparatus as described in its User Guide. 4. Fully open the bypass valve. 5. Start the vacuum pump and wait for it to reach full speed. 6. Shut the bypass valve. 7. Use VDAS@ to record all pressure readings. 8. Use the Schlieren Apparatus to visualize the flow patterns around the model. Use the control under the Portal to rotate the model and change the incidence angle. Use the Schlieren Apparatus to record the images. 9. Fully open the bypass valve and press the stop button. Note: Each time you adjust the model angle, open the bypass valve to reduce the vacuum pressure in the wind tunnel, so you can turn the model angle more easily. Then shut the bypass valve.
  • 27. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 22 Figure 2.8 Typical Schlieren Image - Mach 1.8 Liner with a 50 Double Wedge Model. At low incidence (less than half the total leading-edge-angle) you should see shock waves from the leading and trailing edges and Prandtl-Meyer expansion from the corners. At higher incidences expansion appears above the leading edge and below the trailing edges. The patterns should confirm theoretical predictions quite well, allowing for the boundary layers around the tunnel and models. These will cause somes light effects, listed here: a) Shock waves may appear as a narrow 'fan'. This may seem odd to the student who has learnt that under these conditions a shock wave is very thin (approximately 0.0025 mm). It is because the shock waves are not plane. Boundary layers form on the side walls of the tunnel. The Mach Number decreases near to the boundary layers, so the leading-edge shock waves are at a greater angle to the flow. The shock wave 'fan' is a side elevation of a surface that bends upstream, near the tunnel walls. The downstream edge 'fan' is a relevant part of the shock. b) When the model incidence angle is half the total leading-edge angle, the flow passes over the upper front surface without deflection. The leading edge should only produce a very small disturbance in this flow, showing a Mach line. In practice, a small "fan" tends to appear, for the reasons explained in paragraph (a). Also, the flow very close to the leading-edge is complicated by the growth of the boundary-layer over the upper surface of the model. If the leading edge is thin (up to 0.05 mm) the disturbance near the surface is a weak shock wave graph followed by a region of expansion. If you study your images, you will see this phenomenon, which tends to cancel out near the surface. c) Again, due to the boundary layers on the sidewalls of the working section, the leading edge of a Prandtl-Meyer expansion appears to lie at too great an angle to the flow. d) Shock waves from the trailing edge of a model appear more diffuse than those from the leading edge. This is due to the shocks producing rapid thickening of the model boundary-layer towards the trailing edge, so that
  • 28. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 23 the changes in flow direction become less abrupt. At a fairly small incidence, the boundary-layer separates from the upper surface in front of the trailing edge, producing quite a complicated shock pattern. e) It is important to distinguish between genuine phenomena in the flow such as those mentioned above and spurious optical effects. For example, if the orientation of the Schlieren apparatus is such that a Prandtl-Meyer expansion appears lighter than the background, a small dark region may appear near the corner from which the expansion starts. This is due to "overloading" of the Schlieren apparatus: the density gradient near the corner may be so great that the light rays passing through this region are deflected so far that they miss the final lens altogether. 2.2 Field Testing In this section we will see field testing techniques used to measure the Sonic boom. 2.2.1. Measuring Sonic Booms Sonic booms cover a broad variety of frequencies with a total infrasonic component of less than 1 Hz and a fast pressure of more than 10 kHz. They also give a broad variety of dynamics of more than 200 Pa (140 dB SPL) and a low pressure-ss than 0.1 Pa (74 dB SPL). Initial and final abrupt pressure increases cause impulse noise. Figure 2.9 Acoustic content of a sonic boom
  • 29. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 24 Figure 2.10 Sonic boom signature 2.2.2. Measurement Systems The goals are to check the measuring scheme and identify suitable transducers and installations during five flyovers and three flight conditions. Indoor and outdoor sonic booms were evaluated along with vibration along gates and walls in a site construction. Measures were also produced from a 1000 m suspended weather balloon. Figure 2.11 Test site measurement.
  • 30. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 25 A. Indoor measurement system To satisfy their demands, the Japan Aerospace Exploration Agency (JAXA) chose a NI PXI system with a range of modules. Due to its elevated resolution and wide dynamic range, low cut-off frequency (0.5 Hz for AC coupling), and software-configurable AC / DC coupling and embedded piezoelectric (IEPE) conditioning, the NI PXI-4472B dynamic signal acquisition (DSA) module was used to obtain vibro-acoustic information from microphones and accelerometers. Synchronization via GPS was given by the NI PXI-6682 timing and synchronization module. An NI 8353 controller offers high-speed information streaming via a RAID 0 as well as the high capability required for up to one hour recording of 16 channels. Figure 2.12 Instruments system used for indoor measurements
  • 31. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 26 Figure 2.13 Instrumentation graphical user interface of outdoor recorded Sonic boom The aircraft flew at a peak altitude of 14 km (about 46,000 ft) and at least 6 km (about 20,000ft) for the trials. The sonic boom's overpressure heard inside the test building was about a quarter of what was heard outside. Recent study demonstrates that due to the rattling noise and building vibration, the sonic boom of the present aircraft heard inside a building can cause important annoyance. Figure 2.14 Indoor measurements
  • 32. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 27 The sonic boom will also be heard indoors with overland supersonic flight. Inside a construction, the noise of a sonic boom should be smaller than outside. Looking at the outcomes of JAXA's 2009 sonic boom measurement experiment, the acoustic pressure indoors compared to outdoors is considerably decreased. Also, as seen in the outdoor N-wave, the waveform observed indoors does not have a fast rise in acoustic pressure and has a smooth slope. Secondary noises, such as window rattling owing to the abrupt rise in acoustic pressure and low frequency element of sonic booms, influence human noise perception. Indoors may be bigger the psychological impacts induced by a sonic boom. It is thought that it is essential to explore how to also evaluate these indoor impacts as metrics to be used in global norms for sonic boom noise. JAXA has created a sonic boom simulator and uses its measurement system to perform evaluation tests on test topics using file recording. B. Outdoor measurement system In order to avoid the influence of the turbulence near the ground, a blimp or weather balloon equipped with infrasonic microphones was held at an altitude of 1 km and some other infrasonic microphones are also installed at several points between the blimp and the ground to measure the effect of the turbulence on the sonic boom signature. Using the tethered blimp to prevent the impacts of atmospheric turbulence, a lightweight model was used for aerial readings distributed to 1,000 m. This system is based on stand- alone, wireless LAN-controlled aloft computers with a 4-channel dynamic signal acquisition module NI-9234 for high-precision audio frequency readings.
