AERODYNAMICS AND AEROACOUSTICS SIMULATIONS OF THE AIRBUS

AERODYNAMICS AND

AEROACOUSTICS SIMULATIONS OF

THE AIRBUS A320 FLAP SIDE-EDGE

A thesis submitted to the University of Manchester for the degree of Master of

Philosophy in the Faculty of Science and Engineering

2019

Juan Manuel Cruz Monterrosas

School of Mechanical, Aerospace and Civil Engineering

2

CONTENTS

LIST OF FIGURES ................................................................................................................... 5

ABSTRACT .............................................................................................................................. 7

DECLARATION...................................................................................................................... 8

COPYRIGHT STATEMENT .................................................................................................. 9

ACKNOWLEDGEMENTS ................................................................................................... 10

NOMENCLATURE .............................................................................................................. 11

CHAPTER 1: INTRODUCTION ......................................................................................... 14

1.1 Introduction to the topic. ............................................................................................ 14

1.2 Aims of the thesis. ....................................................................................................... 17

1.3 Structure of the thesis. ................................................................................................ 18

CHAPTER 2: STATE OF THE ART. ................................................................................... 19

2.1 Studies about aircraft noise generation. ................................................................... 19

2.1.1 Flap edge Noise generation ................................................................................. 21

2.2 Computational Aeroacoustics. .................................................................................. 24

2.2.1 Principal Problems ............................................................................................... 24

2.2.2 Acoustic analogies ................................................................................................ 25

2.3 Flap side-edge aerodynamics. ................................................................................... 27

2.3.1 Experiments. .......................................................................................................... 27

2.3.2 Computational simulations. ................................................................................ 28

2.3.3 Grid generation issues. ........................................................................................ 31

2.3.4 Turbulence Modelling Issues. ............................................................................. 33

2.4 Flap side edge aeroacoustics. ..................................................................................... 34

3

2.4.1 Experiments. .......................................................................................................... 34

2.4.2 Computational Studies. ....................................................................................... 37

2.4.3 Vortex Breakdown. ............................................................................................... 39

2.5 Noise Generation Mechanisms. ................................................................................. 40

2.6 Summary. ..................................................................................................................... 43

CHAPTER 3: FLOW PHYSICS ............................................................................................ 44

3.1 Reynolds Number. ...................................................................................................... 44

3.2 Strouhal Number. ........................................................................................................ 45

3.3 Courant-Friedrichs-Lewi condition (CFL). .............................................................. 46

3.3.1 Definition of the CFL Condition. ........................................................................ 47

3.3.2 Definition of CFL Number .................................................................................. 47

3.4 Drag Force. ................................................................................................................... 48

3.5 Lift Force. ...................................................................................................................... 49

3.6 Vorticity. ....................................................................................................................... 50

3.7 Pressure field. ............................................................................................................... 53

3.7.1 Sound Fields .......................................................................................................... 54

CHAPTER 4: APPLICATIONS OF COMPUTATIONAL FLUID DYNAMICS IN

AERODYNAMICS AND AEROACOUSTICS. ................................................................. 57

4.1 Governing Equations of Motion ................................................................................ 57

4.2 Turbulence Models ..................................................................................................... 58

4.2.1 Reynolds-Averaged Navier-Stokes Modelling (RANS) .................................. 58

4.2.2 Large Eddy Simulation (LES) ............................................................................. 60

4.2.3 Detached-Eddy Simulation (DES) ...................................................................... 61

4

4.3 Computational Aeroacoustics ................................................................................... 62

4.3.1 Background ............................................................................................................ 62

4.3.2 Lighthill´s Acoustic Theory ................................................................................. 64

4.3.3 The Ffowcs Williams and Hawkings Equation ................................................ 65

CHAPTER 5: CFD SIMULATION SETUP IN STAR-CCM+ ........................................... 68

5.1 Geometry specification ............................................................................................... 68

5.2 Grid Generation ........................................................................................................... 69

5.2.1 Surface Mesh. ........................................................................................................ 69

5.2.2 Mesh Sensitive Study ........................................................................................... 70

5.2.3 Verification and Validation. ................................................................................ 75

5.2.3 Boundary Conditions ........................................................................................... 80

CHAPTER 6: SIMULATIONS AND RESULTS ................................................................ 81

6.1 Overview ...................................................................................................................... 81

6.1.1 Computational details .......................................................................................... 82

6.2 Aerodynamic Analysis of Results ............................................................................. 84

6.3 Acoustic Analysis of Results ...................................................................................... 89

Chapter 7 CONCLUSIONS AND RECOMMENDATIONS ........................................... 95

7.1 Summary ...................................................................................................................... 95

7.2 Flap side-edge .............................................................................................................. 95

7.3 Recommendations ....................................................................................................... 96

BIBLIOGRAPHY ................................................................................................................... 98

23731

5

LIST OF FIGURES

Figure 1: Sound waves behave differently in the near field (A) and far field (B) [89].

.................................................................................................................................................. 54

Figure 2: The far field begins at 2 wavelengths away from the source [89]. ................ 55

Figure 3: The near field is complex, with sound energy both circulating and

propagating [89]. ................................................................................................................... 56

Figure 4: Acoustic arrays featuring many microphones can be used close to a source

to accurately measure sound energy in the near field [89]. ............................................ 56

Figure 5: Lateral overview of the on-surface grid at flap ................................................ 68

Figure 6: On-surface grid at flap´s top ............................................................................... 69

Figure 7: Lateral overview of the grid composes by the flap and the nearfield. ......... 72

Figure 8: Detail of the grid at the tip of the flap ............................................................... 73

Figure 9: Detail of the grid at the flap ................................................................................ 73

Figure 10: Isometric image of the complete mesh and boundary conditions location74

Figure 11: Lateral view of the mesh and airfoil location ................................................. 74

Figure 12: Lift Coefficient comparison between Angland's results and our simulations.

.................................................................................................................................................. 76

Figure 13: Drag Coefficient comparison between Angland's results and our

simulations. ............................................................................................................................ 77

Figure 14: Oil flow of flap side edge showing major flow features. View looking

starboard, flow is from left to right. [26]............................................................................ 78

Figure 15: Vorticity at the edge of the flap. ....................................................................... 79

Figure 16: SPL results at 30m/s with an angle of attack of 30 degrees. Angland VS our

results. ..................................................................................................................................... 79

6

Figure 17: Y+ values on the flap .......................................................................................... 82

Figure 18: CL of our simulations. ....................................................................................... 85

Figure 19: CD of our simulations. ....................................................................................... 86

Figure 20: Velocities contour in a series of y-z planes showing vortex merging and

separation of vortex from flap. ............................................................................................ 87

Figure 21: Details of the merging vortex at the edge of the flap. ................................... 88

Figure 22: Details of the vortex generation at the edge of the flap. ............................... 88

Figure 23: Vector plot around the flap side-edge in X direction. ................................... 89

Figure 24: Location of the point of evaluation for Sound Pressure Level (SPL) .......... 90

Figure 25: Sound Pressure Level (SPL) of simulations at 40 m/s whit different angles

of attack taken from the side of the flap side-edge. ......................................................... 91






of attack taken from the bottom of the flap side-edge. .................................................... 93





7

ABSTRACT

A computational investigation was carried out to study and determine the

aerodynamics and aeroacoustics of an Airbus A320´s flap side-edge. A detached eddy

simulation was performed on geometry that was based upon the airfoil of the flap; in

order to understand the flowfield and furthermore develop a future mathematical

model that would describe the generation of aircraft on the noise in the flap side-edge.

One main source of vorticity in the flowfield was identified from the computational

research; the flap side-edge vortical system. This source of vorticity interacted to

produce a significantly unsteady flowfield above the solid flap surface. One potential

acoustic source on the flap was identified. This was a turbulent shear layer that rolled

up to form the flap side-edge vortex, reattaching firstly on the side-edge and secondly

on the suction surface of the flap. Measurements taken as part of the computational

study were forces, on-surface pressures, sound pressure levels and a vectors

simulation were performed to visualise the on-surface flow.

8

DECLARATION

No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or of any other university or

institute of learning.

9

COPYRIGHT STATEMENT

I. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and s/he has given The

University of Manchester certain rights to use such Copyright, including for

administrative purposes.

II. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy,

may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as

amended) and regulations issued under it or, where appropriate, in accordance with

licensing agreements which the University has from time to time. This page must form

part of any such copies made.

III. The ownership of certain Copyright, patents, designs, trademarks and other

intellectual property (the “Intellectual Property”) and any reproductions of copyright

works in the thesis, for example graphs and tables (“Reproductions”), which may be

described in this thesis, may not be owned by the author and may be owned by third

parties. Such Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of the relevant

Intellectual Property and/or Reproductions.

IV. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant

Thesis restriction declarations deposited in the University Library, The University

Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations)

and in The University’s policy on Presentation of Theses.

http://www.manchester.ac.uk/library/aboutus/regulations

10

ACKNOWLEDGEMENTS

To CONACyT (Consejo Nacional de Ciencia y Tecnología), for providing me with the

financial support to study this master.

To all the Mexican friends that I have made in Manchester.

To those friends that I met in the George Begg building and who to introduced me to

a wider circle of friends.

To all of my friends from football, salsa classes, the pubs and everyone whom I shared

a pint with. Thank you to all for sharing this time with me and for helping me feel at

home in the distant and cold place of Manchester. ¡Salud!

A special acknowledgement to Charlotte (My Honey Bunny) for all the help, love and

support at this last stage of my master. Las palabras no me alcanzan para agradecerte,

Papita.

To my family: my grandparents, and especially, my parents and my brother Julio. I

will never be able to repay you for all the sacrifices you have made for me. Gracias de

todo corazón.

11

NOMENCLATURE

A Area, m2

CD Drag coefficient

Cdes Constant in DES model

CL Lift coefficient

Cp Pressure coefficient

c Speed of sound, m/s

C Courant number

𝑐 Mean aerodynamic chord, m

cF Flap chord, m

cp Specific heat at constant pressure, J/g.K

𝐷𝑘 Dissipation term in DES model

𝐸𝑖𝑗 Deformation rate

E Total energy, J/kg

e Internal specific energy, J/kg

Fdes Switching function between RANS and LES models

f Frequency, Hz

H(f) Heavy side unit function

I Acoustic Intensity, W/m2

k Turbulence kinetic energy, m2/s2

L Lift Force

l0 Correlation length of acoustic source, m

lt Turbulent length scale

Pij Compressive stress tensor, N/m2

p Pressure, N/m2

Q Convective heat transfer, W

Re Reynolds number

𝑅𝑖𝑗 Reynolds stress tensor

r Farfield distance, m

r0 Vortex radius, m

S Planform area, m2

𝑖𝑗 Main strain rate tensor

Stf Strouhal number based on flap chord

T Temperature, K

Tij Lighthill stress tensor, N/m2

t Time, s

tF Thickness of flap, m

u+ Non-dimensional velocity

𝑢𝑖′ Reynolds fluctuating quantity

𝑢𝑖′′ Favre fluctuating quantity

𝑖 Mean Reynolds averaging

12

𝑖 Mean Favre averaging

ui i-th component of velocity

V Velocity magnitude, m/s

V0 Non-linear region in acoustic analogy

V1 Linear region in acoustic analogy

xF Distance along flap chord, m

xi Generic direction

x, y, z Cartesian coordinates, x positive downstream,

y+ Non-dimensional wall distance

α Flap deflection angle, degrees

∆x, ∆y, ∆z Cell dimensions in x, y and z directions, m

δ(f) Dirac delta function

δij Kronecker delta function

∆ Maximum grid dimension between cell centers

∆t Physical timestep size, s

δ∗ Boundary layer displacement thickness, m

γ Ratio of specific heats

μ Molecular viscosity, Ns/m2

μt Eddy viscosity, m2/s

ν Kinematic viscosity, m2/s

Modified eddy viscosity in SA model, m2/s

ϑ Specific dissipation rate

θ Angle, rad

τij Viscous stress tensor

ρ Density, kg/m3

Ω Non-dimensional vorticity based on flap chord

ω Vorticity, 1/s

ω∗ Dimensionless angular frequency

Acronyms

AIAA American Institute of Aeronautics and Astronautics

CAA Computational Aeroacoustics

CFD Computational Fluid Dynamics

CFL Courant Number

CTA Constant Temperature Anemometry

DES Detached Eddy Simulation

DNS Direct Numerical Simulation

13

FWH Ffowcs-Williams Hawkings

LES Large Eddy Simulation

MICS Microphones

PSD Power Spectral Density

RANS Reynolds-Averaged Navier-Stokes

SADA Small Aperture Directional Array

SPL Sound Pressure Level

SST Shear Stress Transport

14

CHAPTER 1: INTRODUCTION

1.1 Introduction to the topic.

The regulation of noise generation within airports is becoming increasingly stringent.

Year on year the subject of noise reduction is becoming more pertinent, both from the

public and from the manufacturer's point of view. Noise is not only an annoyance, but

has been related to multiple effects on health and secondary to noise pollution. For

example, From the beginning of the 70’s Leibowitz[1] and De Vany [2] describes how

the Noise pollutions around the airports affects People and their property and made

an extensive research to prove it. Another researchers like Haines [3], Stansfeld [4],

Morrell [5], Franssen [6] and Ozkurt [7] in the last 20 years focus their research in

different health issues related to aircraft noise and presents important evidence from

different cases. For this reason, science and industry need to focus on reduction of any

noise generated by the aircraft. This issue did not start to attract attention until 1995,

despite being identified in the early 1970s, when it came to light because of the

increasing demands in air traffic. Furthermore, this attention was generated following

the steadily increasing demands placed on air travel, thus leading to the increase in

the size of airports and generating news regarding increased air traffic. [8] [9].

Noise emission at airports is regulated by various associations; an example being the

International Civil Aviation Organisation (ICAO). This is a complex problem that

originally involved a different part of the aircraft. Therefore, the new airplanes that

are under development are going to have improvements in noise reduction involving

every part of the aircraft, from the engine to every part of the airframe. This begs the

question as to what should happen with the old airplanes; can they continue to be

used?

For this reason, research must be focused on the existing aircrafts. The issue

surrounding noise generated by an aircraft started to gain attention when the turbine

15

engine was developed. This engine is only used for long trips and generates a lot of

noise. But as a consequence of the increasing demand for long haul flights, the airplane

manufacturers developed small airplanes with a jet turbine, that were able to carry

more weight in a shorter time. Subsequently, the organisations previously mentioned

developed new regulations in the early 1960s. Therefore, the airports’ owners were

forced to establish a noise level ceiling that the aircrafts were not allowed to exceed

[10].

Over the subsequent years, research was focused on how to decrease the noise

produced by the engines, but leave behind the noise produced by the airframe, until

the turbofan engine was created [11] [12]. As a result, a number of experiments

developed under the patronage of the Royal Aircraft Establishment (RAE) were

undertaken, with the participation of many companies. Accordingly, these

experiments took place between 1974 and 1978, identifying the principal source of

airframe noise and dependence of the aircraft speed [13] [14].

As previously stated, during 1970s the airplane noise emitted by airframe started to

draw the attention of some research groups [8]. Consequently, the first semi-empirical

airframe noise prediction method was created by Fink [15]. Actually, the classical rank

order of priority for commercial airframe noise is as follows: landing gears, slotted

slats, flap and slat side edges, flap and slat tracks, spoilers, and component interaction

noise sources. [15]

During the first attempts to find the origin of the Airframe noise, all the work was

empirical and they found that the noise produced by deflection of the flaps was

assumed to vary directly with flap area, inversely with far field distance squared, and

directly with airspeed to the sixth power [16].

At the end of the last century, the German national program on airframe noise

reduction was started [17]. A great aim was achieved; not solely by this program. For

16

example, the publication of the Airframe noise reduction challenge at the beginning

of this century resulted in a decrease in the noise generated by the Airframe [18]. A

new aircraft noise prediction program (ANOPP2) is now under development [19].

The Airframe noise prediction methods are divided into four categories and are

presented in order of complexity: fully numerical methods, Computational Fluid

Dynamics (CFD) methods coupled with the acoustic analogy, fully analytical methods

and semi-empirical methods [20]. This field has been led by empirical experiments,

despite this having limited physics. [9].

The high-lift devices (that are integrated by trailing edge flaps and leading edge slats)

increase the overall airframe noise level on the landing approach by around 10 dB and

these form one of the most important parts of aerodynamic noise [8] [10] [21] [22].

Accordingly, there are three items of research interest in the high-lift system: trailing-

edge noise, flap-edge noise and leading-edge slat noise [9].

At the beginning of the 21st century, Guo [23] developed an analytical model for the

study of flap fences on the flow and he produced data that showed a possible

reduction of noise generated by the flap-edge. However, he was not the only

individual to research into this particular part of the high-lift device; also, and more

recently, Angland and Zhang [24] found a high frequency noise reduction in the flap

side edge with a porous material. The same applies to Plata and Martini [25], resulting

in the immediate change from a structure “jet-like” (higher speed in the core) to a

“wake-like” (lower speed in the core) structure by the addition of a plate porous

material in the edge-flap. In all the cases, the authors recommend continuation of

further research into noise generation.

