combined effect of ground presence and heaving motion on a race car wing

Combined Effect of Ground

Presence and Heaving Motion on

a Race Car Wing

Matteo de’Giovanetti

Faculty of Engineering and the Environment

University of Southampton

A thesis submitted for the degree of

Master of Science in Race Car Aerodynamics

2013 09

mailto:[email protected]

http://www.something.net

http://southampton.ac.uk

To Time

Abstract

The purpose of this thesis is to investigate, experimentally, the be-

haviour of an inverted wing in ground effect undergoing a sinusoidal

oscillatory motion. In order to do so, a rigid structure has been built

and connected to an existing 80% model of a F1 front wing mainplane.

The experimental procedure has been validated against existing data

and values computed from widely accepted theories.

The tests included the acquisition of time-history of the aerodynamic

loads for three cases: clean wing, wing with a Gurney flap, wing with

a Gurney flap and transition fixed on the suction side. The inde-

pendent variables included Reynolds number, reduced frequency and

ride height. When possible, the results for lift and drag, average and

fluctuation, were compared with computational analyses carried out

on a similar layout, and good agreement was shown. The phase shift

between motion and lift coefficient was studied at different amplitudes

as well. It was possible also to shed light on the effects triggered by

the presence of a Gurney flap on lift and drag, as an increased bene-

ficial effect was observed at very low frequencies, with respect to the

clean wing case.

Non exiguum temporis habemus,

sed multum perdidimus.

Lucio Anneo Seneca, De Brevitate Vitae

Acknowledgements

There is not a single achievement, in the history of mankind, that was reached by a

man on his own. When a theorem, a discovery, a formula is named after someone,

we are forgetting all the people that made it possible. Every time we meet another

element of our species, that individual shapes who we are and what we think, for

the best or the worst, in a sort of large-scale interpretation of quantum mechanics.

It is my intention to mention, in the next paragraphs, all the people that helped

me, in the most diverse manners, throughout this year.

My sincerest gratitude goes to my supervisors, Professor Xin Zhang and Dr. Dave

Marshall, the first for his invaluable insights and life lessons, the second for his

continuous support and feedback on every topic of the project. Similarly, this

thesis as such would not have been possible without the help of Dr. Oksana

Stalnov, Mr. Dave Cardwell, Mr. Mike Thomas.

On a more personal note, the final days of this project have been incredibly

stressful for me. As my laptop and hard drive were stolen from my house, all the

thesis had to be rewritten in the short span of ten days, while re-analysing all

the wind tunnel data. There are not any words in the English dictionary, or any

other dictionary on this planet, that can describe the encouragement, assistance

and backing that I received from my family, and my parents in particular. As it

is my precise purpose of referring to them as a single entity, I have to thank them

for always being a propulsive force behind my actions, a guidance and a model. I

should also be grateful to my sisters, for they to have always been there. As far as

family goes, I also have to thank Mac, for teaching me that there is always time

to play with a ball, and He-Who-Shall-Not-Be-Named, for he knows why.

Many thanks to the few true friends I can count on, and in particular to the one

who bears my same name, and who shared the (few) crests and (many) valleys

of this year, and the greatness of a forgotten Italian painter. I would like also to

thank my coursemates, for they sharing ideas, knowledge and occasionally despair.

Last but not least, it is my firm intention to mention the name that will be echoed

in eternity: BUZZINI!

i

Contents

List of Figures v

1 Introduction 1

1.1 Background and Motivations . . . . . . . . . . . . . . . . . . . . . 2

1.2 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Dissertation Layout . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Literature Review 7

2.1 Aerodynamics of Racing Cars . . . . . . . . . . . . . . . . . . . . 8

2.2 Inverted Wings in Ground Effect . . . . . . . . . . . . . . . . . . 10

2.3 Unsteady Aerodynamics of Wings . . . . . . . . . . . . . . . . . . 16

2.4 Combined Effect of Oscillations and Ground Presence . . . . . . . 26

3 Research Description 29

3.1 General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Test Programme . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Results and Discussion 43

4.1 Preliminary Study . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Clean Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3 Gurney Flap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5 Conclusions and Further Work 61

iii

CONTENTS

References 65

iv

List of Figures

2.1 Chaparral 2C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Modified pressure distribution for double-element wing in ground

effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Spanwise velocity vectors for wing in ground effect . . . . . . . . . 12

2.4 Time-averaged momentum in the wake of a plunging aerofoil in

freestream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Dynamic stall mechanism for pitching aerofoil . . . . . . . . . . . 20

2.6 Phase shift as a function of reduced frequencies at different ride

heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1 CAD rendering of entire wing assembly . . . . . . . . . . . . . . . 35

3.2 Wing in the wind tunnel . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Example of task decomposition . . . . . . . . . . . . . . . . . . . 38

3.4 Block diagram for Labview software . . . . . . . . . . . . . . . . . 41

4.1 FFT of vertical-force signal . . . . . . . . . . . . . . . . . . . . . 44

4.2 Lift signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Example of lift signal post-processing . . . . . . . . . . . . . . . . 46

4.4 CD and CL vs. wind speed, freestream . . . . . . . . . . . . . . . 47

4.5 Phase shift between lift and motion, comparison between experi-

mental and computed values . . . . . . . . . . . . . . . . . . . . . 48

4.6 Lift coefficient, comparison between experimental and computed

values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.7 Lift and drag coefficients vs. ground clearance . . . . . . . . . . . 49

4.8 Efficiency vs. ground clearance . . . . . . . . . . . . . . . . . . . 50

v

LIST OF FIGURES

4.9 Average lift coefficient vs. frequency and Reynolds number . . . . 51

4.10 Average drag coefficient vs. frequency and Reynolds number . . . 53

4.11 Average lift coefficient vs. reduced frequency and ride height . . . 54

4.12 Phase shift vs. reduced frequency . . . . . . . . . . . . . . . . . . 55

4.13 Phase shift vs. motion amplitude . . . . . . . . . . . . . . . . . . 56

4.14 Lift and drag coefficients vs. wind speed, GF and TFX . . . . . . 57

4.15 Non-dimensional oscillation factor, lift and drag, GF and TFX . . 58

4.16 Non-dimensional lift and drag vs. reduced frequency, GF and TFX 59

4.17 Phase shift vs. reduced frequency for different cases . . . . . . . . 60

vi

Glossary

CAD Computer Aided Design

CFD Computational Fluid Dynamics

GF Gurney Flap

F1 Formula 1

FFT Fast Fourier Transform

FW Front Wing

KVS Karman Vortex Street

LDA Laser Doppler Anemometry

LE Leading Edge

MAV Micro Aerial Vehicle

PIV Particle Image Velocimetry

RVKS Reverse Karman Vortex Street

TE Trailing Edge

TFX Transition fixed

UAV Unmanned Aerial Vehicle

LIST OF FIGURES

Nomenclature

α0 Geometric angle of attack ◦

αeff Effective angle of attack ◦

a Motion amplitude mm

C(k) Theodorsen function

CDD

1/2ρSU∞Drag coefficient

CLL

1/2ρSU∞Lift coefficient

c Wing chord mm

D Drag N

E Young’s modulus Mpa

E Average increase in energy per unit time W

f Motion frequency Hz

k πfcU∞

Reduced frequency

h/c Non-dimensional ground clearance

h Wing position

h −cos(φ) Non-dimensional phase shift

h ac

Non-dimensional motion amplitude

L Lift N

q Freestream dynamic pressure Pa

M U∞c

Mach number

Px Propulsive power W

viii

LIST OF FIGURES

φ Phase shift ◦

Re ρU∞xν

Reynolds Number

ρ Flow density

S Planform area m2

σ Standard deviation

t Time s

Tu√u′2

U∞Turbulence intensity

U∞ρU∞xν

Freestream velocity m/s

u′ Velocity fluctuation m/s

W Weight kg

W Average power W

y Half length of the strut mm

ix

LIST OF FIGURES

x

1

Introduction

Without any doubt, the best researcher in the world is Nature itself. There is

not a more decisive incentive for improvement and advancement than the quest

for survival, which requires animals, and most of the living creatures, to be-

come faster, stronger, tougher as time goes by, and while Nature itself, with

the evolutionary process, provides their predators with increasingly powerful and

dangerous weapons to ultimately kill them. This mechanism is not unlike any

sport, where the smallest detail can make the difference between winning and

losing, rather than living or dying.

It is therefore sensible to look with curious and inquisitive eye at what Nature

shows us, and try to extract all the lessons we can. In science and engineering

especially, Nature can represent an incredible and invaluable source of inspiration

and provide the basis for technological breakthroughs. Fluid mechanics makes no

exception, as the first to gain an insight from biological creatures was arguably

Leonardo da Vinci himself, who tried, somehow successfully, to reproduce the

wing of a bird and to understand the mechanisms that allow such beautiful crea-

tures to fly and glide. Nowadays, many features of living creatures are being

studied in an attempt to improve both our knowledge and our resource man-

agement; for what concerns fluids, it is valuable to mention the studies on the

compliant surfaces of dolphins (1) (2) (3), rough surfaces (riblets) on sharks (4)

(5) (6), wavy leading edges on whales (7) (8) (9) (10), and the overall dynamics

of flight, from the sheer speed of the peregrine falcon to the gracious nimbleness

of the swallow.

1

1. INTRODUCTION

Regarding biological flight, many attempts have been made to comprehend and

reproduce it in laboratory, both from a dynamical and structural point of view.

For the former, it is possible to state that the wing motion for a bird is a combi-

nation of heaving, pitching and fore-aft motion, commonly referred as flapping.

Applications of these findings range from nano-UAVs (Unmanned Aerial Vehi-

cles), to small MAVs (Micro Aerial Vehicles) and larger-sized UAVs; recently, the

influence of these types of motion has been studied in relation with even larger

structures, including racing cars, with the final aim of improving efficiency and

performance.

1.1 Background and Motivations

The influence of aerodynamics in the design of racing cars has steadily increased

in the last decades, and, nowadays, is doubtlessly the most influential factor for

performance. The front wing is one of the most important devices on the entire

car, and is responsible for the production of downforce, as well as being the only

element to encounter freestream conditions. The wing is generally static, and

is rigidly connected to the rest of the car through two pillars mounted at the

centre of the wing. Apparently, the safety factors employed in the dimensioning

of these pillars are not high, as it has been proven by a number of failures in

these components (see for example Alonso at Sepang 2013). As a matter of

fact, the high levels of downforce produced by the wing, as well as the internal

compliance of carbon fibre, induce modifications in the shape at high speeds:

the wing endplates tend to get closer to the ground, introducing a curvature in

the wing. Another effect that can be triggered is the vibration of the wing, as a

further consequence of the flow-structure interaction coupled with the anisotropic

stiffness of carbon fibre. It is therefore interesting to investigate the influence

that these vibrations-oscillations can induce, from two standpoints mainly: one

is the gain in pure performance, the other is on the maximum forces that can be

generated, in order to prevent dramatic failures.

The topic of heaving and pitching wings has been widely investigated from the

point of view of applicability to Micro Aerial Vehicles (MAVs), small and light

devices that operate in Reynolds numbers in the order of magnitude of 102−103:

2

1.2 Project Objectives

unsteady effects are exploited to produce thrust, without any other streamwise-

aligned power device to generate motion. The related increase in lift, with respect

to static conditions, is also a research subject. Many of the inspirations for the

design of these small devices come from biological flyers, such as dragonflies,

similar insects and small birds.

Very few studies have been realised merging these two topics, or with particular

focus on motorsport applications; moreover, CFD has always been the preferred

method to carry out these investigations. The combined influence of unsteady

aerodynamics and ground effect on a generic race car front wing has not been

widely explored yet from an experimental point of view, especially in the range of

Reynolds number of 105. This deficiency has been the main driving force behind

the project.

