Motorcycle Cornering Improvement: An Aerodynamical Approach based on Flow Interference

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Motorcycle Cornering Improvement: An Aerodynamical Approach based on Flow Interference

A Master Thesis in Fluid Mechanics

Author: Vojtech Sedlak

Supervisor/Examiner: Alessandro Talamelli Technical Advisor: Stefan Wallin

Department of Mechanics and

Department of Aeronautical and Vehicle Engineering

Royal Institute of Technology

KTH 2012

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After a brief overview on why standard downforce devices cannot be used on motorcycles, the new idea is introduced and a simplified mechanic analysis is provided to prove its effec- tiveness. The concept is based on the use of anhedral wings placed on the front fairing, with the rider acting as an interference device, aiming to reduce the lift generation of one wing.

Numerical calculations, based on Reynolds-averaged Navier-Stokes equations, are performed on simplified static 2D and 3D cases, as a proof of concept of the idea and as a preparation for further analysis which may involve experimental wind-tunnel testing. The obtained results show that the flow interference has indeed a significant impact on the lift on a single wing. For some cases the lift can be reduced by 70% to over 90% - which strengthens the possibility of a realistic implementation.

Abstract in Swedish: Sammanfattning

Ett nytt aerodynamisk koncept som nyttjar effekter av flödesinterferenser är utvärderat i syfte att p˚a ett noterbart sätt förbättra en roadracing-motorcykels kurtagningsmöjligheter.

Efter en kort genomg˚ang av varför diverse klassiska “downforce” lösningar ej är applicerbara p˚a motorcyklar, presenteras det nya konceptet. Varp˚a en mekanisk analys genomförs i syfte att se över dess tillämpbarhet. Konceptet bygger p˚a anhedrala vingar som placeras p˚a den främre k˚apan, där föraren agerar som ett interferensobjekt, och försöker störa ut lyftkraften som den ena vingen genererar. Numeriska beräkningar baserade p˚a RANS-ekvationer är utförda i förenklade statiska 2D och 3D fall. Som ett vidare steg rekommenderas vindtun- neltester. Resultaten visar att flödesinterferenser är ytterst märkbara för vingar och i vissa fall kan lyftkraften reducerats med 70–90%. Detta förstäker möjligheten för en realistisk implementering.

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Nomenclature

Symbols

Aw area of a wing [m²] bw half-span of a wing [m²]

C_d, C_D drag coefficient for 2D, 3D case [-]

C_f friction coefficient [-]

C_I interference coefficient [-]

C_l, C_L lift coefficient for 2D, 3D case [-]

c_r airfoil chord length [m]

dc diameter of interference device[m]

F , F~ force vector, force [N]

g0 sea level gravity constant, 9.81 [m/s²] K turbulence kinetic energy [m²/s²] k number of fundamental dimensions [-]

l∗ viscous length scale [m]

M , M~ moment vector, moment [Nm]

M_∞ free stream Mach number [-]

m mass [kg]

m₀ mass motorcycle [kg]

m_r mass rider [kg]

N normal force [N]

n number of independent physical variables [-]

P mean static pressure [N/m²] p static pressure [N/m²]

p⁰ fluctuating pressure part [N/m²] R, R~ reaction force vector, reaction force [N]

rc radius of a corner [m]

~

r distance vector [m]

Recr Reynolds number for an airfoil chord[-]

Re_L Reynolds number for specific lenght[-]

S_ij mean strain rate tensor [s⁻¹]

T temperature [K]

U mean velocity [m/s]

u⁰ fluctuating velocity part [m/s]

uτ friction velocity [m/s]

v velocity [m/s]

xc position of interference device in x-direction [m]

yc position of interference device in y-direction [m]

yn wall-distance [m]

y+ normalized wall-distance [-]

α angle of attack [^◦] δij Kronecker delta [-]

µ dynamic viscosity [kg/(m s)]

µs static friction coefficient [-]

ν kinematic viscosity [m²/s]

ν_t turbulence eddy viscosity [m²/s]

Π dimensionless product [-]

Π_count number of dimensionless products [-]

ρ density [kg/m³]

τw wall shear stress [N/m²] φwing anhedral angle of wing [^◦, rad]

ϕlean lean angle of motorcycle [^◦, rad]

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Acronyms

CAD Computer Aided Design CFD Computational Fluid Dynamics

FIM F´ed´eration Internationale de Motocyclisme

FL Finish Line

RANS Reynolds-averaged Navier-Stokes equation VLM Vortex Lattice Method

Constant values

To avoid any misconceptions, due to different definition-style in various literature, following values yield throughout this document. They are mainly based upon the standard values provided by Ansys Fluent.

g0 9.81 [m/s⁻²] ρ_∞ 1.225 [kg/m³]

µ_∞ 1.7894e-05 [kg/(m · s)]

T∞ 288.16 [K]

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Chapter 1

Introduction

A first thing to identify is what motorcycle type should be subjected for improvement.

Clearly when aerodynamics is the topic, the fast going road racing machines are the ones with most to gain. The road racing motorcycle is a definition that includes all types of motorcycles that may compete by doing laps or sprint races on paved, closed down, purpose built race tracks. These tracks have a high number of corners, thus making cornering speed and agility a key element for success.

Within road racing, there are several different categories in which motorcycles may compete.

Mainly there are two premier classes. One that is referred to as MotoGP - a category purely focused on prototype racing with less strict regulations in an attempt to encourage creative thinking and development. The other category is Superbike World Championship where the focus is to get as much racing for as small cost as possible. This results in production bikes that are heavily regulated.

As this thesis aims to provide a plausible aerodynamic cornering improvement, the aim is to be within the more lenient MotoGP regulations. However, the aim is not to present a final concept, but merely to provide some basic analysis whether the idea is at all realistic or not.

1.1 Early History of Motorcycle Aerodynamics

In the early years much of the focus regarding aerodynamics for motorcycles, was simply focused on streamlining. And very much so, various concepts that were brought to light, would challenge different speed-records of the day. The idea was basically to create a tear- drop shaped faring that would cover the rider as much as possible. They also tried to build the motorcycle as low and narrow as possible to reduce the frontal area.