17

1.2 Aims of the thesis.

The main focus of this work is to generate initial data and knowledge in order to

understand how noise generation is associated to flowfield around the edge of the

flaps in future work. In the past, important experiments were developed to

understand the generation of noise [26], [24]. Contrary to these experiments, this work

did not require a big wind tunnel or expensive sensors and microphones to run.

Previously published works were continually used to validate the results.

As part of the simulations we considered the measurement of the drag and lift forces,

on surface pressures and sound pressure to analyse the noise generation. Simulations

were performed with Detached-eddy model and the nearfield unsteadiness

determined by using Ffowcs-Williams Hawkings solver to obtain the farfield

acoustics.

18

1.3 Structure of the thesis.

This thesis is divided into 3 main sections. Firstly, in chapter 2, a review of the most

relevant information is presented, and there is a brief discussion of the work

performed in the aerodynamic, aeroacoustics, noise generation, noise reduction

experiments and computational studies related to noise prediction. Chapter 3 explains

the principal flow physics related to aerodynamics and aeroacoustics as is Reynolds

number, Strouhal Number, Courant-Friedrichs-Lewi condition, drag and lift forces,

vorticity and pressure fields.

Secondly, in the fourth chapter, the principal equations used by Computational Fluid

Dynamics (CFD) software are mentioned as well as the principal models used in our

research. Additionally, in chapter five, the setup and most relevant specifications for

the simulation of the flowfield around a flap side-edge are described. Furthermore,

the validation of the mesh that we use for the simulations is discussed here.

Thirdly, the sixth chapter presents and discusses the results obtained from the

aerodynamic and aeroacoustics study of the flowfield around flap side-edge are

presented.

Finally, chapter 7 presents the conclusions as well as some recommendations for

future work.

19

CHAPTER 2: STATE OF THE ART.

In this chapter, a literature review of flap side-edge aerodynamics and aeroacoustics,

as well as related topics has been conducted. Section 2.1 discusses the generation of

aircraft noise and focus especially in the noise generated by the flap side-edge, which

has been identified as a major source of noise. Section 2.2 shows a review in the

computational aeroacoustic field. Section 2.3 contains references concerning the

aerodynamics of the flap side-edge and the fluid mechanics involved. Section 2.4

describes the aeroacoustics, as well as some experiments in the field of computational

simulations and progress made by several researchers. Section 2.5 describes the

current progress of the reduction in the generation of aeroacoustic noise produced by

the airframe of the plane (with particular focus in the flap side-edge), as well as

discussing some previous experiments. Finally, in section 2.6 a summary of key points

in the chapter is presented.

2.1 Studies about aircraft noise generation.

At the beginning of the 70’s of the last century, the first cycle bypass turbofan engine

had begun operations, part of a series of efforts of reducing fuel consumption. As a

side effect of this improvement in jet airplanes, the noise generated by the airframe of

the aircraft at the approach and landing gained equal importance. Some of the first

efforts focused in quantifying airframe noise generated by different parts of the

airplane [27] [28] [29] [30] [13] [31]. As a consequence, at the end of that decade,

research from Fink [32], Ahyte [33], Brooks [31] and Kendall [34] was developed,

focusing in the generation of noise by the airframe in a particular region, which

showed that a strong and complex generation of noise is linked with the high lift

system.

20

As previously mentioned, Fink [15] developed a semi empirical model in which he

relates both landing gears and high lift device as two major airframe noise generators.

He calculated the noise that is radiated by each part of the airplane individually,

without any interference of another noise source. Using the trailing edge flap spectra

study on a Vickers VC-10 from Fethney [13] in which he measured the spectra at three

different flap deflection angles, Fink conclude than the sound pressure level varied

with the square of the sine of the flap deflection angle. Fink also assumes than the

sound pressure level varies in a direct way with the flap area and airspeed to the sixth

power and inversely vary with the square of far-field distance. By the contrary, Chow

[35] mention than the noise generated by the flap vary with velocity to the eight power

and combined with the high lift device the velocity law is 𝑉5.5. Chow gets this data by

a series of experiments developed by flight test in a full-scale Airbus A340 aircraft.

Also, he developed an experimental noise prediction model, he demonstrates that

noise generated from gears during landing dominates over noise generated by the

high lift device and that noise from slats dominates over noise from flaps.

Another contribution was provided by Howe [36] [37], in which he describes that an

unsteady flow in the vicinity of an edge is an important source of aerodynamic sound.

Also identifies a strong vortex that exists at the outboard flap side-edge as a strong

source of airframe noise. In the vicinity of the flap side-edge, there is an unsteady,

turbulent flowfield that produces hydrodynamic perturbations. The sharp edge of the

flap side-edge leads to acoustic scattering of these hydrodynamic perturbations.

Therefore, unsteadiness in the flap side-edge region is efficiently converted to noise

and is radiated to the farfield.

The presence of a component of mean flow near the edge is related to the unsteady

motion in the neighbourhood of a side edge et al Howe [37]. As a result, this flow

generates the formation of a conventional tip vortex due to the forward motion of a

lifting airfoil. This comes from the lower to the upper surfaces of the flap (from the

21

pressure to the suction respectively); often in the upper surface of the edge a

separation bubble is formed.

Brooks [31], developed an entire prediction method at the end of the 80’s for the self-

generated noise of an airfoil blade encountering smooth flow. These predictions

methods for individual self-noise mechanisms are made based on previous theoretical

studies and self-noise data available on that time, an important relevant point is that

the models are semiempirical and generates new data that has been used until this

time.

2.1.1 Flap edge Noise generation

The source of high frequency broadband noise generated on the flap side-edge is

considered by Molin as the instability of two detached shear layers [38]. Therefore, to

form a single side-edge vortex, these two vortices merge further downstream.

Some analyses were performed by Angland and Davy in an Airbus A320 flap [26] [39].

On one hand, Davy made a series of experiments on a 1/11th scale Airbus A320 model

in an open anechoic wind tunnel and he characterise the airframe noise sources. By an

arrange of microphones he determine that at low and mid frequency range flap noise

contributes in a lower way to the overall noise than slat noise. But at high frequencies,

the flap side-edge noise contributes in a significant way to the overall airframe noise.

On the other hand, Angland develop a series of experiments and numerical techniques

to understand the physics responsible for noise production at the flap side-edge and

the mechanism by which a porous material applied to the flap side-edge reduced the

noise.

Angland [26] identifies a low frequency source radiation at the flap side-edge vortex

by interaction with the flap surface, essentially the suction surface nearest to the

trailing-edge. Consequently, the low frequency noise source mentioned was

22

correlated with the upper surface at the connection line where the post-merged vortex

encroaches on the flap upper surface. During the same experiments, Angland found

another low frequency noise source and this was related to instabilities in the vortical

structure itself in the stream wise direction. This was broadband in nature over a range

of 1 – 10 kHz (2.4 ≤ stf ≤ 24). A vortex bursting that is broadband and with tonal features

at high frequencies was associated with a noise mechanism.

Sound generated from dipole and quadrupole sources close to a sharp edge follows a

scaling law of 𝑉5. In the absence of a sharp edge they would radiate proportional to

𝑉6 and 𝑉8 respectively [40]. The Brooks and Hodgson [41] formula, which is based on

a flat plate at zero incidences with a sharp trailing-edge, gives the far field intensity

as:

𝐼−𝜌∞V5

2𝜋3𝑐2 (𝑢′)5

𝑉

𝑆

ℎ2 ℓ0

𝑐 (2.1)

Where the fluctuation in velocity near the sharp edge is 𝑢′, ℎ is the distance from the

trailing-edge to the observer and ℓ0 is the corresponding correlation length of the

acoustic source near the sharp edge. An important characteristic of this formula is that

it does not have angular dependencies and ignores Doppler effects associated with

1convection. Brooks and Hodgson used the boundary layer displacement thickness

δ∗ at the sharp edge for the correlation length. This relationship shows that the noise

emitted is proportional to the volume of turbulence crossing the sharp edge [42].

Hardin [43] suggested that convective turbulences in the boundary layer that was

around the flap side-edge was responsible for noise production. The magnitude of

sound radiation was related to the strength of vorticity of the convected flow and its

distance from the sharp edge. Convective turbulence travelling past a sharp edge

follows a 𝑉5 scaling law. However, in the measurements performed by Meadows and

Chow [44] [35], the scaling law was found to be 𝑉5.5or higher at high frequencies.

23

Since vortex merging and breakdown are low frequency phenomena, this led to

Meadows to conclude that shear layer instabilities were responsible for the bulk of the

concentrated audible noise generation.

Khorrami [45] performed a linear stability analysis in the vicinity of a flap side-edge,

based on a local mean flow determined from a RANS calculation. The conjecture of

Khorrami about the curved shear layer was that it was supported by large scale flow

perturbations. These fluctuations were brought closer to the flap surface by the vortex

velocity field. In addition to this, the fluctuations amplified unsteady modes in the

vortex. The next equation describes the peak amplification rates of vortex instabilities

in the flow studies.

2 <𝜔𝑟

∗𝑟0

𝑉< 4 (2.2)

Where: 𝜔𝑟∗ = Dimensionless real part of the angular frequency, 𝑟0 = Vortex radius. The

highest value in the amplification rates correspond to 11 ≤ Stf ≤ 22. The potential

acoustic sources are summarised by Khorrami as follows [45].

The free shear layer emanating from the flap bottom edge and spanning the entire

flap chord supports a fluctuation from a large-scale flow.

Large scale flow fluctuations supported by the post merged vortex downstream of

the flap midchord region.

Convection of turbulent boundary layers past a sharp edge resulting in scattering

and broadband sound radiation.

Vortex merging.

Vortex breakdown.

As is presented, the gap between the side-edge flap and the undeflected main element

of the wing is the main influence on the intensity of the generated noise.

24

2.2 Computational Aeroacoustics.

2.2.1 Principal Problems

The Navier-Strokes equations dictate the Computational Aeroacoustics (CAA), which

are comprised of accurate numerical prediction of aerodynamic problems.

Notwithstanding, the nature, characteristics and goals of aeroacoustics problems

differ significantly from the aerodynamics. Some computational issues that are

particular to aeroacoustics are presented by Tam [46] in which he demonstrates their

difference to usual CFD problems.

Firstly, aeroacoustics problems are time dependent.

Secondly, in the majority of the noise problems the frequency related is very

high, which means the wavelengths are small.

One of the suggestions that Tam proposed was that normally for direct numerical

simulations, a minimum of six to eight mesh points are required per wavelength. In

reality, a huge amount of mesh points are needed in the computational domain due

to the large spectral bandwidth of aeroacoustics problems. Roe [47] describes that the

velocity fluctuation associated with the radiated sound are many orders of magnitude

less than the mean flow and usually smaller than the error. Consequently, the

aeroacoustics solutions could be corrupted by the computational noise. This is related

to the magnitudes of acoustic waves and the mean flow disparity.

Incidentally, the partial resolution of a Direct Number Simulation (DNS) is important

because of the problem of distinct and well-separated length scale. In order to

maintain the Courant number (CFL) lower than its critical value for a stable finite

difference scheme, the size of the finest mesh controls the computational time step

Angland [26]. Something that generates an excessive CPU time is a very small spatial

resolution. Speaking about aerodynamic simulations, one of the principal difficulties

of interest is in determinating the loads and moments acting on the body being

25

modelled. Accordingly, the allotment of interest is focused in the solution only

needing to be the spectrum of the radiated sound in the farfield. It is compulsory that

the numerical scheme must be free of numerical dispersion, dissipation and

anisotropy. This is in consideration of the fact that the distance between the noise

source and the boundary is comparably long. These demanding requirements only

can be satisfied by few time-marching schemes as Tam mentions [46].

Radiation and outflow boundary conditions must acquiesce the acoustic and flow

disturbance to reduce to a minimal reflection the computational domain. For instance,

it is necessary for the radiation conditions to be within boundaries of inflow to allow

the acoustics wave propagates out of the computational domain. It is necessary to set

the outflow conditions along its boundaries, with the purpose of facilitating the exit

of disturbance acoustics, vorticity and entropy [46]. A direct consequence of having a

high-order spatial derivative is that the resulting finite difference equation will be

higher than the original partial differential equation. In this case, the number of

boundaries conditions needed for a unique solution is greater. Tam describes two

conditions that generate spurious numerical solutions near wall boundaries;

extraneous boundaries conditions and use of high-order equations.

2.2.2 Acoustic analogies

As Angland [26] mention, an acoustic analogy can be applied in order to avoid a

significant computational cost produced by resolving the acoustic waves propagating

into the farfield. The steps that describe the process of the acoustic analogy are the

following:

• Extract the necessary information out of an unsteady CFD calculation.

• Performs integration and computes the next tree important issues: time

dependent density, pressure fluctuation in the farfield and related frequency

spectra.

26

Recognize an outer region, mentioned as V0, wherein the acoustic waves estimates to

propagate linearly is the ground of the acoustic analogy. V1 that is a non-acoustic

region is surrounded by the acoustic region, where the governing linear equation does

not apply and the flowfield has to be either simulated by numerical methods or

measured by detailed experimental tests. For this reason, Morfey [48] explains two

approaches that matches the acoustic field to the “non-acoustic” region. The first is

where the non-linear region V1 is replaced by an extension of the linear region V0, with

equivalent sources added to represent the flow. The second is where the numerical

solution in the nonlinear region V1 is matched directly to a linear acoustic solution in

V0 by applying appropriate matching conditions across the interface.

Lighthill mention in his acoustic analogy [49] how the noise generation and

propagation allow to be divided into the computation of fluctuations in the near-field

and a separate computation of the generation and propagation of noise. Navier-

Stokes’ compressible equations can be written to describe the propagation of sound in

a uniform medium at rest due to externally applied fluctuating stress:

∂2𝜌′

∂t2 − 𝑐2 ∂2𝜌′

∂t𝑖2 =

∂2𝑇𝑖𝑗

∂x𝑖 ∂x𝑗 (2.3)

The left-hand side is the linear wave equation and the right-hand side is a source term

to the medium outside the region of the fluctuating flow. This term results from the

nonlinear convection and viscous terms in the momentum equation. This source term

is assumed known from the solution of the nearfield fluctuating flow.

As Ffowcs-Williams and Hawkins [50] (now mentioned as FWH) says that an

unsteady flow in the vicinity of an edge is an important source of aerodynamic sound.

The equation called after them [51] is an extension of the Lighthill-Curle’s theory of

aerodynamic sound to include arbitrary convection motion. As has been mentioned

in the previous analogy, is an integral technique that can predict the farfield signal

27

based solely on nearfield input. Now we present the diferential form of the FWH

equation:

(∂2

∂t2− 𝑐2

∂2𝜌′

∂x𝑖2 ) (𝐻(𝑓)𝜌′) =

∂2

∂x𝑖 ∂x𝑗(𝑇𝑖𝑗𝐻(𝑓))

−∂

∂x𝑖((𝑃𝑖𝑗 + 𝜌𝑢𝑖𝑢𝑗)𝛿(𝑓)

∂𝑓

∂x𝑗) +

∂

∂t(𝜌0𝑢𝑖𝛿(𝑓)

∂𝑓

∂x𝑖) (2.4)

The Heavyside unit function is defined as unity when f > 0 and zero when f < 0, where

the function f = 0 defines the surface outside which the solution is required. Equation

2.4 is usually solved using a Green function technique. Acoustic analogies calculate

the density or pressure fluctuations in the farfield and related frequency spectrum.

The acoustic analogies are more desirables, because they are less expensive in

computational cost than resolving the acoustic waves all the way out to the farfield.

2.3 Flap side-edge aerodynamics.

As first point is important to mention that are relevant and related work with

experimental studies are listed in the first part of this chapter, after this discussion we

follows the work related with computational fluid dynamics studies, to end with the

relevant computational issues related with our investigation.

2.3.1 Experiments.

As one of the most relevant work we start with the one performed by Spaid and Lynch

[52], were they performed experiments to illustrate some of the most important flow

physics associated with high-lift geometris at full scale of Reynolds numbers. Some of

the data included in their research are, static pressure distribution, lift and drag

measures, boundary layer and wake surveys. Some of their suggestions are that the

28

data could be useful for CFD code calibration since CFD have difficulties to model

complex flowfields related with high lift configurations such as confluent boundary

layers and merging wakes in an accurate way. Furthermore, Valarezo [53] and Lynch,

noted that important performance parameter did not scale simply with Reynolds

numbers experiments to full scale difficult. As conclusion Spaid and Lynch mention

that is was important to make measurements at Reynolds numbers representative of

flight conditions (this has been pointed in this thesis).

Gursul [54] present in his research a review of unsteady flows over different delta

wings. Kelvin-Helmholtz instabilities were identified in the shear layers that rolled up

to form the vortices. In order to explain the vortex wandering was freestrem

turbulence by Baker and Barker [55]. Nonetheless, the vortex core is bigger than those

caused by freestream turbulences as Menke and Gulsup [56] demonstrates. Finally,

Gulsul and Wensheng [57] shows that exist a correlation between the vortex

wandering and the presence of Kelvin-Helmholtz instabilities in the shear layer that

formed the vortex.

Angland and Zhang [24], also developed Wind-tunnel experiments to investigate a

flap side-edge vortex. The flowfield investigation showed that the peak turbulent

stresses were contained in the shear layer that rolled up to form the flap side-edge

vortex. The wake from the main element was also entrained by the side-edge vortex.

