Flow Analysis of Apache Wingsuit

Karl Nyberg

LIU-IEI-TEK--12/01507--SE

ii

Abstract This thesis is a study of the aerodynamics of a generic model of the Apache wingsuit subjected to angle displacements at high velocity. The Apache wingsuit is a wing equipped jumpsuit, used to enhance the experience of skydiving by producing glide capability. The origin of this case is from an event were unstable behaviour was experienced by the pilot when a dive at 83 m/s (~300 km/h) was followed by an increase of angle of attack which triggered the incident. Aerodynamics regards a big number of phenomena. Many studies have been done on airplanes but not many on wingsuits and an important feature is that it is made out of fabric, which separates it a lot from the physical attributes which apply to an airplane. Basic divergence was considered for it applies well also for a wingsuit regarding physical features. The study aims to recreate these circumstances to determine whether the aerodynamics of the wingsuit are of unstable nature. A generic wingsuit model CAD model was generated in symmetry and in asymmetry through ANSA based on manufacture measurements and visual reference. Moments and forces were monitored while angle displacements were performed in CFD simulations in STAR-CCM+. Solutions were performed in steady state and seemed to show unreliable convergence above 40 degrees angle of attack were stall was introduced. The model did not reveal any unstable characteristics of the symmetric wingsuit and the asymmetric model did not show of any profound force generation. There seemed to be an overproduction of head-down pitch moment, but whether this was a mistake in design of an actual feature of the Apache is not confirmed.

iii

Acknowledgement This thesis has been produced at FS Dynamics Stockholm for Tony Wingsuits and I would like to show my gratitude to the people who have helped me to get to this point of adding my last letters to this thesis. Thank you Marcus Christiansson, my primary supervisor at FS, for recognizing my enthusiasm and curiosity for this project, spending your time and energy to give me this chance and helping me to advance in the field of CFD at FS Dynamics. And thank you Per Birkestad, assisting supervisor at FS, for showing such interest and involvement with so many rewarding and brainfrying discussions. Thank you Matts Karlsson for your commitment and inspiring attitude at LiU, giving me belief in a colourful future of engineering. And sincere gratitude to Jonas Lantz, my official supervisor, for all the good advice and hard work you have put into helping me to pull through this project. Last but not least, all my fantastic new friends at FS Dynamics who has helped me through the project with technical advice and cheerful shouting! Thank you Emelie Lagerkvist, Alex Loubenets and Miriam la Vecchia!

iv

Contents

1. Introduction 1

1.1 Background 1

1.2 The Apache Wingsuit 2

1.3 Problem Formulation 4

2. Theory 6

2.1 Background: Fluid Dynamics 6

2.1.1 Turbulent and Laminar Flow 6

2.1.2 Reynolds Number 7

2.2 CFD - Computational Fluid Dynamics 7

2.2.1 Background: CFD 7

2.2.2 How it Works – A Simplified Explination 7

2.2.3 Navier-Stokes Equations for a Newtonian Fluid 8

2.2.4 Finite Volume Method and Discretization 9

2.2.5 y+ 10

2.2.6 RANS – Reynolds Averaged Navier-Stokes 11

2.2.7 RANS Turbulence Models 11

2.2.8 Time Dependency 12

2.3 Aerodynamics applied on Wingsuit 14

2.3.1 Angles 14

2.3.2 Lift and Drag 14

2.3.3 Separation and Stall 15

2.3.4 Vortex Shedding 16

2.4 Aerodynamic Stability Theory 18

2.4.1 Flutter 18

2.4.2 Buffeting 18

2.4.3 Divergence 19

v

2.4.4 Line of Action 20

2.5 Approach 21

2.5.1 What is Experienced as Instability? 21

2.5.2 Consideration of Phenomena 21

2.5.3 Parameters of Investigation 21

2.5.4 Restrictions and Consideration of Error 23

3. Method 24

3.1 Geometry 24

3.1.1 Wingsuit Geometry 24

3.1.2 Domain 27

3.2 Mesh 29

3.2.1 Boundary Growth Rate 29

3.2.2 Boundary Layer and Wall treatment 30

3.3 Solver Setup 31

4. Results and Discussion 32

4.1 Drag and Lift 32

4.2 Line of Action 34

4.3 Pitch 35

4.4 Yaw 37

4.5 Roll 39

4.6 Asymmetry 41

5. Conclusion 43

6. Future Work 44

Appendix 45

References 49

vi

List of Figures 1.1 “The Flying Man” by Fausto Veranzio, representing a man falling from a tall building wearing

an early version of a parachute.

1.2 Apache Wingsuit viewed form top side.

1.3 Top view of flying Apache with wing segments pointed out.

1.4 Front view of Apache with air intakes pointed out.

1.5 Sequence of events from the occurred problem when an increase in angle of attack was

followed by an instability of the wingsuit.

2.1 Visualization of boundary velocity profile along a flat plate with laminar and turbulent flow

with the viscous sub-layer represented at the three velocity vectors closest to the surface.

2.2 The three angles which describe an airplanes alignment to the direction of travel pitch α, yaw β

and roll γ.

2.3 The three angles which describe an airplanes alignment to the direction of travel pitch α, yaw β

and roll γ.

2.4 Flow over an airfoil with force components and air stream divided in top and bottom stream at

leading edge and merged again at the trailing edge.

2.5 Flow over an airfoil, representing attached flow (a), separating flow (b) and fully separated

(stalled) flow (c).

2.6 Flow over a cylinder create vortex sheddning (von Karman street) which cause oscillating

forces, represented by the vertical arrows.

2.7 Graph demonstrating diverging moment (a) and representation of flow scenario (b) were the

moment causes deflection which can be described as forcing the leading edge to turn up and

backwards.

2.8 An airfoil with the restabilizing moment effect (left) and deflecting moment effect (right) as a

result of the positioning of the Line of Action.

2.10 Moment direction drawn from the centre of mass (a), placement of centre of mass in x-axis (b)

and z-axis (c).

2.11 Representation of moment with respect to angle of air stream, with roll (a) yaw (b) and pitch

(c).

3.1 Outline of the original Apache measurements (a) and perspective view of the unmorphed

Apache model (b).

vii

3.2 Model with morph boxes previous (a) and during (b) morphing session.

3.3 Final model with morphboxes.

3.4 Top view of real Apache lying on ground (a), wingsuit model (b) and real flying Apache (c).

3.5 End view of real Apache lying on ground (a), wingsuit model (b) and real flying Apache (c).

3.6 Asymmetric model front view.

3.7 Domain perspective and measurements.

3.8 Domain measurement from top (a) and side (b).

3.9 Pressure plot along the right side wall presenting a less than 10 Pa pressure difference.

3.10 Volume mesh at full view symmetryplane

3.11 Symmetry plane side view volume mesh around wingsuit model profile (a) and boundary layer

mesh at trailing edge (b).

3.12 Oscillating coefficients due to transient flow.

4.1 Drag to lift plot with 83 m/s and 40 m/s samples shows different values at 40 degrees pitch.

4.2 Velocity plots of symmetryplane profile for 40 degree pitch at 40 m/s (a) and 40 pitch at 83 m/s

(b).

4.3 Line of action with respect to the centre of mass in a pitch angle sequence at 83 m/s.

4.4 Pitch moment with respect to pitch angle.

4.5 Pressure plot around arm segment profile at 0 degree (a) and 30 degree (b) pitch angle.

4.6 Plots of angular accelerations with respect to yaw angle displacement at 30 degree (a) and 60

degree (b) pitch.

4.7 Pressure plot of the wingsuit at 30 pitch/50 yaw (a) and 60 pitch/50 yaw (b) with top view to the

left and bottom view to the right.

4.8 Plots of angular accelerations with respect to roll angle displacement at 30 degree (a) and 60

degree (b) pitch.

4.9 Pressure plot of the wingsuit at 30 pitch/50 roll (a) and 60 pitch/50 roll (b) with top view to the

left and bottom view to the right.

4.10 Plot of angular accelerations to pitch angle for asymmetric and symmetric model.

4.11 Pressure plot of asymmetric wingsuit with pitch at 15 degrees (a) and 45 degrees (b).

5.1 Suggestion of modification to resemble forward swept wing for the purpose of improved high pitch handling.

viii

A.1 Morphed and unmorphed geometry.