1.2 Project Objectives

The principal target of this project is to improve the existing knowledge on the

behaviour of an inverted wing in close proximity to the ground while undergo-

ing oscillatory motion, with the employment of wind tunnel testing. The results

are to be referred to F1 cars and, more broadly, to motorsport applications.

This requires a careful assessment of the suitability and feasibility of wind tunnel

testing for such a case, with specific reference to Reynolds number and motion

frequency, and the technological bounds that are posed by state-of-the-art facil-

ities. The main goals can only be achieved if some intermediate objectives are

met, as listed below:

1. As the nature of this project is completely experimental, the required layout

has to be specified and, if necessary, designed and built. Since the wind

tunnel to be used was known from the start, the first goal was to prepare an

experimental setup capable of providing the required data: this involves all

the aspects connected with experimental testing, such as physical models,

control software and data acquisition.

2. The second objective is strictly connected with the first and indeed intrinsic

to the primary intent as well: understanding the current state of knowledge

3

1. INTRODUCTION

in the field of unsteady aerodynamics, in particular for the cases of ground

effect and heaving motion. This entails the careful review of existing liter-

ature of the subject, in order to correctly steer the ensuing research.

3. Once the first two objectives are completed, the actual testing can begin.

The acquisition of a coherent, consistent and accurate set of data is con-

sidered as an inevitable step and objective, and one not to be overlooked.

It is to be noted how an initial appraisal of wind tunnel capabilities is

of the foremost importance. This will entail the comparison of a simple

case to existing theories, to the positive outcome of which all the following

investigation is subordinated.

4. All the data acquired need to be analysed, taking into account what was

defined in the second step as of primary importance. Again, only a well-

documented and precise data processing can lead to meaningful results. The

objective here is therefore to prepare a programme capable of handling all

the data in a consistent and unique way, and to return significant quantities

and results, as required by the specific objectives outlined in the previous

steps.

5. The final and foremost objective is to draw conclusions based on the infor-

mations from the previous step, compare them with what was extracted in

step two and provide the reader with brief conclusions and suggestions to

steer further work.

1.3 Dissertation Layout

Where possible, this dissertation tries to follow a logical order in the first place,

and a chronological one where not possible, in order to make it as understandable

as possible. This document is consequently structured as follows:

• The second chapter is a survey of the relevant literature. A quick overview

of the influence of aerodynamics on racing cars serves as the introduction to

the two main features that pertain to this study: inverted wings in ground

effect and wings undergoing one or two-degree-of freedom motion, mainly

4

1.3 Dissertation Layout

heaving. A review of the few articles dealing with these two configurations

in conjunction follows.

• The third chapter involves an explanation of all the main facilities, models

and data processing techniques employed during the entire course of the

project. Relevant assumptions for the validity of the study and the testing

programme respectively open and close the chapter.

• The fourth chapter is a comprehensive account of all the results obtained,

both for the preliminary investigation and the main one, including addi-

tional testing.

• The fifth chapter winds up the dissertation by presenting the conclusions

and suggestions for further work. It can be observed how the objectives

described in the previous section and the chapters contents are very similar,

which allows every part to be logically meaningful as a stand-alone section.

5

1. INTRODUCTION

6

2

Literature Review

This chapter presents an overview of the available literature that can be helpful

in building the fundamentals of the project. Given the inclination of this study

towards motorsport applications, a brief overview of the history and current role

of aerodynamics in racing cars is offered. The remainder of the chapter is more

pertinent to the actual physics of this study, and is divided into three sections:

the first presents an introduction to the ground effect for inverted wings, and

effort was made in order to cover every and each of the significant points of this

topic. The second section is an account of the recent progress made in the field

of unsteady aerodynamics, when plunging and pitching wings are considered. In

contrast with the previous part, it was deemed as unreasonably time-consuming

and verbose to display all the research carried out with regards to the aforemen-

tioned problems, as a comprehensive review would encompass the entire field of

unsteady aerodynamics. In attempt to be both exhaustive and concise, the fun-

damentals of the discipline are presented, which date back to the 1920s and 1930s.

Afterwards, the main research of the last 15-20 years is put forward, in order to

illustrate the most recent findings; obviously this means that, time-wise, a gap is

present, but care was made to bridge it with small introductory paragraphs. The

third and final section details the little existing research already carried out on

the combination of these two broader topics.

7

2. LITERATURE REVIEW

2.1 Aerodynamics of Racing Cars

The field of aerodynamics can be considered relatively young, especially when

compared to the subjects of solid and fluid mechanics in general. Aerodynamics

as a separate subject became relevant as aircraft technology advanced, and the

main findings have been successfully applied to race cars in the last 50 years.

More recently, the particular conditions in which a race car finds itself, i.e. being

in contact with a surface that constrains the flow under the car, has justified

the existence of research specifically focused on this topic. It is worth mention-

ing that, as a consequence of the increased attention and awareness towards the

environment, in the last years a number of studies have been carried out on pas-

senger cars as well, mainly aimed at reducing the drag at moderate speed, to cut

large-scale fuel consumption.

Taking a step back in time, at the very beginning of automotive history, aero-

dynamic effects were not considered to be an issue of any sort for cars, given,

basically, the very low speeds that were involved. As technology progressed, these

vehicles were able to attain higher speeds, with the first car to actually break the

100 km/h barrier being the Jamais Contente, driven by Camille Jenatzy (11). In

these early days, the only aerodynamic-driven focus was to reduce the drag as

much as possible, which meant that cars were shaped as bullets or even styled as

raindrops, an example of this being the well-known A.L.F.A. 40-60 HP Castagna

Siluro Aerodinamica commissioned by Count Ricotti in 1914 (12). Perhaps the

first man to understand the potential of aerodynamic loads perpendicular to the

ground produced by a car, Ettore Bugatti designed the 1923 Type 32 Tank de

Tours to be fitted with an aerofoil-shaped bodywork, which produced lift. The

intuition was bright, the application was not. Many incidents, and even notable

fatalities, were triggered by aerodynamic effects, in particular when land speed

record were attempted and the speeds quickly rose up to 400 km/h and beyond,

the most famous case being the death of Auto Union driver Bernd Rosemeyer.

The main instance continued to be drag reduction, and even the studies by two

pioneers of automotive aerodynamics, Dr. Wunibald Kamm and Baron Reinhard

von Koenig-Fachsenfeld (13), were focused on this matter exclusively.

Despite an early, soon-to-be-forgotten attempt made by Opel, it was not until

8

2.1 Aerodynamics of Racing Cars

the 1960s that effective aerodynamic device were fitted to a racing car, the first

example being the number of features that appeared in a short time on the Cha-

parral 2 (14). Specifically, the 2C is more often than not believed to have started

the legacy that still endures today, with the introduction of air dams at the front

and an adjustable, inverted wing at the rear end. This car, and its successors,

enjoyed such a number of victories that the idea of inverted wings was picked up

by Formula 1 teams in 1968, and by the end of this year all the cars on the grid

were equipped with these devices. In order to improve balance, a further wing

was added to the front end, close to the ground (15). The first wings were im-

ported directly from aeronautical industry: this procedure proved to be initially

effective, but engineers soon realised that working condition on aeroplanes and

racing cars were very much diverse (16).

The second big aerodynamic revolution in F1 was represented by the increasing

comprehension of ground effect, with the first car designed around this concept

being the Lotus 78, which was then perfected and raced as the iconic Lotus 79.

The introduction of skirts, that sealed the underbody creating perfect channels

under the car, made possible to reach massive amount of downforce and conse-

quently cornering speeds (17).

The influence of aerodynamic devices on modern F1 cars performance is higher

than any other component, be it the engine, suspensions or electronics. The

downforce generated in high-speed bends can reach up to 3 or 4 times the weight

of the car, and the aerodynamic efficiency is well above three, depending on track

characteristics; wings and diffuser play a major role in the downforce genera-

tion process. It is interesting to point out that also the location of the centre of

pressure can highly affect the performance of the car, making the aerodynamic

balance another significant parameter to monitor during the design process (18).

A number of researches have been carried out on particular components of racing

cars, in an attempt to utilise an academic approach to an industrial problem,

consequently focusing not only on the pure performance, but also on the funda-

mental physics and features governing the flow: besides several articles published

on front wings, studies have been published on diffusers (19) (20) (21) (22) and

on wheels (23) (24), also with reference to their influence on the front wing (25)

9


(26). It is anyway clear how the research into new concepts, and the continu-

ous, systematic betterment of the known ones, is pushed to the limit, and even

infinitesimal improvements can make the difference on track. It is consequently

clear how this dissertation places itself into this continuous strive for advance.

Figure 2.1: Chaparral 2C

2.2 Inverted Wings in Ground Effect

The purposes of a front wing are mainly three: increase the total downforce of

the car, bring the centre of pressure forward, and shape the flow in a beneficial

way for the downstream components, such as diffusers, sidepods and rear wing.

The front wing of a racing car produces a considerable portion of the total down-

force generated by the car, and in general can be assumed to be around 30% and

40% of this value (27) (28). The wing is placed very close to the ground, with

distances that are normally lower than 100 mm (29), and therefore smaller than

the chord of the wing itself. This means that the effect of the ground cannot

be neglected, and that the influence of this wall on wing performance is of the

highest importance.

First mention of the modified pressure distribution of an inverted wing in prox-

imity of a wall is to be found in Zahm and Bear (30), who noticed how both lift

and drag substantially increased with respect to free-stream conditions. It was

not until the 1980s that systematic investigations of inverted wings in ground

effect began. A quantitative description of the modified pressure field for a wing

10


Figure 2.2: Modified pressure distribution for double-element wing in ground ef-

fect, from (18)

and flap configuration can be found in Dominy (31), who also stresses the impor-

tance of tip effects and consequently the necessity of endplates. The influence of

the aspect ratio of the wing has been studied by Katz (32) (33), who showed a

remarkable influence of finite-span effects, while the effects of wing geometrical

parameters, such as thickness and camber, has been explored by Coulliete and

Plotkin (34).

The first comprehensive set of tests on a wing in ground effect was carried out

by Ranzenbach and Barlow: a number of experimental and computational simu-

lations was carried out, both on single-element wings (35) (36) (37) and double-

element wings (38). The influence of ride height on wing performance was ex-

plored, at a constant angle of attack. The point of maximum downforce was

found to be at a non-dimensional ride height of 0.08, for a single element. The

reason for the subsequent downforce reduction was believed to be the merging

of aerofoil and ground boundary layers. It is to be noted how the wind tunnel

used in these tests employed a fixed ground, meaning a thicker boundary layer is

formed. This could have affected the transferability of results to race conditions.

The first introduction of a moving ground is linked to Knowles et al. (39), but the

results obtained are of little interest for real-case scenarios, as three-dimensional

effects are not discussed. It is worth mentioning that the incompressibility limit

11


Figure 2.3: Spanwise velocity vectors for wing in ground effect, from (41)

for ground effect is M = 0.15, as detailed by Doig et al. (40); shockwaves appear

from M = 0.4 onwards. These former results on the effect of compressibility

can help to explain the discrepancies that sometimes are observed between ex-

perimental and computational studies: at very low ground heights and Mach

numbers in the order of 0.1, an underprediction of force coefficients is a char-

acteristics of incompressible solvers, that are often used in order to make the

computational cases quicker to solve. The most complete set of studies in this

field was published as a result of the research completed by Zhang and Zerihan.