Figure 1.1: Left: In early 1950’s the typical “dustbin” fairing were popular as shown by Giulio Carcano’s Moto Guzzi. Right: In 1957 FIM banned these types of fairings and the

“dolphin” shape quickly became the norm. [5]

However, these massive fairings turned soon out to be dangerous in crosswinds and cumber- some when cornering. It soon became clear, that to make fast and safe motorcycles, which

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can go around twisting race tracks, many other considerations had to be taken into account.

This led to motorcycles with more open, yet sleek, fairings. A concept which seems to have stood the time, since the basics layout, appears to be similar to even todays machines.

Knowing this, raises the question whether the industry is reluctant to change or if this basic concept is actually so good, that any radical changes will most likely fail. What is known, is that countless attempts have been made to improve on this classic design. How many and with which ideas, is something one can only speculate, since these sort of things are usually close guarded secrets.

1.2 Focus on cornering

It is clear that if one would find a way of how to improve cornering, the advantage would be substantial. A typical MotoGP track consists of a high number of sweeping corners. Even the majority of road sections that are between corners, that may look like straights, are actually no real straights since the motorcycle has to prepare for the next corner right away.

In section 2.3, an example is given of the traditional racing track TT circuit Assen. Notice how turn 1 to 4 can be considered as a one sweeping corner.

Cornering can obviously be improved by aerodynamic means. Placing a wing that creates negative lift (downforce) increases the normal force, thus enabling the static friction force to reach higher values.

v [km/h]

C = –2_L Influence of Lift coefficient during Cornering

on a vehicle for unbanked turns

r [m]_c

C = –1_L

C = 0_L equation: μ mg – C ρ v A =s 0 L ∞

(

¹2 ²

(

mv r_c

2

values: μ = 1 m = 600 kg A = 1.47 m

s

2

50 100 150 200 250 300

100 200 300 400 500 600

w

Figure 1.2: Visualization of the great speed advantage a higher downforce can provide. In some cases the speed can be more than doubled.

In figure 1.2 an example is given where a simplified vehicle is cornering at various corner radii. The figure shows that if the downforce is increased (CL= -2) the vehicle may go more than twice as fast through corners with low curvature.

There are some radical concepts that have been implement in the past, based on this way of thinking and some of them reached the public attention and curiosity. One of these concepts was conceived by a university student, Rodger Freeth in 1977 (figure 1.3). He added two horizontal wings, in the front and back with the hope that it would create extra downforce on the tires in mid-turn, to improve cornering speed. The largest wing was placed behind the rider, mounted on the back of the rear sub-frame and had a span of 700 mm with a chord of 245 mm. The front wing was attached to the lower fork sliders and had a span of 660 mm and chord of 130 mm. [10]

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Figure 1.3: Rodger Freeth and his concept “Aerofoil Viko TZ750A” from 1977 [10]

Naturally, when a motorcycle is leaned into a corner, this wing will generate negative lift (downforce) at the angle at which the bike is leaning. This will not only generate a vertical force component which will make the bike stick to the ground. It will also add to the lateral force component, pushing the bike of the track. Perhaps back in 1977, when Freeth was racing his bike the lean angles were not so great, maybe not even scraping his knees. Today these lean angles can typically reach over 50^◦. In such case the lateral force component becomes greater than the desired vertical one. On top of all that this concept got banned by the controlling body, due to the great risk of entanglement in close racing.

As many have pointed out over the years a far better concept would be to mount the wings on a gyroscopic tilting device. Thus making sure that no matter what lean angle, the wings would always be parallel to the ground. This way the lateral force component would be eliminated. Even if such device would be allowed, the placement would remain a problem.

It is important to place the wings in the undisturbed free-stream. That would mean either placing it above the bike or on the sides. The bike itself is usually about ∼500 mm wide (excluding handlebars), so to put them on the sides would add major width (since they have to be of a significant size). On top of all that they would have to be movable, which adds additional level of complexity to the design and makes them unusable in competitive racing as MotoGP due to regulations (Appendix B).

Wing

Vertical force component Lateral force

component Tilting Wing

Vertical force component

Front/rear view Front/rear view

N

μ N

F_x

F_y

N

μ N

F_y

s s

Figure 1.4: These are the forces generated by a fixed- and a tilting-wing, during cornering.

The idea is that a tilting wing is stabilized and is always positioned parallel to the ground.

This way it would not produce any lateral force components.

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1.3 Serious Attempts on Wing Use

However, there are applications where small wings (or devices more similar to bulges) in the front of a bike can make themselves useful. It is when there is a need to reduce front-end lift at high speeds. A phenomenon which occurs due to the fact that a motorcycle always has a relatively high profile in the vertical direction compared to its wheelbase. Therefore a pitching moment, created by the drag of the airflow is far more noticeable than for e.g a low car. [5]

Figure 1.5: This type of front wing is made to reduce front-end lift. Here it can bee seen on Barry Sheene’s Suzuki RG500 from 1979. [10] [11]

This type of device can be seen on motorcycles as the BMW R100RS (1977) and on Grand Prix road-racing machines as the Suzuki RG500 from 1979 (see figure 1.5). This trend has apparently not made the desired impact, since this concept was dropped only a short time later, or at least Suzuki did not implement them on GP bikes the following seasons. Most likely, the trade-off was an inferior cornering ability, which simply was not worth it.

At the end of the 2009 season, in Sachsenring, Ducati introduced a similar concept. Here the wings were far more distinctive and placed in the front of the fairings. They also featured small winglets. The concept only lasted though the rest of that season and was abandoned after the next years pre-season testing.

Figure 1.6: From 2009 to 2010 Ducati attempted to use straight small wings at the front of the fairings. Unfortunately the idea was abandoned. [2]

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Regarding the Ducati wings, there are also some unofficial claims and speculations, that the mounting of such wings also creates a low pressure area where the radiator outflow is normally situated. This will then increase the flow through the radiator and helps the cooling. One can argue if there perhaps are not easier ways to achieve the same effect.