A.2 Mach plot of top side wingsuit, 35 degree pitch at 83 m/s showing big areas subjected to

velocities above 0.3 mach.

A.3 Coefficient plot for symmetric case 35 pitch at 83 m/s.

A.4 Zoomed coefficient plot for symmetric case 35 pitch at 83 m/s.

A.5 Residuals for symmetric case 35 pitch at 83 m/s.

List of Tables

3.1 Cell size and cell count

3.2 Boundary layer features

A.1 Moment of inertia

A.2 Reynolds number

A.3 Mesh validation

ix

Nomenclature

Roman Letters dS Segment length change m i Internal energy J k Thermal conductivity W m-2 K-1

k Turbulent kinetic energy, TKE J kg-1

m Mass kg p Pressure N m-2

t Time s u,v,w Velocity scalars m s-1

u’,v’,w’ Fluctuating velocity scalars m s-1

u Velocity vector m s-1

v∞ Free stream velocity m s-1

y+ Non-dimensional wall unit - ΔyP First node wall distance m Capital Roman Letters A Area m2

CD Drag force coefficient - CL Lift force coefficient - Cv Volumetric heat capacity J m-3 K-1

D Energy dissipation J kg m-3 s-1

FD Drag force N FL Lift force N I Moment of inertia kg m-2

L Characteristic length m M Moment N m P Mean pressure N m-2

R Ideal gas constant J mol-1 K-1

S Segment length m SM Momentum source kg m s -2

Si Energy source J kg m-3 s-1

T Temperature K U,V,W Mean velocity scalar m s-1

U Mean velocity vector m s-1

x

xi

Greek Letters α,β,γ Angles Degree δ Kronecker delta - ε Dissipation of TKE m2 s-3

μ Dynamic viscosity Pa s μt Turbulent viscosity kg m2 s-1

ν Kinematic viscosity m2 s-1

ω Specific dissipation of TKE s-1

φ Scalar term ρ Density kg m-3

τw Viscous shear stress N m-2

Subscripts i,j Spatial indices P First layer node w Wall x,y,z Direction

1 Introduction

1.1 Background: Wingsuit

As far back as in the Renaissance people have been trying to invent new creative ways to defy the law of gravity. But for the previous centuries, the scene has consisted of more or less fanatic pioneers who often were considered feeble-minded by their spectators, see figure 1.1.

Figure 1.1. “The Flying Man” by Fausto Veranzio, representing a man falling from a tall building wearing an early version of a parachute.

During World War II it proved to be very successful fly in and drop troops with parachutes in areas with restricted accessibility due to tough terrain or enemy threat.

More and more people started to jump just for fun and year 1952 skydiving became an international sport. The technology has continued to develop through the years, transforming and improving functionality greatly. People early started experimenting with their jumpsuits to improve glide capabilitiy and the concept of the wingsuit has been around since the mid twentieth century. 2006 Tony WingSuits launched their first commercial wingsuit for the public, the Z-wing, one of many to come.

A wingsuit is a suit with wings you use in combination with skydiving for a more exciting experience. The wingsuit slows the fall and allows the pilot possibility to enjoy longer airtime and to navigate more freely. What distinguishes it from other inventions such as paragliding, hang gliding or flying regular airplane, is the combination of speed, flexibility and absence of external power sources such as propeller or jet engine.

Tony WingSuits is a part of Tony Suits which was founded in 1976 by Tony Uragallo. At first the

1

company made equipment for regular skydiving but today they offer a wide range of different wingsuits. Whether you want to do acrobatics, fly in formation or just cover the most miles there is a wingsuit for every purpose.

1.2 The Apache Wingsuit

Wing size is mainly what varies between wingsuits with different purpose. The Apache model in figure 1.2 is built to give the best glide and cover large distances, which it has proven to be rather successful at with several 1st places in long distance competitions as proof. At this time the Apache is the model with the largest wing segments in the Tony Wingsuit’s collection.

Figure 1.2. Apache Wingsuit viewed form top side.

No one have deliberately and unharmed managed to land a wingsuit without a parachute up until this year 2012. The race of being the first pilot to achieve this goal was surrounded by rumours and anticipation. Some had plans to build huge runways to land on but the first one to eventually cross the finish line was Gary Connor, using the Rebel wingsuit from Tony Wingsuits, landing in a field of cardboard boxes. The attempt was successfully and Gary was able to walk away uninjured from the event.

There is a lot of groundwork to be done before you can put yourself in the Apache wingsuit. To fly a wingsuit demands a lot of experience and even with a beginner class wingsuit it is recommended to

2

have done at least 200 regular skydives. To fly the Apache, which is an expert class wingsuit, it is recommended to have 200 wingsuit jumps [8].

There is a strong resemblance between the Apache Wingsuit and a flying squirrel. Both have segments fitted from the arms to each leg and in between the legs, see figure 1.3. On the wingsuit the segments are double layered like an inflatable mattress, which makes it possible for the wingsuit to inflate and gain thickness. This is accomplished through air intakes positioned at the bottom side of the wingsuit. During regular flight, like any other air plane the bottom side is exposed to high pressure. The high pressure forces air into the intakes and inflates the wingsuit, see figure 1.4. The segments are designed as airfoil profiles which will help to give the Apache better flying properties, such as higher lift to drag ratio, i.e. better glide. The inflation also gives rigidity which helps to support the posture of the wingsuit pilot. At normal circumstances, flying velocities for the apache is around 140 to 210 km/h and the average glide ratio is up to 3:1, leaving a fall at 44-66 km/h. Without a wingsuit a regular skydiver reaches terminal fall velocity around 200 km/h vertical speed.

Figure 1.3. Top view of flying Apache with wing

segments pointed out. Figure 1.4. Front view of Apache with air

intakes pointed out. The big wings are the essence of this wingsuit but they are also the reason why pilots need so much experience before jumping with the Apache. And the preparation recommendations are very motivated indeed. The physique and mind of a human is simply not very well qualified to flying without aids and the consequences of mistakes at 200 km/h towards solid ground are unforgiving to say the least. Big wings give larger windbreak, meaning aerodynamic forces such as moment, drag and lift are greater on a pilot flying the Apache rather than a wingsuit with smaller wings. The pilot uses the forces to provide the wingsuit with lift and steering when desired. It is crucial for the pilot to master the wingsuit to be able to perform these tasks. But larger forces require more delicate handling which is why the Apache is an expert class wingsuit. A poorly executed steering manoeuvre could result in an

3

enormous imbalance in the force distribution over the wingsuit and initiate a violent rotational force, leaving the pilot disoriented in a spinning fall. Deploying the parachute in this state is a last resort as the spinning pilot risk tangling into the parachute preventing it from extracting and function properly. More to the specifics of handling a wingsuit, the main feature is to find the point where you balance the body weight to the aerodynamic forces and have the best experience. For the Apache it is the best glide which is the most sought feature, which is the ratio of how much distance covered along the ground in relation to every meter you drop in altitude. 1.3 Problem Formulation

The problem of this study originates from an actual event during a wingsuit skydive when the pilot attempted to break and pull up from a dive at 300 km/h. The pilot in question is one of the most experienced in the wingsuit community, but when he executed the manoeuvred he experienced unstable behaviour from his Apache wingsuit, demonstrated in figure 1.5. Fortunately the mishap occurred at high altitude and the pilot was able to regain control and land uninjured.

Figure 1.5. Sequence of events from the occurred problem when an increase in angle of attack was followed by an instability of the wingsuit.

In order to pull out of the dive a pull-up motion had to be performed, which is initiated by increasing the angle of attack. Though the pilot has described the handling to be extremely sensitive to imbalanced or asymmetric movement at these high velocities it cannot be established that the reason to the accident was an error in handling. The given information yields that the angle of attack was increased at a high velocity when some aerodynamic force made the wingsuit unstable. However it does not say whether the position of the pilot was in an asymmetric, awkward position in some manner or if there was some external source, e.g. if one of the wings caught a sudden side wind. There has been extensive done in the world of

4

aerodynamics, though most cases concern air planes which makes it hard to draw any direct conclusion based on these theories because of the many different properties between the materials of a wingsuit and airplane. This thesis aims to use CFD to investigate the forces and moments acting on of the Apache wingsuit. Similar conditions from the event of accident will be applied, such as increasing angle of attack at 300 km/h, but there will also be some further input parameters such as additional rotation and asymmetry of the pilot posture to investigate how the wingsuit would respond to such possible influences. The results from CFD will yield forces which possibly could correlate with some known aerodynamic instability, e.g. spinning, oscillation and vibrations, and will help to pinpoint features of the wingsuit that may be causing the instability.