This study included a single-element wing (41) (42) and a double-element wing

(43) and (44). Subsequent overviews of the characteristics of the wake for these

two cases were performed by Mahon and Zhang (45) (46). The influence of inflow

conditions was investigated by Soso and Wilson (47) (48). Remarkable results

were obtained; only the ones regarding the particular geometry used in this study

will be reported.

For a single element wing, three clear regions, depending on ground clearance,

were pointed out: force enhancement, enhancement slowdown, force reduction

(41). The first is related to the downforce growth experienced by the wing when

moving closer to the ground; at a certain distance, depending on other parame-

ters such as angle of attack and Reynolds number, the rate of downforce increase

is reduced. The enhancement slowdown region ranges from 0.15c to 0.3c, with

the latter value valid for a near-stall angle of attack. The maximum downforce

is obtained at ride heights between 0.1 and 0.15, with the gains in downforce

being more relevant at lower angles of attack. After this peak, the values for

downforce drop systematically: the reason for this is postulated to be the in-

12


creasingly large adverse pressure gradient encountered by the flow on the suction

side, with regions of separated flow appearing at the trailing edge. Drag is found

to grow continuously when reducing ride height, and the rate of increase is ac-

tually larger in the force reduction region: it is therefore clear that this region

should be avoided, as the wing performance drops dramatically. From the point

of view of flow features and aerodynamic coefficient, the presence of the ground

can be modelled to work analogously to an increased angle of attack for a wing

in freestream (49).

Two main features are believed to affect the force generation process: the Venturi-

like channel formed between the suction side and the ground, and the edge vortex

that is being formed beneath the two spanwise extremities of the wing. The first

is responsible for the further acceleration experienced by the fluid shortly down-

stream of the leading edge, as the region between the lowest point of the wing and

the trailing edge effectively forms a diffuser, thus increasing the suction peak by

means of pressure pumping. Another significant feature is represented, as said,

by the lower edge vortices, which effectiveness can be enhanced by the presence

of endplates. As a matter of fact, the pressure differential across the two sides of

the endplate attracts fluid from the external side, fluid that rolls up and forms a

vortex beneath the wing itself, further reducing the pressure. The separation on

the suction surface is also delayed as a consequence of the increased mixing gener-

ated by this vortex. Induced drag is also raised by this flow feature. Overall, this

type of flowfield is remarkably different from the almost two-dimensional one that

can be observed at centre span. As the ground height is further reduced, the vor-

tex moves inboard and grows in size (42). Vortex meandering is observed in the

enhancement slowdown region, and the vortex ultimately breaks down right after

the maximum downforce peak, triggering instantaneous and large-scale separa-

tion. The interaction existing between the lower and upper edge vortices created

by the endplate has been studied by Galoul and Barber (50): they showed how

the lower vortex has a strength remarkably higher than the upper one, which is

in turn bent downwards. At a certain point the two vortices merge.

Reynolds number effect on lift and drag was investigated by Jasinski and Selig

(51), who performed a comprehensive analysis including various type of wings

from Champ cars and F1 cars. They showed how an increase in this parameter

13


corresponds to a slight reduction in drag and a marginal increase in lift. De-

spite mentioning that, at low angles, the net positive changes in induced drag

are actually lower than the reductions in profile drag, they also proceed to state

that, when a flap is installed, front wing drag generation is dominated by in-

duced effects; no definitive conclusion seems to be reached. A reduction in peak

downforce has been found as the Reynolds number decreases (41), as well as an

increase in drag at all ride heights.

A further analysis on the Tyrrell 026 wing in ground effect was put forward by

Vogt and Barber (52), in particular on the pressure distribution on the wing: the

stagnation point was measured to move towards the ground as the wing is low-

ered. Consistently with previous research, an increase in suction on the pressure

side was shown; the pressure on the upper side is almost unchanged as the wing

approaches the ground, especially with respect to the suction side.

2.2.1 Gurney Flap

The Gurney flap is a small device generally fitted to the trailing edge of the last

element of a wing, in order to increase maximum lift. It consist of a strip that is

mounted perpendicular to pressure side, with a size between 1% and 5% of the

wing chord. Documents showing a device of this type appeared across the 30s

and 40s (53) (54). It was Dan Gurney, an American driver, who first introduced

this strip on racing cars in the 1960s, and it was then widely adopted by teams all

over the world, taking the name of the inventor. Despite its broad employment,

the reasons for improved performance are not yet a clear phenomenon.

One of the very first investigations on the Gurney flap was carried out by Liebeck

(55), who performed wind tunnel testing, observed a decrease in drag and, at the

same time, an increase in lift. Reversed flow was also detected over the back sur-

face of the Gurney flap, as well as behind it. Two little counter-rotating vortices

are supposed to be the source of this latter flow reversal. The actual improve-

ments in performance are indicated to be a function of aerofoil thickness and

trailing edge shape, as already suggested by Duddy (54). Further research (56)

(57) showed that the Gurney flap has the same effect as increasing the camber of

the aerofoil, changing the angle of attack of zero lift, but not modifying the slope

14


of the lift curve. Furthermore, the Kutta condition is not valid when the flap

is fitted (58); its effectiveness is higher when its height is equal to the boundary

layer thickness at the trailing edge, on the pressure surface (59). The increase

in lift has been explained with the fact that the wake is turned downwards by

the presence of the flap. Additionally, a decrease in pressure on the suction side,

coupled with an increase on the pressure side, was detected.

A more recent research showed that the drag is slightly increased by the presence

of the Gurney flap, associated with a growth in maximum lift coefficient. An

investigation into three-dimensional wings showed that an inboard placement is

more effective that an outboard one.

The first study to include a time-history visualization of the flow structures of

a Gurney flap was carried out by Jeffrey et al. (60), opposed to the previous

ones, that focused solely on time-averaged data. Vortex shedding is observed to

take place, as a consequence of the interaction between the free-shear layers; the

separation point on the pressure side is fixed, whereas it moves upstream on the

suction side as the angle of attack increases: this is believed to affect the size and

motion of the shed vortices, but indeed not their presence in the wake. More-

over, the finite distance existing between the two surfaces at the trailing edge is

designated as the cause for the increase in circulation, and ensuing increase in

lift. The increase in lift is also believed to be a direct consequence of the vortex

shedding, which enhance the suction peak on the lower surface. The maximum

improvement in lift coefficient was measured to be +90% at null angle of attack,

and around +30% at stall angle, for a 4% Gurney flap. Drag increased as well,

but did not overshadow the gain obtained in lift, meaning that increased effi-

ciency was measured. These improvements are not directly proportional to the

height of the Gurney flap, as a 0.5% GF shows already remarkable enhancement

with respect to the baseline; the rate of increase of lift reduces as the height is

raised. It is postulated that beyond a height of 0.05 times the chord, the benefits

of further increasing Gurney flap dimensions would be negligible. The beneficial

effect measured on single-element wings is generally replicated by double-element

wings (61), even thus the maximum increase in downforce is somewhat lower in

this latter case.

An examination on the effects of the aerofoil on the effectiveness of Gurney flaps

15


Figure 2.4: Time-averaged momentum in the wake of a plunging aerofoil in

freestream, from (63)

has been carried out by Cole et al. (62): profiles that feature a very early sepa-

ration on the suction surface show a lower rate of lift growth, or even a reduction

in lift coefficient. This is in accordance to what observed before on the effect of

vortex shedding on the suction peak of the wing.

2.3 Unsteady Aerodynamics of Wings

The literature on heaving-pitching wings is vast and spans within a disparate

range of Reynolds numbers, shapes, applications and so on. Where possible, only

16


the aspects relevant to this study have been investigated. Analytical expressions

for potential flow involving heaving and pitching motion for an aerofoil have been

developed by Theodorsen (64) and Garrick (65) respectively, and constitute the

basis for all subsequent studies.

The first aspect related to a moving wing is the reduction in drag that can ul-

timately result in drag reversal and thrust production, a phenomenon that was

first observed by Knoller (66) and Betz (67) independently. Karman and Burgess

(68) proceeded to postulate the dependence of this force on the the structure of

the wake, and in particular on the presence of alternate vortices behind the wing.

The existence of a vortex sheet downstream of a heaving wing has been therefore

studied and then decisively proven in a number of articles (69) (70) (71). The

presence of vortices in the wake is not only related to heaving motion but can

take place also for a stationary aerofoil because of a number of causes, all leading

to shear instabilities at the trailing edge (72). In the case of a Karman Vortex

Street (KVS), vortices that are shed in the wake are aligned in such a away to pro-

duce a momentum deficit, thus generating drag. Heaving and pitching motions

have the potential to modify the relative distribution of these vortices, leading to

different wake structures. This changes can lead to a RKVS (Reverse Karman

Vortex Street), where the time-averaged momentum shows a jet-like momentum

gain, which defines thrust production. In particular, the vortex with positive

circulation is moved to the upper part of the wake, and the one with negative

circulation is moved to the lower part (73). Young and Lai (74) also noticed how

the VKS can actually be substituted by a wake containing multiple vortices per

cycle, thus denying the fact that the non-dimensional amplitude kh can be used

as the only parametre to assess the type of wake structure.

The dependence of the wake structure on the Strouhal number St was proposed

by Lai and Platzer (75); experimental tests performed using this similarity pa-

rameter for comparison yielded good accordance to the computational efforts of

Triantafyllou and Grosenbaugh (76). Both computational and experimental ap-

proaches have been tried to understand the complicate process of drag reversal.

It is to be noted how the VKS is an intrinsically unsteady process, with all the

vorticity concentrated in different points in the wake, thus making modelling a

very complicated matter (77).

17


Interestingly, the range of St capable of producing constant and well-behaved

thrust is exactly the one in which fish and biological flyers operate, as detailed

by Drucker (78) and Wolgang et al.(79).

The actual parameters governing the drag-thrust transition have been widely

discussed, and still represent a partially open question. Godoy-Diana et al. (80)

studied the wake of a flapping aerofoil by means of PIV, at Re in the order of 103.

It was found that the type of the wake closely depends on two parameters, these

being the Strouhal number St and the amplitude AD of the motion itself. For

neutral and reverse wake to take place both the values should be above a certain

threshold, measured to be 0.1 for StA and 0.5 for AD. The regions containing

the same wake are delimited by curves similar to parabolae. This result justifies

the introduction of a new parameter, the amplitude-based Strouhal number StA,

capable of containing both informations at the same time: the sole value of StA

is enough to mark the lower boundary for thrust production. Another feature

indicated by PIV is the deflection of the wake as the frequency and amplitude of

motion are further increased. The existence of a neutral type of wake, with per-

fectly aligned vortices and negligible drag has been confirmed by He et al. (81).

The deflection of the wake at St > 0.5 has been observed by von Ellenrieder et al.

(63), who postulated that the onset of asymmetric wake depends on both reduced

frequency and non-dimensional heave velocity. Results were in accordance with

what already proposed by Lewin and Haj-Hariri (82). Wake deflection seems to

dependent on the initial motion (whether upwards or downwards) and influenced

by the flow features in the very first moments of the heaving motion. They also

confirmed the results obtained previously by Liang et al. (83), who discovered a

positive correlation between deflection angle and Re at fixed St.

It is worthwhile to mention that the vast majority of these studies is computa-

tional, and has been carried out on two-dimensional models. Three dimensional

effects include the suppression of vortex shedding for very low aspect ratio wings.