Another difficulty that aerodynamic concepts, as the ones mentioned, has to face is that eventually the rider is the one who has to feel all the advantages. This is the only way it may be added to the motorcycle and incorporated into the riding. A good example of how a good theoretical idea can end up in a blind alley is the Hossack suspension concept. It showed a lot of promise in theory. In the end it did not become a success due to its higher weight with combination of the riders dislike towards the different front-end feel. The thing is that riders spend most of their careers adapting, getting used to and trying to understand a certain system (e.g. telescopic-forks). A change can throw them of too much if the gain is not clear.

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Chapter 2

Project Overview

This thesis aims to present an idea – a concept – and provide initial estimations of what it might be like, when it has reached a prototype stage. As is usually the case, this idea is fairly simple in theory, but to attain it practically may be a bit of a challenge.

First stage will be to present an overall theoretical idea, on which this concept is build upon.

In a brief way it will show the advantages and the weak points. To give a quantitative first look, simple mechanical estimations will be given to see what can be achieved in an ideal scenario.

The main phase will then be to see if these mechanical goals can be achieved by the use of certain aerodynamic hypotheses. These hypotheses will be put to test in several CFD calculations and their prospective validity will be obtained and quantified.

Conclusively, all of the above considerations will be put together in a final concept. It will show what it is all about, but there will obviously be room for plenty of further improvements.

2.1 Concept

To begin with, when a motorcycle is cornering it will do so at a significant lean-angle. With the rider hanging-out, which is typically done to reduce the lean angle, the airflow around the rider and the bike becomes asymmetric.

On one side the flow is moving relatively smoothly and on the other, the rider acts as a sort of interference mechanism. The rides is interfering with the streamlined flow, making it deviate which in turn alters the resulting reaction forces. Since the flow is subsonic and acts in streamlines, it is highly sensitive to interactions occurring up and downstream.

The great thing about this is that in practically all motor racing, mechanically movable aerodynamic devices are prohibited. However the rider on a motorcycle, is to some extent movable and is affecting the flow around the motorcycle.

What this concept is all about, is that one could greatly improve cornering by placing highly anhedral wings on both sides of the motorcycle (see figure 2.1). Making sure they are placed close to the rider – at such an anhedral angle, when the bike is cornering, one of the wings will become horizontal and the other, vertical. This way, the horizontal wing is generating negative-lift (downforce) and the other one is adding to the unwanted lateral force.

However, with the rider acting as a movable interference device (see figure 2.2), the wing which is generating the lateral force, is now partially disturbed. Thus there will only be a small addition to the lateral force.

An important thing to note here is that the wings will have to be placed on the front fairing, after the radiator inlet and in front of the riders knee and/or elbow. To place wings behind the rider is not recommended due to low maximum width restrictions and the high risk of the rider getting tangled up in it during a crash.

When the motorcycle is going down the straight at full throttle, the increased drag on the wings will naturally deprive it of its maximum speed. The wings will however be of use during the acceleration and braking by pressing the front to the ground.

The most important question is, whether this interference effect is significant enough. A question which will be evaluated in this report.

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Front view Front view, while cornering

Anhedral wings on both sides

While cornering, one is horizontal

...the other one is vertical

Figure 2.1: The idea is to place anhedral wings on each side of the motorcycle, which will generate lift in the direction of the arrows. When the bike is leaned into a corner, ideally one wing is horizontal and the other one is vertical...

but, the rider may interfere the flow around the vertical wing

Figure 2.2: ...The rider will then interfere with the flow around the vertical wing, reducing the horizontal force component.

Furthermore, there are other areas which may have a crucial impact on the actual appli- cability. One of them is stability during transition from uninterfered state to a interfered one. The risk is that too sudden movements or changes of rider’s position may unsettle the bike. Similar risk may occur when the rider enters someone else’s slipstream. The slipstream problem is a well known phenomenon in F1 racing, at least a well debated one.

The solution there, seems to simply cope with it. To be aware, but not to concern too greatly.

Advantages:

- Downforce increased during cornering, i.e increased cornering speed.

- Acceleration improved by decreasing pitching and roll moment.

- Breaking distance shortened.

Downsides:

- Higher drag will reduce top speed.

- Interference effect may not be significant enough.

- Due to geometry restrictions, wings may have to be small in size.

- The motorcycle might get unstable when the rider moves into cornering position quickly.

- Slipstreaming may disrupt stability.

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2.2 Mechanical aspects

To get a more clear understanding of how this idea may be of use, a simple clarification of the mechanical forces is in order. What will be looked at is how the cornering may be affected with such wings mounted. This suggests that a 2D example with a frontal view of the bike is in order. Where the horizontal x-axis is pointing in the direction of the centripetal acceleration and the y-axis is the vertical component (see figure 2.3). The z-axis is pointing out of the plane and is only used to show the moment. To simplify things even more, straight line flow is assumed.

c0 = 600 c1 = 700

c2 = 800

c3 = 200 c4 = 70 b = 300_w

x

y φ_lean

F_m F_r

F_w2 F_w1

mass center motorcycle

mass center rider

downforce point 2 downforce point 1

r_r r_w1

r_w2 r_m ϕ_wing

N

M0

μ N_s

Figure 2.3: A simplified model of a cornering motorcycle.

This figure introduces a fair amount of variables which all follow a very simple system. All vectors denoted ~F contains forces in x and y direction and in the same manner, vectors denoted ~r contains positions. When trying to obtain the moment (see equation 2.11) the crossproduct of these two vector types will give the result.

The most fundamental force components are the ones acting on the bike and rider. These two forces could have been merged together, but it is more flexible to keep them separated should one desire to investigate other rider positions.