5

2 Theory

2.1 Background: Fluid dynamics Fluid dynamics describes the motion and behaviour of fluids. The common fluids, liquids and gases, are involved in many everyday routines, some more obvious than others. Building an airplane quite risky business without the knowledge of the properties of air, i.e. aerodynamics, but how to fill a cart with yoghourt the fastest is an equally important task to fulfil for the food industry companies in order to be productive. Knowledge of how fluids behave grants the possibility to manipulate flow in ways of desire. 2.1.1 Turbulent and laminar flow There are two kinds of forces to consider for an object in an air stream. First there are tangential wall stresses induced by the fluid passing along the surface. Viscosity magnitude indicates the fluid’s sluggishness and how much shear force it utilizes to try to drag the object along. Second are normal stresses, i.e. pressure, created when the fluid collide with the surface. Turbulent flow can be described as random and chaotic flow, consisting of small eddies. Turbulence magnitude indicates the relation between pressure and shear inflicted force, with pressure increasingly dominant with more turbulent flow. The opposite is laminar flow which is a state when the fluid has a more uniform motion and the viscous effects of the fluid has more significant role [1]. Surface boundary layers always have a part laminar region, seen in figure 2.1, called viscous sub-layer, because vertical movement is limited and viscous force dominates at the proximity of the wall.

Figure 2.1. Visualization of boundary velocity profile along a flat plate with laminar and turbulent flow with the viscous sub-layer represented at the three velocity vectors closest to the surface.

6

2.1.2 Reynolds Number The turbulence magnitude is measured by Reynolds number, which is a function of free stream velocity, dynamic viscosity, density of the fluid and the characteristic length of the object or area of interest, seen in equation (1.1). Higher Reynolds number indicates more turbulence, meaning more randomness and smaller eddies within the flow. In external flow turbulence is considered to be fully developed approximately at Re > 1 000 000 for a flat plate, and at Re > 2300 for in internal pipe flow [1].

LvRe (1.1)

2.2 Computational Fluid Dynamics - CFD 2.2.1 Background CFD is a method were computational numerics is used to calculate flow in models of real fluid systems, such as aerodynamics, internal combustion systems or blood flow in the cardio vascular system. CFD is a relatively new tool to the industrial world in comparison to solid mechanics and automatic control. The theory has been around as early as the 60’s but the delay in utilizing the possibilities of the technology is simply because the method requires a larger amount of computational power which has not been available up until the last two decades. Even today the amount of computer power play a restricting roll to what is possible to simulate and at what level of detail. Unlike solid mechanic’s finite element method, CFD has to consider motion of a fluid which adds more equations to the system and demands higher resolution to the cost of CPU power. Additionally the equations in CFD are more complicated to solve and increases the workload even further. 2.2.2 How it works - Simplified procedure A geometry is created in CAD and setup with conditions defined with a desired level of detail by dividing the domain into a finite number of elements. Thereafter the case is run and the computer calculates how the fluid should behave from what information, i.e. boundary conditions, that are given. When the procedure is done it is possible to move around and surgically investigate the fluid in a frozen state, with no risk of instrument or human error and no environmental inconvenience, such as investigating aortic blood flow when the object is very delicate and experiments are inappropriate. A weakness of CFD is the need to know the influencing factors before being able to perform a simulation. An experiment will produce different results compared to corresponding CFD simulation if there is some input which is not accounted for in the simulation boundary conditions. The models which are within reasonable computation costs are still only approximations and demands to be carefully set up for each different case. The matter of the right experience is essential in order for a simulation to yield reliable results will only be as good as the . Also as mentioned before, there are still some cases which suffer from major CPU bottlenecks, waiting for technology to provide with new more efficient simulation aids. However, regarding both costs and convenience, CFD can be superior to experimental methods, given that simulations generate accurate results.

7

2.2.3 Navier-Stokes equations for a Newtonian fluid The Navier-Stokes equations (2.1a-c) are derived from the momentum equations which originate from Newton’s second law. Substituting the assumptions of a Newtonian fluid, were the viscous stresses are proportional to the rates of deformation, into the momentum equations yields the Navier-Stokes equations (2.1):

xMSugraddivx

pudiv

t

u

)()(

)( u

yMSvgraddivy

pvdiv

t

v

)()(

)( u

zMSwgraddivz

pwdiv

t

w

)()(

)( u

I II III IV

(2.1a)

(2.1c)

(2.1c)

With velocity vector u = [u v w], pressure p, density ρ, viscosity μ. Where (I) is the rate of fluid momentum increase, (II) is net rate of momentum out of fluid element, (III) is rate of momentum increase due to diffusion and (IV) is the rate of momentum increase due to sources.

0)(

udiv

t (2.2)

The continuity equation for a compressible fluid (2.2), derived from the law of conservation of mass, keeps the mass constant in the system, meaning that fluids cannot spontaneously disappear or be created in an element. The equation balances the mass flow through the cell to the rate of pressure change.

iSDTgradkdivdivpidivt

i

)()()(

uu (2.3)

The energy equation (2.3) has the same term structure as equation (2.1) but applies to energy balance, which is for the purpose to conserve energy in the system, considering temperature, pressure and internal energy.

RTp

(2.4)

TCi v

(2.5)

Pressure (2.4) and specific internal energy (2.5) for a perfect gas are equations needed to describe the physical attributes of the fluid, were R is the ideal gas constant, T the temperature and Cv the heat capacity for a constant volume.

8

2.2.4 Finite Volume Method and Discretization The Finite Volume Method, FVM, divides the room into a finite number of volumes, also referred to as cells. Each cell is given a set of properties, such as pressure, velocity, temperature etc. FVM is one of the tools used in CFD to give an approximate picture of how fluids move in the room. When the room has been divided into a finite number of elements, it is called a mesh. The point of this method is to treat every cell as a separate unit with ability to affect and adapt to its neighbours. If one cell differs from its neighbours it will create a domino effect and the entire domain will adjust to some degree. As an example, a straight open ended pipe with filled with a fluid is given a velocity inlet on one side and a pressure outlet on the other. 5 elements, preferably equally sized divide the fluid space along the inside of the pipe. Before the inlet is activated the fluid is stagnant because the outlet has the same pressure as the fluid. When the inlet is activated, new momentum is forcing itself into the first element. The second element experiences the difference and adjusts to the momentum increase. The third element repeats the same procedure of the second element and so on, i.e. creating the domino effect. When the fifth element is reached the excess pressure is released through passing fluid to the outlet. When all elements have adapted there will be a constant flow through the pipe and the system has reached equilibrium. In reality a room can be divided into an infinite amount of volumes which is not feasible for our technology at this time. Yet, a good approximation through CFD has proved to suffice in many fluid dynamic scenarios when knowing the main flow is enough to determine what causes problems, such as fluctuations, stagnant points or turbulence. There are several ways to calculate the properties of every cell. Each method is called discretization methods. The general idea is, for each cell, to look at the state of mass and energy flow in its neighbouring cell and use that information combined with the properties of the medium to calculate the new state in the current cell. In this project an upwind discretization is used because. Upwind method focuses on upstream neighbouring cells to have the most influence on the current cell. The algorithm recognizes the stream direction and uses it to choose which neighbouring cells to take influence from. Cases were flow is the main concern is a good fit with the upwind method, though some cases regarding diffusive flow may cause errors using the upwind method. Thermal energy travels through diffusive flow which also goes up stream, a feature the first order upwind simply does not include, leading to inaccurate results [1]. If a case would include a heat source down stream would be unable to affect its up stream neighbouring cells. There are different orders of discretization which refers to the amount of neighbouring cells to consider. A second-order upwind is used in this investigation, as higher order method gives more information about the currents cell’s adjacent surrounding than a first order method. But taking extra cells into account comes to the cost of longer iteration time and in some cases it could make the solution become unstable. When every cell in the mesh has considered its neighbours and acquired new set of property values through discretization, an iteration has been completed. The solver repeats the procedure until the cell values seize to change to some desired degree, meaning that the solution has converged and the results are ready to be extracted and analyzed.