Another effect triggered by a vertical motion of a wing is the dynamic stall,

which includes the dramatic increase in post-stall lift as the wing pitches and

plunges. This effected is believed to be triggered by the existence of a Leading

Edge Vortex (LEV), consisting of a small spanwise vortex close to leading edge

18


on the suction side of the wing. A comprehensive discussion on this subject has

been presented by Shyy et al. (84). The dynamic stall mechanism has been

thoroughly explained by McCroskey and Fisher (85) (see figure 2.5): as the stall

angle is exceeded, flow reversal first appears on the surface of the wing (b); as

the angle further increases, large eddies start to appear in the separated zone (c),

inducing an additional separation and flow reversal over the majority of the wing

surface (e). At this point the LEV appears, which role is to further reduce the

suction peak and consequently improve lift (f-g). The only mechanism capable

of breaking this cycle is the occurrence of moment stall (h), which induces a lift

stall as well. Deep stall ensues (j). When the angle of attack is reduced below

the stall angle, the full stall ends and the boundary layer reattaches (k), in order

for the entire process to happen again in the following cycle (l).

The presence of a LEV is highly critical to the total lift enhancement, and in

addition is a highly unstable mechanism, which is worth analysing in depth. The

size and position of LEVs changes with the time, as the wing undergoes its mo-

tion; lift enhancement is believed to be higher during downstroke and the final

part of the upstroke, as detailed by Liu et al. (86). Actual figures were proposed

by Warrick et al. (87), who claimed that 75% of the total lift of the cycle is pro-

duced in the downstroke, whereas only the remaining 25% is due to the upward

motion. This is probably a consequence of the time frame in which the vortex

formation happens, namely at the beginning of the downstroke, as detailed by

Usherwood and Ellington (88). It is to be stressed how different models, based

on different types of flyers, can yield very different results for what concerns axial

flow in the vortex, which influences its stability, and other parameters such as

spanwise flow, as explained by Birch and Dickinson (89). It is anyway clear how

a requirement for actual lift increase is the attachment of the LEV for an amount

of time that is higher of at least half stroke. As an upper limit, vortex breakdown

seems to occur after 3 of 4 chords of travel. The mutual interaction between the

LEVs phenomenon and the propulsion efficiency of a heaving wing is detailed in

Ashraf et al. (90): the LEV can be shed in the wake of the wing and thus modify

its thrust characteristics. It is observed how, at a fixed kh, the thrust grows

with increasing reduced frequency. The dependence of drag and lift on reduced

frequency, on a NACA0012 aerofoil, was investigated by Medjroubi et al. (91): it

19


Figure 2.5: Dynamic stall mechanism for pitching aerofoil, from (85)

was found that both coefficients bear a positive correlation with k. Interestingly,

altering the Reynolds number only does not result in any appreciable change in

these two coefficients, whereas an incidence increment has high influence on the

flow field. The influence of leading edge shape is investigated by Kang et al. (92):

it was shown that a sharp LE can lead to the formation of a stronger LEV, and

in general has an effect on the entire flow structure around and downstream of

the aerofoil. Furthermore, the differences in flow characteristics between a flat

plate and a cambered aerofoil is studied: the sensitiveness to Reynolds number

is higher for the aerofoil; remarkably, the flat plate shows a higher maximum lift

coefficient; phase shift is similar.

Another mechanism capable of significantly increase lift is the rapid pitch-up, i.e.

the rapid rotation experienced by the wing at the two extrema of the motion.

The first peak force, the one experienced during the upstroke-downstroke transi-

tion, introduces a component of rotational circulation that adds up to the already

existing value (93), thus increasing lift. The second peak force, happening at the

end of the downstroke, is part of a more complex phenomenon called wake cap-

20


ture. All the effects due to the interaction between the wing and the wake fall

under the wake capture nomenclature: in particular, the features that influence

flow characteristics on the suction surface are hereby discussed. The increase

in lift during this inversion is considered to be a consequence of the increased

velocity on the suction side (94); some doubts still exist on the real nature of

this force peak, as detailed in Sunada and Ellington (95), who postulate that this

improvement is only a consequence of the added mass effect.

The relative magnitude and influence of various flow phenomena, at different St,

has been studied by Andro et Jacquin (96): when the Strouhal number is lower

than 0.1, the only significant lift enhancement mechanism is represented by the

presence of the leading edge vortex, which accounts for a quasi steady circulatory

force. As St in increased, both added mass and wake capture start to play a

relevant role too. As St is beyond 0.5, the acceleration grows accordingly, thus

increasing the importance of the added mass effect, which becomes the only sig-

nificant source of lift enhancement. Moreover, the wake capture seems to work

best at St = 0.4, and as this value is surpassed, the vortices being shed decrease

in size, thus reducing the mean lift.

Another important factor in the process of leading edge vortices shedding is the

thickness of the wing, which strongly affects both the formation and the shedding

timing. As explained by Yu et al. (97), aerofoil below a certain thickness do not

shed the LEV in the wake; instead, the LEVs remain close to the leading edge

for the entire cycle. This introduces an aperiodic component in the aerodynamic

loads, and in particular in the thrust production.

2.3.1 Theodorsen’s Theory

In 1935, Theodore Theodorsen performed a comprehensive theoretical analysis

of the unsteady aerodynamics of an aerofoil and aerofoil-aileron (sic), using non-

stationary potential flow theory and applying the Kutta condition at the trailing

edge. A theory based on infinitely small oscillations was developed, which should

not be affected by the aerofoil characteristics such as thickness and camber. Three

forces were considered, as explained by Theodorsen himself: the inertia forces,

the restraining forces and the air forces. A rigorous mathematical tractation of

21


Theodorsen theory will not be put forward here, as the referenced paper already

contains it, and it is widely available. Only the relevant steps will be presented.

For the non-circulatory part, six potential velocities are introduced to completely

model the flow around the aerofoil: these velocities are computed from a number

of sources placed around the geometry. Once the velocity potentials are known,

it is possible to compute pressures and therefore, by integration, obtain the forces

and moments acting on the aerofoil. The circulatory flow is solved through the

introduction as a vortex element moving with respect to the aerofoil; Kutta con-

dition is used to determine the total circulation. Vertical forces and moments are

then derived.

The Theodorsen function C is introduced as the ratio of the integrals introduced

in the circulatory component computation. Furthermore C is defined as being a

function of the reduced frequency only, hence

C = C(k)

The Theodorsen function is further divided into two terms such as

C(k) = F (k) + iG(k)

The function can also be expressed as the ratio of Hankel functions, which in

turn are complex combinations of Bessels functions. The role of the Theodorsen

function is to return the lift variation, with respect to static conditions, as a

function of the reduced frequency only. Moreover, it is possible to derive the

phase shift with respect to the oscillation. The total lift, for a heaving and

pitching wing, can be written as

CL = π[h+ α− aα

]+ 2π

[α + h+ α

(1

2− a)]

C(k) (2.1)

as detailed by Brunton and Rowley (98). The first term accounts for the added-

mass effect, whereas the second is an expression of the quasi-steady lift compo-

nent. The term a represents the position of the pitch axis. For the case of pure

heaving, the total lift can be written as

L =1

4πρc2y + πρU2

∞cC(k)y

22


It is also possible to express this quantity as a function of a complex variable

(99), such that

L = 2πρU2∞

[−k

2

2−Gk + iFk

]aei2πft = 2πρU2

∞

[−k

2

2−Gk + iFk

]y

and the phase shift between the position and the lift waves represented as

φ = atan

(F (k)

k2

+G(k)

)

For the sake of consistence with previous research, the phase shift will not be

referred as an angle, but as a pure number h, such that

h = −cos(φ)

Another study was carried out by Garrick (65) in order to assess the energy

required by the system to produce and maintain thrust. The conditions, and

assumptions, under which this work holds are the same as Theodorsen’s, and the

methods employed are very similar. The proposed formula is

W = E + Pxv (2.2)

The quantity W represents the average power required to maintain oscillations; E

is the increase in energy, per unit time, in the wake. The third term is the propul-

sive power. After a number of mathematical manipulations, the ratio between

the propulsion energy and the total energy given to the system from outside the

system is shown to bePxv

W=F 2 +G2

F(2.3)

2.3.2 Aeroelasticity

One important feature to be taken into consideration, when dealing with unsteady

aerodynamics, is the concept of flutter, defined as ”amplitude of oscillation in-

crease caused by negative damping” (100). A one degree of freedom motion, such

as heaving, should not be subjected to this phenomenon, unless separation takes

place (101) (102). As separation is not predicted to be a factor to this study,

23


given the expected ride heights and angles of attack, flutter can be considered

not to be an issue. Conversely, static aeroelasticity has to be taken into account.

An aeroelastic analysis of the structure employed in this study will developed

from the examples presented by Hodges and Pierce (103).

The model can be considered to be a cantilever beam hinged to the top of the

wind tunnel, with the beam perpendicular to the flow. For a static condition, the

focus is on the deflection angle induced by the compliance of the structure, which

adds up to geometric angle of attack, and can induce failure of the structure,

if the moment induced by pitching becomes uncontrolled. The total deflection

angle is

θ = θF + θM

with

θF =F0 (2y)2

2EI; θM =

M0 (2y)

EI

with F0 and M0 being the horizontal force and the moment due to the strut

internal stiffness, if 2y is the total length of the strut. A further vertical force

introduced by the strut can be called R0. Horizontal balance gives only

D − F0 = 0 (2.4)

where D is the drag. Vertical balance yields

L+R0 +W = 0

with L being the lift, pointing upwards, and W being the weight. It is to be

noted how this equation does not contain any term including the deflection angle.

Momentum balance gives:

M0 − 2Wysinβ −Mac = 0 (2.5)

with β being the angle between the strut vertical and the line passing through

the hinge and the centre of mass. Mac is the moment due to aerodynamic forces.

Drag and moment appear in the previous equations. It is decided, given the low

overall incidence and the presence of ground effect, to assume the first as linear,

24


and in case apply a a safety factor, if necessary, later in the process. Drag is

expressed as

D = qSCDααeff

where q is the freestream dynamic pressure. Since the calculations are carried

out at the aerodynamic centre, the momentum contribution from the aerofoil is

independent from angle of attack, leading to

Mac = qScCMac

Substituting the definition of deflection angle and solving 2.4, it is possible to

obtain

θF = qSCDα (α + θM)

[4y2

2EI − 4y2qSCDα

]The moment balance gives the solution for the second deflection angle

θM = (2Wysinβ − qScCMac)2y

EI

Summing the two terms results in the elastic part of the increase in incidence θ,

as

θ = qSCDα

[EI

2yα + 2Wysinβ − qScCMac

] [8y3

EI 2EI − 4y2qSCDα)

]+

2y

EI(2Wysinβ − qScCMac)

It is now sufficient to study the denominator of this equation to find when the

effective angle of attack is expected to blow up, i.e. when

(EI)2(2EI − 4y2qSCDα

)Since the dependent variable here is velocity, which is comprised into the dynamic

pressure term, it is possible to define the divergence pressure qd as the minimum

pressure that leads to the uncontrolled increase in effective angle of attack, as

qd =2EI

4y2qSCDα(2.6)

For this structural configuration, there is not a course of action capable of making

the negative pressure negative, as it is sometimes the case. As expected, in order

to increase this pressure, and the divergence velocity accordingly, the overall

stiffness has to be increased, or the vertical distance decreased.

25


2.4 Combined Effect of Oscillations and Ground

Presence

The studies presented in the previous subsection cannot be fully applied to the

conditions of this study, since they lack in two fundamental features: ground

presence and Reynolds number. This last quantity is generally limited to 104 in

the best case, as a result of experimental constraints and researchers’ interest.

As proven by Isaac (104), the extrapolation of high Re results from low Re flows

would be completely inaccurate, as a consequence of the particular flow features

involved.

Indeed, the topic of an inverted wing in ground effect undergoing an oscillatory

motion has enjoyed little popularity: just a few articles exist. Some interest has

been displayed in the phenomenon of hysteresis, under which name fall all the

effects connected with the differences observed at a certain ground clearance de-

pending on the direction of approach, i.e. whether moving upwards or downwards.