Force vector ~Fm is acting on the motorcycle and ~Fr on the rider. Both are affected by centripetal acceleration and gravity, only the mass is different. 160 kg estimated for the motorcycle [4, §2.5] and 70kg for the rider (it should be noted that some of the MotoGP riders weigh closer to 60 kg)

F~_m= m₀





−v²/r_c

−g₀ 0



 (2.1)

F~_r= m_r





−v²/rc

−g0

0



 (2.2)

For a standard bike – here, referred to as the “reference case” – these forces would be the only ones acting on it in this simple example (if one excludes resultant normal forces). A bike equipped with anhedral wings, will also get contributions from the force components caused by lift.

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F~w1=1

2CLρ_∞v²Aw





cos(φw1) sin(φw1)

0



 (2.3)

F~w2=1

2(1 − CI) CLρ_∞v²Aw





cos(φw2) sin(φw2)

0



 (2.4)

These equation introduce a new set of variables and to make estimations easier to follow, these are the values they have been set to.

Used values for wings C_L = 1.7 (lift coefficient)

b_w = 0.3 m (span of one wing-part) c_r = 0.2 m (root chord of the wing) A_w = c_r· b_w = 0.06 m² (area of one wing)

What differentiates the interfered wing with the other one is the interference coefficient CI. This variable may typically attain values between 0 and 1. Where 0 is no interference – the wing is generating lift in an undisturbed fashion. If the value reaches 1, the wing generates no lift, i.e. it is fully interfered. Further details are explained in section 3.1.

CI = ∆CL

CL

= 0 . . . 1

The angle for the uninterfered wing φw1and the interfered wing φw2 is the resulting angle of both the lean angle ϕlean and the anhedral angle of the wings φwing.

φw1= −ϕlean+ φwing−1

2π (2.5)

φw2= −ϕlean− φwing+3

2π (2.6)

It is clear that the above approach results in a complex geometry which can be significantly simplified. This can be done by creating a “center of pressure”. A point where all of the different lift forces intersect and can be converted into a single force (figure 2.4).

A new vector is formed ~Fw and replaces the old force vectors acting on the wings. This vector can be describes as a function of the lean angle and of the interference coefficient.

The ~F_w vector will then point from the center of pressure, r_cp, in a direction ϕ_cp.

F~_w= f (C_I, ϕ_lean) (2.7)

The problem here is that if the anhedral angle φ_wing is changed, both the position of the center of pressure r_cp will be moved and the angle ϕ_cp will be affected. Therefore, if one intends to keep the geometry fixed, the simplification by the use of center of pressure is suggested. In following sections however, different choices of anhedral angles are investigated thus making the initial setup more flexible, despite its greater complexity.

2.2.1 Calculations

To establish a resultant force, denoted ~F₀in the both the x and y direction is fairly straight forward. Summarize all the force vectors and introduce normal forces. The resultant force for a bike with no wings has the index “ref ”, suggesting it is a reference case. Equilibrium is reached when the resultant force, ~F₀ is equal to zero.

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c0 = 600 c1 = 700

c2 = 800

c3 = 200 c4 = 70 b = 300_w

rcp

x

y φ_lean

F_m F_r

F_w2 F_w1

mass center motorcycle

mass center rider

downforce point 2 downforce point 1

r_r r_w1

r_w2 r_m ϕ_wing

N

F = f(C ,φ )_w φ_cp

I lean center of pressure

M0

μ N_s

Figure 2.4: The same model with the use of center of pressure.

F~0,ref= ~Fm+ ~Fr+



 µsN

N 0



 (2.8)

F~0,concept= ~Fm+ ~Fr+ ~Fw1+ ~Fw2+



 µsN

N 0



 (2.9)

Next step is to set the equation for the moment. This way the roll-moment of the bike can be established. The result is simply obtained by adding crossproducts of distance vectors ~r and force vectors ~F .

M~_0,ref= ~r_m× ~F_m+ ~r_r× ~F_r (2.10)

M~0,concept=

~

rw1× ~Fw1+ ~rw2× ~Fw2

+ ~rm× ~Fm+ ~rr× ~Fr (2.11) These equations are then combined, solved and used for all of the following mechanical estimations in this chapter.

2.2.2 Evaluating the Effect of Interference

Primarily, the idea behind the anhedral wings is to give the motorcycle additional downforce. The downforce increases the vertical normal force N , which will give it the ability to go through a corner faster. It will also reduce the needed static friction coefficient µsif the cornering characteristics are kept the same.

Another interesting feature is that the anhedral wings can help to reduce the lean angle by generating a negative roll moment. It counteracts the moment caused by centripetal forces acting on the mass center of the motorcycle and the rider.

This advantage can give two different favorable outcomes. It can either let the rider go faster through the corner, yet keeping the same lean angle as the standard bike. A very useful advantage when going through very long sweeping corner (figure 2.5).

The other option is to maintain the same speed through the corner, but with the bike more upright thus enabling more aggressive throttle roll-on and braking, enabling faster entrance and exit of the corner. This is refered to in motorcycle terms as “squaring it off” (figure 2.6).

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v [km/h]

C = 1 (ideal case)I

C = I 0.9

C = 0.7 (realistic case)I

reference case Cornering speed over radius of curvature

at const. lean angle of 50°

r [m]_c

100 200 300 400 500

100 150 200 250 300

Figure 2.5: A noticeably increase of speed in long sweeping corners is noted if the interference effect is high. rc is the curvature radius of the corner.

0 10 20 30 40 50

100 150 200 250 300 350

v [km/h]

C = 1 (ideal case)_I C = 0.9_I

C = 0.7 (realistic case)_I reference case

φ [°]

Cornering speed over lean angle

at const. radius of curvature r = 600 m

lean

Figure 2.6: With a high interference effect, the lean angle is noticeably decreased.

A noticeable detail is the significant difference between the reference case and the concept bike, when reaching high speeds. This is simply due to the fact that a wing generates more lift when the dynamic pressure is higher. As a result the advantages of the wings becomes more apparent. Unfortunately at low speeds, where the bike usually does a lot of its cornering, the help of the wing is very small. A characteristic which all wings have in common and is far from ideal in any motor racing.

It is also clear that the higher interference coefficient CI we have, the better is the result.