9

2.2.5 y+ To acquire the correct wall shear stresses the viscous sub-layer needs to be resolved and y+ is a tool to appreciate whether your mesh is sufficient or not. The value is a function depending on the first node height, kinematic viscosity, viscous shear stress and density of the adjacent flow, seen in equation (2.6). The more turbulence means increased rate of inertial dominance closer to the wall, slimming of the viscous sub-layer and as a consequence finer mesh will be needed to resolve it.

wPy

y

(2.6)

It often requires a too big number of cells to produce an adequate resolution along a surface. Wall functions have been developed for the purpose to remedy this with an approximation of the boundary layer flow. At certain y+ interval, wall function is triggered in the program and replaces the ordinary flow calculations. A wall function is an analytical model of how tangential velocity of the fluid varies as it comes closer to the wall. The models use wall distance, adjacent fluid velocity, max fluid velocity, wall shear stress, density, viscosity, roughness of the wall and the addition von Karman’s constant as input to perform these approximations [1]. There are different models depending on region of the boundary layer and depending of software, implementation of the models can vary. However, the use of wall functions is an effective way to reduce the amount of cells in a mesh. If boundary layer is predicted to be important in the study, it may not be suitable to rely too much on wall functions as it may ignore influences of dramatic flow which can generate misleading results such as underestimated separation bubbles. There are different wall functions describing the flow depending on the distance to the wall and a finer mesh will give lower y+ which denies the use of the outer boundary layer wall functions, giving better possibility to resolve circulating or separating flow.

10

2.2.6 Reynolds Averaged Navier-Stokes (RANS) Velocity in turbulent flow can be divided into two components, mean velocity and fluctuating velocity , called the Reynolds decomposition. The fluctuations are usually of less interest because most investigations focus on mean flow, but there are some attributes brought by the fluctuations that cannot be neglected. The RANS equations (2.7a-c) are derived through introducing the Reynolds decomposition to the original N-S equations (2.1), followed by a time average of the expressions.

),( txu )(xU),(' txu

xMSz

wu

y

vu

x

uUgraddiv

x

PUdiv

t

U

)''()''()'()()(

)( 2 U

yMSz

wv

y

v

x

vuVgraddiv

y

PVdiv

t

V

)''()'()''()()(

)( 2 U

zMSz

w

y

wv

x

wuWgraddiv

z

PWdiv

t

W

)'()''()''()()(

)( 2U

(2.7a)

(2.7b)

(2.7c)

The result looks as if the regular N-S with the regular velocity u replaced by the mean velocity U, with the addition of three new terms called Reynold stresses which are the remaining features from the fluctuations that has considerable effect on turbulent flow but have proved to be very hard to measure. 2.2.7 RANS Turbulence models A RANS turbulence model’s role is to simplify and translate the effects of the Reynold stresses into the time averaged Navier-Stokes equation. The physical flow contributed by the Reynold stresses is extremely complex and costly to recreate, which is why the stress terms are substituted by models representing the effects of the Reynold stresses. The Reynolds shear stresses are modelled with the Boussinesq proposition derived from the assumption that they are proportional to mean rates of deformation:

iji

j

j

itji k

x

U

x

Uuu

3

2

(2.8)

Where )'''(2

1 222 wvuk is the turbulent kinetic energy per unit mass, μt is the turbulent viscosity

and the Kronecker delta, to edit the equation (2.8) whether to calculate for normal or

shear stress.

jiif

jiif

0

1ij

11

Dissipation of mean flow is a main feature brought by the turbulence models. For instance when a laminar jet stream is projected into a stagnant fluid, the viscous force tear the jet apart into smaller and smaller eddies. Models are often developed in relation to certain types of flow. A turbulence model produced for pipe flow might not be suitable for aerodynamic application, which raises the requirement to select the appropriate model for the intended flow. The Navier-Stokes (2.1a-c) and energy equation (2.2) uses a term structure which can be translated into general form, called a transport equation (2.9).

Sgraddivdiv

t

)()()(

u (2.9)

Where is a scalar property of the fluid and Γ is the diffusion coefficient. RANS turbulence models, k-ε and k-ω, refer to further modelling of the eddy viscosity μt using transport equations.

k-ε The k-ε model is a two transport equation, RANS turbulence model, regarding turbulent kinetic energy k and dissipation, ε. The model works well for internal flow simulations and has been use extensively in industrial connection [1]. However, the model has some trouble to catch external and more violent flows with large pressure gradients and often under predict separation. Later on through the years the k-ε realizable modification was produced and has proven to manage previous disadvantages well [2]. k-ω The k-omega model is also, similar to the k-ε model, a two transport equation RANS model. The first equation is for turbulent kinetic energy k and second for dissipation rate ω. The model works fairly well for general purpose but is most suitable for wall bounded external flow, such as backward-facing step. Though, use of this model will come with a considerable risk to over predict separating flow.

Shear Stress Transport, SST (Menter) k-ω The SST (Menter) k-ω uses both k-ε and k-ω with a blending function which alters between the models depending on the surrounding flow. The model combines features from both models where they perform best, i.e. k-ε for confined flows, and k-ω for free stream flow. The model is recommended for general purpose in the aerodynamic industry which applies quite well to the wingsuit case [1] [2].

2.2.8 Time dependency Time dependency adds another feature to the analysis of flow. Simulation can be executed with or without time as a variable. The time regarded solution, i.e. transient solution, reveals how the system would develop as time progressed. Without time it is called Steady state solution, which can be translated as the state of a system that has reached its equilibrium, given that there is such. Use of transient solution requires a lot more CPU time than the steady state solution which states that use of steady state solver is preferred to save time.

12

Problems occur with steady state when the simulation does not converge, which can indicate a number of things. The mesh could be too coarse or have inadequate cells, meaning it is unable to resolve the flow. The setup, such as boundary condition and solver settings could be inaccurate. Selecting a turbulence model inappropriate for the type of flow can also be followed by a badly converged or even false solution. Another advantage with steady state is that the results are often easier to survey and draw conclusions from. But ultimately it is not possible to catch all the phenomena from flow in steady state as it is a simplified version of the transient solution, which concludes that it simply will not converge well if the transient character of the flow is too dominating.

13

2.3 Aerodynamics applied on Wingsuit 2.3.1 Angles In aerodynamics there are three angles which describe the aircraft’s alignment with the air stream, pitch, yaw and roll, seen in figure 2.2. Pitch is used to gain or decrease altitude and turning is done with yaw and roll. The same features apply to the wingsuit among a number of additional degrees of freedom, due to the fact that the wingsuit consist of a pilot with adjustable limb position.

Figure 2.2. The three angles which describe an airplanes alignment to the direction of travel pitch α, yaw β and roll γ. 2.3.2 Lift and Drag An airfoil is the shape of a wing profile seen from the side of the airplane, see figure 2.3. For an air plane to fly it needs a certain amount of lift to counteract the gravitational force. To obtain lift the airplane needs to catch the air stream and manipulate its direction which creates over pressure at the bottom side and under pressure at the top side of the wing. The pressure difference between bottom and top surfaces will give the airfoil lift force.

Figure 2.3. Flow Flow over an airfoil with force components and air stream divided in top and bottom

stream at leading edge and merged again at the trailing edge.

14

Depending on the purpose of the plane, different airfoils are used because depending on the shape of the airfoils it gains different properties. Fighter planes which need mobility and speed have slim airfoils while cargo planes which need maximum lift are blunt and curved. The shape of the wingsuit airfoil is diffuse and deforms with external influence, which makes it hard to determine which category it belongs to. Similar applications such as the intakes at the leading edge of a paraglider wing support that the inflation technique serves its purpose to provide a functional airfoil profile. The air stream connecting to the leading edge of an airfoil is divided into either the top or the bottom side. Connecting with the airfoil the air stream is forced to adjust to the airfoil profile. The reason why wings have an airfoil is that it is shaped to increase the amount of lift and very little drag. It creates an over pressure on the bottom side because the air stream is redirected and pushed down. Under pressure is created on the top side because the curved surface descends towards the trailing edge and manipulates the attached air stream to turn downwards. The shape of the curving of the top surface is delicate because if it turns too aggressively it might cause the air to separate from the wing which will increase drag and reduce lift. The momentum equation (2.9), derived from Newton’s third law, helps to confirm that if air, m1, is directed down 0 > v1, the wing, m2, has to go up 0 < v2.