It is to be remarked how this behaviour is different from an harmonic, oscillatory

motion, from both the standpoints of flow physics and aerodynamic loads. An

early study was carried out by Moryossef and Levi (105), using a one-equation

turbulence model coupled with a Euler/Navier-Stokes flow solver. It was found

that the average downforce was very close to the static value at the same ground

clearance, whereas the amplitudes of oscillation for both lift and drag increase as

the reduced frequency grows. Only the first mode is found to be important for

lift, whereas, for drag, higher modes (generally second and third) are of the same

order of magnitude of the first, and can not be neglected.

Two comprehensive articles have been published by Molina and Zhang (99) and

Molina et al. (106), investigating both the magnitude of lift and drag coeffi-

cients, and their behaviour in time with respect to the oscillatory motion. From

the point of view of lift, the proximity to the ground seems to yield more increase

in downforce at higher frequencies than at lower ones; furthermore, it is estab-

lished that if k < 1.09 the frequency variations do not have any tangible effect.

Thrust in freestream is said to be generated at k = 2.31, a value that rapidly

increases as the wing is brought close to the ground: at h/c = 0.33, the boundary

between drag and thrust is beyond k = 4. Peak forces are shown to increase as

26

2.4 Combined Effect of Oscillations and Ground Presence

reduced frequency increases and ground effect decreases. Peak to peak amplitude

increases as well, and for some conditions (provided k > 2) positive lift can be

produced in some parts of the cycle. Instantaneous switch from lift to drag can

take place at reduced frequencies as low as 0.34, with this value strongly depend-

ing upon the ride height.

Another parameter to be taken into account is the phase shift between motion

and downforce waves. This is influenced both by the initial position of the aero-

foil (its mean ground height) and the reduced frequency. Three main effects can

be isolated: ground presence, increased angle of attack and added mass; the last

two are already present in Theodorsen’s theory and account for the circulatory

and non-circulatory elements respectively.

At very low reduced frequencies, the flow can be considered quasi-stationary, and

the downforce generated at each position depends only on this quantity, as no

dynamic effects play a role; the boundary between quasi-stationary and unsteady

regions is set at k = 0.11. In this range of frequencies the ground presence is

therefore the only element that affects performance. As the reduced frequency is

increased, the velocity at the central point of the motion starts to be significant,

introducing an effective angle of attack, defined as

αeff = α0 + atan

[dhdt

U∞

](2.7)

The role of this increased angle of attack is to increase the lift of the wing, thus

moving the point of maximum downforce towards the centre of the motion, with

a null phase shift. The magnitude of maximum phase shift depends on both

reduced frequency and ride height: as the wing is moved closer to the ground, its

presence is more influential, therefore bringing the two waves closer and increasing

the reduced frequency at which this is reached. The limiting case is when the

motion occurs for the most part in the force reduction region, and the effect of

increased incidence induces a different shape in the h vs. k plot, as detailed in

figure 2.6. Since the presence of the α0 term in the previous equation, it is clear

that the geometrical characteristics of the wing, and its initial angle of attack,

can influence the effectiveness of the increased angle of attack phenomenon. As a

matter of fact, an α0 close to stall angle could trigger a separation-reattachment

27


Figure 2.6: Phase shift as a function of reduced frequencies at different ride

heights, from (99)

cycle different from free-stream, as the ground would both worsen the effect of

separation and reduce the effectiveness of the diffuser. As the reduced frequency

is further increased, an inviscid effect starts to move the phase shift back to 0,

and therefore the point of maximum downforce back to the lowest position of the

oscillatory motion, this time regardless of the initial ground height. The added

mass effect is related with the amount of fluid that has to be displaced by the wing

during its movement; the force generated by this phenomenon is proportional to

the acceleration of the wing, with the following law:

Fmass = ρθd2h

dt2(2.8)

Depending on the frequency, at the beginning of the upstroke a positive lift can

be experienced by the wing; in racing conditions, this would mean that the car

is highly unstable and almost impossible to drive. It is to be noted how this

phenomenon has the same effect on all the ride heights, meaning that all the

curves in Molina merge at a reduced frequency higher than 1.01.

28

3

Research Description

This chapter presents a description of the methods used in this research, including

the overall methodology, the relevant assumptions, an account of the model and

software used, as well as the initial programme for the wind tunnel testing. This

chapter is conceived as a series of information that can help understanding the

following one, and as a reference in case similar experiments are to be repeated.

3.1 General Approach

It has already been mentioned how, to the best knowledge of the author, this is

one the first experimental studies of a heaving wing in ground effect at a Reynolds

number in the order of 105. A careful planification is therefore highly necessary,

as well as a clear definition of the objectives.

As customary with experimental testing, the first variable to consider was the

availability, and in second order the specifications, of a wind tunnel. The RJ

Mitchell wind tunnel at the University of Southampton features is commonly

used for motorsport, aeronautical and sport-related research, making this the

preferred choice. The dimensions and principal characteristics of this facility are

described later in this same chapter. Once this is settled, the actual model to

be employed has to be decided. Contemporary F1 front wings are extremely

refined, and feature an incredible numbers of flaps, appendages and other micro-

aerodynamic devices. Beside the obvious manufacturing complication of building

such a model, two main problems exist: the first is to actually get a blueprint for

29

3. RESEARCH DESCRIPTION

such a component, and the second is to eventually discern the main factors that

influence performance. As a consequence, a simple single-element wing model

was used, for which static experimental validation (for the stationary case) and

computational validation for dynamic cases, is available in literature. The rela-

tive simplicity of this model makes possible to eliminate non-fundamental flow

features and force behaviours, and to concentrate only on the desired variables.

The validation data available constitute the baseline cases as well, to which the

following results are to be compared, when possible. The selection of the model

allows to design all the relevant components that need to transmit the alternate

motion to the motor to the wing, transforming it into a linear, vertical, displace-

ment. The role of this structure is also to ensure the required rigidity and stiffness

at design conditions.

The last part of this preliminary analysis is to determine what are the quanti-

ties to be analysed. As flow visualization techniques are not available, the focus

is shifted on the investigation of drag and lift principally, and their dynamic

behaviour. The independent variables to be changed are four: ground height,

wind speed, motion amplitude and motion frequency; these, in turn, define other

non-dimensional parameters such as reduced frequency, Reynolds number and

Strouhal number. The actual test programme is presented in the next subsec-

tion.

3.2 Test Programme

The test programme was prepared bearing in mind that one of the principal ob-

jectives was to reach a reduced frequency as high as possible, which can be done

by varying two quantities: wind speed and motion frequency. In particular, an

increase in frequency and a decrease in speed will obtain the same net change.

Both the quantities are indeed limited by practical constraints: the motor needs

a finite amount of time to invert its motion, and the wind tunnel speed is only

constant throughout the entire cross-section at a determinate value. This latter

was placed at 5 m/s, which was is considered to be the lower operational limit of

the wind tunnel, where the maximum frequency that was possible to obtain from

the motor (with an amplitude of 10 mm) was of 5 Hz. These two restrictions,

30

3.2 Test Programme

along with the chord of the wing, limited the maximum attainable reduced fre-

quency to 0.73.

Another objective was to examine the influence of different parameters on lift and

drag: namely, the ride height, the Reynolds number (governed by the wind speed

only) and the motion frequency. It was therefore decided that a comprehensive

set of test was needed. The wind tunnel velocities spanned between 5 and 40 m/s,

with steps of 5 m/s, the ride heights went from the lowest allowed by geometric

constraints (0.45) to one almost in free-stream (1.35), with three intermediate

values to bridge the gap (0.60, 0.75 and 0.90). Once this grid had been created,

all the different speed/clearance configurations were explored at various motion

frequencies, from 1 to 5 Hz, with 1 Hz steps, thus creating a three-dimensional

matrix.

Additional tests were performed with a 2.2% Gurney flap fitted to the trailing

edge of the wing and a rough strip on the suction side, as already listed in the

relevant section. Only two motion frequencies (3 and 5 Hz) beside the static con-

figuration, were investigated. Moreover, at a fixed frequency of 3 Hz, the effect of

different amplitudes, and therefore different Strouhal numbers, was studied. The

angle of attack of the wing was kept constant at 0.5◦ for all the duration of the

experiments, since it was not possible to alter it, as the geometry of the motor

plate did not allow to design a structure that could implement a mechanism to

modify this quantity. Further details are presented where relevant in the next

chapter.

Once in the wind tunnel, after the initial static tests, it was decided to start from

the lowest speed and then build up to the higher ones. For every speed, data

for all the frequencies were sampled at a given ride height; after this, the ride

height was changed. Gurney flap and transition-fixed runs were performed after

the initial set of tests was completed. Repeatability tests were performed both

in the same day at different times, and at different days. The condition chosen

to perform these tests was at a wind speed of 10 m/s, frequency of 2 Hz and

lower ride height. Lift and drag coefficients were both with a ±1% boundary of

the initial measurement.

31


3.3 Assumptions

As it always happens when dealing with physical components, the overall layout

of the experiment is just a model of the conditions that are to be analysed, and

some assumptions are made, in order for the experiment to be meaningful. In

particular, a number of assumptions are worth mentioning for this study, from

different point of views:

• The motion input was designed to be a sinusoidal wave. As obvious, this

means that the actual motion transmitted to the wing is the sum of very

small discrete movements of the motor, and it is not a perfect sinusoidal

wave; nonetheless, the frequency at which the motor transmits the motion is

at least two orders of magnitude higher than the motion to be transmitted,

which allows the wave to be treated as sinusoidal.

This assumptions also involves the hypothesis that the oscillatory motion in

a racing car is purely sinusoidal: although not exactly so, this is still a good

approximation that does not interfere with the validity of the outcome.

• Similarly, the sampling procedure is assumed to be continuous: the actual

sampling frequency (1000 Hz) is again much higher than the maximum

frequency of any physical feature the flow is expected to show.

• The impact of the plates, struts and stings on the flow characteristics around

the wing is assumed to be negligible. A great effort was made to isolate the

wing from external influences as much as possible, for example by stream-

lining the vertical struts and designing the horizontal ones far away from

the pressure side. It is here to be recalled that on racing cars pillars exist to

support the wing, and that in ground effect the most significant features are

due to the pressure distribution on the suction side, which is barely affected

by any structure above the wing. Therefore, the aerodynamic loads were

deemed to be solely a result of the wing interaction with the flow. Cali-

bration runs were carried out to assess the drag of the structure (without

the wing), assuming that the drag generated by it and by the wing were

actually independent, and therefore the system to be linear in these two

components.

32

3.3 Assumptions

• All the forces reported in this study were measured by an overhead bal-

ance, which has already been calibrated, and is habitually used for similar

configurations. This assumed that the structure is perfectly rigid. As a

consequence of the material used (carbon fibre is very anisotropic), the

structure is effectively rigid to vertical loads (lift), whereas cannot be con-

sidered completely as such when streamwise forces are taken into account.

Therefore, maximum care was taken to design mountings capable of re-

straining the rotation motion around the central joint, thus reducing the

degrees of freedom.

• From the point of view of applicability of this study to racing cars, a couple

of distinguo need to be made. First, the maximum Reynolds number en-

countered in race conditions are normally higher than what can be obtained

in a wind tunnel, for a number of reason, and are of the order of 106. Sec-

ond, the flow around a wing is influenced by the components downstream,

primarily the wheels. Despite these two differences, the results can be ex-

trapolated to have relevance for these practical conditions as well. At the

same time, the flow has a very low turbulence intensity, a conditions that

can cease to exist if the wake of a preceding car is present. Again, this is

a singular case that cannot be analysed in a wind tunnel, but is still worth

remembering.