If however the interference would not be there, i.e. CI = 0, the curve would be exactly the same as for the reference case. Even though there would not be a difference in moment, one has to take into consideration that these wings also affects the lateral force. With the the

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vertical wing undisturbed, the result would be far from favorable.

Here it is also suggested that value of CI = 0.7 is consider realistic. This has not been verified but it is nonetheless an unwritten goal in further chapters. If better values can be achieved it will only be favorable, but this value will be referred to when doing estimations.

2.2.3 Anhedral angle effect on Vertical and Horizontal Forces

An essential part of the wing layout is the selection of the anhedral angle. The initial proposal was to use an anhedral angle which matches the maximum lean angle of the bike, typically around 50^◦. A reason is that if the anhedral angle is too small, even the uninterfered wing will provide a certain negative lateral force component and work in a similar way as Rodger Freeth’s wing (see figure 1.3, left picture).

Too high anhedral angle and the downforce during straight line braking and acceleration will be reduced. Since the wings may not be mechanically movable (Appendix B), one has to make compromises.

Beginning with the vertical forces (see figure 2.7) it is clear that a high anhedral angle is far from the best choice. An interesting detail is also how all of these different setups have their own peak points regarding downforce. The very high anhedral angle setups naturally have their peak points far behind the maximum lean angle of the motorcycle.

lean

0 10 20 30 40 50

2300 2350 2400 2450 2500

N [N]

Vertical force on tires

at velocity 65 m/s (234 km/h), r = 600 m, C = 0.7

φ [°]

ϕ = 40°_wing ϕ = 50°_wing ϕ = 60°_wing reference case

ϕ = 70°_wing

c I

Figure 2.7: A high anhedral angle provides a lower vertical force component In this case the interference effect C_I has been kept constant at a realistic value of 0.7, but if reduced further, the peak point of the curve will move to the left and drop off very quickly.

For the horizontal force, however, the aim is to keep this force as small as possible (figure 2.8).

A lower horizontal force means less force pushing the bike of the track. In this case it is rather the setup with the high anhedral angle which shows best results. If CI would be reduced, all of the the curves would increase in value and cut the reference curve at a lower lean angle.

2.2.4 Overall performance

Thus far the force components and moments have been examined individually, showing different characteristics. The next step is to put them together so that a complete overview can be visualized.

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0 10 20 30 40 50 1450

1500 1550 1600 1650 1700

μ N [N]

Horizontal force on tires

at velocity 65 m/s (234 km/h), r = 600 m, C = 0.7

ϕ = 70°_wing

c I

φ [°]lean s

Figure 2.8: Horizontal component will be lower with a high anhedral angle.

A good way to illustrate the total advantage of a certain setup, is to look at the total static friction coefficient µs, which will keep one from loosing grip, when the friction force is at its maximum. If one can manage with a lower µs, one can conclude that the rider on that particular bike can use a bit worse or more deteriorated tires.

140 160 180 200 220 240

0.4 0.6 0.8 1.0 1.2 1.4

ϕ = 70°_wing Friction coeff. for different velocities

up to maximum lean angle (50°), r = 300 m, C = 0.7c I

v [km/h]

μ [-]_s

Figure 2.9: Comparing the speed and the friction coeff. required to go through a fast corner To bring this to a conclusion it is of interest to plot the friction coefficient over speed. This way all of the mentioned equations can be satisfied. The corner radius is 300 m which could be estimated to a 5th gear corner doing 230+ km/h through the apex. This scenario is similar to the 8th corner of the TT Circuit in Assen, which is mentioned in the upcoming section (see figure 2.11).

What one can tell from this, is that if one can go through the corner at the maximum lean angle, the reference bike is 9 km/h slower, and requires a bit higher static friction coefficient

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Figure 2.10: Jonathan Rea’s (WSBK) rear tire after race one in Misano 2010, shows great signs of deterioration. Notice that most of the deterioration occurs out on the edges of the tire, suggesting it has been exposed to very high loads at high lean angles. [3]

(better tires) to stay on the track. Since one may expect the tires to be completely finished after a race (which in MotoGP may last over 40 minutes), it should be considered a great advantage if one can stay competitive even on worse tires.

An important detail to keep in mind, is that this mechanical model is very simple, so no considerations has been taken to the fact that the friction coefficient changes over lean angle due to the shape of the tire. This model is only intended for comparison with the reference case.

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2.3 Speed estimation

A very important factor to clarify, is in which speed spectrum the motorcycle may typically travel, when doing a lap of a generic road-racing circuit, in this case TT Circuit Assen. This circuit has a good mix of slow and fast corners and will show what Reynolds numbers are relevant and what dynamic pressure one may expect.

Since the variation of speed is usually great it is helpful to divide it up in different categories.

A typical procedure is to split it up, to see which gear is used for which corner. That way one can separate the fast corners from the slow ones. Obviously this entire process is merely an estimation, but should provide general characteristics.

N

TT Circuit Assen

MotoGP 2012, Qualify, V.Rossi

1 2

3

4 5

6 7

8

9

10

11 12

13 14

15 16 17

18 19 20 21

#2:119 km/h

#4:195 km/h

#3:110 km/h

#3:116 km/h

#2:70 km/h

#4:219 km/h

#5:246 km/h

max 309

km/h

#4:162 km/h

#3:130 km/h

#2:111 km/h

#2:106 km/h

#3:153 km/h

#5:227 km/h

#4:184 km/h

#2:103 km/h

#2:143 km/h

max 240

km/h

max 285

km/h

max 291

km/h

Figure 2.11: Current gear and lowest corner speed at the TT Circuit Assen. The values are from Valentino Rossi’s qualify lap 2012. It was not his fastest lap, but shows the generic character of given sections.

TT Circuit Assen, 2012, qualify rossi

Corner Gear Speed

– 291 (max speed in section i1/FL)

1 2 119

2 4 195

3 3 110

4 3 116

5 2 70

7 4 219

– 309 (max speed in section i2)

8 5 246

9 4 162

10 3 130

11 2 111

12 2 106

13 3 153

14 5 227

17 4 184

18 2 103

20 2 143

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From previous table one can get an idea of the average speed for each corner-type based on gears and the minimum corner speed. This will give an estimation of relevant Reynolds number if the chord length of the used airfoil is cr= 0.2 m.