The near-field pressure fluctuations where the turbulent shear layer impinged on the

flap side edge were broadband in nature from a Strouhal number of 10 to 50. During

the hot-wire measurements on the downstream vortex they identified a broadband

instability centered around a Strouhal number of 13.2.

2.3.2 Computational simulations.

In order to understand the prominent flow structures associated with both the inboard

and outboard flap side-edges, numerous computational solutions have been

29

performed on the flow over a three-dimensional high lift wing. According to

Khorrami [58] these efforts were motivated by a lack of understanding of noise

producing fluid dynamical processes at the flap side edge.

For this reason, he performed an extensive computational investigation of a generic

high-lift configuration comprising of a wing and a half-span flap at flap deflection

angles of 29 and 39 degrees. The steady computational solutions were obtained using

the thin-layer form of the Reynolds Averaged Navier-Stokes (RANS) equations and

the Spalart-Allmaras turbulence model [59]. Several reasons have been cited by the

authors to justify the use of this turbulence model; specifically, its robustness,

efficiency and ability to handle flows where separation and reattachment occur.

Eventually occupying the entire flap side-edge, the primary vortex that was generated

rapidly grew in size in the stream wise direction. Contrary to this, the second vortex

designed as the weaker vortex only grew moderately. Khorrami postulated that the

separated shear layer at the bottom flap side edge was a constant source of vorticity

that was wrapped around the vortex and “fed it”. This is because close to a point near

the flap mid-chord, he noted that the primary vortex, which was detached from the

side-edge, moved to the upper surface and merged with the top vortex to form a single

strong vortex. These shear layers were formed due to boundary-layer separation at

both bottom and top sharp corners on the flap side edge. This constant feeding of

vorticity resulted in a stronger vortex with a low-pressure core, which caused the axial

velocity in the core to obtain a speed up to twice the freestream speed [26].

Khorrami [60] founded that according to the acoustic array measurements, the

outboard flap side-edge was found to be a more potent noise source than the inboard

flap side-edge. The reason postulated was that the outboard vortex path remained

closer to the side-edge than the inboard path and vortex breakdown first occurred at

the outboard edge and at lower flap deflection angles. Khorrami´s conclusion of this

30

study was that vortex breakdown was not unique to these simple generic

configurations and in reality could occur at any flap side-edge in a high-lift setting.

Streett [61] also noted two separation bubbles, similar to the previous studies

discussed, with associated stream wise vorticity and roll-up at the upper and lower

corners of the flap edge. The reattachment point of the side-edge vortex moved up the

side edge as the flow progressed along the flap chord until it reached the upper corner.

The side-edge vortex then travelled over the upper corner interacting and then

merging with the upper-surface vortex. This single vortex was fed with vorticity from

the cylindrical shear layer that emanated from the lower edge. The mechanism of

continually feeding vorticity into the vortex produced a strong jet-like flow in the core

of the vortex.

Sensitivities of the computed solutions were categorised by Moitra [62] as those

dependent on the grid and those depending on the flow solver. Grid attributes such

as surface point distribution, normal spacing near the surface, and grid stretching ratio

and grid density in the wake regions have large effects on the accuracy of the

computed solution for complex high-flows. Moitra stated that turbulence models and

transition location were the principal sources of flow solver sensitivities. Subtle

differences in turbulence modelling caused differences in the prediction of wake

growth, particularly for wakes in adverse pressure gradients which characterise high-

lift flow fields. Since the location and extent of separation was strongly influenced by

the transition location, it was important to accurately predict the location of the

transition from laminar to turbulent flow.

As one of the most recent works, Cummings [63] performed a detached-eddy

simulation on a high-lift wing on an unstructured grid. The geometry consisted of a

half-span flap and a three quarter span slat. He applied a grid refinement to the slat,

main element leading edge, and main element flap cove and flap regions. The largest

31

grid size was 5.2×106. Although some unsteadiness was found in the slat region, the

flap-tip vortex was found to be steady. The authors concluded that there was a

necessity to improve the grid density of the simulation.

2.3.3 Grid generation issues.

Moitra [62] during his research obtained important grid attributes for computing high

lift flowfield. He get them by systematically varying grid parameters until an increase

in grid density no longer produced appreciable variations in surface pressure and

skin-friction coefficients as well as integrated quantities such as lift, drag and pitching

moment. He mentioned that the most difficult part is to ensuring sufficient grid

density in the area of interest of our flow phenomena happens, while you prevent a

deterioration of grid density and smoothness in other areas. Moitra focuses in three

principal areas: The resolution of the boundary layer, grid density on the surface of

the geometry, and resolution of wakes including regions of merging or separation.

As Moitra [64] shows in his review, during a research leaded by Boeing, the maximum

limits on surface spacing were established to be 0.1 and 0.3 percent of the chord at the

leading and trailing edges respectively. This has been an important data to determine

our grid clustering in the present study.

Also during this review, Moitra shows important information about the grid

resolutions requirements for boundary layers, and he pointed to two important

considerations: the initial normal spacing and the stretching ratio. He stated that the

initial normal spacing at the surface must be small enough to provide at least three

points in the linear sublayer (y+ < 5). This implied an upper bound of approximately a

y+ of 1.5 on the upper surface. And, Fluent recommends in his User’s Guide [65] that

when the laminar sublayer was being resolved, then the y+ at the wall adjacent cell

should be y+≈ 1. However, a higher value of y+ was acceptable as long as it was well

inside the viscous sublayer (y+ < 5).

32

As Moitra [62] mentions the resolution of the wake regions was the most crucial

requirement for accuracy of CFD predictions of high-lift flows. The usual method was

to assume a priori the location of the wake in the form of lines in the flowfield and to

cluster points in the vicinity. The difficulty was in predicting the location of the wake.

As a result in the best option this method may result in a waste of grid points and in

the worst of the cases, corruption of the solution as a result of a lack of resolution.

Moitra [62] stated that the origin of wakes was in the boundary layer, submerged in

the boundary layer grid, and therefore were well resolved. As it moved downstream

it moved away from the airfoil surface. Crucially a lack of grid resolution caused a

rapid dissipation of the wake in this case. The wake half-width grows directly

proportional to the streamwise distance [66] [67]. Also, in the boundary layer the

velocity gradients are hundreds and often thousands of times larger than the wake

velocity gradients [62]. This led Moitra to conclude that it should be enough for grid

spacing of several orders of magnitude greater than the boundary layer to resolve

wakes.

Special attention was paid to the region behind a highly deflected flap where the flow

was characterised by flow separation and massive flow reversal. These phenomena

occupy a large spatial extent and cannot be adequately resolved by grid refinement of

the near-body alone. The widely varying length scales associated with the flow

phenomena in this region caused a solution-adapted grid to approach a uniform grid

[64] seen in the solution adapted grid results presented by Walsh and Zingg [41].

A guideline for the creation of detached-eddy simulation (DES) grids for external flow

applications has been presented by Spalart [68]. The DES method is aimed at

modelling high Reynolds number separated flows. Spalart suggested a y+ = 2 or less

and a stretching ratio of 1.25 or less, for the RANS resolved attached boundary layer.

The grid spacing should be chosen to give adequate spatial resolution in the area of

primary interest. As Spalart mentions in his work, the best way to spend less

33

computational resources and obtain the desired resolution was to have cubic cells. For

time step considerations, five-time steps per period were recommended for the

smallest resolved eddy in the LES region. Is important to mention than we use this

guideline to obtain the create our grid in this work.

2.3.4 Turbulence Modelling Issues.

For the Spalart-Allmaras one equation [59] and the Menter two equation [69] [70]

turbulence models Godin and Zingg [71] has been evaluated for RANS computation

of high-lift aerodynamic flows. Is important to mention the cases considered: A

separated flow over a single element airfoil at a high angle of attack, a fully-attached

flow over an airfoil with a flap, and a separated flow over an airfoil with a flap. The

Spalart-Allmaras turbulence model is a one-equation transport model for eddy

viscosity. The Menter model combines the k−ω model with the k − ǫ model in a

manner that exploits the best features of both [69]. This blends the robust and accurate

formulation of the k−ω model in the near-wall region with the free-stream

independence of the k − ǫ model in the far field. Godin [71] shows in his results that

the Menter model is more accurate in separated flow regions. The Spalart-Allmaras

model was more accurate in attached flows and wakes, including merging boundary

layers and wakes. According to Godin and Zingg, the Spalart-Allmaras model was

somewhat more robust and is therefore preferred for general computations of

aerodynamic flows while the Menter model is the better choice if separated flows are

of primary interest. Khorrami in his works [60] used the Spalart-Allmaras turbulence

model [59] with a solid-body rotation modification which produced better results for

vortex dominated flows.

34

2.4 Flap side edge aeroacoustics.

During this part of the chapter the most relevant data about the aeroacoustics will be

explained. Focusing principally in experimental and computational experimentation.

2.4.1 Experiments.

As one of the most important investigations during the beginning of noise generation

and trying to understand the generation of it, Macaraeg [72] performed a research at

the NASA Langley research centre specifically focus into airframe noise mechanism

associated with high-lift devices. The measurements taken during this research

include steady and unsteady pressure measurements, hot films, oil and pressure

sensitive paint for flow visualization, also were taken five hole-probe measurements,

particle-image velocimetry, laser velocimetry and laser light sheet measurement. In

order to obtain an acoustic source map of the model as a quantitative spectra an array

of microphones were used. Is important t mention that the targeted frequency during

the research was 2-30 kHz. To start the hypothesis of the noise generation mechanism,

a vibration of flap side edge vortical structure was proposed. However, Macareg

pointed that the laser light sheet data did not reveal significant vibration of the

structure, nonetheless, the flap side-edge noise dominate at low frequencies.

The maps obtained by the large aperture microphone array showed on the edge of the

flap a higher frequencies source. Macareg mention that this was consistent with the

primary vortex grazing to the edge of the flap. As the frequency decreased, the source

moved downstream and inboard. This was due to the merged vortex system spilling

over the side-edge and impinging on the upper surface of the flap. The shear layer

instability was broadband in nature as the disturbance remained significant from 5

kHz (Stf ≈ 10) to 30 kHz (Stf ≈ 63)2. Apparently as the frequency decreases the vortex

instability start to get more strength than that of the shear layer instability. From the

5 kHz noise map the maximum intensity occurred inboard of the flap side-edge at the

35

location where the vortex moved rapidly over the side-edge and onto the suction

surface. Furthermore, Macaraeg founded that a sudden rise in noise intensity occurred

following an increase in the flap deflection angle due to vortex bursting on the flap

side edge system. Important to mention that this reference was useful in determining

noise generation mechanisms for a flap side-edge, namely cylindrical shear layer

instabilities, instabilities in the primary vortical structure and vortex bursting.

Another important part was in detailing acoustic source maps and quantitative

spectra.

In order to investigate the sound generation mechanism of a flap side edge an

experimental study was performed by Brooks and Humphreys [22]. A Small Aperture

Directional Array (SADA) of microphones was used to obtain farfield noise spectra

and directivity acoustic database. The measurements revealed a dominant flap vortex

structure that resulted from the merger of two upstream vortices; one strong vortex,

formed on the pressure side which dominated the flap side-edge, and a weaker vortex

formed at the flap side edge on the suction surface. Brook and Humphreys observed

that as the flap side-edge was approached from inboard, the surface spectral levels

increased. However, the classical turbulent-boundary-layer trailing-edge noise scatter

problem is opposite to Humpherys and Broook’s trend of increasing spectral levels

approaching the edge. Therefore, a different mechanism other than edge scattering is

suggested [41].

In order to develop their research Brooks and Humphreys [22] hypothesised a

different mechanism consistent with shear layer instability models for noise

production [58] [61]. This shear layer instability resulted in shedding of unsteady

vortices from the flap side-edge and related pressure scatter. For higher flap angles

the measured noise levels exceeded the predictions, which suggested additional

contributions from surface sources that were not localised to the immediate flap side-

edge region. This additional source was related to vortex bursting that occurred at

36

high flap angles as observed by Khorrami [58]. Focusing in the flap side-edge, a simple

dipole directivity pattern at low frequencies were founded by Brooks and Humphreys

and an approximate cardioid pattern for high frequencies at the same region.

Notwithstanding the cardiodid pattern was reserved with higher levels being found

away from the extended flap side-edge, which is contrary to thin edge scatter theory.

The authors offer an explanation, it was related to edge thickness and to acoustic

wavelength effect.

Working over the field of high-lift wing, Meadows [44] performed aeroacoustic

measurements to investigate sound generation. The tests were performed on a NACA

652 − 215 airfoil with a 30% chord half-span fowler flap. Reaching a speed up to March

0.17 and Reynolds numbers up to 1.7 x 106 were tested. This research used a Large

Aperture Directional Array (LADA) in order to identify locally dominant noise source

by producing high spatial resolution noise source location maps along the airfoil

surface; a SADA also were used to measure the directivity and spectra of selected

portion of wing flap model, and unsteady pressure sensors, to quantify the

wavenumber spectra over the surface and to correlate the surface pressure

measurement with the farfield acoustic measurements. As has been mentioned

previously in other researches, Meadows noted the presence of a dual vortex system.

For the 39 degree flap deflection case the vortices were stronger and the side-edge

vortex spilled over to the upper surface sooner. More interesting according to

Meadows was the vortex bursting that occurred. Acoustic field maps obtained from

the LADA measurements showed that the locally dominant noise source changed

with frequency. A trend existed for low-frequency sound sources to be located near

the flap trailing-edge. High-frequency sound sources were located near the flap mid

chord for the 29 degree flap deflection case and near the flap-main element juncture

for the 39 degree flap deflection case. According to Meadows this trend of decreasing

frequency with increasing streamwise distance was consistent with an increase in the

37

scale of the dominant flow structures. Furthermore, this trend was also noticed by

Kendall and Ahyte under their research [34].

Related with the SADA measurements Meadows founds that for the 39 degree flap

deflection angle, all spectra uniformly increased, typically 10 dB from the 29 degree

flap deflection case, except for the very lowest frequencies. This level increase

included the high frequency tonal features of the spectra. Another peculiarity noted

by Meadows was the broadband noise for the higher flap deflection angles that

seemed to have a distinct Strouhal number dependence. This is characteristic of flow-

surface interaction noise. The appearance of multiple broadband tonal features at high

frequencies suggested that there was an altered flow condition at the flap side-edge

that dominated the radiated noise field.

An overlap region between the trailing edge of the main element and the side edge of

the flap has an split flap configuration. Choudhari [73] referes this one to as the side

lap region. This side lap region generates a high speed jet which flows throught the

gap region. As a result a strong shear layer separates the main element with an

opposite sign of vorticity to that of the flap side edge vortex. The explanation of

Choudhari is that this caused a flattening of upper surface flap vortex and delayed

merging between the two vortices.

2.4.2 Computational Studies.

Related with this area, Streett [61] obtained a computational solution of the fluctuating

flow field associated with the complex vortex system at the side of a flap in a multi-

element wing system.

In order to calculate the spectrum of noise generated by such flowfield the spectral

content of these fluctuation has been estimated. The fluctuations at the flap side-edge

are broadband in frequency. Since the computational effort required to simulate

38

unsteady phenomena is roughly proportional to the ratio of the highest to the lowest

frequency, this led Streett to declare that the use of unsteady RANS to simulate these

fluctuations was “out of the question” [61]. Using the Lighthill acoustic analogy [49]

the first approximation to the origin and frequency content of the fluctuations has

been obtained. As Streett mentions, the primary noise generating fluctuations resulted

from instabilities in the flow. As an example, we can mention: inflectional instabilities

in shear layers resulted in the reorganisation of steady mean vorticity into fluctuating

vorticity of potentially large amplitude. Streett suggested that the non-linear

interaction of these fluctuations in a rapidly-varying mean flow would be the

mechanism for noise generation.

Streett found two basic families of disturbance modes. The first was associated with

the instability in the cylindrical shear layer, which overlies the side-edge separation in

upstream stations, and feeds the trailing vortex in downstream stations. Streett

proposed that the instability, strength, location and thickness of the cylindrical

boundary layer were functions of configuration and loading. For the configuration

examined by Streett, the shear layers over the two vortices present were relatively thin

at 10 percent of the flap chord, which led Streett to expect higher frequencies to

dominate. At 50 percent of the flap chord, the two vortices had merged and the

cylindrical shear layer/vortex system was well established. The instability of the

cylindrical shear layer was broadband in nature. Streett also noted that 5 kHz (StF ≈

12) disturbances persisted with significant magnitude even as they were convected

over the vortex. The second disturbance mode was associated with the instabilities of

the vortex and its “jet-like core” which possessed a significant oscillatory structure in

the streamwise direction. The dominant frequency band for these disturbances was

considerably lower than that for the shear-layer instability. From the measured

frequency spectra, the shear layer instability band was roughly 5 kHz (Stf ≈ 12) to 30

kHz (StF ≈ 73), while for the vortex instability Streett found the band was roughly 1

39

kHz (Stf ≈ 2.4) to 10 kHz (Stf ≈ 24) with wavelengths corresponding to the order of 1/4

to 1/2 of the vortex diameter.