3.3.1 Sources of Error

It is useful to also discuss the sources of error that could have affected

the accuracy of the tests. First of all, the Re was computed from the

wind speed, which has an intrinsic fluctuation due to the fan motion, of

±0.3 m/s. At the same time, the ground is supposed to move at wind

speed. Ground speed uncertainty was measured to be ±0.1 m/s. Besides,

the pressure transducers, from which the wind speed is measured, have an

accuracy of ±0.15%. As a consequence, the maximum discrepancy between

ground and wind speed, at 30 m/s, is ±0.45 m/s, and decreases at lower

speeds. Other sources of error include the measurement of the angle of

33


attack, performed with an inclinometer with an accuracy of ±0.1◦. The ride

height was initially measured using a ruler, perpendicular to the ground,

with a resolution of 1 mm. Only the minimum ride height was measured,

and then all the other ground clearances were obtained by displacing the

wing, using the electric motor, by a known quantity. The resolution of the

motor is much better than the ruler, and will not me discussed, since the

inaccuracies due to it would be negligible. Since all the quantities were

measured through the overhead balance, the accuracy of this component

has to be taken into account as well. It is anyway postulated that this

represents only a small part of the total errors.

3.4 Experimental Setup

3.4.1 Wing Assembly

The tests wee performed on an untwisted, untapered single element rectangular

wing. The wing profile is derived from the main element of the front wing used in

the 1998 Tyrrel 026 Formula 1 car. This aerofoil was developed starting from a

NASA GA(W)-1 profile, type LS(1)-0413, in order to reduce the magnitude of the

wake, by changing the position of the suction point, which was moved upstream

(41). A finite trailing edge has been introduced as well. The wing used was the

test is an 80% model, with a chord of 233 mm and a span of 1100 mm, with a

corresponding aspect ratio close to 5. The model is hollow and made of carbon

fibre. This wing was used for testing in ground effect a number of times already,

and validation data is widely available. Specifically, since its first appearance

this profile has quickly become the reference for the niche of inverted wings for

motorsport applications, and the vast majority of research on this topic has been

carried out on it.

A 2.2% Gurney flap was added after the first round of wind tunnel runs; it

consisted of an L-shaped aluminium strip that was glued, on one side, to the

wing. An adhesive stripe covered with grit was subsequently added to induce

transition on the suction side, this being centred at 10% of the chord, and with

a width of 4% of the chord approximately. Two aluminium-made, 2-mm thick

34


Figure 3.1: CAD rendering of entire wing assembly

35


endplates were fitted at each end of the wing, with a length of 250 mm and a

height of 100 mm; the lower edge of the endplate was placed at 1 mm from the

lowest point of the suction side.

The existing parts were reverse-engineered and translated into a CAD file, from

which the mountings were developed: the connection between the horizontal

struts and the wing was designed to be performed using two aluminium plates,

bolted to the wing using two existing cavities on the pressure surface, at a distance

of 32% of the span from the centre point. These were connected through two

streamlined struts to a carbon fibre sting, which aim was to transmit the motion

from the motor to the wing. The cavities on the wing were covered with tape

during testing, to prevent any unwanted interaction with the incoming flow.

3.4.2 Wind Tunnel

Figure 3.2: Wing in the wind tunnel

All the tests were performed in the RJ Mitchell Wind Tunnel at the University

of Southampton, which has been already employed for industrial, motorsport

(Formula 1 and Indycar) and academic research. This wind tunnel features a

return circuit design and a closed test section, with cross-sectional dimensions of

36


3.6 x 2.5 m (11” x 8”). The test section is approximately 10.5 m long. On the

four corners of the testing section side fillets, with an angle of 45◦, are present.

The speed range of the wind tunnel is between 5 and 40 m/s, and the maximum

turbulence intensity, defined as

Tu =

√u′2

U∞

is of 0.2%. A moving ground is present, capable of velocities up to 40 m/s,

and with dimension of 4.0 x 1.9 m. A moving belt is the only known way to

correctly simulate real-life conditions and ground effect. The belt is made of

polyurethane and PVC, which makes is possible to keep a flat and predictable

road surface (107); lifting is avoided by means of suction under the belt. The

movement is transmitted by a roller system, which keeps the belt under tension

and in the right position in the middle of the test section. A separate cooling

system is employed to keep the belt temperature low, both for safety reasons and

in order not to change the test conditions. The wind tunnel itself is equipped

with a system to keep constant temperature in the test section. A double-staged

boundary layer removal device exists, with suction applied to small slots drilled

in an aluminium plate right upstream of the belt. The bulk of the incoming

boundary layer is removed by a forward-facing step placed further upstream,

which has incorporated suction. This boundary layer control allows a velocity

correspondent to 99.8% of free-stream at only 2 mm from the belt itself.

A 6-component balance is mounted above the test section and connected to the

wing through an ad hoc strut. The motion is generated by an electric motor,

already present in the wind tunnel, and connected to a eight-hole plate that

moves vertically. The motor is connected to a National Instruments chassis, that

can be controlled by a Labview programme. Specifically, the chassis is a PXI-

1044 model, and it is connected to the motor through a 3-axis PXI-7350 Motion

Controller port. The chassis also acquires the readings from the overhead balance,

through a PXI-4472 port.

37


Figure 3.3: Example of task decomposition

3.4.3 Software

Two different softwares were employed in this study: Labview and Matlab. The

first one was used in situ to control the wing motion and acquire the desired data,

while the second was the preferred tool for data analysis. It is useful to present

a brief summary on their relevance in the tests.

As already mentioned, two main functionalities were needed in the wind tunnel:

motion control and data acquisition. This meant that a programme capable of

performing both tasks was needed. The approach followed in order to meet this

goal was the so-called functional decomposition (or top-down approach), which

is a standard in computer science: this involves breaking down big tasks into

smaller commands, and iterating this process until the basic instructions can be

easily written. The opposite process was carried out to build the entire software,

with the linkages between these constitutive parts being provided by the logic of

the software, that was conceived separately. In some sense, the entire procedure is

not dissimilar from the analysis-synthesis dichotomy, used throughout all fields of

science, and inspired by Descartes himself. An example of the first approach can

be found in figure 3.3, while the building process, along with the interface between

the two major software blocks, is visually represented in figure 3.4. Everything

was prepared with the objective of minimising human intervention and therefore

reducing the possibility of errors.

The actual data processing required the capability of handling massive amount

of data in an ordered, consistent and time-effective manner. The huge potential

38


of Matlab, which couples user-friendly interface and endless possibilities for plots

and figures with the potential of user-defined functions, made it the first choice

for this task. Since a number of manipulations was carried out on each file to

extract the relevant informations, an example of this procedure will be detailed

hereafter, in order to make next chapter more comprehensible to the reader.

1. The output file of the Labview programme is a .txt file with the various

columns representing the readings of the overhead balance. The first step

is therefore to isolate the sets of data that are to be examined later: the

output file is imported into Matlab using the built-in textscan function,

implemented into another ad hoc function. Three vectors are then obtained,

corresponding to the total vertical force, total horizontal force and vertical

position of the wing. This last value is important to compute the phase

shift between wing motion and lift generation, as detailed in the previous

chapter.

2. These vectors are then processed in order to obtain the steady part of the

measurement, for the static case, or the stable one for dynamic tests. This

involves applying a windowing procedure, that produces a coherent set of

data that can further manipulated later. Broadly speaking, the objective

is to get rid of the initial overshoot and correlated effects, and make sure

that the oscillations have taken place within certain boundaries. It is to

be noted how the settling period of the lift and drag signals was generally

lower than two cycles. This step produces two additional vectors, called Lift

and Drag, that can assume the required length, which cannot be, obviously,

higher than the original one.

3. It is then necessary to isolate the aerodynamic loads from the inertial effects.

The inertia force is computed from solid mechanics: for a sinusoidal motion

Finertia = mappk2Ax

where k is the frequency in Hz, A the amplitude in m , and x is the

normalised position of the wing (between -1 and 1). It is to be noted that the

39


apparent mass was computed from runs carried out at no wind conditions,

and was different for all frequencies and amplitudes, since it did depend on

internal, non-linear resistances of the motor as well as the actual mass of the

components. Therefore, calibration runs for frequencies and amplitude were

carried out before the dynamic and wind-on tests. The actual accuracy of

this procedure was tested for freestream conditions at various frequencies,

comparing the results with what predicted by Theodorsen theory.

After the inertia is computed, a simple subtraction provides the actual

aerodynamic load, provided all the undesired effects are included into the

vector accounting for inertial effects. This step is needed for Lift only, as

the Drag vector is assumed to carry values due to the wing drag only, since

no horizontal motion takes place. The result is the Aero vector.

4. The Aero vector contains the values of the vertical aerodynamic load. It

is now possible to compute all the statistical quantities that are needed,

such as the average values meanlift and meandrag, as well as the motion

amplitudes peaklift and peakdrag.

5. At this point, a further step involves the interpolation of the Aero vector in

order to obtain an actual sinusoidal wave. This wave is then re-normalised

used the maximum value for the inertia vector, and then the phase shift

between the two waves is computed.

All these steps were unified in a single function, that needed as inputs only

the initial text file and the motion characteristics, and produced the mentioned

quantities, plus other that were used for other considerations. This highly au-

tomatised method has the potential to allow great flexibility in examining the

inter-dependence of different quantities.

40


Figure 3.4: Block diagram for Labview software

41


42

4

Results and Discussion

This chapter deals with the experimental results obtained in the wind tunnel. It

is to be stressed that more than 200 runs were carried out, with the independent

variables being altered as detailed in Chapter 3. After the data were processed,

the main results were selected and reported in this chapter, with the obvious or

non-relevant outcomes being neglected, for the sake of conciseness.

The preliminary results, used to validate the experimental set-up, in situ acqui-

sition and motion control software, and data processing technique are shown in

the first section. Next, the outcome of the main part of the experiments are

displayed. A brief account of the additional testing on Gurney flap influence and

transition fixing ensues.

4.1 Preliminary Study

As anticipated, a preliminary study was carried out in order to assess the suit-

ability of the experimental conditions to this case, and to prepare and verify the

Matlab functions that are required to extract the desired quantities, as detailed

in Chapter 3. It was not possible to employ the wing that has been used for the

subsequent tests, since the manufacturing process was not concluded yet. Instead,

a similar wing was mounted in the wind tunnel, with same profile but slightly

different dimensions; in any case, the purpose of this initial runs was not to find

values that could be compared with following data, but of appraising the capa-

bilities of the wind tunnel, motion and acquisition programmes, and overhead

43

4. RESULTS AND DISCUSSION

Figure 4.1: FFT of vertical-force signal

balance. Another goal of this test was to detect any significant trends that could

be studied more in depth with the other model. One feature of this wing-strut

assembly was its weight, since the material used to build it was aluminium, with

respect to the lighter composite fibre used in the main tests. This limited the

maximum motion frequency to 3 Hz.