Summary of velocities for each corner type

Definition km/h m/s Re_c_r Comment

v_c2g 109 30.2 4.13e5 Average 2nd gear corner

v_c3g 127 35.3 4.84e5 3rd gear corner

v_c4g 190 52.8 7.23e5 4th gear corner

v_c5g 237 65.7 8.99e5 5th gear corner

2.3.1 Airfoil Selection: NACA 23015

v∞

x

y c_r

c_r

1 4

Figure 2.12: A standard NACA 23015 positioned upside-down.

This generic type of airfoil is good for low Reynolds numbers, especially around mentioned velocity regions. It has a small camber which gives it a very standard feel, with a typical stall point at 14^◦. Another advantage is that it is a very well tested airfoil and offers no surprises. Simply ideal for initial test cases when one would like to test the validity of a theory. Following velocities were obtained from available Reynolds numbers. [1, pp500-501]

Summary of available velocities for NACA 23015

Definition Re_c_r km/h m/s Comment

v_ref1 2.6e5 68.4 19.0 ∼1st or 2nd gear corner speed.

v_ref2 6.0e5 157.8 43.8

v_ref3 8.9e5 234.00 65.0 ∼5th gear corner speed.

The vref3 is particularly interesting due to the fact that that will be the speed region where the anhedral wings will be most helpful. For those reasons it is extensively used throughout this document.

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Chapter 3

Problem Specification

In the previous chapter it has been concluded that there is much to gain from a concept utilizing anhedral wings in terms of improved cornering. What has also been concluded, is that this concept fully relies on whether the flow around the wings can be interfered.

The greater this change, between a normal and an interfered wing, can be made, the more substantial will the effects of this concept be.

As a result of this, the main focus of this work will be to fully identify the effects of the interference. By knowing what causes it and how it can be fully maximized, a well working concept can be derived.

To archive this the best approach is to start with a very simple static examples and identify all the variables that are important.

3.1 Identifying Variables - The Buckingham Pi Theo- rem

First question one may ask when trying to quantitatively identify the cause of a certain effect, is which variables it depends on. Then the next step is to isolate them , except for one variable – which is being systematically manipulated. This manipulation will reveal the cause and effect of the specific variable.

In this case there is a body which is being subjected to aerodynamic forces. The body is in the most simplified case, an airfoil or a wing and some device which is interfering the wing.

This device will in this text be referred to as an interference device and will in its most simple case be modeled as a cylinder (sized approximately as a human knee to represent the rider).

These aerodynamic forces can be simplified to a one single force, a reaction force ~R. [7, §1.7]

R = f (ρ~ _∞, v_∞, cr, µ_∞, α, dc, xc, yc) (3.1) This force is then a function of several different physical variables. Many of them may look very familiar, apart from the last 3 ones. These are related to the interference device and are the size dc (which may be the diameter size if the device is a cylinder), position in x-direction xc and y-direction yc.

The strength of the Buckingham Pi Theorem is that both the amount of independent variables can be reduced and they can also be made dimensionless which will significantly simplify further calculations.

A first step is to rearrange the previous equation (3.1) so that the function equals 0. This results in a new function definition.

g(ρ_∞, v_∞, c_r, µ_∞, α, d_c, x_c, y_c, ~R) = 0 (3.2) Now the new function also depends on the reaction force, thus there is a total of 9 independent physical variables. This amount is here referred to as n, i.e. n = 9.

The other value k, equals the number of fundamental dimensions. In mechanics, all physical variables can be expressed in terms of the dimensions of mass, length, and time. Thus the value k = 3.

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This gives a relation for the amount of dimensionless Π products.

Πcount = n − k = 6 (3.3)

By setting up and solving all of the 6 dimensionless Π products it is possible to obtain a coefficient of the reaction force. The exact procedure is well explained in literature. [7, §1.7]

CR= f

Rec_r, M_∞, α,dc

cr

,xc

cr

,yc

cr

(3.4) The same procedure can be done for the other coefficients, of lift, drag, moment etc.

CL = f

Rec_r, M_∞, α,dc

cr

,xc

cr

,yc

cr

(3.5) CD= f

Rec_r, M∞, α,dc

cr

,xc

cr

,yc

cr

(3.6) CM = f

Recr, M∞, α,d_c cr

,x_c cr

,y_c cr

(3.7) This paves the way for the definition of the Interference coefficient. It has been said that this coefficient simply goes, in most cases between 0 and 1. Here it becomes clear that the definition is a bit more complex.

C_I =∆CL

C_L (3.8)

It is defined as the change of lift coefficient ∆CL, divided by the lift coefficient CL of the uninterfered wing. The ∆CLrepresents the difference in lift coefficient between the interfered and uninterfered wing.

The interference coefficient may typically go between 0 and 1, but is not limited to only that. If the values are negative it will mean that not only has the reduction of lift failed, but it has done the complete opposite – it has made it increase. Assume on the other hand that the value is larger than 1. This will mean that not only has the wing been completely interfered, but now a lift force, going in the other direction has been created. This latter effect may never happen for wings at high angles of attack with high lift coefficients, but rather for wings generating low lift in the uninterfered state.

3.2 Problem Overview

As the variables are identified, the next step is to have a plan on how to proceed. The best thing to do would be to make a model and test it in a wind tunnel. This is however a great undertaking which may consume a lot of time. Therefore it is a good idea to start with some calculations and establish if this idea works in theory.

First thing to notice that this problem is in the region of high Reynolds numbers. Assum- ing the chord of the wing is 2 decimeters, the Reynolds numbers may vary from 200 000 to up over 1 million (see section 2.3). This with the combination of a bluff body, the rider, interfering the aerodynamic device, the wing, results in an unsteady problem. What this means is that there are no analytical solution methods that can be used on this problem.