02211 vmvm (2.9) Drag describes the force which acts on the air craft in the same direction as the air stream. In aerodynamics an airfoil should have as low drag as possible when flying straight through an air stream. Equations of coefficients from drag (2.10) and lift (2.11) are used to compare aerodynamic properties from different cases.

Av

FC D

D 2

2

(2.10)

Av

FC L

L 2

2

(2.11)

Where FD is drag force and FL lift force. For general fluid dynamics the area considered in A is the profile area from the engaging angle. But in aerodynamics the top aerofoil area is used which will will apply for this investigation as well.

15

2.3.3 Separation and Stall Stall and separation is most often an unwanted phenomenon in aerodynamic context because it increases drag and decreases lift. If the shape of the airfoil is too rough, the velocity too high or the angle of attack too big, it could cause the air stream to separate from the surface and create a recirculating flow at the separation. If the recirculation reaches the state were separation covers the whole upper side of the airfoil, it is fully stalled, see figure 2.4 and applies to wingsuits as well.

(a)

(b)

(c)

Figure 2.4. Flow over an airfoil, representing attached flow (a), separating flow (b) and fully separated (stalled) flow (c). Increasing the pitch to a certain point will also create stall and break the wingsuit instead of turning it. This manoeuvre is called flairing and is used with purpose of slowing down. It was the same procedure the wingsuit pilot performed as he tried to break out of the high velocity dive. The technique is also used by birds to break before landing. 2.3.4 Vortex shedding When an object, e.g. a cylinder, passes through an air stream and flow will separate from both sides and create vortices as visualized in figure 2.5. The two sides will take turns to build vortices and leave the opposite side to decrease and reattach for a moment. Eventually the vortex will release and the vortex on the opposite side will grow and imitate the same event, and so on. The routine is called vortex shedding or von Karman street and is repeated as long as the flow is constant. The alternating vortex generation is a time dependent phenomenon with a stable frequency. When the flow is attached to one side its surface serves the same purpose as the upper side of an airfoil, steering flow down. The cylinder is now subjected to a counterforce in the opposite direction, due to the momentum equation (2.9). The attached flow is not stationary and will eventually start to separate as well followed by a new vortex created from the separated flow, disengaging the momentum effects on the current cylinder side surface. Meanwhile the flow will reattach on the opposite side and perform the same procedure. The alternating attachment of the flow creates an oscillating force on the object, perpendicular to the direction of the flow. Vortex shedding can also be initiated by other shapes such as flat plates, which can be considered to have similar features as a high pitched airfoil, i.e. this phenomenon is physically applicable to wingsuit instability, but would require a transient solution since the phenomenon is time dependent.

16

Figure 2.5. Flow over a cylinder create vortex sheddning (von Karman street) which cause oscillating forces, represented by the vertical arrows.

17

2.4 Aerodynamic Stability Theory 2.4.1 Flutter Flutter is an instability caused by an aerodynamic force and the reacting force from the elastic structure [3]. Together the forces create oscillations and at a certain wind speed the oscillation meets the structure’s natural frequency becomes self feeding. Unless the situation is mended the oscillation will build up amplitude and the structure will eventually fail. There are famous examples were this phenomenon has been the cause for disastrous events, such as Tacoma Narrows bridge. One day the bridge, not built with enough precautions to tough winds, was hit with hard weather and fell into flutter which lead to it eventually tearing itself apart. Flutter is also a problem to aircrafts, not only for the risk of structural failure but also because the oscillations can cause difficulty to manage the steering properly [3]. This might be an application to a wingsuit, although the stiffness and structural dynamics is far from similar to an airplane. The phenomenon is a time dependent and would require such investigation, i.e. transient solution, to be detected. 2.4.2 Buffeting Buffeting is similar to flutter except that it is not dependent on the structure elasticity [3]. For example, when you leave the back seat window open while driving, you can experience wind creating a beating sound. It is caused by the cyclic shedding of the wind where the window is roller down, creating a pressure oscillation inside the car which is experienced as sound. The danger of buffeting is mainly material fatigue damage due to longer periods of exposure.

18

2.4.3 Divergence When a displacement is caused to a system, three things can happen. The system will fall back into its initial state, the system will remain at its new state or it will accelerate the displacement. An example is how to balance an egg. If it is positioned carefully it is possible to balance the egg on its top. But the slightest movement will make the egg fall over. In this case the top represents a divergent state of the egg. Placing an egg on its side is a much easier task. And even if it is given a little nudge, it would eventually fall back on its side. This state is called convergent. If the egg is rolled along its round side no forces from the egg will act to change its direction and it will continue to roll until some outer force stops it. This is an indifferent state [4]. The danger of divergence in aerodynamics is expressed as deflection, a force which causes the aircraft to start to turn in an undesired manner and cause the pilot to loose control. This problem applies to the wingsuit in the same manner as an aircraft and could be investigated in a steady state solution. The model in figure 2.6 (a) shows how the moment is in the opposite direction of the angle α and how the graph shows an increasingly negative moment is developing with α in figure 2.6 (b). The demonstrating figure shows how a deflecting moment would appear when looking at the moment as a function of the pitch angle.

(a)

(b) Figure 2.6. Graph demonstrating diverging moment (a) and representation of flow scenario (b) were the moment causes deflection which can be described as forcing the leading edge to turn up and backwards.

19

2.4.4 Line of action When an airborne body is engaged by an air stream it is subjected to two kinds of forces, pressure and shear force. These two combines into one resulting force vector which produces different moments on the body depending on where it acts [4]. The moment acts on the centre of mass and the further apart the force vector and centre of mass is, the more lever there will be to produce moment around the centre of mass. The feature can be used to determine whether an airfoil has divergent behaviour. If the line of action passes in front of the centre of mass it will create a deflecting moment and create restabilizing moment if it is behind the centre of mass, as in figure 2.7.

Figure 2.7. An airfoil with the restabilizing moment effect (left) and deflecting moment effect (right) as a result of the positioning of the Line of Action. The line of action will differ for every degree in pitch and makes it possible for an initially stable object to switch into being deflecting. A quantified investigation of the lines of action for a interval of degrees will help to determine the character of the wingsuit as it increases the angle of attack.

20

2.5 Approach

2.5.1 What is experienced as instability? Describing the problem with instability leaves a huge amount of possible phenomena to look for. What might be experienced as instability to the pilot may not be recognized likewise by an engineer. At high velocity the aerodynamic forces will be large and the slightest movement or asymmetric distribution will create a reaction. If the pilot makes an unsubtle movement and does not manage to react to an unexpected following event it could send him or her into a spin. This is technically not instability as much as sensitive handling. 2.5.2 Consideration of phenomena Because flutter is a transient (time dependent) problem it is excluded from this investigation for the reason of steady state priority. The application of buffeting on a wingsuit for this problem might not be so obvious. Although vibrations may be inconvenient it probably will not cause any instant unmanageable handling issues to a wingsuit. Like von Karman, flutter, buffeting would require transient solutions to be reproduced because of its time dependent behaviour and is therefore not considered in this investigation. Determination of divergence can be done by observing moments on the wingsuit subjected to an air stream while increasing the pitch. The moment around its centre of mass could be extracted and if it forces the wingsuit to deflect from the air stream direction, i.e. increase in pitch, it is divergent. 2.5.3 Parameters of investigation Two geometries are to be considered, one symmetric and one asymmetric. The investigation will aim to reconstruct a flairing manoeuvre in normal speed 40 m/s (144 km/h) and high speed 83 m/s (300 km/h), by increasing pitch from 0 to 90 degrees and look for deflecting characteristics for the symmetric and asymmetric model. Cases of yaw and roll displacement between 0 and 50 degrees will also be incorporated but only for the symmetric model. The asymmetric geometry is created with purpose to determine how slight limb displacement could affect the outcome of a flair event which is why no yaw or roll angles are added to the investigation for the asymmetric geometry cases. A free body rotates around three axes, X-, Y- and Z-axis, each running through the centre of mass, see figure 2.8 (a), and because the human body is non isotropic it has different moment of inertia on each axis as can be seen in table A.1 in appendix. Positioning of the centre of mass and moment of inertia, seen in figure 2.8 (b-c), is based on a statistics study of astronauts by NASA were the average pilot was 190 cm and weighed 98.5 kg [6].