  • 33. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 28 Figure 2.15 Outdoor measurement systems C. Infrasonic microphones Modern measurement microphones have vent holes to equalize changes in atmospheric pressure. This functions as a filter with a high pass that cuts below 3-5 Hz. A condenser microphone's reduced limiting frequency is acoustically regulated by the microphone's inner volume and air equalization vent, which guarantees that tiny atmospheric differences are equalized while rapid differences in sound pressure are not equalized as we want to assess them. A good measuring microphone should equalize to cut off unwanted pressure fluctuations that surround us in many respects as quickly as possible. Wind turbulence-door slam-movement of the ground etc. For many high-quality measuring microphones, the normal cut-off is 3-5 Hz. It should be 0.1-0.5 Hz for infrasound. Pre-polarized microphones deliver important benefits over polarized price, weight and energy usage, making them helpful as used here for mobile field measurements. A microphone system's low-frequency reaction is provided by the preamplifier's electrical cut-off and the microphone capsule's acoustic cut-off. These newer microphones have stiffer diaphragms that decrease the mechanical cut-off A- field Microphone System, Infrasound Type 40AZ-S1 is provided with a unique adaptor that reduces the preamplifier's reduced cut-off frequency and has been used in these trials. It also
  • 34. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 29 has the thermal noise that increases. The elevated input-frequency 3-dB limit f L= 0.2 Hz for the GRAS Type 40AZ microphone capsule capability (20 pF). Figure 2.16 Infrasonic microphone used D. Drop Test Measurements The D-SEND project consists of drop trials for D-SEND #1 and D-SEND #2. Two distinct axisymmetric bodies were placed in the D-SEND #1 drop experiment and the sound booms were analyzed and compared. An experimental supersonic aircraft model (unmanned aircraft with no engine and low sonic boom design technology will be dropped and the sonic boom will be measured in the D-SEND #2 drop test. This is planned for the summer of 2013. The sonic booms will be measured and recorded by the microphone system which is linked to a line between the ground and the blimp (altitude=1 km). Two sample bodies were dropped from an altitude of 30 km at a 20-second interval in D- SEND #1. The test bodies were the NWM (N-Wave Model) generating a N wave's pressure signature, and the LBM (Low-Boom Model) generating a low boom wave's pressure signature.
  • 35. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 30 Figure 2.17 drop test Diagram Both men trace nearly the same history of Mach numbers and produce forward and perpendicular sonic booms to the angle of the Mach cone. The sound booms are evaluated 1 km from the floor by a boom measuring scheme (BMS). The telemetry scheme transmits information such as velocity (speed) and position information of the drop test designs to the floor. Figure 2.18 N-WAVE and Low-Boom models being prepared for drop Through this experiment, JAXA proved its axisymmetric design concept technology with low sonic boom that halved the sonic boom.
  • 36. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 31 Figure 2.19 constracting Sonic Boom signatures recorded with NWM and LBM test bodies The information from the experiment is useful as a reference for validating the technique of assessment of sonic boom propagation and is anticipated to contribute in the future to low- sonic boom research. JAXA has also developed a fresh technique for showing the notion of low sonic boom design in the form of a balloon drop test for the first time. For D-SEND #2, using J-boom design technology, an experimental supersonic airplane (S3CM: S-cube Concept Model) will be used. On the front and bottom of the fuselage, the aircraft has a shaped boom mark. Figure 2.20 Experimental Supersonic airplane model to be used in D-SEND #2
  • 37. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 32 The aircraft will be dropped from a 30 km altitude and gliding at Mach 1.3 over one of four boom measuring devices and a 50° flight path angle. The formed boom signature produced by the aircraft is projected vertically towards the sonic boom scheme at this angle of flight path. The objective is to set values for low-sonic boom design technology and to develop the so far advanced low-boom wave procurement technology. Figure 2.21 Diagram of D-SEND #2 test planned for 2013 JAXA experiments in Sweden have validated that the measuring system can measure sonic booms and work well with a variety of microphones optimized for measuring infrasound. In order to decrease the impacts of atmospheric turbulence, the ground-based measuring scheme was extended to include an aerial measuring system distributed at altitudes up to 1,000 m. In the next scheduled drop test, JAXA hopes to speed up the growth of civil supersonic aircraft by showing low-boom design technology. 3. Whitham Theory (Analytical) Known people attempted to create theories after the origin of sonic boom to predict the propagation of the sonic boom through the atmosphere and to minimize the power of the sonic boom. The Whitham's theory is the most relevant theory that is still used today from theoretical components to wind tunnel experiments and CFD methods. According to this theory, the wavefront from the aircraft to the ground can be divided into three regions; near- field, midfield and far-field flow, see the Figure below, the Figure is a schematic of the coalescence of near-field shock waves, leading to a so-called far-field N-wave. From this figure it is possible to draw some significant points of attention:
  • 38. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 33 A pressure disruption in the footprint characterizes the sonic boom described by the Whitham's theory, which has an original rapid pressure increase and a second instantaneous increase back to the local pressure. There is also a linear reduction in pressure to below local pressure between these two abrupt pressures. The observer on the floor actually perceives the bow shock and the tail shock as the effects of the two abrupt jumps of stress described above. It is now apparent that the amplitude and duration of this N-wave shape sonic boom is linked to the airplane's geometry. The loudness of the booms to be heard can be determined by the pressure disturbance rate as well as by the pressure disturbance rate. In addition, when the time between these two shocks is very short, only one boom will be heard by the ground observer. As stated above, the following figure basically demonstrates three distinct wave fronts and the respective signatures at three distances away from the aircraft. There are usually two waves for an axisymmetric body as a well-known airfoil, the bow shock connected to the nose and the tail shock connected to the tail. However, as we understand that an aircraft is not a smooth and axisymmetric body, what happens in the near-field is that the shock wave pattern includes many shock waves, corresponding to the different compressions induced by the aircraft's geometry. However, the shock wave patterns will develop away from the aircraft due to nonlinear effects such as atmospheric turbulence and gradients of air temperature. The shock wave patterns combine in the far-field and essentially form two primary waves, the shock wave of the bow and tail. Whitham created this operation to determine the shock formation and calculate the associated distortion and is known as the theory of sonic boom by the Whitham. From earlier research, Figure 2.22 Pressure signature diagram It can be concluded that there are many variables affecting the power of the sonic boom, namely airplane weight, size and shape, as well as altitude, attitude and flight route and climate or atmospheric conditions. A heavier aircraft causes a greater sonic boom than a light