2.4.3 Vortex Breakdown.

One of the most relevant mechanism for noise generation has been the vortex

breakdown at high flap deflection angles. The next part will outline the examination

of the phenomenon. Vortex breakdown classically refers to the appearance of a

stagnation point on the vortex axis followed by a region of reversed flow [74],

Benjamin [75], identify two category of vortex breakdown: the axisymmetric bubble

type and the asymmetric spiral type. Both involve a sudden expansion of the vortex

core. Benjamin also shows that the phenomenon was a transition between two

dynamically conjugate flow states. Harvey [76] performed a series of experiments and

determined that vortex breakdown to be an intermediate stage of two types of rotating

flows.

Bossel demonstrate in his work [77] that Harvey and Benjamin were wrong. He

showed that that the phenomenon was a regular solution to the linearised version of

the axisymmetric incompressible Euler equations when retardation of the axial

velocity and high swirl were introduced. Bossel also showed that the breakdown was

essentially an inviscid phenomenon and the swirl parameter was the determining

factor as to whether or not vortex breakdown would occur.

Another important point was done by Grabowski and Berger [78], were they solved

the Navier-Stokes equations for the breakdown of an unconfined viscous vortex. Whit

this results they refuted the theory that the vortex breakdown was a finite reversible

transition between two states. Further numerical results showed that the swirl was the

dominant parameter in axisymmetric breakdown, this has been performed by Salas

and Kuruvila [79].

40

Gursul [58] founds at the beginning of the century in his experimental and theoretical

explanations that swirl level and external pressure gradient outside the vortex core

affected the occurrence and movement of vortex breakdown. Flow downstream of the

vortex breakdown exhibited hydrodynamic instability. It was also observed in several

experiments that the vortex breakdown location was not steady and exhibited

fluctuations along the axis of the vortices.

2.5 Noise Generation Mechanisms.

During the previous parts of this chapter we have discussed a long all the literature

review about the noise generated by the flap side edge of the airframe and identified

them. Choudhari and Khorrami [80] listed in the next way the noise producing

features near the flap side-edge: free shear layers and their rollup, formation of

multiple vortices, vortex merging, and vortex bursting when the flap deflection was

sufficiently large. Another relevant noise source is the one pointed by various

researches that we have pointed during this chapter, two detached shear layers which

roll up from the flap side-edge to form primary vortices. Molin [38] mentions,

instability of these detached cylindrical shear layers, especially close to the lower

surface, are considered as the source of high frequency broadband noise localised on

the flap side-edge. Both vortices merge further downstream to form a single side-edge

vortex. Also Molin says that this pairing, in itself, does not contribute significantly to

the generation of noise.

Two low frequency sources have been identified. Firstly, the flap side-edge vortex

source radiated by interaction with the flap surface, mainly the suction surface close

to the trailing-edge. This low frequency noise source was associated with the upper

surface at the attachment line where the post-merged vortex impinged on the flap

upper surface. Secondly, the next low frequency noise source was associated with

41

instabilities in the vortical structure itself in the streamwise direction. This was

broadband in nature over a range of 1 – 10 kHz (2.4 ≤ Stf ≤ 24). A noise mechanism

was associated with vortex bursting that was broadband and had tonal features at

high frequencies. The effect of edge scattering has been mentioned in the preceding

discussion. Sound generated from dipole and quadrupole sources close to a sharp

edge follows a scaling law of 𝑉5. In the absence of a sharp edge they would radiate

proportional to 𝑉6 and 𝑉8 respectively [40]. The Brooks and Hodgson formula, which

is based on a flat plate at zero incidence with a sharp trailing-edge, gives the farfield

intensity as,

𝐼−𝜌∞𝑉5

2𝜋3𝑐2 (𝑢′)5

𝑉

𝑆

ℎ2 ℓ0

𝑐 (2.5)

where 𝑢′ is the fluctuation in velocity near the sharp edge, h is the distance from the

trailing-edge to the observer and ℓ0 is the corresponding correlation length of the

acoustic source near the sharp edge. This formula has no angular dependencies and

ignores Doppler effects associated with convection. Brooks and Hodgson used the

boundary layer displacement thickness δ∗ at the sharp edge for the correlation length.

This relationship shows that the noise emitted is proportional to the volume of

turbulence crossing the sharp edge. Possible noise reduction methods would be to

reduce the volume to turbulence convecting past the sharp edge and to change the

scattering by modifying the sharp edge [42].

Hardin [43] suggested that turbulence in the boundary layer that was convected

around the side-edge was responsible for noise production. The magnitude of sound

radiation was related to the strength of vorticity of the convected flow and its distance

from the sharp edge. Turbulence convected past a sharp edge follows a 𝑉5 scaling law.

However, in the measurements performed by Meadows [44], the scaling law was

found to be 𝑉5.5 or higher at high frequencies. Since vortex merging and breakdown

are low frequency phenomenon, this led the authors to conclude that shear layer

42

instabilities were responsible for the bulk of the concentrated audible noise

generation.

A mechanism for sound production at the side-edge was proposed by Sen [81] as the

oscillation of the side-edge vortex. The frequency was dependent on circulation, edge

thickness and mean distance from the edge. In Sen’s model, the base vortex was

perturbed using a smaller vortex to simulate the interaction between the side-edge

vortex and upstream unsteady flow structures. The principal conclusions of Sen about

his vortex oscillation model was that when the vortical region was compact, i.e. far

away from the flap surface, the vortices tended to move in a mutually cancelling

manner, which resulted in low acoustic production.

Khorrami and Singer [45] performed a linear stability analysis in the vicinity of a flap

side-edge, this was based on a local meanflow determined from a RANS calculation.

The two models proposed were cylindrical shear layer instabilities and streamwise

vortex instabilities. Khorrami and Singer conjecture that the curved shear layer

supported large scale flow perturbations. The fluctuations in the shear layer were

brought close to the flap surface by the vortex velocity field. The fluctuations also

amplified unsteady modes in the vortex. In the flow studied, peak amplification rates

of vortex instabilities occurred for,

2 <𝜔𝑟

∗𝑟0

𝑉< 4 (2.6)

where ω∗r is the dimensionless real part of the angular frequency and r0 is the vortex

radius. The peak amplification rates correspond to 11 ≤ Stf ≤ 22.

Khorrami and Singer [45] listed on their work the potential acoustic sources in the next

order.

43

1. Large scale flow fluctuations supported by a free shear layer emanating from

the flap bottom edge and spanning the entire flap chord.

2. Large scale flow fluctuations supported by the post merged vortex

downstream of the flap midchord region.

3. Convection of turbulent boundary layers past a sharp edge resulting in

scattering and broadband sound radiation.

4. Vortex merging.

5. Vortex breakdown.

Finally, in relation with the split flap configuration, Howe [37] formulated a model for

the flow through the slot between the flap and the undeflected part of the main

element. The gap between the side-edge of the flap and the undeflected main element

was the main influence on the intensity of the radiated sound.

2.6 Summary.

During the last five decades, the reduction of airframe noise has been the principal

focus of the manufacturers in this domain. Several had achieved important successes

by different methods over the last two decades. The literature shows that an important

source contributing to airframe noise has been located along the flap-side edge. The

previous work identified a mid-frequency noise source and described the major flow

characteristics of the flap side-edge. The present work contributes to the

understanding of aeroacoustics in the flap side-edge by several simulations and

experiment reviews. The combination of experimental and computational approaches

was used to attempt a better understanding of flap side-edge noise.

44

CHAPTER 3: FLOW PHYSICS

In order to understand the physics related with this field a chapter has been created.

In the following chapter we will discusse: Reynolds number (Re), Strouhal number

(St), Courant–Friedrichs–Lewy (CFL) condition, drag and lift forces, pressure field

and Vorticity. Is important to mention that the following information has been

extracted from the next books [82] [83] [84].

3.1 Reynolds Number.

Reynolds (1874) studied the flow characteristics of fluids by injecting a tracer into a

liquid flowing through a pipe. At low liquid speeds, the tracer moves linearly in the

axial direction. However at higher speeds, the fluid flow lines become disorganized

and the tracer disperses rapidly after its injection into the liquid. The linear flow is

called Laminar and the erratic flow obtained at higher liquid velocities is called

Turbulent.

The characteristics that determine the laminar flow depend on the properties of the

liquid and the dimensions of the flow. As the mass flow increases, the momentum or

inertia forces increase, which are counteracted by friction or viscous forces within the

flowing liquid. When these opposing forces reach a certain equilibrium, changes in

the characteristics of the flow occur. Based on the experiments carried out by Reynolds

in 1874, it was concluded that the forces of the moment are a function of the density,

the diameter of the pipe and the average speed. In addition, the friction or viscous

force depends on the viscosity of the liquid. According to this analysis, the Reynolds

Number was defined as the relationship between inertial forces and viscous (or

frictional) forces.

45

𝑅𝑒 =𝜌𝑢𝐿

𝜇=

𝑢𝐿

𝑣 (3.1)

where:

• 𝜌 is the density of the fluid (SI units: kg/m3)

• u is the velocity of the fluid with respect to the object (m/s)

• L is a characteristic linear dimension (m)

• 𝜇 is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s)

• 𝑣 is the kinematic viscosity of the fluid (m2/s).

This number is dimensionless and can be used to define flow characteristics within a

pipeline.

The Reynolds number provides an indication of the loss of energy caused by viscous

effects. Observing the above equation, when viscous forces have a dominant effect on

energy loss, the Reynolds number is small and the flow is in the laminar regime. If the

Reynolds Number is 2100 or less, the flow will be laminar. A Reynold number greater

than 10,000 indicate that viscous forces have little effect on energy loss and the flow is

turbulent.

3.2 Strouhal Number.

In dimensional analysis, the Strouhal number (St) is a dimensionless number that

describes the oscillatory behaviour of a flow. This parameter takes its name from the

Czech physicist Vincenc Strouhal, who experimented with the detachment of wire

vortices in 1878. Strouhal's number is a fundamental parameter in fluid mechanics.

The Strouhal number is usually written as follows:

𝑆𝑡 =𝑓𝐿

𝑈 (3.2)

46

where

• 𝑓 is the frequency of the vortex shedding.

• 𝐿 is the characteristic length (for example, the airfoil thickness).

• 𝑈 is the velocity of the flow.

For high values of the Strouhal number (of the order of 1), the flow is dominated by

viscosity. For low values (of the order of 10-4 and smaller), the quasi-stable part of the

flow (at high speed) dominates the oscillation. The intermediate values of the Strouhal

number are characterized by the appearance of vortices.

For spheres in a uniform flow in the range of the Reynolds number 800 <Re <200 000

two values of the Strouhal number coexist: one associated with the low frequency of

the large-scale instability of the wake (independent of the Reynolds number) whose

value is approximately 0.2; and another associated with the instability on a small scale

of the separation of the boundary layer.

3.3 Courant-Friedrichs-Lewi condition (CFL).

The Courant–Friedrichs–Lewy or CFL condition is a condition for the stability of

unstable numerical methods that model convection or wave phenomena. As such, it

plays an important role in CFD (computational fluid dynamics). The section below

confers the numerical discussion that derives the CFL condition. After this discussion,

the CFL condition is presented, and in later sections, its used in CFD simulations of

our dissertation.

47

3.3.1 Definition of the CFL Condition.

Culbert B. Laney’s definition of the CFL condition, from the book “Computational

Gasdynamics” [85], is as follows: the full numerical domain of dependence must

contain the physical domain of dependence.

Therefore, the CFL condition expresses that the distance that any information travels

during the timestep length within the mesh must be lower than the distance between

mesh elements. In other words, information from a given cell or mesh element must

propagate only to its immediate neighbours.

The CFL condition is commonly confused with linear stability conditions or nonlinear

stability conditions. However, it is important to emphasize that it is not a sufficient

condition for stability, and other stability conditions are generally more restrictive

than the CFL condition.

3.3.2 Definition of CFL Number

The Courant number can be defined as follows:

𝐶 = 𝑉∆𝑡

∆𝑥 (3.3)

Where, 𝑉 is the velocity magnitude, ∆𝑡 is the timestep and ∆𝑥 is the length between

mesh elements.

The Courant number must be equal or smaller than 1, otherwise, the numerical

viscosity would be negative. An article by Courant, Friedrichs, and Lewy first

introduced this condition in 1928 [86]. This derivation is considered one of the most

influential works for the development of CFD techniques.

48

3.4 Drag Force.

In fluid dynamics, fluid drag, or friction is the friction between a solid object and the

fluid (a liquid or gas) through which it moves. For a solid that moves by a fluid or gas,

the drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of

the flow of the external fluid. Therefore, it acts opposite to the movement of the object,

and in a motorized vehicle this is solved with the push. Although there is generally

talk of air resistance, because air is the medium through which bodies move, the same

considerations apply for other gases and even liquids.

The drag force is proportional to the square of the relative velocity v of the object with

respect to the fluid and the proportionality constant called the CD drag coefficient,

which in turn depends on the Reynolds number.

In this section, we study the cases that the drag force is proportional to the speed and

the square of the speed.

The formula of the drag force is:

F𝐷 = 𝐶𝐷1

2𝜌𝑓𝐴𝑣2 (3.4)

Where 𝐶𝐷 is called drag coefficient, 𝜌𝑓 is the density of the fluid, 𝐴 is the area of the

cross section perpendicular to the direction of movement (in the case of a sphere is

πD2 / 4) and 𝑣 is the relative velocity of the object with respect to the fluid.

The drag coefficient is a function of the Reynolds number, Re. This number is

important to define the behaviour of a fluid and, the transition from laminar to

turbulent flow.

49

3.5 Lift Force.

The lift is the force generated on a body that moves through a fluid, perpendicular

direction to the speed of the incident current. The best known application is the wing

of a bird or an airplane, surface generated by a wing profile. It is the main force that

allows an aircraft with wings to stay in flight. This, being greater than the total weight

of the aircraft, allows it to take off.

For the lift the L notation is used, and CL for the lift coefficient, which always seeks to

be as large as possible.

In addition, the lift, and consequently its coefficient, directly depend on the angle of

attack, increasing as it increases to reach a maximum point or a critical angle of attack,

after which the air flow passing over the extrados (upper surface wing) can not travel

in its entirety and stay attached to the aerodynamic profile, leading to stall. To increase

the lift, there are hyper-lift devices such as flaps and slats to continue with the pressure

difference and therefore increase the lift by modifying the curvature of the profile

(generally used when low speed lift is needed). A correct explanation of the origin of

the lift requires the use of the boundary layer theory developed by Prandtl.

Differences in the behaviour of objects at different speeds are usually expressed with

the 'Reynolds Number', a number without dimensions that describes the relationships

between viscosity and inertia in a fluid.

As with other aerodynamic forces, in practice, dimensionless coefficients are used that

represent the effectiveness of the shape of a body to produce lift and are used to

facilitate calculations and designs.

The mathematical model of the lift force is:

L =1

2𝜌𝑉2𝐴𝐶𝐿 (3.5)

50

where:

• L is the lifting force in newtons.

• 𝜌 is the density of the fluid, in kg / m3.

• 𝑉 is the speed, in m/s.

• 𝐴 is the reference area of the body, represented in m2.

• 𝐶𝐿 is the lift coefficient. Like the rest of the aerodynamic coefficients, it is

dimensionless. This coefficient is found experimentally in accordance with:

𝐶𝐿 =𝐿

1/2𝜌𝑉2𝐴 (3.6)

3.6 Vorticity.

Vorticity is a physical quantity used in fluid mechanics and in the meteorological

world to quantify the rotation of a fluid. Mathematically, vorticity is the vector field

defined by the rotational velocity field:

𝜔 = ∇ × 𝑣 (3.7)

The presence of vorticity in a fluid always implies the rotation of the fluid particles,

accompanied or not by some transverse deformation. In a real fluid its existence is

intimately linked to the tangential tensions. The equation for studying the kinetics of

this field (called the vorticity transport equation) is obtained by taking the rotational

on both sides of the momentum equation of the Navier-Stokes equations and

expressing the local derivative in terms of the substantial derivative.

𝐷𝜔

𝐷𝑡= 𝜔 ∙ ∇𝑢 + 𝑣∇2𝜔 (3.8)

The vorticity originates fundamentally in the solid contours because the fluids are not

able to slide on them, and then it propagates to the interior of the fluid following the

law of variation described by the previous equation. The first term corresponds to the

51

variation of vorticity by deformation of the vortic lines. This phenomenon occurs in

both viscous and non-viscous fluids, however it is a remarkable fact that when the

fluid is non-viscous (ideal) this is the only way in which vorticity can vary. As Kelvin

showed in one of his theorems, this variation always occurs so that the flow of vorticity

associated with an open surface that moves with the fluid remains constant, which

also implies that the variation of the velocity Γ of the velocity along the contour of that

same surface is null.

To find a simple explanation for this vorticity variation mechanism, let us imagine that

a vortex region in the form of a tube with a variable section in its length has been

formed in some non-viscous fluid. Since there is no viscous diffusion within it, the

flow of vorticity associated with any transversal surface is identical and constant, so

when the section varies there must be a variation in the intensity of the vorticity.

The second term of equation 3.8, which unlike the first is only evaluated in viscous

fluids, corresponds to the variation of vorticity by viscous diffusion and has an

analogy (similar differential equation) with the phenomenon of heat conduction in

solids. Due to this phenomenon, particles that do not have vorticity acquire it from

neighbouring particles that do have it, producing a diffusion of vorticity towards the

interior of the fluid.