The approach is naturally use some form of numerical method on both the continuity equation and Momentum equation, also known as Navier-Stokes equation. The Energy equation is not needed, since we can assume incompressible flow due to low Mach numbers. A good choice is to use the Reynolds-averaged Navier-Stokes equation which is a time averaged momentum equation that uses Reynolds decomposition. The turbulence model was chosen to be Spalart-Allmaras which is a very simple model, yet sufficient since the main task is to determine lift and not drag.

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Wind tunnel

idea Calculations

• Reynolds Number too high

• Unsteady problem

• No analytical solution

RANS

• Good for lift estimations

• Can not resolve drag correctly

Fluid Domain

• Domain size restrictions

• Cell count restrictions

Simplifications

• Focusing only on the principle

• Setting up a static problem

Proof of Concept

Numerical Methods

To be on the safe side, key points have been solved using a more advanced viscous model, the SST (Menter’s Shear Stress Transport).

As a numerical approach is used it also means that a fluid domain has to be defined and meshed. This brings limitations to both the sizing of the domain and the amount of cells that can be computed.

All the limitations mentioned will force one to try simplifying the problem as much as it is possible and only focus on the basic principles. This also means to set up a static problem even thou we know that the real problem will be a dynamic one. The rider is moving into the interference position and this movement could cause some Hysteresis effects. For now one may neglect such effects to see if the concept even works at this stage.

3.3 Predicting Near-wall Cell Size

The following section may be considered as slightly unnecessary, due to the fact that the aim of this project is not to resolve any turbulent vorticity which is needed for any accurate values of drag. However it is a good idea to have the knowledge of the desired mesh sizing and to know how far off, the actual mesh is.

To figure this out one may evaluate the mesh grid type, which is used to resolve the viscous sublayer, and to consider the normalized wall-distance, y+.

The normalized wall-distance can be expressed as a ratio between the wall distances ynand the inner viscous length scale l_∗. At the first grid cell, y+ needs to have the value of 1. [6,

§12] [14, L06] If this can not be achieved the grid should be remeshed.

Since the inner viscous length scale can be rewritten as kinematic viscosity divided by friction velocity, the equation becomes as following.

y+= y_n

l_∗ = ρ_∞u_τy_n

µ_∞ (3.9)

Where the u_τ is the friction velocity, defined by the wall shear stress, τ_w. Also note that the kinematic viscosity has been replaced by the dynamic viscosity µ_∞ divided by density ρ_∞ to prepare the equation for further steps and also because these specific variables have known values.

u_τ=r τw

ρ∞

(3.10) The wall shear stress, τw can be obtained from the friction coefficient, Cf, which in turn can be found in various literature. The one here is for the skin friction of a plate. [14, L06]

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τ_w=1

2C_fρ_∞v² (3.11)

Cf = 0.058Re^−0.2_L (3.12)

Re_L =ρ_∞vL

µ_∞ (3.13)

With following values, y+ = 1

v = vref3

L = cr

Then the yn = 5.19e-6 m. In the preliminary 2D test-case (chapter 5) the value that has been used is 1e-5. In the following 3D case the first grid cell has a size of 5e-6, but here the inflation (or prism-layer as it is called) uses wb-exponential growth rate which has a bit different characteristics. The total thickness of the inflation layer is about 1 cm. [15, L5]

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Chapter 4

Numerical Approach

The solver for the fluid dynamics part in this study is Ansys Fluent. A platform used by many companies in the automotive industry which makes it the ideal working tool. It provides a wide variety of different solver settings which will be considered.

An important thing to note is that the author only has access to one workstation and not a powerful cluster of any kind. This somewhat limits the number of details, precision and the amount of different types of calculations that can be made. Fortunately the task is to investigate lift and not drag, which means that a coarser mesh and lot more simple calculations are required.

4.1 Work Flow

Within each solver package, that one may choose, there are certain compability considerations. Usually there is one program to generate the geometry, another one to mesh it, another one to solve it and finally a program to present all the results. Naturally none of these programs communicate with each other very well and one may consider it a great feat if one program can read what the other one has produced.

Despite this there are ways of how go through all these steps in a fairly efficient manner.

Obviously different users have their own preferences and may rather do most of the work in a single application, rather than split it all up. It is typically possible to do most of the simple geometry building in a meshing applications, if one prefers to do so.

Nevertheless, the process is to start with the generation of an airfoil and place it in a fluid domain. Then generate a mesh from the domain and then solve it.

Airfoil generator (XFLR5)

CAD (e.g. Solid-Works/Edge)

2D-Mesh (Ansys Mesh)

3D-Mesh (Ansys ICEM CFD)

CFD Solver (Ansys Fluent)

Figure 4.1: Schematics of the work flow.

When generating airfoils it is recommended to use XFLR5, a freeware aimed at model- plane builders and provides features to quickly calculate simple incompressible flow. This application is especially useful when there is a need to generate standard NACA airfoils, as it has a build-in generator for those. Once the airfoil is generated it is exported to a DAT file which is then converted to a curve-geometry file. This part is made using a own developed converting application, which has not only a capability to transform it, but also to project it onto a desired plane.

The curve-file is then imported into a CAD-program to create the surrounding fluid domain and add additional geometrical details that might be needed for the simulation.

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As the geometry is set, it is necessary to mesh it. Depending on if it is a 2D or a 3D problem, different approaches are suitable. For the simple 2D case a more easy-to-do approach is to use the Ansys Workbench and set up a project schematics. Starting with importing the geometry to the Ansys Geometry and then move to Ansys Mesh. Using the project schematics is actually very convenient since all parts are connected and can be updated from changes made upstream.

For 3D cases the Ansys Mesh is just not practical enough. To have full control over inflation sizing and other elements it is preferable to use Ansys ICEM CFD, which provides far more options and control. However, to import something into ICEM the best format to use turned out to be IGS. Note that this format has a tendency to flip normal vectors of surfaces. Also when the mesh is exported to a Fluent CAS file it can sometimes be corrupted. This is usually caused by corrupt mesh orientation, which may occur during volume mesh generation. Each of these meshing approaches are discussed extensively in respective chapters.