  • 39. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 34 aircraft due to the former displacing more air and creating more lift. One of the most efficient strategies to reducing the intensity of the sonic boom is altitude, as it determines the distance the sonic boom travels before it reaches the floor. Wind, airplane velocity and direction, air temperature and pressure influence the direction and strength of shock waves. The point has been reached in all these classical studies on the sonic boom that any enhancement in the parameters that regulate the effectiveness of the output of the aircraft will result in a decrease in the weight of the aircraft. As a result, this weight decrease results in a decrease of the sonic boom. In the (proportion) not just weight but also improvements weight thrust, drag lift (ratio), structural effectiveness and specific fuel consumption lead to minimization of sonic boom. Going to this topic is beyond the scope of this thesis, minimizing the sonic boom and achieving better aerodynamic efficiency. A brief summary of the theoretical part of the theory of Whitham will be given in the following and its implementation and limitations will be discussed in addition. The theory of Whitham is selected to be explained in this thesis because it is an analytical predictive technique on which almost all of today's continuing research is based. Furthermore, the theory of the Whitham can be used to explore the trait of sonic boom induced by a straightforward 2D body with a certain thickness. 3.1. 2D shape method (2D Diamond wedge) The first step to apply the theory of Whitham to the optimum contours (diamond wedge) is to discover the respective feature of Whitham's F-function. This feature actually reflects the body's flow disruption. In other words, the geometry of the contour is the primary consideration for the Whitham F-function magnitude. The potentially troubled speeds are provided as follows: (2.1) According to the Whitham theory, the variable can determine any distinctive curve that originates from the body surface. This variable is a function of x and y perpendicular to the boundary wall y= y(x) respectively. In 2D continuous supersonic flows, F(j) is equivalent to the border curve at the stage where the characteristic line crosses it, i.e. F(j)=y'(X). The distance to this characteristic line X(a) from the tip of the nose can be determined by X- βy(X)=al. Figure 2.23 is a sketch of the distinctive line that emanates from the body at point b and passes through point p in the field of flow.
  • 40. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 35 Figure 2.23 Sketch of a characteristic line, Whitham’s theory Knowing the Whitham’s F-function enables us to approximate the pressure jump or pressure signature for the occurred shock wave as follows: (2.2) Figure 2.23 represents the Whitham’s F-function with the corresponding overpressure for a first variant contour with a volume of approximately V≈ 0.0571 at M0= 2.0. The top plot demonstrates that the F -function resulting from the inclination of the surface reduces from the nose to the level of the shoulder. The lower plot 2.23 represents the values for the near- field overpressure ∆ by considering a distance of r=1.0 away from the x-axis. From lower plot 2.23 that the first value for ∆ indicates in fact the leading shock power for this body at M0= 2.0. From this, by using the Whitham theory for distinct contours, we can now acquire the leading shock power.
  • 41. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 36 Figure 2.24 Upper plot: F-function, Lower plot: Pressure Jump  3.2. Limitations of Whitham’s Theory Complete application of conventional sonic boom theory is very complicated, so a computer program evaluation is preferred. Up to now, a few computer programs have been created to implement the theory of Whitham. All of these programs treat the F-function as an input and execute the calculation of ray tracing and signature aging. The input of the F-function can be obtained from a distinct linear flow calculation acquired from wind tunnel or computing systems. Between the years 1969 and 1972, two computer programs were created from which both of them are currently being used or at least they have become the main component of all other programs up to our moment. The first program was Hayes ' ARAP model that regarded all the information from the conventional theory in a horizontal, non-uniform and windy environment for a particular maneuvering aircraft. Thomas created the second program in a manner that could be input straight from wind tunnel experiments. Noting that each of these programs has its own capacities and constraints is of great significance. More recently, as an option to wind tunnel testing, CFD techniques have become considered. These CFD schemes were needed to calculate the near-field F-function. But getting a full near-field signature from CFD needs a very big spatial grid that was used for aerodynamic design reasons as never before. Men expect to be able to calculate the entire flow field of any aircraft even to very big distances with the rise in computing energy in the future. While the theory of the Whitham is the most applicable 3D flow theory, it can not yet be used to find an precise relationship between the aircraft's geometry and the near-field signature. That's
  • 42. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 37 because the near-field pressure disturbances are heavily non-linear that the theory neglects. Scientists have lately created higher-order alternatives of the governing differential equations by maintaining higher-order terms in the equations in order to take these non-linear effects into account. But these techniques are not yet used sufficiently advanced to allow practical issues to be predicted using such techniques. And also, because their results are based on improved linearized theory, these greater order approximation methods like the Whitham's theory can not be used at higher Mach numbers. There are also phenomena such as hypersonic flight speeds, concentrated booms, shock wave rise times, and atmospheric turbulence impacts beyond the Whitham theory's capabilities. The theory of the Whitham neglects the non-linear effects in the near-field as they decrease quickly moving away from the aircraft, allowing the linear flow area rule theory to be implemented in the far-field. The forecast of the Whitham has been validated at mild supersonic Mach numbers for slim bodies. It implies that the flow field must be analyzed in one way or another for the hypersonic speed car. When an aircraft accelerates, turns, or other maneuvers, it appears that the focus of the shock waves leads to the amplification of the intensity of the sonic boom. The observed overpressure on the floor is about 2-5 times greater than those in a typical N-wave when boom concentrating happens. This phenomenon allows the region of the ray tube to disappear at certain points so that the ray tracing technique used by the Whitham theory can no longer be used. Furthermore, the theory of the Whitham does not take into consideration the structure of the shock waves and therefore utilizes the concept of soft shock that actually means thin waves. However, recent flight experiments indicate that shocks from the sonic boom are significantly thicker than anticipated. Some issues stay open about turbulence propagation in the reduced air, ab-sorption and dispersion owing to the impacts of non-equilibrium and viscosity. The impacts of atmospheric turbulence are also beyond the ability of the Whitham theory to trace rays because the Whitham theory neglects the existence of turbulence in the atmosphere. 4. BASS Theory (Analytical) First, a summary will be provided in this section for the BASS principle, which is a measure of the asymptotic shock intensity of an item in a supersonic flow field with a very tiny density. Subsequently, the geometry of a 2D diamond wedge body will be implemented with a certain thickness for which this report will determine the asymptotic shock power.