21

(a)

(b)

(c) Figure 2.8. Moment direction drawn from the centre of mass (a), placement of centre of mass in x-axis (b) and z-axis (c). To make results easier to interpret, moments are in the opposite direction of the corresponding angle, see figure 2.9. If Mx increases with the roll angle, γ, it acts as a re-stabilizing moment to the displacement. If the moment shows negative value, a deflecting moment is present and the model indicates divergent characteristics of the wingsuit.

(a) (b)

(c) Figure 2.9. Representation of moment with respect to angle of air stream, with roll (a) yaw (b) and pitch (c). Moments are extracted in STAR-CCM+ from the pilot’s centre of mass and will not represent the actual magnitude of moment produced in real flight. For such an investigation, consideration of the direction of gravity force and body momentum to have to be included and because there is no input of how the pilot was aligned with the ground surface during the incident it is not possible to determine the direction of gravity force and thereafter calculate the actual moment. Though with the assumption that the pilot was not flying upside down, the moment direction will not depend on whether the force of gravity is included and the simulation will still be useful for determination of instabilities.

22

2.5.4 Restrictions and uncertainties The flexible nylon in the suit adds a big challenge in translating the shape of the real Apache into a CAD geometry. In reality the material is flexible and will give the wingsuit a different shape for each different flow case and different pilot. No experiments for validation of the model were possible to perform because the resources were simply not available and time was also a factor. With that said, the investigation does not aim to optimize or extract any exact values, it is simply a model to help determine whether the generic shape of the Apache wingsuit prohibits it from fulfilling its purpose, which is stable flying. There are many kinds of instabilities in the world of aerodynamics. However a big proportion regarding structure failure are negligible because of the difference in structure stiffness and design between wingsuit and a classic airplane from which these are derived. Steady state will be priority in this investigation because the need to produce solutions faster which will give more samples to compare.

23

3 Method 3.1 Geometry The model seeks to investigate behaviour of a generic geometry of a wingsuit that stays in one static shape regardless of flying angles. Proceeding with this assumption, geometry details will be included with motivation that it likely has purpose for the flow. A simpler model might also help filter and bring main feature’s aerodynamic impact forward. 3.1.1 Wingsuit Geometry The wingsuit is drawn from top profile measurements of an Apache wingsuit lying on the ground, see figure 3.1 (a) were the human body is not included. Some additional features are necessary to represent the presence of the pilot. The head, feet, segment inflation and parachute are body parts considered most likely to have influence on the aerodynamics and are therefore included in the geometry, seen in figure 3.1 (b).

(a)

(b) Figure 3.1. Outline of the original Apache measurements (a) and perspective view of the unmorphed Apache model (b). Furthermore, the shape of the suit in real flight is not very flat. A general symmetric geometry with curving of the wing segments is therefore generated through morphing tools in ANSA [9], see figure 3.2 and 3.3. The modifications through morphing such as camber height and the thickness of the suit inflation are approximated from videos and photos. The final model, seen in figure 3.3, shows the final geometry with morph boxes.

24

(a)

(b)

Figure 3.2. Model with morph boxes previous (a) and during (b) morphing session.

Figure 3.3. Final model with morphboxes.

The shape generated by morphing tools is focused on the wing segments which are inspirited by boat sails, which appears in similar flow scenarios were flexible material, mounted along a rigid body is subjected to an air stream to convert into forward momentum [10].

25

When comparing the geometry to the photo in figure 3.4, the geometry (b) appears to have higher apect ratio, i.e. higher width-to-length ratio, than the real wingsuit in flight (c), but not the one on the ground (a).

(a)

(b)

(c)

Figure 3.4. Top view of real Apache lying on ground (a), wingsuit model (b) and real flying Apache (c).

(a) (b) (c)

Figure 3.5. End view of real Apache lying on ground (a), wingsuit model (b) and real flying Apache (c). This is not an error in the original measurements, but it can be explained by the unelasticity of the wingsuit material. The nylon in the real wingsuit may be flexible, but it does not extend as much as the model does when the morph is executed. The curving of the wing segment during flight leads to a contraction of the hand to foot to foot distance, see figure 3.5. Thereby the feet are forced closer together with every increase in camber which is a measure which in simplified terms can be expressed as the wing segment curving. Although the model wingsuit differ in width from the real one, it still serves the purpose to include some main features of a wingsuit, such as outline, camber, and influencing body parts. To find out how asymmetric movement affects the wingsuit model, an asymmetric geometry is generated were the right hand of the pilot is lowered 0.12 m using morph in ANSA, seen in figure 3.6.

Figure 3.6. Asymmetric model front view.

26

3.1.2 Domain A number of different cases have to be simulated and the domain should to be designed to be suitable all cases. The domain should also render the same conditions as when the incident occurred. To resemble outdoor conditions the domain boundary walls should have no influence on the flow round the wingsuit. To confirm this, pressure is monitored along the side wall. Preferably the side wall should experience as little pressure variation as possible to represent outdoor flying.

Figure 3.7. Domain perspective and measurements.

(a)

(b)

Figure 3.8. Domain measurement from top (a) and side (b). To setup every case with different angles of the air stream, the inlet direction will be altered instead of moving the wingsuit. Thereby no re-meshing will be needed. The full model is necessary for asymmetric wingsuit, yaw- and roll-cases and lastly to give a more observable design. Velocity inlets are set at the front and bottom, pressure outlet at the top and back, and free slip wall at the sides for regular pitch cases. In case of asymmetric flow such as yaw and roll, the left side (seen from wingsuit) is converted to velocity inlet and the right side to a pressure outlet.

27

The domain, shown in figure 3.7-8, has a 10 Pa variation along the side walls, seen in figure 3.9, which is considered acceptable considering the inlet velocity.

Figure 3.9. Pressure plot along the right side wall presenting a less than 10 Pa pressure difference.

28

3.2 Mesh The volume mesh is generated in STAR-CCM+ [2] with Trimmer with prismatic boundary layer elements. A validation of mesh independence is performed using meshes of 16, 8, 4 and 2 million cells, presented in table A.1 in the appendix and the final size of the model is chosen to be 8 million cells, with described attributes in table 3.1. This mesh aims to resolve the model well enough to be able to capture the flow that affects the wingsuit the most and since the Reynolds number in table in appendix A.2 is about 10.5 million, i.e. about ten times the critical Reynolds number for external turbulent flow, inertial forces will be dominating the flow and wall treatment is utilized to save elements. As described in earlier the use of wall treatment risk to under appreciate separation or even letting it go undetected which is something to keep in mind through the investigation as it will experience stalled flow. 3.2.1 Boundary Growth rate Each case will have a new air stream angle which will demand that the mesh can supply sufficient refinement around the wingsuit to satisfy resolution requirements for every case.

Figure 3.10. Volume mesh at full view symmetryplane

29

Boundary growth rate is used to produce a refinement pattern around the geometry shown in figure 3.10, similar to volumetric control but more cell efficient and adaptable to the geometry [5] as seen in figure 3.11 (a). The growth boundary growth rate supplies a 12 element growth layer with growth factor 2.