A simple example that demonstrates this phenomenon is that of a cylindrical

container filled with fluid that starts from rest and suddenly begins to rotate on its

axis at a constant angular velocity. Anyone can sense that the fluid that originally

remained motionless will begin to rotate along with the container. First it will be in

the contour, but after a certain time all the fluid will be rotating as if it were a solid

mass inside the container. What happens in the first instant of the experiment is just a

generation of vorticity due to the appearance of a transverse velocity gradient. That is

to say: suddenly the particles of the contour are turning with the container due to their

52

adherence, while their neighbours still remain immobile. What happens next is a

progressive viscous diffusion that lasts until reaching the regime state; when all the

fluid reaches the same angular velocity and therefore the distribution of vorticity is

constant.

If we repeated exactly the same experiment but with less viscous fluids, we would

notice a longer transition time, while for fluids more viscous shorter times; which is

an indicator that the viscosity is related to the velocity of diffusion of vorticity. This

same mechanism of generation of vorticity is responsible for the generation of the

surrounding layers around the solid bodies. The formation process of these regions is

similar, although in them you can find pressure gradients that modify their

development.

The previous example leaves as a first concept that the viscosity is the capacity of the

particles to infect their vorticity and that depending on it, the fluid will be more or less

dominated by vorticity. However, the field of movement of a fluid is also

characterized by other factors: the scale of the system (its characteristic length), its

characteristic velocity, and its density. The scale effect is an indicator that the size of a

body is one of the determining parameters of the movement field. If you have two

models of the same solid contour but of different scale and circulate through them the

same fluid at the same speed the vorticity will not have to spread the same in both

cases, so the shape and / or intensity of the vortic regions will not necessarily be

identical. If you want to have similar movements, you should circulate a less dense

fluid, or at a slower speed, or a higher viscosity, through the larger body.

A simple example of the scale effect is the circulation of fluid tangent to a solid plane,

where it is concluded that the development of the surrounding layer depends on the

length. Density, on the other hand, is a factor that intervenes dynamically, because by

varying the mass of a fluid particle its response to the actions that are exerted on it

53

varies. From this broader point of view it is evident that the vorticity diffusion level is

closely linked to the Reynolds number of the fluid.

With a very simple mathematical expression Reynolds number allows to distinguish

and compare the movement of fluids. This is because it meets the fundamental

characteristics of movement: the scale of space and time, mass and internal actions. In

general terms, it can be said that when this number decreases, the phenomena

associated with viscosity gain preponderance, and therefore larger vortex regions can

be expected. On the contrary, when it increases, viscous phenomena weaken in

relation to non-viscous phenomena, and therefore more compact vortex regions are to

be expected.

3.7 Pressure field.

Pressure field is a two-component vector force field, which describes in a covariant

way the dynamic pressure of individual particles and the pressure emerging in

systems with several closely interacting particles. The pressure field is a general field

component, which is represented in the Lagrangian and Hamiltonian of an arbitrary

physical system including the term with the energy of particles in the pressure field

and the term with the field energy [87] [88].

The pressure field is included in the equation of motion by means of the pressure field

tensor and in the equation for the metric – by means the pressure stress-energy tensor.

Any forces acting on the matter particles and causing a change in their interaction with

each other contribute to the pressure field, its energy and momentum. The pressure

field is generally considered as a macroscopic field, describing the averaged

interaction of particles in an arbitrary small volume of a system. The cause of the

pressure field emerging at the microlevel is different interactions. For example,

54

electromagnetic forces and strong gravitation hold electrons and nucleons in atoms

together. The action of the external forces causes the matter compression and change

in the volume occupied by atoms and electrons in the matter atoms. This leads to a

change in the energy of the system, which can be represented as a change in the

pressure field energy.

3.7.1 Sound Fields

A sound field is a region where there is sound. It is classified according to the way

and the environment in which the sound waves travel. In the next subsection, the

acoustic terms “near field” and “far field” will be described. These types of field differ

in the physical distance from the sound source (Figure 1). Depending on how far away

an observer is from a sound emitting object, the acoustic energy produced by the

sound source will behave quite differently. It is therefore important to understand

these differences, and design measurements carefully.

Figure 1: Sound waves behave differently in the near field (A) and far field (B).

3.7.1.1 Far Field

The acoustic far field begins 2 wavelengths away from the sound source and extends

outward to infinity (Figure 2). As wavelength is a function of frequency, the beginning

of the far field is also a function of frequency.

55

Figure 2: The far field begins at 2 wavelengths away from the source.

In the far field, the source is far away enough to essentially appear as a point in the

distance, with no discernible dimension or size. At this distance, the spherical shape

of the sound waves has grown to a large enough radius that one can reasonably

approximate the wave front as a plane-wave, with no curvature (Point B in Figure 1).

At this distance, sound pressure level is governed by the inverse square law, and a

single microphone sound recording will give reliable & predictable results. For each

doubling of distance away from the source, the sound pressure will drop 6 dB in the

far field.

In many acoustic standards, measurements are often specified at a distance of at least

one meter from the sound emitting object to ensure that the measurement is taken in

the far field for the most critical frequencies.

3.7.1.2 Near Field

When close to a sound emitting object, the sound waves behave in a much more

complex fashion, and there is no fixed relationship between pressure and distance.

Very close to the source, the sound energy circulates back and forth with the vibrating

surface of the source, never escaping or propagating away. These are sometimes

called “evanescent” waves. As distance increases from the source, some of the sound

field continues to circulate, and some propagates away from the object (Figure 3).

56

Figure 3: The near field is complex, with sound energy both circulating and propagating.

This transition, from circulating to propagating, continues in an unpredictable fashion

until the threshold distance of 2 wavelengths is reached, where the sound field strictly

propagates (the far field). This mixture of circulating and propagating waves means

that there is no fixed relationship between distance and sound pressure in the near

field and making measurements with a single microphone can be troublesome and

unrepeatable. Typically, measuring in the near field requires the use of more than one

microphone (Figure 4), in order to be able to accurately measure the energy from the

circulating and propagating waves.

Figure 4: Acoustic arrays featuring many microphones can be used close to a source to accurately measure

sound energy in the near field [89].

57

CHAPTER 4: APPLICATIONS OF COMPUTATIONAL FLUID

DYNAMICS IN AERODYNAMICS AND AEROACOUSTICS.

This chapter examines background theory in Computational Fluid Dynamics (CFD)

and the understanding of CFD methods applied in noise generation. This chapter

starts with the description of the basic fluid dynamics theory and then follows on to

turbulence modelling in CFD. The CFD code used in this thesis is STAR- CCM+. This

chapter concludes by explaining the CFD equations used by this software in the

aeroacoustics field.

4.1 Governing Equations of Motion

The basic equations of motion used to evaluate any flow problem are the continuity

and momentum equations. Assuming no body forces, equations 4.1 and 4.2 show the

compressible form of both equations, respectively.

𝜕𝜌

𝜕𝑡+

𝜕

𝜕𝒙𝒊(𝜌𝒖𝒊) = 0 (4.1)

𝐷(𝜌𝒖𝒊)

𝐷𝑡≡

𝜕(𝜌𝒖𝒊)

𝜕𝑡+

𝜕

𝜕𝒙𝒋(𝜌𝒖𝒊𝒖𝒋) =

𝜕𝑝

𝜕𝒙𝒊+

𝜕𝜏𝑖𝑗

𝜕𝒙𝒋 (4.2)

where, 𝒙𝒊 (𝑖 = 1, 2, 3) are the cartesian coordinates corresponding to (x, y, z). 𝒖𝒊 is the

cartesian component of velocity, 𝑡 is the time, 𝑝 is the pressure, 𝜌 is the density and 𝜏𝑖𝑗

is the viscous stress tensor. These equations form the basis for any fluid analysis.

However, when turbulent flows are involved, more variables arise that cannot be

solved, due to the lack of equations. As a result, more equations are needed to solve

the turbulence closure problem. [84]

58

4.2 Turbulence Models

This section will discuss the basis of the Reynolds Averaged Navier-Stokes (RANS)

equations and the associated turbulence closure problem. The formulation of some

turbulence models used in STAR-CCM+ simulations is also presented. These models

are: the most used model in CFD, Standard k-𝜺 model, as well as Large Eddy

Simulation (LES), and Detached Eddy Simulation (DES). The advantages and

disadvantages of each model are presented.

4.2.1 Reynolds-Averaged Navier-Stokes Modelling (RANS)

Reynolds-Averaged Navier-Stokes (RANS) equations deal with the unsteadiness of

the flow in average terms. The flow variables are represented as a sum of two terms,

a mean component and a fluctuating component, as shown in equation 4.3 and 4.4.

Both equations represent the notation for the two different types: Reynolds averaging

and Favre averaging, respectively:

𝑢𝑖(𝑥𝑖, 𝑡) = 𝑖(𝑥𝑖) + 𝑢𝑖′(𝑥𝑖,𝑡) (4.3)

𝑢𝑖(𝑥𝑖, 𝑡) = 𝑖(𝑥𝑖) + 𝑢𝑖′′(𝑥𝑖,𝑡) (4.4)

where 𝑢𝑖′and 𝑢𝑖′′are the fluctuation about the averaged value for the different

averaging types. There are two types of averaging used in order to solve 𝑖(𝑥𝑖) in

Reynolds averaging. One method is the time-averaged approach, shown in equation

4.5.

𝑖(𝑥𝑖) = limΤ→∞

1

Τ ∫ 𝑢𝑖

Τ

0(𝑥𝑖, 𝑡)𝑑𝑡 (4.5)

where Τ is the averaging interval and is large compared to the typical time scale of

the fluctuation. The time-averaged approach is mainly used for steady flows.

59

For unsteady flows, another type of averaging is used: ensemble averaging. This

concept involves the averaging of a large set of flows where all the variables are

controlled and identical, but the initial condition for each flow is generated randomly.

The mean flow under ensemble average is shown in equation 4.6, where 𝑁 is the

number of flows in the ensemble.

𝑖(𝑥𝑖, 𝑡) =1

𝑁∑ 𝑢𝑖(𝑥𝑖, 𝑡)𝑁

𝑛=1 (4.6)

Equations 4.5 and 4.6 are used for incompressible flows. For compressible flows, Favre

averaging is used. It is defined as the density-weighted average with the fluid density

denoted as 𝜌(𝑥𝑖 , 𝑡). Equation 4.7 shows the solution for 𝑖(𝑥𝑖).

𝑖(𝑥𝑖) ≡𝜌𝑢𝑖 (𝑥𝑖,𝑡)

(𝑥𝑖,𝑡) (4.7)

For high speed, compressible flows, the Favre averaging is better suited. After

incorporating equations 4.4 and 4.7 into the equations of motion (4.1 and 4.2) and then

considering the Reynolds average, the Favre-averaged conservation of mass

continuity and momentum can be defined as shown in equations 4.8 and 4.9,

respectively.

𝜕

𝜕𝑡+

𝜕

𝜕𝑥𝑖(𝑖) = 0 (4.8)

𝜕(𝑢𝑖)

𝜕𝑡≡

𝜕(𝑢𝑖𝑢𝑗)

𝜕𝑥𝑗= −

𝜕

𝜕𝑥𝑖+

𝜕

𝜕𝑥𝑗(τ𝑖𝑗 − 𝜌𝑢′′𝑖𝑢′′𝑗 ) (4.9)

where the term (−𝜌𝑢′′𝑖𝑢′′

𝑗 ), known as the Reynolds stress tensor, represents the

apparent stress in the mean flow due to turbulent fluctuations. Its presence makes the

turbulence problem difficult to solve due to the introduction of more unknown

variables than available equations. The absence of additional equations is known as

the Turbulence Closure Problem. The Reynolds stress tensor cannot be solved in the

60

same way the viscous stresses are. The reason behind this is that the viscous stress can

be related directly to other flow properties using constitutive equations. This is

possible because the closure approximations of a fluid are averaged over characteristic

length and time scales that are much smaller than those of the flow we are interested

in. At the same time, these scales are much larger than the molecular length and time

scales that characterize the molecular interactions that cause momentum transfer.

However, for Reynolds stress, it arises from the flow itself and the scales of the

fluctuating motion of the flow are the scales we are interested in. As a result, the same

closure concept from viscous stress will not work with Reynolds stress.

To close the system (to solve the turbulence closure problem), the Reynolds stress

tensor needs to be modelled. One of the first people to tackle this problem was

Boussinesq, who introduced the Boussinesq approximation with the model Reynolds

stress tensor (𝑅𝑖𝑗). The Boussinesq approximation replaces the exact Reynolds stress,

as shown in equation 4.10.

𝑅𝑖𝑗 = −𝜌𝑢′′𝑖𝑢′′

𝑗 ≡ 2𝜇𝑡𝑆𝑗 −

2𝑘𝛿𝑖𝑗

3 (4.10)

The eddy viscosity (𝜇𝑡) and the turbulent kinetic energy (𝑘) would then be computed

using the turbulence model to achieve turbulence closure. Even though this

approximation is simple, it does provide the appropriate accuracy needed for simple

shear flows where mean velocity gradients and turbulence develop slowly.

4.2.2 Large Eddy Simulation (LES)

More advanced turbulence modelling approaches have been developed over the years

in order to better simulate complex and real-life phenomena. These approaches are

based primarily on unsteady, transient calculations and on average have higher

computational costs than RANS models. The first that we mention is the Large Eddy

Simulation (LES).

61

Large Eddy Simulation (LES) is a transient approach that solves the large scales of

turbulence and models the smaller scales. Therefore, by modelling less of the

turbulence, this technique results in less error due to turbulence modelling. It is based

on the idea that smaller eddies are self-similar, thereby can be modelled with more

universal models. To achieve closure of the Navier-Stokes equations, the subgrid scale

model is used to model the subgrid scale viscosity, while the Boussinesq

approximation is used to model the subgrid scale stresses. One major disadvantage of

this model is that it is computationally expensive. As a result, the detached eddy

simulation (DES) was explored.

4.2.3 Detached-Eddy Simulation (DES)

The Detached-Eddy Simulation (DES) originated by Spalart [92] in 1997, and was first

used by him 2 years later [93], with the purpose of coping with massively separated

flows at high-Reynolds number. DES combines LES and RANS approaches, based on

the turbulence length scale and the grid spacing. Hence, LES is used for regions of

massive separations and RANS within the boundary layer. The official definition of

DES, in accordance with Travin [94] is “A three-dimensional unsteady numerical

solution using a single turbulence model, which functions as a sub-grid scale model

in regions where the grid density is fine enough for a large-eddy simulation and as a

Reynolds-averaged model in regions where it is not”. More details about the

equations, advantages, limitations and implementation of DES can be found in the

review paper of Spalart [93].

This approach has become well-known and proven for the prediction of massively

separated flows at a lower computational cost than the LES model [95]. In this model,

the dissipation term is modified, as shown in equation 4.11.

𝐷𝑘 = 𝛽∗ ϑk → 𝐷𝑘 = 𝛽∗ϑkF𝐷𝐸𝑆 (4.11)

62

The modification involves the addition of the F𝐷𝐸𝑆 term to distinguish between which

model should be used, 𝛽∗ is a calibration parameter. Equation 4.12 presents the

definition of as a function of turbulent length scale 𝑙𝑡, shown in equation 4.13, model

constant 𝐶𝑑𝑒𝑠, and the largest distance between the cell centre under consideration and

the cell centres of neighbouring cells ∆.

𝐹𝐷𝐸𝑆 = max [𝑙𝑡

𝐶𝑑𝑒𝑠∆, 1] =

1, 𝑖𝑓𝑙𝑡 < 𝐶𝑑𝑒𝑠∆↔ 𝑅𝐴𝑁𝑆 𝑚𝑜𝑑𝑒𝑙1, 𝑖𝑓𝑙𝑡 > 𝐶𝑑𝑒𝑠∆ ↔ 𝐿𝐸𝑆 𝑚𝑜𝑑𝑒𝑙

(4.12)

𝑙𝑡 =√𝑘

𝛽∗ϑ (4.13)

where 𝑘 is the turbulent kinetic energy and ϑ is the specific dissipation rate.

The RANS model is used in the regions near solid boundaries, where the turbulent

length scale is less than the maximum grid dimension [92]. When these conditions are

not in play, the dissipation term in the equation increases which in turn decreases. As

a result, the turbulent eddy viscosity decreases, as does the modelled dissipation. This

process solves, rather than models, a large part of the turbulence, the concept of the

LES subgrid scale model [96].

The formulation of the DES model is very helpful in reducing the computational cost

while allowing the small-scale length scales to be resolved. This model was the one

selected for our research.

4.3 Computational Aeroacoustics

4.3.1 Background

Aeroacoustics is the study of noise generation that develops from turbulent fluid

motion or through the interaction of flow and surfaces (aerodynamic forces). This field

63

originated by Sir James Lighthill [49] during his time as Professor in the University of

Manchester where he studied the noise generation associated with jet engines. Since

that time, this field has grown immensely until the 1980s, when computational

aeroacoustics (CAA) were developed.

Computational aeroacoustics is the subset of aeroacoustics that utilizes numerical

methods to analyse noise generation. There are two methods that can be used under

CAA: direct method and hybrid method. The direct method involves computing the

flow and acoustic fields using the same computational domain using computational

fluid dynamic equations. A large domain would be setup to include the receivers

within, and the mesh would have to be fine enough throughout the entire domain to

prevent any dissipation. This is necessary in order to account for the large differences

in length scale between the acoustic and the flow variables. As a result, the method is

computationally expensive and impractical.