  • 43. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 38 The characteristic lines indicate a convergent trend in a compression flow domain, according to the characteristic theory of features. And a shock wave will be created when the features tend to cross each other. (2.3) This equation represents the slope of a shock wave as the average of the slopes of the characteristic lines υ0 and υ1 merging into the shock. The practical problem with this equation is when the orientation is rotated the characteristic slopes will be changed w.r.t each other. So, in order to analyze the asymptotic shock strength later on in this report a rotational invariant jump equation is required as follows: (2.4) This equation demonstrates that the shock route angle is equal to the character angle bisector before and after the shock. Using the relationships of trigonometry, this equation can be written as follows: (2.5) The power of such a shock wave can be determined by the following expression once the shock route can be modeled by the invariant jump equation (2.4). (2.6) As stated, the distinctive angles behind and before the shock wave, respectively, are range 1 and range 0. Throughout this dissertation this expression will be used to evaluate the shock's asymptotic power.
  • 44. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 39 An object moving at a supersonic speed leads both the shock wave and the expansion waves to occur. The waves of expansion communicate with the wave of shock as they migrate into space. The shock force will be reduced as a result of this interaction and eventually becomes zero when the range gets to infinity. An expression extracted from P.G describes a metric for the decline of shock intensity to zero when the range gets to infinity. Bakker and BASS is referred to. BASS stands for the asymptotic shock resistance of the Bakker and represents the shock resistance asymptotic decline conduct of a body with infinitesimally small density. Below is a brief description of the BASS theory: In order to attain the BASS measure, the features must be projected onto the x-axis and this is only feasible if we are aware of the distribution along the x-axis. According to the simple wave theory all curved Γ − characteristics originate from the undisturbed flow field and therefore the invariant of the isentropic flow V0 − remains constant everywhere in the flow domain. The Γ + characteristics are straight lines and have a slope of υ = tan θ = tan (μ + φ). The profile and the value υ for this point is the following: (2.7) Where ζ is the x-coordinate of point Q(x, y) which itself is the intersection point of the Γ+ characteristic with the object surface. This equation indicates in fact the gradient of the line PQ which equals to υP . The task is now to express ζ as function of x and y. According to the simple wave theory we know already νP = νQ and νQ + φQ = V0 − . This gives us νQ as follows: (2.8) In this equation f−(ζ) is the gradient of the object in point Q which also indicates the flow direction. We can express υ as follows: (2.9)
  • 45. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 40 Figure 2.25 An object in a supersonic flow field Using this equation and knowing the slope of characteristic Mach lines along the x-axis tan (μ) =  we can express the flow direction as follows: (2.10) This equation shows the flow direction φ as a function of υ along the x-axis with the known Prandtl-Glauert factor β which can be defined as follows: (2.11) With knowing the following expression for Prandtl-Meyer angle; (2.12)
  • 46. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 41 It is impossible to express υ in terms of x so we do other way around namely x=x(υ). This means we can express x coordinates as a function of the local flow direction x=x(tanϕ). So, equation 2.10 becomes: (2.13) This equation is called F(υ) function which indicates the x-coordinates in terms of υ along the surface. The x-coordinate of point Q can be defined with ζ= F(υQ) which gives υQ = F−1 (ζ). So, there are now two expressions for υ(x,y) at point Q as follows: (2.14) υ(x, y) = F−1 (ζ) (2.15) From these two equations we are able to write ζas a function of x and y, ζ= ζ(x, y). This result together with equations (2.14) and (2.15) enable us to describe the location of υ(x ,y) along the surface. For the analytical simplicity, the υ-distribution will be projected into the x-axis which means the characteristic lines will continue until they intersect the x-axis. This means that y- coordinate of point Q becomes zero for which the corresponding υ becomes: ( , ) = = ( ) (2.16) From this we know that which results in . And this gives us the corresponding y-coordinates of the characteristic lines as follows: y = υ (x, y) [x – F (υ (x, y))] (2.17) Once the υ-distribution is known along the surface, the next step to make the BASS theory complete is to define an expression for the shock path. The jump equation will be as follows: (2.18)
  • 47. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 42 It should be noted that υin this equation indicates υ1. And the differential equation represents the υ-distribution along the shock wave. Integration of with the known boundary conditions at the leading x=F(υl) =0 results in desired coordinates for the shock path as follows: (2.19) (2.20) The parameter x given in expression (2.19) represents the shock path location which can be determined by integration of the characteristics along the shock wave. As it was earlier explained, the asymptotic shock strength can be defined as a measure that the shock strength decays to zero when the shock wave goes to infinity. This definition is obviously to observe from equation (2.19) which shows when θ→ θo, the shock wave goes to an infinite distance from the object, Υ(θ) → ∞. Earlier it was mentioned the asymptotic shock strength can be determined by equation (2.15). And we know that substitution of equation (2.19) in (2.20) gives us the behavior of the shock strength when y → ∞. So, in order to calculate the asymptotic shock strength, we must express Σ(y) explicitly. For this reason, firstly Υ(θ) must be developed in terms of (tanθ− tanθ0) by using Taylor series expansions. Putting the new Υ(θ) into equation (2.20) gives us a new definition of the vertical path of the shock as follows: (2.21) This result gives us the following expression for Σ. + Higher Order Terms (2.22) As it can be observed, the asymptotic shock strength will decay to zero with the factor kl, where the simplified form of the dominant coefficient l˜ 0 is the following:
  • 48. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 43 (2.23) The influence of higher order terms is very small; therefore, it is decided to neglect the effect of these higher order terms in the asymptotic shock strength Σ. It means the dominant term for the asymptotic shock strength when y → ∞ becomes: (2.24) The term is constant and does not depend on body geometry. As it only gives the Mach number of the undisturbed flow, it is considered as the Mfactor. We already know the characteristic angle of the undisturbed flow θ0 is the sum of the undisturbed Mach angle and undisturbed flow angle θ0=µ0+ϕ0. So, this help us to express Mfactor only in free flow Mach number as follows: (2.25) Thus, Al can be addressed as the only measure for the asymptotic shock strength of the leading-edge shock which depends on the shock wave-expansion interaction: (2.26) This integral shows the asymptotic shock power for an item in a constant and invisible supersonic flow, according to the BASS theory. Al is an integration of the cosθ distribution along the body surface in a domain which is defined from 0 at the nose to x0 at the shoulder point of the body where the θ0 characteristic intersects. At the shoulder point a Prandtl-Meyer expansion wave will occur where the flow expands to the free flow condition. And x0 is in fact the x-coordinate of the intersection of the Γ0-characteristic through the shoulder point for which the slope is zero with the x-axis. So, in this way the x-coordinates which are involved in this integral are actually the x-locations of the projected characteristic lines onto the x-axis.