Before processing any quantity, it is necessary to assess how the actual signal

and the system noise are captured by the balance. Figure 4.1 shows the FFT

of the balance signal for the vertical component of the force, at a motion fre-

quency of 3 Hz: the peak magnitude is exactly as this value, while all the other

frequencies contribute as noise only, and have a magnitude that is at least two

orders of magnitude lower. This peak magnitude includes both the inertia forces

and the aerodynamic loads, as the equality between motion frequency and the

lift wave frequency has been explained in Chapter 2. The streamwise compo-

nent underwent the same procedure, with similar results; it is noteworthy that

no secondary frequency was observed to bear any particular contribution to the

initial signal, unlike what has been computationally found by Moryossef and Levi

(105). Several samples were randomly chosen between all the acquired data, and

the dominant frequency of the signal was always detected to be the motion fre-

44

4.1 Preliminary Study

Figure 4.2: Lift signal

quency, by a margin of at least an order of magnitude, two in most cases. Once it

was established that the signal was correctly captured by the overhead balance, it

was deemed as non necessary to perform this analysis for all signals, as it would

have been incredibly time-consuming. Since the order of magnitude of the forces

did not change throughout the entire study, and the frequencies were in the range

from 1 to 5 Hz, this is a reasonable conclusion.

The balance signal for lift can be observed in figure 4.2. As explained previously,

this reading comprises all the forces that are generated by the moving structure,

i.e. inertia and aerodynamic. The post-processing procedure for this signal has

been detailed in Chapter 3, but a couple of remarks need to be made. First, it

can be observed that the acquisition started before the motion, and ended after.

This was eventually made to measure any changes in the static values for lift and

drag immediately after the wing was stopped. Since no significant change was

observed, this approach was dropped after all ride heights were deemed not to be

influenced by previous history, in order to save time. Secondly, it is interesting to

see exactly how the analysed quantities were extracted from the original vectors,

as shown in figure 4.3. The initial reading is shown as Vertical Force. The inertial

force is then computed from the position of the wing and its apparent mass at a

45


Figure 4.3: Example of lift signal post-processing

determined frequency (measured in the no-wind runs), as detailed in the previ-

ous chapter. A simple subtraction gives the aerodynamic load. The Interpolated

Aerodynamic Load curve is obtain either by means of simple interpolations (with

an ad hoc function) or by ensemble averaging, this last used as a confirmation.

Last, this curve is normalised by centring it at 0 and rescaling it to the same

amplitude of inertial force. This is only an intermediate step used to measure the

phase shift between the two curves. Once this value is known in time, it is enough

to know the frequency for the value of h can be computed. The only passage that

needs validation is when the aerodynamic load is obtained, as explained later in

this section. It was also decided to investigate the dependence of lift and drag

coefficients on speed, as shown in figure 4.4, in order to check that the correct

gain factors and calibrations were made by the programme. The expected trends

are recognised, with both the quantities depending in different measure on wind

speed: the lift changes marginally, whereas the drag notably diminishes. The

technique used to obtain the lift from the initial measurement has been detailed

already, and is based on strong arguments. Nonetheless, validating these results

could further reaffirm the correctness of this method. Theodorsen’s theory was

used for this purpose, as the expectations were to see a good agreement between

theoretical predictions and experimental measurements, both in trends and val-

ues. The phase shift can be observed in figure 4.5, and good concordance is

found: the experimental values seem moved to the right by a small distance, and

46

4.2 Clean Wing

Figure 4.4: CD and CL vs. wind speed, freestream

quantitatively match the computational values very well. The dependence on re-

duced frequency of lift coefficient was investigated as well, as it can be observed

in figure 4.6. Despite some little discrepancies, that have been however seen in

other, similar works (108), the results are comparable, and they corroborate the

validity of the method, that will be consequently used from now on to process all

the following data. It is also to be recalled that Theodorsen’s theory is derived

from non-stationary potential flow, and is therefore to used as a guidance only:

minor differences could indeed be due to the modelling errors in the theory itself.

4.2 Clean Wing

This section describes the results that have been obtained for the wing described

in chapter 3. The first step was to run some static tests in order to ensure that

data obtained agreed with previous experimental results. Figure 4.7 shows the

dependence of drag and lift coefficient on ground clearance, for the clean wing

in static condition, at different Reynolds numbers. As it customary in ground

effect analysis, the distance between the wing and the ground has been non-

dimensionalised using the chord of the wing itself. It can be observed how both

47


Figure 4.5: Phase shift between lift and motion, comparison between experimental

and computed values

Figure 4.6: Lift coefficient, comparison between experimental and computed values

the coefficients show the known behaviour, i.e. they increase noticeably, with the

drag showing a steeper slope as it approaches lower heights. The actual mag-

nitudes of the two coefficients are very close, if not matching perfectly, existing

48

4.2 Clean Wing

Figure 4.7: Lift and drag coefficients vs. ground clearance

values for the same wing (41). The increase in lift is due to the Venturi-like effect

in particular, while the higher drag is due to induced effects mainly. It is here

worth mentioning that the actual figures for drag have been corrected already,

with the drag generated by the bodies in the wind tunnel being subtracted by

the balance reading, in order to derive the drag produced by the wing only. From

a ground clearance point of view, it was unfortunately not possible to enter the

force-reduction zone, as a consequence of the geometrical constraints in the as-

sembly itself. It is also interesting to show that the overall efficiency drops for

all cases when the wing approaches the ground (figure 4.8). Reynolds number

dependence is consistent with what is generally found in literature: an increase of

this parameter is matched by a slight reduction in both coefficients, and induces

a small benefit as efficiency is concerned, at least for the range of ride heights

here investigated. The differences encountered by changing Re are believed to be

a consequence of the different size and position of the separation bubble on the

suction surface.

Once the actual accuracy of the experimental layout was assessed, the focus was

shifted on the dynamic behaviour. The experimental plan was prepared in a

way that could allow to investigate the effect of three different quantities on

a given value, chiefly lift or drag; mathematically speaking, this means having

three independent variables (namely motion frequency, Reynolds number and

49


Figure 4.8: Efficiency vs. ground clearance

ride height) and, assuming that just one quantity at a time is of interest, one

dependent variable. Representing all these variables at the same time would re-

quire a four-dimensional space, which is impossible to represent by conventional

means. Therefore, it was decided to use two independent variables only, obtaining

infinitesimal slices of the aforementioned quadri-dimensional surface; hopefully

these snapshots, taken at convenient positions and orientations (always parallel

to one of the original axes), would represent a valid surrogate of the original plot,

both visually and content-wise. It is also interesting to mention how wind speed

and motion frequency can be merged in a single quantity, the reduced frequency.

However, this quantity is not exhaustive, since a change in viscosity would modify

the Reynolds number but not there reduced frequency. It is therefore clear that,

in whichever way the problem is posed, the independent variable can not be less

than three. As a further remark, coloured two-dimensional plots are used, which

are deemed to be of easier comprehension with respect to a three-dimensional

surface.

Before exploring the results, it is useful to mention a feature introduced by the

heaving motion which is peculiar to inverted wings in ground effect: when the

wing oscillates, the diffuser-like zone that is delimited by the wing and the ground

50

4.2 Clean Wing

Figure 4.9: Average lift coefficient vs. frequency and Reynolds number. Ground

clearance: h/c=0.45

changes continuously, varying both area ratio and characteristic length, as defined

in (19) and (21). Moreover, the pressure difference across the endplate sides is

altered as well, introducing a source of unsteadiness in the edge vortex generation

process. Despite the absence of images or data from flow visualisation techniques,

explanations for the examined results will be presented.

The combined effect of frequency and Reynolds number was explored, as it can

be seen in figure 4.9; it can be postulated that both a reduction in Re and an

increase in frequency lead to an increased generation in downforce, consistently

with what has been presented before. The influence of the motion frequency

seems to be more significant. It is noteworthy to recall that the Theodorsen’s

function C can be expressed as a function of k only. Since k is proportional

to fU∞

, iso-contours of k would appear in figure 4.9 to be parallel, straight lines

with a positive angular coefficient; along this lines, ideally, the increase in lift

would be constant as well. This is very close to what is observed in figure 4.9;

the discrepancies can be explained by the presence of the ground, as the flow

features are influenced at the same time by Re and ride height. The separa-

tion bubble can be postulated to be stable at this ride height, since consistent

51


improvements are achieved. Apparently, the heaving motion is beneficial to the

development of this bubble, since higher improvements in downforce are obtained

at low Reynolds numbers. As the ride height is increased, the Reynolds number

effect becomes less important, and the heaving motion plays a more significant

role. At h/c = 1.35 the effects due to Re on lift generation are almost negligi-

ble if compared with the benefits deriving from the heaving motion. It is to be

noted that, if a larger angle of attack was reached, as a result of either a higher

geometric incidence or motion-induced effects, a higher Reynolds number could

help to prevent large-scale separation and maintain the lift at a pre-stall level.

On the other side, it is possible that in the force reduction zone an increased Re,

along with a higher motion frequency, could disrupt the beneficial flow features,

such as the edge vortex; as a consequence, the lift peak would take place further

away from the ground. Despite being an apparently negative result, this could

actually help when the ground height is fixed by regulations, if the minimum

allowed clearance is still in the force enhancement (or enhancement slowdown)

zone.

The drag coefficient shows a different behaviour, as it is almost negligibly affected

by the motion, and it is more significantly affected by the Reynolds number. The

plot almost represent an extension of the line seen for the line in figure 4.7, with

little to none frequency effects. As a matter of fact, the reduced frequencies here

are deemed to be too low to actually play a noticeable role. Indeed, as already

mentioned in literature (105), a low reduced frequency can actually increase the

drag, in close proximity to the ground. A similar behaviour was observed at

higher ride heights.

Subsequently, the combined effects of ground clearance and reduced frequency

is analysed, as shown in figure 4.11: the remarkable improvements prove how

these two variables can work together to increase downforce, consistently with

what observed before. At low Reynolds number the benefit seems to be higher in

free-stream, whereas at higher Re the improvement is larger for low ride heights.

It can be postulated that this behaviour is due to the different performance of

the diffuser-like effect, as a higher Re induces an improved lift coefficient at all

ride heights. Again, the ability of entering the force reduction zone could pro-

vide a valuable insight on the unsteady phenomena connected with this feature.

52

4.2 Clean Wing

Figure 4.10: Average drag coefficient vs. frequency and Reynolds number. Ground

clearance: h/c=0.45

The overall impact of reduced frequency seems to be more significant at a lower

Reynolds number, at most ride heights, also as a consequence of what previously

presented. For this particular testing configuration, in which the Re is defined

only by the wind speed (as chord, density and viscosity are almost constant), a

reduction in this variable would entail a higher effective angle of attack, at con-

stant motion frequency (see equation 2.5). Moreover, the benefits at a position

closer to the ground, at Re = 448, 00, are slightly higher than what it would be

expected from Theodorsen’s theory. Again, a beneficial interaction between the

ground effect and the heaving motion is detected.

The phase shift was measured as well, and it is presented in figure 4.12, showing

again good agreement with known computational data. The point of maximum

downforce moves to the centre point of the motion as the reduced frequency is

increased. After a maximum, that is reached at a value depending on the ground

clearance, the maximum downforce tends to be generated again closer to the

ground, as a consequence of the added mass effect.

Amplitude effects on the phase shift were investigated as well, at fixed frequency

and ground height. From figure 4.13, it can be observed that the trend, at a given

53


Figure 4.11: Average lift coefficient vs. reduced frequency and ride height.