The alternative approach, hybrid method, splits the flow domain from the acoustic

domain. The flow variables will be solved using the computational fluid dynamic

equations. The flow field is then used to calculate the acoustical sources, which in turn

is used to propagate noise to the receiver location using an acoustic analogy. This

allows the domain to be much smaller and reduces the computational cost

significantly.

The hybrid approach is the basis for all commercial software including STAR-CCM+.

The next two sections discuss the acoustic analogy developed by Lighthill and its

modification to include moving surfaces referred to as Ffowcs Williams-Hawkings

(FW-H) equation.

64

4.3.2 Lighthill´s Acoustic Theory

Lighthill [97] introduced one of the simplest yet powerful concepts into the

aeroacoustic world, known as the acoustic analogy. The purpose, at the time, was to

understand and predict the noise generation by the jet of an aircraft turbojet engine.

The idea of the acoustic analogy is to replace the regions of unsteady fluid flow by an

equivalent distribution of sources in order to derive linear perturbations from the base

flow [97]. The analogy is based on manipulating the momentum and mass continuity

equation to obtain a linear wave equation with nonlinear forcing terms that are

independent of the far-field radiation.

In order to derive the acoustic analogy, consider a jet of air streaming into a quiescent

medium with density 𝜌0 and speed of sound 𝑐. Away from that jet, the perturbation

pressure 𝑝′ can be written in the wave equation form as shown in equation 4.14.

𝑝′ =1

𝑐2

𝜕2𝑝′

𝜕𝑡2 − ∇2𝑝′ = 0 (4.14)

Lighthill derived an exact relationship for perturbation density 𝑝′ showed in equation

4.15.

𝑝′ = 𝑐𝜌′ (4.15)

Manipulating the mass continuity and momentum equations in 4.1 and 4.2, we get a

rearranged combined equation, shown in equation 4.16.

𝜕2𝑝′

𝜕𝑡2 =𝜕2

𝜕𝑥𝑖𝜕𝑥𝑗(𝜌𝑢𝑖𝑢𝑗 + 𝑃𝑖𝑗) (4.16)

Subtracting 𝜕2𝑝′

𝜕𝑥𝑖2 from both sides of equation 4.16 and using equation 4.15, we get an

equation of the same form of equation 4.14 as shown in equation 4.17.

65

𝑝′ =𝜕2Τ𝑖𝑗

𝜕𝑥𝑖𝜕𝑥𝑗 (4.17)

where Τ𝑖𝑗 = (𝜌𝑢𝑖𝑢𝑗 + 𝑃𝑖𝑗 − 𝑐2𝜌′𝛿𝑖𝑗). In equation 4.17, Τ𝑖𝑗 is referred to as the Lighthill

turbulence stress tensor. It is equal to zero at the far-field, thereby satisfying the

definition in equation 4.14. However, its value is not equal to zero in the jet and acts

as a quadrupole noise source that radiates sound in a radial direction [97].

4.3.3 The Ffowcs Williams and Hawkings Equation

The Ffowcs Williams-Hawkings (FW-H) equation is the generalised form of Lighthill’s

acoustic analogy, showed in equation 4.14. It is derived primarily from Farassat’s

Formulation [20], being the exact rearrangement of the generalized derivatives of the

continuity and momentum equations into the form of the inhomogeneous wave

equation.

To understand the formulation, consider a moving, impenetrable body described by

𝑓(𝑥, 𝑡) = 0, such that 𝑓 > 0 is outside the body and ∇𝑓 = (outward normal to 𝑓 = 0).

Inside the body, the fluid is at rest and with the same conditions as the formulation of

Lighthill’s acoustic analogy. Based on this setup, there is an artificial discontinuity at

the body (𝑓 = 0). To consider the jump present at the surface, the mathematical

concept of derivatives of generalized functions is used to make the required

corrections to the conservation laws. The generalized conservation laws of mass

continuity and momentum are shown in equation 4.18 and 4.19, respectively. The bars

over the derivatives denote generalized differentiation.

𝜌′

𝜕𝑡+

𝜕𝑥𝑖(𝜌𝑢𝑖) = 𝜌0𝑣𝑛𝛿(𝑓) (4.18)

𝜕𝑥𝑖(𝜌𝑢𝑖) +

𝜕𝑥𝑗(𝜌𝑢𝑖𝑢𝑗 + 𝑃𝑖𝑗) = 𝑙𝑖𝛿(𝑓) (4.19)

66

where 𝑣𝑛 =𝜕f

𝜕t is the local normal velocity at the surface of the body, 𝑙𝑖 = 𝑃𝑖𝑗𝑛𝑗 is the

local force intensity that acts on the fluid, and 𝜕(f) is the Dirac delta function. Taking

the 𝜕

𝜕t from equations 4.18 and 4.19, and subtracting the result of the latter from the

former, we get to equation 4.20:

2𝜌′

𝜕𝑡2 −2

𝜕𝑥𝑖𝜕𝑥𝑗(𝜌𝑢𝑖𝑢𝑗 + 𝑃𝑖𝑗) =

𝜕𝑡[𝜌0𝑣𝑛𝛿(𝑓)] −

𝜕𝑥𝑖[𝑙𝑖𝛿(𝑓)] (4.20)

Substituting equation 4.15 into equation 4.20 and subtracting 2𝜌′

𝜕𝑥𝑖𝜕𝑥𝑗 from both sides

provides the general form of the FW-H equation as shown in equation 4.21.

𝑝′ =

𝜕𝑡[𝜌0𝑣𝑛𝛿(𝑓)] −

𝜕𝑥𝑖[𝑙𝑖𝛿(𝑓)] +

2

𝜕𝑥𝑖𝜕𝑥𝑗[𝑇𝑖𝑗𝐻(𝑓)] (4.21)

where 𝐻(𝑓) is the Heaviside function. Using the free-space Green’s function [98] to

compute the sound pressure at the observer’s location x, the solution of equation 4.21

can be defined in the form shown in equation 4.22.

𝑝′(, 𝑡) = 𝑝′𝑇(, 𝑡) + 𝑝′𝐿(, 𝑡) + 𝑝′𝑄(, 𝑡) (4.22)

where 𝑝′(, 𝑡) refers to the monopole (or thickness) term. It arises from the

displacement of the fluid as the body passes through. 𝑝′𝑇(, 𝑡) is the dipole (or loading

term). It occurs from the unsteady motion of the force distribution on the body surface.

Both noise sources are surface related. Finally, 𝑝′𝑄(, 𝑡) is the quadrupole (volume

source) term and results from the nonlinearities present in the flow.

There are two types of surfaces that can be used in the formulation. An impermeable

FW-H surface acts as a filter of wall boundary conditions from which the noise

originates. This type will produce sound levels only from the monopole and dipole

sources. A permeable FW-H surface acts as a filter of internal interface boundaries.

67

This surface is a fine mesh region that surrounds all the sources of noise: monopole,

dipole, and quadrupole.

In STAR-CCM+, the FW-H model uses a concept developed by Brentner and Farassat

[99], referred to as the advanced time approach or the source-time-dominant

approach. The algorithm looks forward in time to see when the receiver perceives the

generated sound waves. This advanced time algorithm makes a distinction between

the emission and reception times. The emission times of the acoustic signal from each

surface will be constant while the reception time for those signals will be different. As

a result, the emission times are fixed and the signals arriving to the receiver are

accumulated at their respective emission time slot. The overall acoustic signal at the

receiver is the sum of the individual acoustic signals from each source surface during

the same emission time. The goal of the FW-H model is to predict the small amplitude

acoustic pressure fluctuations at the location of the desired receiver. It predicts the

propagation of sound in free space using analytical integral solution to the generalized

wave equation and does not include any effects such as reflections and refractions.

This approach was used in the simulations performed in this thesis to predict noise

levels of the receivers in the far field.

68

CHAPTER 5: CFD SIMULATION SETUP IN STAR-CCM+

The next chapter will describe the geometric specification of the airfoil used during

the research, as well as the details of the mesh generation and the sensitive study

developed. One last point of interest was the validation of our mesh and the

aerodynamic results obtained, in comparison with the experimental data obtained by

Angland. [26]

5.1 Geometry specification

The geometry was based on the airfoil of the Airbus A320´s flap (for more data about

this model check [100]). The dimension of the span´s flap model was 0.4 m (Figure 5

and Figure 6 ). Angland [26] recommends this, in order to improve the quality and the

spanwise cells number; as a result, a better resolution will be provided using a DES

model. Also, as the focus is on the noise generated by the flap side-edge, it is removed

from the noise generated by the trailing edge or otherwise; it is necessary to keep the

span at the smallest possible in order to save computational resources.

Figure 5: Lateral overview of the on-surface grid at flap

69

Figure 6: On-surface grid at flap´s top

5.2 Grid Generation

The reason to generate a good mesh is to obtain suitable results through analysis. As

a result, the generation of a mesh begins with a description of the geometry surface.

From this description, two cycles of meshing of the geometry need to be done: surface

meshing and volume meshing.

5.2.1 Surface Mesh.

Star-CCM+ contains tools which can be used to help prepare the starting surface

geometry so that a high-quality volume mesh can be created from it. The most utilised

are the surface remesher and the surface wrapper.

There is also a surface remesher in order to improve the overall quality of the surface

and optimise it for the volume mesh models. Typically, the surface remesher is used

for remeshing the surface produced by the surface wrapper.

70

5.2.1.1 Volume Mesh.

In Stars-CCM+, three different types of meshing models can be used to generate a

volume mesh: tetrahedral, polyhedral and trimmed mesh.

The tetrahedral mesh is used to provide an efficient and simple solution for complex

mesh generation problems. It is the fastest of the provided models and uses the least

amount of memory for a given number of cells.

The polyhedral meshes provide a balanced solution for complex mesh generation

problems. They are relatively easy and efficient to build, requiring no more surface

preparation than the equivalent tetrahedral mesh.

The trimmer meshing model utilises a template mesh constructed from hexahedral

cells, from which it cuts or trims the core mesh, based on the starting input surface.

From the mentioned mesh models, the trimmer was expected to produce best results

when working with multiphase on and free surface (due to its ability to describe the

smooth free surface).

5.2.2 Mesh Sensitive Study

In order to establish the accuracy of the CFD solution, and to keep an optimal and low

computational cost, the model has been analysed using: the Detached-Eddy

Simulation (DES) model. This case study was selected because our airfoil had been

used previously by Angland [26] for experimental test and we extracted some of his

data to compare with our simulations. The data was uniform Re = 1.27 x 106, and angle

of attack of 20° degrees. The grid convergence study was performed by developing

three different meshes: a large, medium, and fine grid to predict the drag and lift

coefficients on normalised mesh cells to determine how the mesh quality affects CFD

simulation results. The number of nodes and the simulation time for the three cases

simulated using the model are highlighted in Table 1, as well as the results. Table 1

71

summarises the key characteristics of the meshes, and it is very clear that CFD

simulation time is highly dependent on the number of mesh nodes considered. The 3

meshes generated have near wall resolution i.e. y+ < 10 by using the standard wall

function approach to avoid unsatisfactory results when using the Detached-Eddy

Simulation (DES).

Table 1: Mesh size, CFD simulation time, and estimated CL and CD for DES model at Angle of attack = 20°.

Mesh

Resolution

Number of

Nodes

CFD Simulation

Time CL CD

Coarse Mesh

(M1)

1.2 X 106 nodes 50 hrs 1.45 0.55

Coarse Mesh

(M2)

2.3 X 106 nodes 75 hrs 1.50 0.59

Coarse Mesh

(M3) 3.9 X 106 nodes 110 hrs 1.56 0.64

In our case of investigated meshes, the airfoil has an increased mesh resolution. This

is due to the closer flap side-edge, as could be seen in the Figure 6. This was decided

in order to acquire the most precise data in this spot, as it is the most important part

of our investigation. The mesh is refined in the grids from M1 to M3 where M1, M2,

M3 represent coarse, medium, and fine mesh respectively, generated for the DES

model. The estimated lift coefficient increased from 1.45 to 1.56 and lift coefficient

increased from 0.55 to 0.64 as shown in Table 2. Another important facts to remember

are the coefficients obtained by Angland at similar values, with a Re 1.3 x 106 at 20

degrees CL=1.54 and CD=0.62.

Table 2: Mesh Results VS Angland results at approximately Re=1.3x106 and angle of attack of 20°.

Mesh

Resolution CL CD

Coarse Mesh

(M1)

1.45 0.55

Coarse Mesh

(M2)

1.50 0.59

Coarse Mesh

(M3)

1.56 0.64

Angland Results 1.54 0.62

72

It is important to note that the mesh resolution has one of the main roles in the final

CFD results. The mesh nodes need to be small in order to solve the boundary layer on

the blade surfaces. The highest CL and CD obtained from the mesh study conducted

is 1.56 and 0.64 respectively for M3. Also, M3 is the closest one to Angland’s results in

both coefficients. It is clear from the final CFD simulation results obtained in the mesh

study that the simulation time is highly dependent on the number of mesh nodes, and

the turbulence model selected. M1 relatively leads to reasonable prediction of the

coefficients on the airfoil, whereas M2, and M3 it can be seen than the coefficients of

M3 is better than M2. Due to the closest approximation to Angland values, despite

being the most computationally expensive, M3 is the best mesh and was used for

further research in the work contained in this thesis.

The final grid used for the DES calculation was 14 metres tall, 14 metres long, 16

metres wide, 3.9 X 106 cells, 11.6 X 106 faces and 4 X 106 vertices. Pictures of the

computational grid are shown from Figure 5 to Figure 11.

Figure 7: Lateral overview of the grid composes by the flap and the nearfield.

73

Figure 8: Detail of the grid at the tip of the flap

Figure 9: Detail of the grid at the flap

74

Figure 10: Isometric image of the complete mesh and boundary conditions location

Figure 11: Lateral view of the mesh and airfoil location

75

5.2.3 Verification and Validation.

After the verification and the validation of the CFD analysis was performed, the

quality of the results needed to be assessed. Oberkampf & Tocarno [101], and Mehta

[102] made a quality assessment, and their terminologies are widely accepted in CFD

research community.

Verification has been defined by Mehta as “The process of determining that a model

implementation accurately represents the developer's conceptual description of the

model and the solution to the model”. The verification procedure begins with

assessing the error occurred quantitatively during the discretisation of fine grids,

implementation of the turbulence models, and errors while programming the CFD

codes. Generally, a mesh sensitive study is performed to describe and point out the

errors. The spatial discretization error is analysed by simulating the grids to different

resolutions, a process which increases the computational overhead while increasing

the options in CFD code.

Validation is further defined by Mehta as “The process of determining the degree to

which a model is an accurate representation of the real world from the perspective of

the intended uses of the model”. Validation in CFD refers to comparison of the CFD

simulation with the experimental data in order to examine the modelling errors. CFD

results validation against experimental data can be difficult sometimes, as the

available experimental data might be limited or is complex. Validation can also be

defined as “solving the right equations” which also recognises the quantified errors

and the uncertainty in CFD simulations. Oberkampf & Trucano demonstrated that

validating CFD simulations against experimental data can be complicated, as the poor

experimental data may scatter the CFD simulations.

Keeping in mind the complex nature of the validation process, in order to validate our

simulation, we compared our data with the experimental results from Angland [24].

76

It must be noted: Angland runs the experiments with velocities between 10 m/s to 40

m/s and a Reynolds number from 0.7 X 106 to 2 X 106. For this reason, a 30 m/s case

was calculated with the same values and with angles of attack of 30 degrees.

The results for the lift force are presented in Figure 12, comparing the results of

Angland with our simulations data. Moreover, the drag forces are shown in Figure 13

for the experimental results, compared with our simulations. On one hand, it is shown

that the results are slightly different, with a linear response in both cases when

describing the lift force. On the other hand, it is recognisable in both cases that the

results for the drag forces generated a parabolic graphic.

Figure 12: Lift Coefficient comparison between Angland's results and our simulations.

77

Figure 13: Drag Coefficient comparison between Angland's results and our simulations.

Now, if we focus on the generation of vorticity at the edge of the flap, it is possible to

see the similarities between Figure 14 and Figure 15. A primary attachment line and a

secondary separation line are visible in both Angland's experimental case and in this

study's simulation. The focal point is slightly more difficult to see, but it can be

appreciated in Figure 15 on further examination (this will be discussed in section 6.2).

All these pointed specifications are generated in similar areas of the side-edge of the

flap. It is necessary to compare the sound pressure level generated by the edge of the

flap in this case, and compare it with the experimental cases. Moreover, is important

to compare the sound pressure level (SPL) generated by the edge of the flap in this

study case and compare it with the experimental cases. In Figure 16, is possible to

appreciate the SPL generated by the edge of the flap versus the frequency in the

experimental case at 30 m/s with a deflection of 30 degrees over the flap, versus the

78

results generated by the simulations running the DES model with the configuration

mentioned previously. Is important to mention that the generation of SPL starts with

110 dB at a similar frequency (around 60 Hz), then begins to increase until it reaches

120 Hz, and then ultimately starts to drop. There is a quicker drop in this study's

simulations as the high lift dispositive was not completely simulated. For this reason,

the frequency and behaviour of the SPL has changed, however the important result is

the response of the system in comparison with the experiment.