  • 49. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 44 We have: (2.27) And with the trigonometric identity: (2.28) We can write this: (2.29) In the final and we after we did some calculations this results in: (2.30)
  • 50. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 45 With = 5. CFD (ANSYS Fluent) Fluent software includes the wide, physical modeling capacities required for industrial apps to model flow, turbulence, heat transfer and responses. These vary from air flow through an aircraft wing to furnace combustion, from bubble columns to oil platforms, from blood flow to production of semiconductors, and from clean room design to wastewater treatment plants. Fluent covers a wide variety, including unique designs, capable of modeling combustion in- cylinder, aero-acoustics, turbo machinery, and multi-phase systems. Fluent also provides extremely scalable, high-performance computing (HPC) to assist rapidly and cost-effectively solve complicated, large-model CFD simulations. By scaling to 172,000 cores, Fluent set a world record for supercomputing. The setup of any Fluent study is divided to 5 steps: 1. Geometry: Input of the geometry that you would like to study, and setting the computational domain 2. Meshing: Setting up a dynamic mesh is needed for any coupled analysis where a system receives displacements 3. Configuration: Setting up boundary conditions and restrictions 4. Solution: Mainly this part of the analysis is reserved to plotting the variables, such as the pressure distribution along a surface or the body. 5. Results: Visual representation of the flow and variable variation, for example pressure. Figure 2.26 Fluent CFD For comparison, this work will be conducted on 2D and 3D with different solver models such as Inviscid and laminar. Once all done, we will apply an angle of attack of 5 degrees which is the lifting case and redo the entire study in the different solver models.
  • 51. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 46 CHAPTER 3 : SONIC BOOM RESULTS 1. Introduction In this chapter we will see all the results found by the three approaches of analysis: theoretical, computational and experimental. And a comparison between them. 2. Experimental Results (Wind Tunnel) After conducting the experiment, we were finally able to get schlieren photos and take pressure measurements, the following is the pressure plot for 0° of attack: And the schlieren photo is as follows:
  • 52. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 47 The shock wave shows clearly, these results will be later on compared with the fluent and theory 3. Computational Results 3.1. No Lifting case for diamond shape airfoil (0° angle of attack) The model that will be used as discussed before is the 10° double wedge diamond airfoil, this model is perfect for preliminary studies for sonic boom production and reduction. the model is shown in Chapter 2 There are many models in the CFD that can be used and compute the lift and pressure distribution along the body (the 10° double wedge airfoil in our case). In this research we will only use three models which are: INVISCID, LAMINAR and TURBULENT, and then compare them to get a good idea on which model is best fit for our research. first of all, let's start by modeling the flow only in 2D. once the three models are compared, we will then redo the computation all over again, but this time in 3D. After finishing the 3D modeling and computations, we will then proceed to comparing the 3D results to the 2D. And choose which case gives the more accurate results.
  • 53. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 48 2D MODELING AND COMPUTATION: As discussed before the fluent study will be conducted in three cases: INVISCID, LAMINAR and TURBULENT. Let us start with the first case, which is INVISCID. a. INVISCID FLUENT COMPUTATION First of all, we need to select an analysis system for CFD: it will be "FLUENT" in our case as shown below: Figure 3.1 Fluent CFD a1. Geometry: To get matching results with the wind tunnel, we will take a rectangular computational domain that put the airfoil model in the middle section. the dimensions will be (200mm;100mm) in (x;y) coordinates. In 2D we can cut roots by only plotting half plane, and later use symmetry giving the fact that our body (double wedge is a symmetrical airfoil) as shown in the figure below:
  • 54. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 49 Figure 3.2 Computational domain As a first step in FLUENT, we have to draw the geometry and the computational domain. In 2D CFD, it is as easy as drawing a few lines, setting angles and distances and finally generate A surface from all of it combined as shown below: Figure 3.3 Geometry layout Figure 3.4 Body before symmetry
  • 55. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 50 Next, we need to cut the computational domain into parts, four in our case. So that the program will be made aware each time there is a change in surface. In our case the domain splitting will be made at the level of the start of the double wedge as shown below: Figure 3.5 Face split As we can see the domain is split into four parts and we are all done for the geometry part. a2. Meshing: First up, we need to name the borders of the computational domain, so that we can input boundary conditions in the setup part that will be discussed later. we have three named selections:  Fairfield: is a simulation of the ground, where we will take pressure measurements.  Symmetry: the two lines coming out from the edges parallel to x axis, will be used to create a symmetry and get a view for the entire computational domain  Wall: which is the upper part of our diamond airfoil. As shown below these are the named selections: Figure 3.6 Farfield after named selection
  • 56. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 51 Figure 3.7 Symmetry Figure 3.8 Symmetry Next up, is the meshing configuration. To start with we will assign a face meshing to each computational domain Figure 3.9 Face meshing And afterwards we will assign an edge sizing to each line that split the domains and also the lines that define the wall as shown below and increase the mesh accuracy for the boundary layer:
  • 57. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 52 Figure 3.10 Sizing Once all that is done and checked we will configure the mesh setup by setting function of meshing into "proximity and curvature”, relevance center into "fin", setting the maximum face size and max size and, smoothing to high and then finally generating a grid. The grid generated had a max element of "17200" elements and quality ratio of "0.60409" which good considering the fact that the quality ratio should be below "0.98"As a result of this work we got an accurate grid as shown below: Figure 3.11 Grid/Meshing a3. Setup:
  • 58. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 53 Figure 3.12 Setup Configuration Next up is the setup part, where we will input boundary conditions and select solver model and general settings. These settings and conditions should match the wind tunnel setting, giving the fact that we will compare the results later on. As a general setting we are going to set the solver setting into "density based" and time as "steady”. going into models we are going to set the energy equations into "on" and the calculation model into inviscid. Next is setting the air into ideal gas. in the boundary condition setting: the farfield will be set as a "pressure Farfield and the mach number set to "1.8 mach" to match the wind tunnel speed. the inlet pressure P∞ will be set to "0.23bar" again, as a matching to the wind tunnel conditions. Next the named selection "symmetry "should be set as a symmetry .and the double wedge as "wall". As a reference value, we going to ask the program to start computing from the farfield and select it as a reference domain. As a solution model we going to make it all into second order solving, because it is alot more accurate than first order. In the monitors part we are going to set the residuals into something very low, at least ten to the power mince five. Before starting the calculations, we have to do standard initialization also from the Farfield settings. Next up is the calculations part. But before doing so we hit the check case , to see if we have any problems with the grid or any recommendation from the software, if not we proceed into
  • 59. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 54 the calculations, and start the iterations .Once the program has finished the calculation we move on into the next step which is the solution. In this part we will mainly take the pressure distribution along the airfoil and on the ground to compare it later with the other results. As predicted the pressure distribution on the ground gave us an N-wave shape as shown below Figure 3.13 Pressure plot on the Farfield And the distribution along the airfoil:
  • 60. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 55 Figure 3.14 Pressure plot along the body These results will be later compared with the other results obtained from other models in 2D and finally compared with 3D results to decide which gives the best computation and analysis.
  • 61. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 56 a4. Results plot: Figure 3.15 Pressure Contour As excepted the results are symmetrical and the shockwave shown clearly along with expansion and after shock, once the flow passes the airfoil it returns to its normal value which is the input value. b. LAMINAR AND TURBULENT: The same procedure will be followed in our next computation except one slight detail. inputting the solver model as Laminar and redoing the calculations all over again. Once all done, we will save the results and again redo the calculations but only this time we will use the turbulent model which is "k-epsilon-realizable" and save the results. After plotting and comparing the results we had matching plot as shown below: As a small reminder, the input pressure is "0.23bar" matching the wind tunnel settings-
  • 62. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 57 Figure 3.16 Comparison between Inviscid, laminar and turbulent From this comparison, we can conclude that in 2D computations, it does not make any difference whether we choose INVISCID or LAMINAR or TURBULENT. There for from now on, if we are to do any computation in 2D, we will input INVISCID as a solver model. CATIA conception of the double wedge airfoil:
  • 63. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 58 Figure 3.17 Catia layouts 1. COMPUTATION USING INVISCID SOLVER: a1. Geometry: Same as 2D, in 3D we will use the fluent to do our calculations and conception. After building the double wedge in CATIA, we import it as ".stp” file into geometry and generate the file inside "Design modeler". In the non-lifting case the angle of attack is set to zero, therefore we don't need to input rotation .Next step is Enclosure ,which is the computational domain ,the dimensions of this domain are (100mm;25mm;50mm) in the (x;y;z) coordinates .the figure of the enclosure is shown below:
  • 64. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 59 Figure 3.18 Computation domain for the 3D analysis Next up we need to create a Boolean to subtract the body from the enclosure, this is a very important step that will help us produce a more accurate meshing and accurate simulation of fluid flow over the body (double wedge airfoil). a2. Meshing: Basically, the meshing process is a lot like similar to the 2D, except in 3D there is no domain splitting. We begin with by creating named selection, four to be exact:  INLET: The flow inlet, the setting will be configured in the setup part.  OUTLET: a pressure outlet that defines the exit of airflow.  SURROUNDING: The side and above surroundings of the airfoil.  FARFIELD: the part that represents the ground in our case.
  • 65. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 60 Figure 3.19 Named selections Figure 3.20 Surroundings After defining the named selections, we move on to setting up the meshing. To begin with, we set function of meshing into "proximity and curvature”, relevance center into "fin", setting the maximum face size and max size and, smoothing to high and then finally generating a grid. The grid generated had a max element of "265000" elements and quality ratio of "0.7856" which good considering the fact that the quality ratio should be below "0.98". The generated mesh look like the following:
  • 66. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 61 Figure 3.21 Grid generated This sums up the meshing process. a3. Setup: Figure 3.22 Setup configuration To begin with we select the type of our process as a density-based analysis and time as steady. Next up the energy equation set "on" and solver model as "INVISCID”. Next is the boundary
  • 67. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 62 conditions, just like the 2D, we need to give similar boundary conditions for us to be able to compare results afterwards. As a reminder, the inlet pressure is "0.23" bar and a speed of Mach 1.8. The Farfield and the surroundings, in our case will be selected as "wall", and the outlet as "pressure outlet". Then we will ask the software to take the inlet as a "reference value". Next up is the solution methods, we select second order instead of first order, giving that second order will give more accurate results. Select the residuals to something less than ten to the power mince five and as a final step before is initialization, we choose to initialize from the inlet. Finally, we enter the number of iterations as 1000 and ask the software to compute. This sums up the setup part. a4. Solution: In this part we ask the program to plot the pressure signature on the ground, which is the Farfield in our case showed in the figure below: Figure 3.23 Pressure plot on the farfield As excepted, the N-wave shows on the ground and leaves a pretty significant signature on the ground, later on it will be compared with other results (laminar and turbulent). Next, we ask the program to plot the pressure distribution over the body (double wedge airfoil) and we get the following
  • 68. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 63 Figure 3.24 Pressure plot along the body This figure will be later on compared with the turbulent, and laminar results from 3D. a5. Results: Next up, we insert an isosurface, that can move along the y axis, and set variable as "pressure" we get the following results: Figure 3.25 pressure contour