(a) (b)

Figure 3.11. Symmetry plane side view volume mesh around wingsuit model profile (a) and boundary layer mesh at trailing edge (b). Table 3.1. Cell size and cell count Min surface size [m]

Target surface size [m]

Cell Count 106 [-]

0.002 0.01 8.4 3.2.2 Boundary Layer and Wall treatment The boundary layer of the wingsuit, seen in figure 3.11 (b), is aimed to y+ ~60 in order to acquire wall treatment which is activated by STAR-CCM+ at y+ > 30. The number of boundary layer presented in table 3.2 seems sufficient due to met ~y+ value and smooth transition between boundary layer and regular volume trimmer cell and no residual problem occurring. The wall treatment saves big amounts of cells and suits the project well in terms of detail priority, time and computing cost. Table 3.2. Boundary layer features First boundary layer height [mm]

y+ average (30 pitch at 83 m/s) [-]

Total boundary layer height [m]

Growth rate Number of boundary layers

0.1 – 0.5 43.4 0.05 1.25 15

30

3.3 Solver Setup

The segregated solver is chosen prior to the coupled because previous experience has revealed that solutions can have problems to converge properly using the coupled solver. Cell Remediation tool is used to remove cells with bad quality in the mesh by giving free slip faces to the bad cell. All y+-wall treatment provides low y+ wall treatment where y+ 0 and high wall treatment where y+ > 30. As described in 3.2 Mesh, the feature provides an approximation of the boundary layer flow where mesh resolution is too coarse to resolve flow accurately. The Standard temperature (25 celsius) and pressured (1 atm) air travels at 83 m/s with compressible option selected for the solver as the speed is just slightly below 0.3 mach were compression starts to have more influence on the outcome of the flow. The additional feature of compressibility adds some extra time per iteration but is considered affordable. The decision can also be supported by the mach plot shown in the appendix figure A.2. The SST (Menter) turbulence model is chosen because it is recommended for external aerodynamics [1]. Since the level of detail of the project is pretty rough, the convergence criteria does not need to be excessively fine. The residuals are not only considered to determine whether a solution is valid or not. Coefficient of drag, lift and angular momentum are also monitored until they reach converged state. The residuals are considered to the length that they should be stable and coefficients are permitted to vary in 5% over 1000 iteration interval and can be seen in appendix figure A.3-5. Some angles cause the solution to oscillate as figure 3.12 shows. First at hand one would assume the setup to be insufficient. But as other angles converge perfectly fine an explanation could be that the mesh is resolved well enough to detect that the flow does not have a steady state solution. This will result in fluctuating solution for the steady state with questionable reliability [7], and unfortunately indicates the need of a transient solver.

Figure 3.12. Oscillating coefficients due to transient flow.

31

4 Results and Discussion

4.1 Drag and Lift Plots of lift by drag are used to visualize the aerodynamic attributes of an aircraft. From the figure 4.1 it is possible to determine the highest lift capacity and best lift to drag ratio. The plotted coefficients from both velocities show that most lift is acquired around 35 degrees of pitch. The different velocity samples correspond quite well for all pitch degrees except for 40. The sweet spot in wingsuit context is supposed to be around 30 degrees which is confirmed by looking at the graph where most lift is available. While lift is necessary to stay in the air, the lift to drag ratio seems to be higher at pitch angles around 15 degrees. However it can be seen in the lift force coefficient equation (2.11), assuming all other inputs are constant, that it would require higher velocities or a density drop for 15 degrees to provide the same lift force as for 30 degrees.

Figure 4.1. Drag to lift plot with 83 m/s and 40 m/s samples shows different values at 40 degrees pitch. The reason why the 40 degree velocity samples split up is because the flow is separated for the 83 m/s case but still attached in the 40 m/s case. Velocity plots of the two cases show a significant stagnation at the trailing edge at 40 degree pitch, but not at 35 degrees, seen in figure 4.2. Though caution must be taken when considering theses high pitch flow as RANS has been predicted to be inaccurate and confirmed having trouble to converge these cases [7].

32

(a)

(b)

Figure 4.2. Velocity plots of symmetryplane profile for 40 degree pitch at 40 m/s (a) and 40 pitch at 83 m/s (b). From 45 degrees and above the lift is dropped for both cases and the difference in samples between the velocities at the remaining samples at 45 to 75 degrees pitch could be a consequence for the oscillating solutions. Still, the motivation of the study is not exact numbers, but character like increasing or dropping moment or force patterns.

33

4.2 Line of Action Drag and lift are the two forces measured for the symmetric pitch investigation. When summing these into one resulting vector you will get the line of action. Plotting the line of action through the pitch angles gives you an idea of how the forces act on the pilot. The aerodynamic force direction is mapped in a sequence of normalized force vectors in figure 4.3. From 45 degrees and above, the vector direction has little change.

Figure 4.3. Line of action with respect to the centre of mass in a pitch angle sequence at 83 m/s. The line of action at 0 degrees is positioned outside the region of the model. A flat plate would have a force aligned with the direction but because of the enhanced lift features of the wingsuit shape it provides lift even at 0 degrees. The force vector moves toward the centre of mass with each increase from 0 to 15 degrees. It is possible to observe that from pitch angle 15 to 30 there is little distance between centre of mass and line of action and if centre of mass or line of action was to be moved it could end up switching sides with the line of action, which would make the moment to switch direction and become deflecting. Fact is that the position of centre of mass can differ several centimetres between individual samples [6] and limb movement will also have effect on the positioning of the mass centre. But moving limbs would also have effect on the aerodynamics of the model and would require some extensive further research in terms of parameter studies to yield any perspicuous conclusion.

34

4.3 Pitch The moment shows a steady increase from 10 to 90 degrees in figure 4.4. The angular acceleration is very high but strictly positive. The stall is indicated by a drop in moment from 35 to 40 degrees as we established earlier that this interval experiences a big drop in lift which, combined with the drag, is the cause of the moment and therefore will presented a decrease of it. There are no obvious unstable tendencies to point out with the moment constantly positive the resting point of the model is yet to be found. A resting point is indicated where the moment start at a negative value and become positive as the corresponding angle increased. At the intersection, the moment would counteract displacement in both angle directions.

Figure 4.4. Pitch moment with respect to pitch angle.

From 0 to 10 pitch’s degree there is a drop in angular acceleration and the reason why the moment is dropping could be because the arm segments catch the stream on the top side rather than bottom side. The event is caught in a pressure plot in figure 4.5 were the under pressure at the top of the arm segment in the 30 degree case but not for the 0 degree case. The flow which occurs in the 0 pitch degree case is most likely not in line with what happens in reality. In a 0 pitch scenario the dynamics of the wingsuit material would align it more to the flow denying air to enter the intakes and thereby allowing the inflation to decay. The aerodynamic properties of the model seize therefore to agree with reality between 0 and 10 degrees pitch which will be taken into account in the conclusion of this study.

35

(a)

(b)

Figure 4.5. Pressure plot around arm segment profile at 0 degree (a) and 30 degree (b) pitch angle.

36

One should keep in mind that the velocity in question is extremely high and the force coefficient equations (2.10) and (2.11) show that the forces grow exponentially by with every increase in velocity. Which means at normal speed, about 40 m/s i.e. half of the current speed, the forces and moments would reduce to a fourth from the previous values. However, a condition to this statement is that the flow must be consistent between the cases which means that it is valid only between 0 and 35 degrees pitch were both flows are still attached to the top surface of the wingsuit. Never the less, an oversize of the leg wing is implied as the pitch moment is strictly positive and growing with pitch increase. If this is a consequence of the model being broader than the real wingsuit it is hard to say. But looking at video material one can observe the knees of the pilot are often bent which will decrease the amount of lift produced by the leg-to-leg segment, and thereby imply that excess in pitch moment is actually present in real flight too.

4.4 Yaw When the yaw angle, β, is investigated there is a significant increase in roll angle acceleration for both α = 30 and 60, while pitch and yaw acceleration remains fairly stable. All moments are restabilizing.

(a) (b)

Figure 4.6. Plots of angular accelerations with respect to yaw angle displacement at 30 degree (a) and 60 degree (b) pitch. In comparison, yaw acceleration is not making big appearance in any case and it is hard to determine whether it will have any significant impact, see figure 4.6. However, when displacing the wingsuit in β the angular roll acceleration seems to be affected considerably. In (a) the roll acceleration exceeds pitch acceleration, but not in (b), which means that high pitch lowers the moment around the roll axis when there is a yaw displacement. Further investigation is performed by looking at pressure plots over the wingsuit surface, revealing the pressure distribution.

37

(a)

(b)

Figure 4.7. Pressure plot of the wingsuit at 30 pitch/50 yaw (a) and 60 pitch/50 yaw (b) with top view

to the left and bottom view to the right. A reason to this is presented when looking at the pressure plots at in figure 4.7. The pressure distribution at the bottom side does not show any significant difference. The pressure magnitude varies between the two but the pattern, i.e. distribution, is similar. The top side, on the other hand, shows a remarkable deviation of the pressure pattern between the two cases most likely caused by stalled flow at α = 60 creating a more uniform pressure over the entire top side.

38

4.5 Roll The roll angle, γ, investigation shows decreasing pitch acceleration at γ = 20 to 50 for both pitch cases, in figure 4.8, but initially an increase in γ, which in this case will act as a re-stabilizing moment and forces the wingsuit to decrease in γ. Pitch and yaw acceleration also act restabilizing.