Figure 14: Oil flow of flap side edge showing major flow features. View looking starboard, flow is from left

to right. [26]

79

Figure 15: Vorticity at the edge of the flap.

Figure 16: SPL results at 30m/s with an angle of attack of 30 degrees. Angland VS our results.

80

5.2.3 Boundary Conditions

The wall boundary condition is applied to the flap; this is a no-slip boundary condition

with the gradient of pressure normal to the wall set to zero. The density was calculated

using the ideal gas law and lists the boundary conditions used along the surfaces of

the domain in Table 3.

Table 3: Boundary conditions applied

Boundary Type Value

Inlet Free-stream V and Re are shown in for every

test.

Outlet Pressure Outlet 0 Pa

Flap Wall No – slip smooth

Around Free-stream V and Re are shown in for every

test.

81

CHAPTER 6: SIMULATIONS AND RESULTS

During this chapter, the results for the simulations of a flap side-edge flowfield using

the Detached Eddy model in Star CCM+ are presented and discussed. The main

purpose of these simulations was to generate initial data to model the nearfield flow

and to use the unsteady CFD data as an input to a Ffowcs Williams Hawkings (FWH)

solver to estimate the farfield acoustics in future works. The software used was Star-

CCM+, as previously mentioned, with the FWH solver integrated in the program. The

data and specifications used in the simulations are presented.

6.1 Overview

To capture the significant off-surface unsteadiness in the correct way, the detached-

eddy simulations were chosen. The parameters used for these simulations were with

velocities between 30 and 60 meters per second, a Reynolds number between 0.95 X

106 and 1.91 X 106, all with angles of attack between 10° - 30° degrees. These

simulations are detailed in Table 4. No simulations were run with an angle of attack

of less than 10 degrees, because the average configuration for landing the Airbus A320

is between 15 and 30 degrees. Meanwhile, for take-off, the flap set is between 5 and 15

degrees depending on the company procedures.

Table 4: Set of simulations.

V (m/s) Mach number Reynolds number Flap model deflection

30 0.102 0.95 X 106 30°

40 0.135 1.27 X 106 10°, 15°, 20°, 25°, 30°

50 0.169 1.59 X 106 20°, 25°, 30°

60 0.203 1.91 X 106 20°, 25°, 30°

82

Other important considerations are the parameters used for our simulation. All of

them are listed in Table 5.

Table 5: Meshing parameters for simulation

Parameters Values

Number of Cells 3.9 X 106 cells

Mesher Type Trimmer

Maximum Mesh Size (mm) 680

Minimum Mesh Size (mm) 10

Maximum Y+ 8.3

Figure 17: Y+ values on the flap

6.1.1 Computational details

Table 5 lists the meshing parameters used in the simulation and from Figure 5Figure

11 shows the mesh of the domain, zoomed view of the mesh around the flap, and

isometric pictures of the mesh, as well as the location of the flap inside of the fluid

domain, respectively.

As shown in the figures mentioned in the previous paragraph, the mesh was refined

around the flap and near of the flap side-edge. This was required in order to capture

the wake dynamics of the flow in the important area of interest, as well as to keep the

83

y+ value as lower as possible. Figure 17 shows the y+ values on the flap. The maximum

value of y+ is 8.27. Even though it is greater than 5, it is an acceptable value to get

reasonable results without increasing the mesh cell numbers and computational cost.

An all y+ wall treatment is used in the simulation which also justifies the why the

mesh size is reasonable.

In order to have a positive numerical viscosity, the CFL number must be equal or

lower than 1. The CFL number has been calculated using equation 3.3. The used

velocities are between 30 and 60 m/s, showed in Table 4, the timestep used in our

simulation is listed in Table 7 and the minimum and maximum length of the cells are

listed in Table 5. With these values we have than the highest CFL number obtained is

0.18. Ensuring real viscosities with these results.

Table 6 and Table 7 list the physics model and the stoppage criteria used in the

simulations.

Table 6: Physics parameters for simulations

Parameters Values

Turbulence Model Detached Eddy Simulation (DES)

Wall Treatment All y+ wall treatment

Flow Regime Turbulent Flow

Equation of State Ideal Gas

Acoustic Model Ffowcs Williams-Hawkings (FW-H)

Table 7: Stoppage criteria for simulations

Parameters Values

Timestep Size 3×10-5s

Temporal discretization 2nd order

Iteration timestep 237

84

The physical timestep (∆𝑡) was 3×10-5s. This corresponded to a sampling frequency

of 20000 Hz. According to the Niquest criteria, this meant that the highest frequency

that could be resolved was 10000 Hz. The timestep corresponded to a non-

dimensional timestep of 4.25 ×10-3, which meant 237 timesteps were needed for one

convection length. An implicit dual time-stepping method was used with 20 sub-

iterations for each timestep to ensure convergence. The solution was run to a non-

dimensional time of approximately 0.1s. Convergence was determined by monitoring

global values like lift and drag and pressure monitors around the vortex.

The microphones positions are inputted into STAR-CCM+ at the same locations than

the experiments performed by Angland [26]: 1 meter of distance from the flap side

edge, as well as another positioned under the flap, 1 meter away.

6.2 Aerodynamic Analysis of Results

The lift and drag coefficients were calculated using the equations 3.4 and 3.5.

The drag and lift coefficient are shown in Figure 18 Figure 19 for the different

simulations that are specified in Table 4. As could be seen in Figure 18, there is a small

increase in 𝐶𝐿 as the Reynolds Number was increased from 1.27x 106 to 1.91 x 106. As

we could corroborate, the lift coefficient answer has a linear response with the 3

different Re, with the 3 main sets, from 20 degrees till 30 degrees of deflection of the

flap. With these results, we know that the geometry of the flap did not stall up to these

angles of attack. Regarding the drag values, these ones have a slight dependence with

the velocity and, as shown in Figure 19, once the velocity increases, the drag force

decreases.

85

As shown in the Figure 20, the leading edge of the flap is dominated by a dual vortex

system. Originated by the flap´s pressure surface and located on the side-edge, the

primary vortex dominates the entire side-edge. This happens as a response to its fast

growing in the chordwise direction. We also found a secondary vortex located on the

suction surface; caused by a shear layer that separates from the upper surface of the

side-edge. The shear layer that causes the secondary vortex is reattached on the

suction surface of the flap, which is why the growth of the primary vortex is bigger

than the secondary one.

Figure 18: CL of our simulations.

86

Figure 19: CD of our simulations.

The extension of the primary vortex on the side-edge is formed by the primary

attachment line, where the shear layer that detached from the flap suction surface

attached to the side-edge flap. We can appreciate the development of the merged

primary and secondary vortex in the streamwise direction in the Figure 20. Moreover,

we can visualize how the strength of the vortex is decreased as the vortex grow in size,

also as the vortex moves downstream and separates from the flap surface. Details are

shown in Figure 21 Figure 22. These simulations predicts the theories developed by

Brooks and Humphreys mentioned previously at the section 2.4. [22]

As we mention in the previous chapter, Figure 14 and Figure 15 show a tiny difference

with Angland simulations run with similar configurations than ours. The primary

attached line determined by the DES calculation was located at almost the same place

as the experimental oil flow shown in the first figure, but it shows the disparity with

the information showed by Angland [26] where he mentions: “… the next there were

87

two significant disparities. The primary attachment line determined by the DES

calculation was located further towards the suction surface than the equivalent feature

on the oil flow. This suggested that the size of the primary vortex on the flap side-edge

was larger and grew quicker in the DES calculation. There was also a disparity at the

point where the shear layer, which was wrapped around the primary vortex, attached

on the suction surface. This was the point of vortex merging. In the oil flow, this

occurred at 0.41 < xF /cF < 0.44 (the exact location of this point was difficult to determine

in the oil flow visualization since it moved). The point of attachment on the suction

surface in the DES calculation was xF/cF = 0.38. The difference arose from the

accelerated growth of the primary vortex on the flap side-edge in the simulation. The

point on the flap where the merged vortex system separated from the flap was well

predicted by the simulation.” [26]

Having a closer prediction of the primary attachment line and the secondary

separation line, as well as having a correct prediction of the merging point, allowed

us to follow with the prediction of the acoustic analysis of the simulations.

Figure 20: Velocities contour in a series of y-z planes showing vortex merging and separation of vortex from

flap.

88

Figure 21: Details of the merging vortex at the edge of the flap.

Figure 22: Details of the vortex generation at the edge of the flap.

89

Figure 23: Vector plot around the flap side-edge in X direction.

6.3 Acoustic Analysis of Results

Figure 24 shows the sketch of the location where the sound pressure level is measured

to acquire data from the nearfield acoustics. From Figure 25 to Figure 27, the sound

pressure level (SPL) of the nearfield pressure fluctuation is measured at x = 0.2 m and

y = 0 m and z = 0.7 m, with velocities from 40 to 60 m/s (all the different configurations

are mentioned in Table 4). The results from the bottom probe point (under the flap

side edge) are shown from Figure 28 to Figure 30 with same velocities and deflections

of the flap located at x = 0.2 m and y = -0.5 m and z = 0.2 m.

In general, all the results show a peak at lower frequencies. This was expected, as a

similar behaviour is shown across different experiments like Angland [26], Aythe [33]

and Hardin [43]. The results show also a similar behaviour from the Angland results

with the same flap, but have a particular difference as this last one has been developed

90

within a complete high lift device. For this reason, Angland’s results shows stronger

noise at higher frequencies, as we already know from different analysis previously

mentioned in chapter 2, Flap side-edge only generates high noise at lower frequencies

as is showed in all figures.

Figure 24: Location of the point of evaluation for Sound Pressure Level (SPL)

These results were expected, based on the aerodynamic analysis performed on the

wake and mean pressure coefficient on the flap. A larger and more converged sample

of data is needed for the analysis of the spectra. It can also be seen that there is more

fluctuation in the broadband of the signal. This is expected when using the detached

eddy simulation model. However, the magnitude of the broadband is mostly lower

than the experimental results in the flap. It is higher than the experimental results up

to a 1000 Hz and then falls slightly lower than experiments afterwards.

91

Figure 25: Sound Pressure Level (SPL) of simulations at 40 m/s whit different angles of attack taken from the

side of the flap side-edge.



92



As we can see in Figure 25Figure 26Figure 27, when the velocities are higher the noise

generations increase as well as the same happens when deflection of the angle

increase. Same behaviour is presented in Figure 28Figure 29Figure 30, our simulations

predict in a correct way the behaviour of experimental data like Angland’s [26].

93


bottom of the flap side-edge.



94



95

Chapter 7 CONCLUSIONS AND RECOMMENDATIONS

7.1 Summary

This computational research has been undertaken to determine the aerodynamics and

aeroacoustics of the flowfield near and around the flap side-edge. The principal aim

of the investigation was to understand the generation of noise, and in the future

develop a mathematical model that would be able to describe the generation of the

noise at the edge of the flap. Different configurations for the simulations were ran to

found which the best option as well as following the recommendations from previous

work to acquire the knowledge needed for future progress.

7.2 Flap side-edge

The aerodynamic properties of the flap were determined by means of on-surface

pressures and by measuring the forces and moments in the simulations. This was

made possible by running a detached eddy simulation on a flap side-edge to resolve

the unsteady flow around this geometry with a grid of 3.9 X 106 nodes. The simulation

allowed the identification of sources of unsteadiness in the flow around the flap side-

edge.

The detached eddy simulation captured the major flow features at the flap side-edge

found in the experimental cases from other researchers. For example, a dual vortex

system nears the leading edge, vortex merging and a significantly unsteady off-

surface vortex. As the results were compared with the experimental on-surface oil

flow visualisation and other simulation results, the detached eddy simulation were

found to have similar behaviours, magnitude and growth rate of the primary vortex

96

on the flap side-edge as well as the secondary vortex. The point of separation of the

vortex from the flap surface was well predicted by the detached eddy simulation. One

principal noise source at the flap side-edge had been corroborated with previous

work.

In summary, a dual vortex system near the mid-chord of the flap had merged to

become a single vortex. In addition, an extra source of unsteadiness in the flap side-

edge vortex could be possible as the pressure perturbations in a plane at the flap side-

edge showed us. The primary vortex on the flap side-edge showed significant

unsteadiness. Contrary to this, the weaker secondary vortex on the flap has showed

less unsteadiness. As the vortex grew in strength and separated from the flap surface,

the amplitude of these disturbances were magnified.

7.3 Recommendations

This section discusses briefly what needs to be improved in order to continue with

future research, as well as some recommendations for the reader.

The amplitude of the cases needs to be increased. More cases need to be run, with

configurations at lower speeds to identify the behaviour of the dual vortex system and

start with a mathematical model of it. Once the principal parameters to run the

simulations are obtained, the focus should be on gleaning more data and increasing

the information to develop the mathematical model of the noise generation at the flap

side-edge.

As it is already known that the flap never works alone during the take-off and landing,

another recommendation is to develop a model of the high lift dispositive and

measure the noise generate by all the system. In this way any kind of gap in the

discussed model could be solved, also there are experimental data from Angland in

97

this field [24]. Another interesting simulation could be with different classic methods

at the edge of the flap like a porous treatment or fences to compare with experiment

data and generate enough data to generate a mathematical model of the noise

reduction by this methods.

Finally, more information could be post processed to compare with other

experimental data like chordwise and spanwise pressure distribution on the flap,

between others, and corroborate these if they are well predicted.

98

BIBLIOGRAPHY

[1] H. Leibowitz, "Airport Noise Pollution: A Bibliography of its Effects on People

and Property.," vol. 19, no. 3, 1974.

[2] A. S. De Vany, "An Economic Model of Airport Noise Pollution in an Urban

Environment," 1976.

[3] M. M. Haines, S. A. Stanfeld, R. F. S. Job and B. Berglund, "Chronic aircraft noise

exposure, stress responses, mental health and cognitive performance in school

children," vol. 31, no. 2, 2001.

[4] S. A. Stansfeld and M. P. Matheson, "Noise pollution: non-auditory effects on

health," vol. 68, no. 1, 2003.

[5] S. Morrell, R. Taylor and D. Lyle, "A review of health effects of aircraft noise,"

vol. 21, no. 2, 1997.

[6] E. A. M. Franssen, C. M. A. G. van Wiechen, N. J. D. Nagelkerke and E. Lebret,

"Aircraft noise around a large international airport and its impact on general

health and medication use," vol. 61, 2004.

[7] N. Ozkurt, S. F. Hamamci and D. Sari, "Estimation of airport noise impacts on

public health. A case study of İzmir Adnan Menderes Airport," vol. 36, 2015.

99

[8] W. Dobrzynski, "Almost 40 years of airframe noise research: What did we

archieve?," Journal of Aircraft Vol. 47 No. 2, pp. 353-367, March-April 2010.

[9] A. Filippone, "Aircraft noise prediction," Progress in Aerospace Sciences, vol. 68,

pp. 27-63, March 2014.

[10] M. J. T. Smith, Aircraft Noise, Cambridge, United Kingdom: Cambridge

University Press, 1989.

[11] J. C. Hardin, "Airframe self noise - four years of research," NASA TMX-73908,

1976.

[12] H. H. Heller and W. M. Dobrzynski, "A comprensive review of airframe noise

research," ICAS, vol. GL 03, 1978.

[13] P. Fethney, "An experimental study of airframe self-noise," in AIAA 2nd Aero-

Acoustics conference , Hampton, Va, 1975.

[14] P. Fethney and A. H. Jelly, "Airframe self-noise studies on the lockheed L1011

Tristar aircraft," AIAA, pp. 80-1061, 1980.

[15] M. R. Fink , "Airframe Noise Prediction Method," U.S. Department of

Transportation RD-77-29, Washington, D.C., 1977.

[16] M. R. Fink, "Noise Component Method for Airframe Noise," Journal of Aircraft ,

vol. 16, no. 10, pp. 659-665, 1979.

100

[17] W. Dobrzynski , "The national program on airframe noise reduction- pertinent

wind tunnel experiments on source identification and airframe noise reduction

of wing high lift configurations," in AAAF-DGLR Symposium , Saint-Louis,

France , 1999.

[18] D. P. Lockard and G. M. Lilley, "The airframe noise reduction challenge,"

Langley Research Center NASA, Hampton, Virginia, 2004.

[19] L. V. Lopes and C. L. Burley, "Design of the nest generation aircraft noise

prediction program: ANOPP2," in 17th AIAA/CEAS Aeroacoustics conference

(32nd AIAA Aeroacoustics conference), Portland, Oregon , 2011.

[20] F. Farassat and J. Casper, "Towards an airframe noise prediction methodology:

survey of current approaches," in 44th AIAA aerospace science meeting, AIAA

2006-0210, Reno, NV, January 2006.

[21] W. Dobrzynski, B. Gehlhar and H. Buchholz, "Model and full scale high-lift

wing wind tunnel experiments dedicated to airframe noise reduction,"

Aerospace Science and Technology , vol. 5, no. 1, pp. 27-33, 2001.

[22] T. F. Brooks and W. M. Humphreys Jr., "Flap-edge aeroacoustic measurements

and predictions," Journal of sound and vibration, vol. 261, pp. 31-74, 2003.