  • 69. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 64 As excepted the results are symmetrical and the shockwave shown clearly along with expansion and after shock, once the flow passes the airfoil it returns to its normal value which is the input value "0.23bar". 2. COMPUTATION USING LAMINAR SOLVER: We start all over again and redo the entire steps done in INVISCID, except this time we will use a laminar solvent. this time viscosity will be taken into consideration and many other factors. We input the settings just like before but with slight differences, like considering the viscosity and density in this case. we proceed into initialization of the software from the inlet and we start the computation. After finish the calculations we get the following pressure signature on the ground: Figure 3.26 pressure plot on the Farfield We can notice the pressure fluctuating frequently, and this due the disturbance in the flow and the consideration of viscosity different than zero. this figure will be later on compared to the TURBULENT and INVISCID results. Next up we plot the pressure distribution along the body (double wedge airfoil):
  • 70. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 65 Figure 3.27 Pressure plot along the body Same as the plot on the Farfield, we notice the fluctuation due to disturbance in the airflow above the body. Next up, in the figure below we plot the pressure contour and get an idea on the shape of shock wave: Figure 3.28 Pressure contour
  • 71. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 66 The shockwave and the expansion wave are clearly shown, but we do notice a slight disturbance on the wall, and this is due to boundary layer generated on wall. this is normal considering the fact that viscosity is different than zero. also, we notice a parallel lines coming up from the wall, these lines are called characteristic lines also known as Mach lines, these lines will be explained in the optimization part (final part of the thesis). 3. COMPUTATION USING TURBULENT SOLVER: As we understand, the distinction between laminar and turbulent is that the fluid follows a smooth route in laminar, routes that never interfere with each other, rather in chaotic uneven flow defined by small areas of whirlpool. This fluid's velocity is certainly not continuous at all points. Same as before, we will do the input the geometry and do the meshing, and proceed to the setup. The only difference is, we are going to use a different solver model which is "spalart- allmaras”. we will input the wind tunnel settings as before and start the calculations. Once the calculations are over, we proceed into plotting the pressure distribution on the ground and we get the following: Figure 3.29 Pressure plot on the Farfield The pressure is allot less fluctuating than the laminar, the result will be later compared to the remaining figures.
  • 72. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 67 Next up the plot over the body: Figure 3.30 Pressure plot along the body As a final result we are going to plot the pressure contour around the airfoil: Figure 3.31 Pressure contour
  • 73. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 68 The pressure plot is similar the results obtained before, the shockwave and the expansion clearly shown 4. COMPARISON BETWEEN INVISCID, LAMINAR AND TURBULENT: Next up we need to compare the results of the three models used in 3D computation. Let us start by comparing the pressure signature on the ground: Figure 3.32 Comparison between Laminar, turbulent and inviscid results We can notice that both the LAMINAR and TURBULENT models fluctuate allot, whereas the INVISCID plot is smoother and more accurate. Let us plot the pressure distribution over the airfoil for each model and compare
  • 74. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 69 Figure 3.33 Comparison on pressure plots along the body on Turbulent, Laminar and inviscid Again, we notice the INVISCID model is the smoothest and more accurate model. Therefore, the most logical and accurate solver model to use is INVISCID. From now on, the 3Dresults will be given using INVISCID solver model. 5. COMPARISON BETWEEN THE 2D AND 3D: As a final checkup, we need to choose between the 2D and 3D, let us compare the pressure plots for both: Figure 3.34 Comparison between 3D Inviscid and 2D inviscid
  • 75. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 70 The 3D modeling is known to give more accurate results, giving the fact that it considers all variables and also consider the thickness of the model, whereas the 2D model is based on only 2 axes. For the time being we will compare both results and compare them to the wind tunnel results. Figure 3.35 Comparison between 2D and 3D inviscid and windtunnel results In 2D the flow is moving in one direction, whereas in 3D the kinetic energy in the flow is higher (along with the mass flow) this explains why the 3D results are slightly higher than the 2D. We can see that the ind tunnel limited results giving the fact that it only takes measurements in several points (25 points). Also, from now on the Fluent study will be conducted in 2D solver models for simplicity reasons, and also giving the fact the windtunnel is 2D measurement equipment. 3.2. Lifting case for diamond shape airfoil (5° angle of attack) The second part of this chapter is to study the lifting case, which is applying an angle of attack to our body, first of all we will start with a 5 degree angle of attack ,after conducting the wind tunnel experiment we have a general idea on the pressure signature on the ground and on the body, also we managed to get a clear view of the shock wave and expansion wave. FLUENT MODELING AND COMPUATION:
  • 76. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 71 We will use the same model there for we will not need to rebuild the model in CATIA all over again, all we need to do import the "doublewedge.stp" and apply a rotation, the remaining steps are the same as the steps taken before in the 3D computation for non-lifting case. Only this time we will use only the INVISCID solver model, giving the results and analysis obtained before. Let us start by setting up the angle of attack Figure 3.36 Rotation along ZX axis (5 degrees) The angle of attack is set to 5 degrees with a rotation around the ZX Plane as shown in the figure above. Following the same steps as before we get a mesh of roughly 100 thousand elements and quality of 0,897 which is acceptable considering the fact it should be lower than 0.9. Figure 3.37 Grid generated
  • 77. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 72 We can notice the grid is more concentrated around the body, which is a good thing, that will give is a more accurate reading on the pressure distribution along the body and on the farfield (the ground). Next up is the setup, just like before, inputting the settings that match the wind tunnel, we initiate the calculation and plot the pressure distribution on the ground and get the following result: Figure 3.38 Pressure plot on the farfield Lifting case Next up is plotting the pressure distribution along the body:
  • 78. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 73 Figure 3.39 Pressure plot along the body (lifting case) Now, we need to compare these results with the wind tunnel, let us start by comparing the farfield results: Figure 3.40 Comparison Fluent vs wind tunnel results (Lifting case)
  • 79. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 74 The results of the wind tunnel compare to Fluent, the distance between readings in the wind tunnel between measurement point inside the test section, there is a 25 mm distance between each point. The results are correct and match. we can now increase the angle of attack a little bit. As a final result, we will plot the pressure contour: Figure 3.41 Pressure contour (lifting case) From this pressure contour we can see that when applying angle of attack the N-shape wave tend to disappear.