Reynolds number: 79,000 (left), 448,000 (right)

reduced frequency, is increasing as the amplitude is enlarged, regardless of the

frequency: this is postulated to happen as a result of the increased angle of attack

at the mid-point: in fact, αeff depends on the velocity as shown in equation 2.5

αeff = α0 + atan

[dhdt

U∞

](4.1)

For an harmonic sinusoidal oscillation, velocity can be expressed as

dh

dt= x(t) = afcos(ft) (4.2)

From 4.1 and 4.2

αeff = α0 + atan

[afcos(ft)

U∞

]which entails that the effective angle of attack is maximum for cos(ωt) = 1

(central point of oscillations) and equal to the geometrical one for cos(ωt) =

0 (extrema of oscillation). It is possible to plug in the definition of reduced

frequency k = πfcU∞

to obtain

αeff = α0 + atan

[akcos(ft)

πc

](4.3)

thus introducing a direct dependence on reduced frequency, at least for a sinu-

soidal motion; it is possible to reproduce this derivation every time the motion

54

4.2 Clean Wing

Figure 4.12: Phase shift vs. reduced frequency, h/c=0.45

can be defined as a continuous function. It is also to notice how the introduction

of a new variable, namely

h =a

c

could non-dimensionalise the motion amplitude with respect to the chord, in order

to obtain a further similarity parameter. The behaviour in 4.13 can be explained

from 4.3, as the phase shift is dependent on reduced frequency, at least in the

range of k were the increased angle of attack is expected to play a significant role.

Moreover, an increment in the maximum amplitude shows an analogous response;

both are non-linear effects since the presence of the trigonometric function.

The effective angle of attack at a given position can be derived by knowing the

quantitykh

π

which is just a rescaling of the Strouhal number. It would be anyway inaccurate

to use only this parameter to compute the phase shift, as the added mass effect

has a different dependence. From 2.6

Fmass = ρθd2h

dt2

55


Figure 4.13: Phase shift vs. motion amplitude

In a similar fashiond2h

dt2= x(t) = −af 2sin(ft)

and

Fmass = −ρθaf 2sin(ft)

Following these steps, the expression for the added mass force is found, depend-

ing only on the known parameters ρθaf 2. If the reduced frequency and non-

dimensional amplitude are introduced

Fmass = −ρθ hkU∞fπ

sin(ft)

It is clear that the added mass effect cannot be derived from non-dimensional

parameters only, but that some other quantities need to be known as well.

4.3 Gurney Flap

As additional tests, it was decided to fit the wing with a Gurney flap placed on

the trailing edge. The dimension of the flap was approximately 2.2% of the chord,

56

4.3 Gurney Flap

Figure 4.14: Lift and drag coefficients vs. wind speed, GF and TFX

well in the range of what is commonly used on racing cars. Afterwards, a strip

with fine grit was placed at 0.1c (consistently with (41)) on the suction side of

the wing, in order to trip the boundary layer and force the formation of boundary

layer through roughness and consequent by-pass transition.

As with the clean wing, the first runs were aimed at assessing the consistency with

existing data. As it can be observed in figure 4.14, the lift coefficient is increased

by a considerable factor with respect to the clean wing, while the transition-fixing

condition has a negative effect on both lift and drag. Still, the lift values for this

last case overshoot what was observed for the clean wing with free transition.

Drag increases as well. It is noteworthy to point out how the drag is almost

constant when the transition is fixed, which entails that the skin friction is critical

for this case. Drag for the transition-free case grows with Reynolds number,

similarly to the clean wing.

For this particular setup, a new, non-dimensional parameter was introduced,

called oscillation factor, defined as

OF =σFF− 1

which is the ratio between the standard deviation and the mean of the desired

quantity (in this case, lift or drag). From a practical point of view, it is useful

to know how much the lift and drag values vary, especially when compared to

57


Figure 4.15: Non-dimensional oscillation factor, lift and drag, GF and TFX

the mean quantity. It can be seen how an increment in reduced frequency highly

increases the oscillation amplitude, as it is expected, since the flow is experiencing

more unsteadiness, a quantity for which the reduced frequency is an accurate

indicator. In particular, oscillations in lift are higher when the transition is fixed,

whereas the opposite situation is observed for drag. This latter behaviour can

be explained by the fact that a higher component of the drag is skin friction

(since transition is forced), which remains almost constant throughout the entire

oscillating regime, reducing the non-dimensional factor. The higher variability in

lift can be explained by a thicker boundary layer, more prone to separation at

higher effective angles of attack, which induces a more pronounced separation-

reattachment mechanism.

As a further investigation, lift and drag obtained at dynamic conditions were

compared with the static value. The lift displays an interesting behaviour: the

dynamic cases show a remarkable improvement, at least at reduced frequencies

higher than a threshold, that appears to be around 0.4. A peak in this quantity is

observed around 0.5 for the highest Reynolds number, whereas a steady growth

is seen at Re = 79000, but with a decreasing rate as the reduced frequency is

increased. Drag shows the opposite behaviour: for k > 0.4, the drag starts to

constantly decrease for all Reynolds number, reducing to around 80% of the initial

value. It is interesting to notice how this type of behaviour is something that is

58

4.3 Gurney Flap

Figure 4.16: Non-dimensional lift and drag vs. reduced frequency, GF and TFX

encountered at higher reduced frequencies for a clean wing, which would suggest

that the addition of a Gurney flap can be considered, in some sense, similar to

an increase in reduced frequency. It is to be remembered that the wake of a

wing equipped with a Gurney flap features a discrete vortex shedding in static

conditions already. The reduction in drag can be explained with the different

alignment of shed vortices when an oscillatory motion is applied, a situation that

does not take place with the clean wing at reduced frequencies below 1. The

role of the Gurney flap in this drag reduction is therefore indirect, as it is simply

needed to trigger the vortex shedding in the wake. It is indeed more complicated

to explain the increase in lift; it can be postulated that the pressure difference

at the trailing edge is increased by the oscillatory motion, thus inducing a higher

base suction.

Figure 4.17 shows the phase shift for all the three main cases considered, at a

constant ride height h/c = 0.45 . It is observed that the peak is both anticipated

and increased, as the increased angle of attack plays a more prominent role at

a lower reduced frequency: the presence of Gurney flap induces a higher lift as

the effective incidence grows. The slope is also steeper, for the same reason.

The presence of transition fixing can introduce separation at the trailing edge,

introducing new flow features in this zone, especially if the presence of the Gurney

flap is considered. As a consequence, at low reduced frequencies the behaviour

59


is very similar, since the increase in angle of attack is low, as shown in 4.17.

Afterwards, the difference is more noticeable. The two curves the remain at an

almost constant distance. Furthermore, the three curves seem to tend back to

h = −1 with different slopes, lower for the Gurney flap-equipped wings, higher

for the clean wing. This is again a consequence of the more powerful influence of

the effective angle of attack, triggered by the presence of the Gurney flap at the

trailing edge.

Figure 4.17: Phase shift vs. reduced frequency for different cases

60

5

Conclusions and Further Work

The present study falls in the line of a research sector aimed at shedding light on

the possible improvements attainable by introducing unsteady flow features, by

means of externally-actuated motion on a lifting surface, such as a wing. Specifi-

cally, the focus of the project was to assess the suitability of wind tunnel testing to

the case of a planar, rectangular wing in heaving motion, at Reynolds numbers in

the order of 105. Subsequently, to investigate the influence of ground presence on

the aerodynamic loads produced by the wing itself, at different Reynolds number,

frequencies and wind speeds, with particular reference to the available literature.

A model capable of carrying the predicted loads has been designed and built, as

shown in Chapter 3. The preliminary tests, aimed at appraising the suitability of

the available facilities, have been undertaken as a necessary step towards the com-

pletion of the project. In particular, lift measurements for a wing in freestream

conditions were compared with what is predicted by the Theodorsen theory, in

order to validate the procedure that has been followed in the following tests.

Good agreement was found between the two sets of data, at least for the range of

reduced frequency that were permitted by the intrinsic limits posed by the avail-

able facilities, wind tunnel and electric motor in primis. It is worth mentioning

that one of the main constraints of wind tunnel testing for similar cases is the

upper boundary of reduced frequency, which is limited by the maximum motion

frequency that can be transmitted to the wing, and the minimum wind tunnel

speed at which a steady flow is obtained. These two technological bounds are

61

5. CONCLUSIONS AND FURTHER WORK

remarkably difficult to overcome, especially if the importance of Reynolds num-

ber is considered: an hypothetically smaller, and therefore lighter, model would

allow for higher frequencies to be reached; however, this would mean lowering the

Reynolds number. As a matter of fact, the trade-off between these two quantities

is something to be carefully considered when preparing a test programme, or even

defining project objectives.

An important step of the project was to assess the suitability of the selected wind

tunnel for this type of research, by comparing the theoretical values predicted by

Theodorsen’s theory with the experimental results. Once this was done, it was

possible to move the wing closer to the ground, in order to investigate ground

influence. The relative influence of three quantities on lift and drag coefficients

was studied: Reynolds number, ride height and reduced frequency. It was found

that all variables can play a significant role, and their combined influence was

assessed as well. The magnitude of force fluctuations is found to be qualitatively

similar to what was observed with CFD; the phase shift showed good agreement

as well. The dependence of the effective angle of attack on the Strouhal number

was demonstrated. Additional tests were performed on the same wing, adding a

Gurney flap at first, and then placing a rough strip on the suction side to trip

the boundary layer. The maximum phase shift (expressed as h) was observed to

increase, while the reduced frequency at which it occurs decreased. A beneficial

effect of increasing the reduced frequency was discovered on both lift and drag, as

a consequence of the vortex shedding introduced by Gurney flap presence even at

k < 1. The maximum oscillation in lift and drag was observed to be dependent

on reduced frequency too, as predicted.

Overall, the project proved the possibility of performing tests on non-stationary

wings at Re in the order of 105, and M in the order of 0.1. The calibration proce-

dure, to obtain the inertial forces, was validated against theoretical results. The

effectiveness of oscillatory motion to reduce drag is negligible, at least for k < 1,

as from existing literature. Conversely, it was first shown that the presence of a

Gurney flap, which induces significant vortex shedding even at very low frequen-

cies, can help to reduce drag and improve downforce, as the vortices respective

positions are modified by the wing motion, with respect to the static condi-

tions. The distribution of vorticity could lead to thrust characteristics at a much

62

lower value of reduced frequency than a clean wing. The contribution towards

downforce generation of the increased angle of attack effect grows in magnitude.

Similar trends, quantitatively less marked, are observed when the boundary layer

is tripped on the suction surface. In particular, a lower sensitivity to the effective

angle of attack and Reynolds number can be detected. Finally, from the results

of this investigation, improvements in aerodynamic efficiency and performance

in racing conditions are deemed as definitely possible; the study performed on

Gurney flap presence are particularly encouraging from this standpoint.

This research showed very promising result, especially for what concerns the

employment of experimental-based procedures for unsteady analysis, at a scale

significantly bigger than what is commonly employed. One of the limits, as men-

tioned, is the relatively low reduced frequency that can be achieved. To increase

this, the simplest method would be to have a higher motion frequency, which

could be attained with either a different motor or a lighter model. Covering up

to k = 3 would mean increasing the motion frequency to 15 Hz, at fixed chord

and wind speed. Another extension would be to build a model that could inves-

tigate lower ride heights, and eventually go as low as the force reduction zone.

Furthermore, a more comprehensive analysis of the influence of motion ampli-

tude would help to shed more light on the phenomenon. Eventually, the effect of

non-sinusoidal and even random oscillations is to be taken into consideration.

This project, for the most part, considered the effect of oscillatory motion and

ground presence from the standpoint of two quantities, lift and drag. Employing

visualisation techniques to explore the flow features in the wake of the wing is

of primary importance, given the importance of vortex shedding for this partic-

ular case. Pressure measurements on the two wing surfaces would arguably be

helpful as well. From the point of view of actual results, further studies on the

contemporaneous effect of Gurney flap and oscillatory motion is surely required,

as it was observed to be very promising and carrying a lot of potential, as it could

result in a much improved aerodynamic efficiency with a very little mechanical

input from the outside. Further research would, ideally, include double-element

wings, or even more complex layouts, in order to approach actual F1 wings.

63

5. CONCLUSIONS AND FURTHER WORK

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