[23] Y. Guo, "On noise reduction by flap side edge fences," Journal of sound and

vibration, vol. 277, pp. 369-390, 2004.

101

[24] D. Angland and X. Zhang, "Measurements of flow arounf a flap side edge with

porous edge treatment," AIAA Journal, vol. 47, no. 7, pp. 1660-1671, 2009.

[25] F. Plata Moraleda and F. Martini Catalano, "Experimental analysis of the

aerodynamics of porous flap side-edge for noise reduction," in 22nd

International congress of mechanical engineering (COBEM 2013), Ribeirao Preto, SP,

Brazil, 2013.

[26] D. Angland , Aerodynamics and aeroacoustics of flap side-edges, Southampton,

UK: University of Southampton, 2008.

[27] J. S. Gibson, "The Ultimate Noise Barrier: Far Field Radiated Aerodynamic

Noise," Inter-Noise 72 Proceedings, pp. 332-337, 1972.

[28] G. J. Healy, "Measurement and Analysis of Aircraft Far Field Aerodynamic

Noise," NASA CR-2377, 1974.

[29] J. S. Gibson , "Non-Engine Aerodynamic Noise Investigation of a Large

Aircraft," NASA CR-2378, 1974.

[30] J. D. Revell , "The Calculation of Aerodynamic Noise Generated by Large

Aircraft at Landing Approach," Journal of the Acoustic Society of America , vol. 55,

p. 73, 1974.

[31] T. F. Brooks, D. S. Pope and M. A. Marcolini, "Airfoil Self-Noise and Prediction,"

NASA Reference Publication, no. 1218, 1989.

102

[32] M. R. Fink and M. H. Schlinker, "Airframe Noise Component Interaction

Studies," vol. 17, no. 2, pp. 99-105, 1980.

[33] W. F. Ahyte, W. R. MIller and W. Meecham, "Wing and Flpa Noise Measured

by Near and Far Field Cross Correlation Techniques," 1979.

[34] J. M. Kendall and W. F. Ahyte, "Noise Generation by a Lifting Wing/Flap

Combination at Reynolds Numbers to 2.8 x 10^6," AIAA Paper, vol. 35, p. 80,

1980.

[35] L. C. Chow, K. Mau and H. Remy, "Landing gear and high lift devices airframe

noise research," AIAA Paper 2002-2408, 2002.

[36] M. S. Howe, "A review of the theory of trailing edge noise," Journal of sound and

vibration , vol. 61, pp. 437-465, 1978.

[37] M. S. Howe, "On the generation of side-edge flap noise," Journal of sound and

vibration , vol. 80, no. 4, pp. 555-573, 1982.

[38] N. Molin, M. Roger and S. Barre, "Prediction of aircraft high-lift device noise

using dedicated analytical models," AIAA, pp. 2003-3223, 2003.

[39] R. Davy and F. Noens, "Aeroacoustic Behaviourof a 1/11 Scale Airbus Model in

the Open Anechoic Wind Tunnel CEPRA 19," AIAA , no. 2412, 2002.

[40] M. S. Howe, Theory of vortex sound, Cambridge, UK.: Cambridge University

Press, 2002.

103

[41] T. F. Brooks and T. H. Hodgson, "Trailing-edge Noise Prediction from

Measured Surface Pressures," Journal of Sound and Vibration , vol. 261, no. 1, pp.

31-74, 2003.

[42] G. M. Lilley, "A study of the flight of the owl," AIAA, pp. 98-2340, 1998.

[43] J. C. Hardin, "Noise radiation from the side edge of flaps," American Institute of

aeronautics and astronautics journal , vol. 18, pp. 549-552, 1980.

[44] K. R. Meadows , T. F. Brooks, W. M. Humphreys, W. W. Hunter and C. H.

Gerhold, "Aeroacoustics measurements of a wing-flap configuration," AIAA,

pp. 97-1595, 1997.

[45] M. R. Khorrami and B. A. Singer, "Stability analysis for Noise-Source modeling

of a Part-Span flap," AIAA Journal , vol. 37, no. 10, pp. 1206-1212, 1999.

[46] C. K. W. Tam, "Computational Aeroacoustics: Issues and Methods," AIAA

Journal, vol. 33, no. 10, pp. 1788-1796, 1995.

[47] P. L. Roe, "Technical Prospects for Computational Aeroacoustics," AIAA Paper ,

1992.

[48] C. L. Morfey, "Fundamental Problems in Aeroacoustics," Seventh International

Congress On SOund and Vibration, Germany, 2000.

[49] M. J. Lighthill, "On sound generated aerodynamically. I. General Theory.," M.

H. A., pp. 564-587, 1951.

104

[50] J. E. Ffowcs-WIlliams and D. L. Hawkings, "Aerodynamics Sound Generation

by Turbulent Flow in the VIcinity of a Scatting Half-Plane," Journal of Fluid

Mechanics , vol. 40, pp. 657-670, 1970.

[51] J. E. Ffowcs-Williams and L. H. Hawkins, "Sound Generation by Turbulence

and Surfaces in Arbitrary Motion," Philosophical Transactions of the Royal Society

of London, vol. 342, pp. 264-321, 1969.

[52] F. W. Spaid and F. T. Lynch, "High Reynolds Number, Multi-Element Airfoil

Flow-field Measurements," AIAA Paper, vol. 96, p. 682, 1996.

[53] W. O. Valarezo, C. J. Dominik, R. J. McGhee, W. L. Goodman and K. B. Paschal,

"Multielement Airfoil Optimization for Maximum Lift at High Reynolds

Number," AIAA Paper, 1991.

[54] I. Gursul, "Review of Unsteady Vortex Flows over Delta Wings," AIAA Paper,

2003.

[55] G. R. Baker, S. J. Barker, K. K. Bofah and P. G. Saffman, "Laser Anemometer

Measurements of Trailing Vortices in Water," Journal of Fluid Mechanics, vol. 65,

no. 2, pp. 325-336, 1974.

[56] M. Menke and I. Gursul, "Unsteady Nature of Leading Edge Vortices," Physics

of fluids, vol. 9, no. 10, pp. 1-7, 1997.

[57] I. Gursul and X. Wensheng, "Origin of Vorte Wandering over Delta Wings,"

Journal of Aircraft, vol. 37, no. 2, pp. 348-350, 2000.

105

[58] M. R. Khorrami, B. A. Singer and R. H. Radeztsky Jr., "Reynolds-Averaged

Navier-Strokes Computations of a Flap-Side-Edge Flowfield," AIAA Journal,

vol. 37, no. 1, pp. 14-22, 1999.

[59] P. R. Spalar and S. R. Allmaras , "A One-Equation Turbulence Model for

Aerodynamic," AIAA Paper, 1992.

[60] M. R. Khorrami, M. E. Berkman, F. Li and B. A. Singer, "Computational

Simulations of a Three-Dimensional High-Lift Wing," AIAA Paper, 2002.

[61] C. L. Streett, "Numerical Simulation of a Flap-Edge Flowfield," AIAA Paper,

1998.

[62] A. Moitra, "Automated CFD Analysis of Two-Dimensional High-Lift Flows,"

AIAA Journal , vol. 39, no. 4, pp. 662-667, 2002.

[63] . R. M. Cummings, S. A. Morton and J. R. Forsythe , "Detached-Eddy Simulation

of Slat and Flap Aerodynamics for a High-Lift Wing," AIAA PAper, 2004.

[64] A. Moitra, "Unstructured Grid Issues in 2-D High-Lift Computations,"

Proceedings of the 7th International Conference on Grid Generation in Computational

Field SImulations. International Society of Grid Generation., pp. 263-274, 2000.

[65] F. Inc., FLUENT 6.0 User's Guide, 2001.

[66] P. T. Meredith, "Viscous Phenomena Affecting High-Lift Systems and

Suggestions," High Lift System Aerodynamics, vol. 19, 1993.

106

[67] F. T. Lynch, R. C. Potter and F. W. Spaid, "Requirements for effective High-Lift

CFD," International council of the Aeronautical Sciences Proceedings, 20th Congress,

AIAA, vol. 2, 1996.

[68] P. C. Spalart, "Young-Person’s Guide to Detached-Eddy Simulation Grids,"

NASA, 2001.

[69] F. R. Mentor, "Improved Two-Equation k-w Models for Aerodynamic Flows,"

AIAA Paper, vol. 93, no. 2906, 1993.

[70] F. R. Mentor, "Two-Equation Eddy-Viscosity Turbulence Models for

Engineering Applications," AIAA Journal, vol. 32, no. 8, pp. 1598-1605, 1994.

[71] P. Godin and D. W. Zingg, "High-Lift Aerodynamic Computations with One

and Two-Equation Turbulence Models," AIAA Paper , no. 96, p. 562, 1996.

[72] M. G. Macareg, "Fundamental Investigations of Airframe Noise," AIAA Paper,

pp. 98-2224, 1998.

[73] M. Choudhari, D. P. lockard, M. G. Macaraeg, B. A. Singer, C. L. Streett, G. R.

Neubert, R. W. Stoker, J. R. Underbrink, M. E. Berkman, M. R. Khorrami and S.

S. Sadowski, "Aeroacoustic Experimens in the Langley Low-Turbulence

Pressure Tunnel," NASA TM-2002-211432, 2002.

[74] S. T. Smith , "Flap Side-Edge Vortex Bursting and Airframe Noise," AIAA Paper

, 2002.

107

[75] T. B. Benjamin , "Theory of the Vortex Breakdown Phenomenon," Journal of Fluid

Mechanics, vol. 14, no. 4, pp. 593-629, 1963.

[76] J. K. Harvey, "Some Observation of the Vortex Breakdown Phenomenon,"

Journal of Fluid Mechanics, vol. 14, no. 4, pp. 585-592, 1963.

[77] H. H. Bossel, "Vortex Breakdown Flowfield," Physics of Fluids , vol. 12, no. 3, pp.

498-508, 1969.

[78] W. J. Grabowski and S. A. Berger, "Solutions of the Navier-Stokes Equations for

Vortex Breakdown," Journal of Fluid Mechanics , vol. 75, no. 3, pp. 525-544, 1976.

[79] M. D. Salas and G. Kuruvila , "Vortex Breakdown Simulation: A Circumspect

Study of the Steady Laminar Axisymmetric Model," Computers and Fluids, vol.

17, no. 1, pp. 247-262, 1989.

[80] M. Choudhari and M. R. Khorrami, "Computational study of porous treatment

for altering flap side-edge flow field," in 9th AIAA/CEAS Aeroacoustics conference

and exhibit , Hilton Head, South Carolina, 2003.

[81] R. Sen, "Vortex-Oscillation Model of Airfoil Side-Edge Noise," AIAA Journal,

vol. 35, no. 3, pp. 441-449, 1997.

[82] B. W. McCormick, Aerodynamics, Aeronautics, and Flight Mechanics, New

York: Wiley, 1994.

108

[83] R. Shepherd Shevell, Fundamentals of flight, University of Michigan: Prentice-

Hall, 1983.

[84] L. J. Clancy, Aerodynamics, New York: Longman Scientific & Technical, 1986.

[85] C. B. Laney, Computational Gasdynamics, London, UK.: Cambridge University

Press, 1998.

[86] R. Courant, H. Lewy and K. Friedrichs, "Über die partiellen

Differenzengleichungen der mathematischen Physik," Mathematische Annalen,

p. 100, 1928.

[87] S. G. Fedosing, " The Concept of the General Force Vector Field," OALib Journal,

vol. 3, pp. 1-15, 2016.

[88] S. G. Fedosin, "Two components of the macroscopic general field.," Reports in

Advances of Physical Sciences, vol. 1, no. 2, 2017.

[89] M. J. Crocker , Handbook of Acoustics, John Wiley & Sons, 1998.

[90] B. Launder , G. Reece and W. Rodi , " Progress in the development of a Reynolds

stress turbulence closure. Journal of Fluid Mechanics.," AIAA Journal, vol. 68,

pp. 537 - 566, 1975.

[91] D. C. Wilcox, Turbulence Modeling for CFD, CA: Griffin Printing, 1994.

109

[92] P. Spalart, W.-H. Jou, M. Strelets and S. Allmaras, "Comments on the feasibility

of LES for wings, and on a hybrid RANS/LES approach," Advances in DNS/LES,

pp. 137-147, 1997.

[93] P. R. Spalart, "Detached-eddy simulation," Annu. Rev. Fluid Mech., vol. 41, pp.

181-202, 1999.

[94] A. Travin, M. Shur, M. Strelets and P. Spalart, "Detached-eddy simulations past

a circular cylinder," Flow Turbul. Combust., vol. 63, pp. 293-313, 2000.

[95] M. Strelets, " Detached Eddy Simulation of Massively Separated Flows," AIAA,

2001.

[96] R. B. Kotapati, K. D. Squires and J. R. Forsythe, "Prediction of the Flow over an

Airfoil at Maximum Lift," AIAA Paper, vol. 259, 2004.

[97] M. Lighthill, "On Sound Generated Aerodynamically. I. Turbulence as a Source

of Sound," Proceedings of the Royal Society of London. Series A, Mathematical and

Physical Sciences, pp. 1-32, 1954.

[98] F. Farassat, " Derivation of formulations 1 and 1A of Farassat. Technical

Memorandum TM-2007-214853," NASA Langley Research Center (USA), 2007.

[99] K. S. Brentner and F. Farassat, "Modeling aerodynamically generated sound of

helicopter rotors.," Prog. Aero. Sci., vol. 39, pp. 83-120, 2003.

110

[100] W. J. R., "The HIgh Lift Development of the A320 Aircraft," ICAS Conference

1986, no. 2.3.2, 1986.

[101] W. Oberkampf and T. Trucano , "Verification and Validation in Computational

Fluid," Progress in Aerospace Science, vol. 38, pp. 209-272, 2002.

[102] U. Mehta , " Credible Computational fluid dynamics simulation.," The American

Institute of Aeronautics and Astronautics (AIAA) Journal., vol. 36, pp. 665-667, 1998.

[103] H. V. Fuchs and A. Michalke, "Introduction to aerodynamic noise theory,"

Progress in Aerospace Sciences , vol. 01, no. 14, pp. 227-297, 1973.

[104] N. A. Chigier and V. R. Corsiglia, "Tip vortices-velocity distributions," NASA

TM X-62 087, 1971.

[105] Y. Guo, "Aircraft flap side edge noise modeling and prediction," in 17th

AIAA/CEAS Aeroacoustics conference, Portland, Oregon, 2011.

[106] Y. P. Guo, K. J. Yamamoto and R. W. Stoker, "Component-based empirical

model for high lift system noise prediction," Journal of Aircraft , vol. 40, no. 5, pp.

914-922, 2003.

[107] Y. Guo and M. Joshi, "Noise characteristics of aircraft high lift system," AIAA

Journal, vol. 41, no. 7, pp. 1247-1256, 2003.

[108] K.-S. Rossignol , "Development of an empirical prediction model for flap side-

edge noise," in 16th AIAA/CEAS Aeroacoustics Conference , 2010.

111

[109] W. R. Miller , W. C. Meecham and W. F. Ahtye, "Large scale model

measurements of airframe noise using crosscorrelation techniques," J. Acoust.

Soc. Am., vol. 71, no. 3, pp. 591-599, March 1982.

[110] D. G. Crighton, "Airframe Noise," Aeroacoustic of Flight Vehicles: Theory and

Practice , vol. 1, p. 1258, 1991.

[111] F. Lynch, "Experimental Necessities for Subsonic Transport Configuration

Development," AIAA Paper, 1992.

[112] F. T. Lynch, R. C. Potter and F. W. Spaid, "Requirements for Effective High-Lift

CFD," in International Council of the Aeronautical Science Proceedings, 20th

Congress, AIAA, 1996.

[113] H. J. Morch, S. Enger, M. Peric and E. Schreck, "Simulation of lifeboat launching

under storm conditions," in 6th International Conference on CFD in Oil & Gas,

Metallurgical and Process Industries, SINTEF/NTNU, Trondheim, Norway, 2008.

[114] J. Ferziger and M. Peric, Computational Method for Fluid Dynamics, Berlin:

Springer, 2003.

[115] CD-adapco, USER GUIDE STAR-CCM+ Version 10.04.011, CD-adapco, 2015.

[116] M. Shur , P. R. Spalart , M. Strelets and A. Travin, "Detached-Eddy Simulation

of an Airfoil at High Angle of Attack," in 4th Symposium on Eng. Turb. Modelling

and Experiments , Corsia, France, 1999.

112

[117] J. Dacles-Marian, G. G. Zilliac, J. S. Chow and P. Bradshaw,

"Numerical/Experimental Study of a Wingtip Vortex in the Near Field," vol. 33,

no. 9, 1995.

[118] J. D. Revell, H. L. Kuntz, F. J. Balena, C. Horne, B. L. Storms and R. P. Dougherty,

"Trailing edge flap noise reduction by porous acoustic treatment," AIAA paper

97-1646, 1997.

[119] D. Wilcox, Turbulence modelling for CFD 2nd Edition, California: DCW

Industries, 1994.

[120] T. F. Brooks and M. A. Marcolini, "Airfoil Tip Vortex Formation Noise," AIAA

Journal, vol. 24, no. 2, p. 246, 1986.

Documents

AERODYNAMICS AND AEROACOUSTICS SIMULATIONS OF THE AIRBUS