(a) (b)

Figure 4.8. Plots of angular accelerations with respect to roll angle displacement at 30 degree (a) and 60 degree (b) pitch. The reason why the γ -increase produces more roll acceleration at α = 60 , figure 4.8 (b), compared with the β study, in figure 4.6 (b), is because the roll movement aligns the wingsuit more to the air stream which allows the flow to reattach on the top side and produce more roll moment, viewed in figure 4.9.

39

(a)

(b)

Figure 4.9. Pressure plot of the wingsuit at 30 pitch/50 roll (a) and 60 pitch/50 roll (b) with top view to the left and bottom view to the right.

40

4.6 Asymmetry The asymmetric geometry is expected to generate some angle acceleration in roll and yaw, but what is noteworthy is that the roll acceleration switches to negative direction when α > 30, seen in figure 4.10. Since γ = 0, both negative and positive angular acceleration indicates deflecting character which states the wingsuit to be divergent in the current event. In a real event the switch of moment direction might be problematic for the pilot to counter act.

Figure 4.10. Plot of angular accelerations to pitch angle for asymmetric and symmetric model.

The yaw plot shows a slight moment in positive moment counter-clockwise viewed from the top. This moment is modest in relation to pitch but the following yaw displacement it causes might lead to increased roll moment, judging from the yaw displacement study in figure 4.6.

41

A pressure overview of the 15 degree sample in figure 4.11 (a) reveals that the lowered right hand results in slightly higher pressure at corresponding arm wing top side implying to push the right side down and produce roll moment in the positive direction. The asymmetric modification responds in the opposite manner at 45 degrees pitch, decreasing pressure at right wing top surface, indicating negative roll moment. The bottom sides shows very uniform pressure distributions for both cases and are hard to determine whether they are producing any forces contributing to the roll moment.

(a)

(b)

Figure 4.11. Pressure plot of asymmetric wingsuit with pitch at 15 degrees (a) and 45 degrees (b).

42

5 Conclusion The investigation has aimed to determine whether the shape of a stiff generic model of the Apache wingsuit has a divergent stability problem. The highest lift coefficient is found around 35 degrees of pitch but the best lift to drag ratio is found at the small angles. Because both lift and drag coefficients are relatively small at low pitch angles, it requires higher velocity to gain the necessary lift to counteract the gravity force. Displacement of yaw at 30 pitch proves to have major affect of increase in roll moment, although the yaw acceleration itself was restabilizing. At 60 degrees pitch the roll moment did not increase as much when increasing yaw angle. A possible explanation could be that high pitch relieves some moment through stagnation, distributing wake pressure evenly at the top side of the wingsuit. Displacement of roll showed lowered pitch moment but restabilizing character by all moments. The lowering of pitch moment can be explained by the roll motion aligning the wingsuit with the air stream, leaving less profile area to produce moment. Not very surprising, the asymmetric model showed distinct deflecting roll characteristics when running the pitch analysis. The small moment of inertia for roll allows moment more impact on angular acceleration than for yaw and pitch, which concludes that asymmetric movements could induce aggressive roll acceleration at high velocities. Whether it is possible for the pilot to react in time to handle the rotations is not possible to determine without further studies with mechanics included. This study implies that if the wingsuit starts from a stable symmetric position it remains stable. But at events such as jumping out of the plane or performing aerobatics when the wingsuit could initiate at an asymmetric position or angle the following would include large rotational forces which very well could disorient the pilot. Due to the stiffness in the model, low pitch angles may give misleading results because the wingsuit is generated from cases where the Apache is flow with pitch angle more than 10 degree. At lower degrees the wing segments will adapt to the air stream and loose camber. Neither will inflation work because there requires higher pressure on the bottom side which is generated through a higher angle of attack. The uncertainty of the wingsuit shape leaves a big question mark whether this study correlates with the actual event. An interesting future project would be to validate the model through acquiring the actual shapes at specific angles and also to perform experimental studies to compare with the model. Due to the oscillating solution further studies would be appropriate to perform in transient solvers to investigate time depending phenomenas. Whether the oscillations indicate flutter is not possible to determine from the oscillating steady state solver. As far as the study goes, regarding different angles of roll, yaw and pitch at 300 km/s, there are no divergent tendencies to the symmetrical Apache wingsuit model.

43

6 Future work

Suggestions of future modifications of the model would be to reduce or reshape the flap of the leg-to-leg wing. Its is highly doubtful that it maintains its shape when subjected to high pressure forces, as it does not have any rigid support other than the inflation. Modifying the flap would possibly lower the pitch moment and possibly produce a more agreeable result. An even better option would to obtain the real wingsuit shape at a specific flow. Studies have shown that airplanes with forward swept wings can endure higher angle of attack than regular ones with backward swept wing [11]. An interesting modification to investigate would be a reduction of the leg wing width and to increase the arm wing to give the wingsuit a shape more similar to a forward swept winged airplane, demonstrated in figure 5.1.

Figure 5.1. Suggestion of modification to resemble forward swept wing for the purpose of improved high pitch handling. A transient RANS, Large Eddy Simulation or Detached Eddy Simulation should be performed to capture the true events in stalled flow, considering the fact that steady state RANS solution does not appear to be appropriate for separated flow. The investigation struggles to show any reason to instability. It does however imply that steady RANS produces results with considerable relevance in the interval between 10 and 35 degrees pitch, where the flow remains attached and the shape of the wingsuit agrees with reality in terms of inflation and deformation. With previous statement, the investigation model proves satisfactory in predicting glide properties of the wingsuit at normal flight angles which could work as a tool to localize and develop such desired properties of the wingsuit.

44

Appendix

Geometry

Figure A.1. Morphed and unmorphed geometry.

45

Solver Setup

Figure A.2. Mach plot of top side wingsuit, 35 degree pitch at 83 m/s showing big areas subjected to

velocities above 0.3 mach.

Figure A.2. Coefficient plot for symmetric case 35 pitch at 83 m/s.

46

Figure A.3. Zoomed coefficient plot for symmetric case 35 pitch at 83 m/s.

Figure A.4. Residuals for symmetric case 35 pitch at 83 m/s.

47

Calculations and Tables Table A.1. Moment of inertia [6] Ix = 61.3 kg m2 Iy = 185.2 kg m2 Iz = 243.3 kg m2

Table A.2. Reynolds number

Dynamic viscosity μ = 18.27 · 10-6 [kg m/s] Free stream velocity v = 83 [m/s] Characteristic length L = 1.95 [m]

Density ρ = 1.184 [kg/m3] Reynolds number Re = 10 488 801 [-]

Table A.3. Mesh validation

Cells CL CD My [Nm] Average y+ Base Size [m] 2 M 1.1 0.61 -1624.79 33.3 1 4 M 1.37 0.58 -1395.72 43.7 0.04 8 M 1.37 0.58 -1356.18 43.4 0.01 16 M 1.38 0.58 -1320.7 24.5 0.005

48

49

References [1] H.K. Versteeg, W. Malalasekera. An introduction Computational Fluid Dynamics - The Finite Volume Method, second edition. [2] Adapco. STAR-CCM+, Version 6.06.017. [3] Raymond L. Bisplinghoff, Holt Ashley, Robert L. Halfman. Aeroelasticity 1996. [4] Richard von Mises. Theory of Flight, 1959. [5] Nor E. Ahmad, Essam Abe-Serie and Adrian Gaylard. Mesh Optimization for Ground Vehicle Aerodynamics 2010. [6] NASA. Anthropometry and Biomechanics, Volume I – Section 3. [7] R. Wokoeck, A. Grote, N. Krimmelbein, J. Ortmanns, R. Radespiel and A. Krumbein. RANS Simulation and Experiments on the Stall Behaviour of a Tailplane Airfoil [8] Tony Wingsuits. www.tonywingsuits.com [9] ANSA. Version 13.2.0. [10] Ignazio Maria Viola. Downwind sail aerodynamics: A CFD investigation with high grid resolution. [11] NASA. X-29 Ship #2 in Flight at an Angle that Highlights the Forward Swept Wings. http://www.dfrc.nasa.gov/gallery/Photo/X-29/HTML/EC90-039-4.html