  • 80. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 75 4. Analytical Results of Whitham’s theory Figure 3.42 Pressure signature in the ground along the length of the working section in the wind tunnel 5. Conclusion 5.1. 0° angle of attack Pressure angle measurement:
  • 81. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 76 Figure 3.43 Shock wave angle measurement for 0° angle of attack Figure 3.44 Schlieren photo for 0° angle of attack We can come to the conclusion that the wind tunnel and fluent results (angle measurement) tend to match. therefore, the Fluent results are confirmed. 5.1. 5° angle of attack
  • 82. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 77 Figure 3.45 Theta-beta-mach curve In theory the angle of attack for 5°, beta should be equal to 38.56444, we will compare them with the results obtained from the fluent and wind tunnel experiment. Figure 3.46 Fluent angle measurement at 5° angle of attack
  • 83. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 78 Figure 3.47 Schlieren Photo at 5° angle of attack We can come to the conclusion, that the results match! CHAPTER 4 : MINIMIZATION OF SONIC BOOM 1. Introduction The idea behind the technique that we will use is adding a spike to the body, this way we can direct the shock in a different direction or at least minimize it. First of all, we came up with a Matlab code that predicts the and pressure variation, this way we can come up with a shape that produces minimum pressure signature and acceptable lift. the Matlab code result is shown in the following section. 1.1. Diamond Wedge
  • 84. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 79 Figure 4.1 Lift coefficient versus Pressure signature (flight conditions) The red line represents the angle of attack, and the blue line represents the Mach number. Now, for diamond wedge we are able to predicts the and pressure variation for different input Mach number and angle of attack. this way if we are to modify the shape, we can do the same analysis and predict the and pressure variation. Let us plot the following conditions:  Mach 1.8 and angle of attack 0°  Mach 1.8 and angle of attack 5° The following is a plot of the previously mentioned flight conditions:
  • 85. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 80 Figure 4.2 flight conditions in theory From the previous figure we got the following results for specified flight (Mach 1.8) conditions: Mach 1.8 DPmax Alpha = 0° 0 1.7 Alpha = 5° 0.24 2.7 Let us now compare these results with the results obtained from CFD Fluent. Mach 1.8 DPmax Alpha = 0° -0.0005 1.8 Alpha = 5° 0.214 2.5
  • 86. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 81 2. Minimization techniques to reduce Sonic Boom 2.1. Sonic boom reduction technique using Matlab Contour for diamond wedge 2.1.1. Sketch of the Diamond wedge (Lambda and t) “t” Modification λ Modification  Optimized Shape 2.1.2. Lift Coefficient Flight conditions: Mach 1.8 5° Angle of attack P∞= 0.23 bar
  • 87. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 82 2.1.3. Drag Coefficient Flight conditions: Mach 1.8 5° Angle of attack P∞= 0.23 bar
  • 88. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 83 2.1.4. Pressure signature and Lift Coefficient Flight conditions: Mach 1.8 5° Angle of attack P∞= 0.23 bar
  • 89. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 84 2.1.5. The Minimized Pressure Signature = 0.05 = 0.72 2.2. Scheme of the new optimized shape Shape corresponding to: t = 0.05c λ = 0.72c = 0.025c λ = 0.72c
  • 90. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 85 3. Results of minimization for 2D shape 3.1. Diamond wedge results 3.1.1. Geometry of the new shape 3.1.2. Grid generated Number of elements: 50 k roughly Quality ratio: 0.6 < 0.9 Run time: less than 10 minutes
  • 91. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 86 3.1.3. Results pressure plot on ground 3.2. Minimization technique inspired from F-15b NASA's modified supersonic aircraft Introduction to the idea The following proposed solution is inspired from the modified F-15b supersonic aircraft, this modification was geometry based, a spike was added at the nose of the aircraft to help reduce and spread the sonic boom and pressure signature on the ground. the following figure is a picture of the modified supersonic aircraft. 3.1.4. Pressure contour P (bar) 15% reduction
  • 92. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 87 3.2. Quiet spike sonic boom reduction technique 3.2.1. Introduction of the idea After understanding the sonic boom and the way it spreads, we can illustrate the sonic boom propagation in the following figure: Figure 4.3 Sonic boom Illustration The idea behind the technique that we will use is adding a spike to the body, this way we can direct the shock in a different direction or at least minimize it. First of all, we came up with a Matlab code that predicts the and pressure variation, this way we can come up with a shape that produces minimum pressure signature and acceptable lift. the Matlab code result is shown in the following section.
  • 93. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 88 Figure 4.4 F-15b Spike As you can see, the spike added is divided into several parts. We will apply the same analysis to our diamond wedge. the following is an illustration of the modifications we will add to the airfoil. Adaptation of the idea to our problem Figure 4.5 Modified diamond double-wedge airfoil Our added spike consists of two parts, with a main objective: reduce the sonic boom impact on the ground. Let us plot this geometry in ANSYS and follow the same steps as in the chapters before. Note that the analysis will be conducted in 2D for simplicity reasons. a1. Setup:
  • 94. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 89 As done before we will only plot half of the wing in the geometry and use symmetry later, due to the fact that our body is symmetrical. Moving on to the meshing we generate a precise grid by following the same steps as in the chapters before. The generated mesh had a number of elements of 50 thousand elements with a quality element of 0.85 which is less than 0.9 an acceptable rate. The grid generated is as follows: Next up is the setup part, we will use the same flight conditions as used before, A mach 1.8 as an inlet velocity and density-based analysis. once the setup is all done, we move on into the pressure plot and pressure contour illustration. a2. Results: The following figure is a pressure distribution plot on the farfield, we can see that the N-wave signature on the ground is disturbed
  • 95. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 90 Let us compare this signature with the double wedge airfoil on the same conditions: Figure 4.6 comparison between normal shape and optimized We can see that delta P max is significantly reduced (from 0.41bar to 0.36 bar) We conclude that the technique works and is a promising solution for our problem. The following is an illustration of the pressure contour:
  • 96. Experimental and Computational Study on Sonic Boom Reduction UNIVERSITÉ INTERNATIONALE DE RABAT 2018/2019 91 Figure 1.7 Pressure contour of optimized airfoil A close up on the modifications added and their effects: We can see that the spike added helped spread the shock wave into several ones, which helped to reduce the pressure signature on the ground. An adequate solution for a complicated problem.