Eventually the mesh is imported into Fluent where it is solved using desired schemes. For 3D cases it is convenient to use the CFD-Post tool to clearly see the different contour plots and other visualizations.

4.2 Meshing

When dealing with airfoils the typical meshing approach is to have a coarse structure near the edges of the fluid domain and increase the quality near the objects, which are to be investigated.

The first step is to decide whether to use structured or unstructured mesh. The advantaged of the structured mesh is that it can be solved much faster and there is rarely a noticeable transition between the free stream an the boundary layer. In fact, when using structured mesh one may even skip the process of creating a inflation layer (to properly resolve the boundary layer) and merely dense the mesh near a given surface.

A clear disadvantage is the creation of a structured mesh, which usually is a tedious work.

The cells get easily skewed and to fix this can be very tiresome. In this case there will be a lot of moving around of a certain interference device which will undoubtedly present new challenges for each position.

It is much more manageable to to use the flexibility of an unstructured mesh together with inflation layers, despite the extra solving time.

Figure 4.2: The unstructured mesh between the trailing edge of the airfoil and the interference device.

For those reasons an unstructured mesh is chosen and to resolve the boundary layer, which forms at the wall of a given object, a inflation layer is constructed. The inflation layer is typically smallest in thickness near the wall and then it grows exponentially (or in any other

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desired way) in the normal direction from the wall. It should do so until it covers the entire boundary layer. To achieve this one may have to go back after obtain the solutions from the solver and modify the specific mesh.

If one uses a standard exponential grow, starting at reasonably small value (see section 3.3) with at least 30 layers, there is usually no problem to enclose the boundary layer.

Then there is also the question of necessity, since this work mainly focuses on lift and not drag. Lift is typically much less sensitive to a poorly made mesh, thus one may not have to be all that concerned with the details.

4.3 Numerical Solver

Since only the lift is of the main interest, this part is way more easier than it normally would have been. Because drag force is of little use, the vorticity generated mainly by the bluff body does not need to be resolved in high detail. Also the Mach number is low which means that the flow can be treated as incompressible.

The main problem with vorticity is that in reality it is transient, which means that there is a need to incorporate times-steps into the solution process for good accuracy. However if one uses time averaged solution models as the Reynolds-averaged Navier-Stokes equations (RANS), which uses Reynolds decomposition, one will get a time-averaged approximation of the problem. Here is the incompressible version:

ui= Ui+ u⁰_iand p = P + p⁰

∂Ui

∂t + Uj

∂Ui

∂x_j = −1 ρ

∂P

∂x_i + ∂

∂x_j

ν∂Ui

∂x_j − u⁰_iu⁰_j

(4.1) To further simplify the problem one may use Boussinesq expression for the turbulent stress tensor, which is used in Spalart-Allmaras one-equation model.

u⁰_iu⁰_j= 2νtSij−2

3Kδij (4.2)

Here the Sij is the mean strain rate tensor, K is the turbulence kinetic energy and δij is the Kronecker delta. All of these variables used standard values provided by Fluent and are described in the user manual. There are naturally many details to this, that could be discussed further. Unfortunately such topics are also out of the scoop of this thesis, but hopefully the provided references will encourage further reading [6, §4] [13, §4.2].

Nevertheless, this gives a low-cost RANS model which is known to give good results for boundary layers subjected to adverse pressure gradients. To validate the results a number of key-points have also been solved by the use of a more complex solution model, the 4- equation model SST (Menter’s Shear Stress Transport). This more complex version of RANS has the ability to predict transition from laminar to turbulent flow.

The solution method is selected to Coupled Pressure-Velocity scheme with the use of 2nd Order Upwind for Momentum and Modified Turbulent Vicosity. A coupled scheme uses up more memory but converges faster. In some cases the convergence was improved with the use pseudo-transient settings where correct length-scales were provided. This is particularly the case for 3D problems.

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Chapter 5

Preliminary 2D test-case

In this part, initial tests will be made using CFD. The focus will be on the positioning of the interference device behind a generic airfoil. Initially values for the uninterfered case will be obtained (a case where you only have the wing and nothing is disrupting it). The next step is to place an interference device behind it and see what will happen to the interference coefficient C_I or as it also can be referred to, ∆C_L/C_L.

To gain a deeper understanding, the angle of attack α of the wing will be varied to see how this affects the outcome.

5.1 Geometrical Setup

The geometry has been made with simplicity in mind. A 2-dimensional C-grid fluid domain around an airfoil of standard type, NACA 23015 and a 2-dimensional cylinder. The dimensions of the fluid domain are 20 times the size of the airfoil chord, crin all directions. With a value of cr= 0.2 m, the domain is 4 m in all directions from the center of the airfoil.

x y

v∞

flow inlet

flow outlet

4 m (20·c )r

4 m (20·c )r

airfoil 2D cylinder

Figure 5.1: A C-grid fluid domain containing an airfoil (NACA 23015) and a 2-dimensional cylinder.

The center of the airfoil is defined at the 1/4 cr (one quarter of the chord length) and is pitched around that point to acquire the desired α. From the trailing edge of the airfoil

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(when at α = 0 position) the distance to the center of the cylinder are measured. The distance is then defined as xc in the horizontal direction and yc in the vertical. Since the interference device is a cylinder, it has a diameter defined as dc.

Due to the criteria of having dimensionless values, all the cylinder diameter and distance values are divided by the chord length of the airfoil (details are in section 3.1). This way it will be easier to compare values in graphs.

v

_∞

x

y

x

_c

y

_c

α

Ø = d_c

c

_r

c

_r

14

Figure 5.2: A close up of the internal relations between the NACA 23015 airfoil and the 2-dimensional cylinder.

With the given geometry and the flow velocity of v∞= vref3 = 65 m/s. (see section 2.3.1) the next phase is to go through all of the different changes to obtain the comparable results.

Following table shows which values are altered and with how much at each step.

Variables Min Step Max

α 0^◦ +4^◦ 8^◦

x_c/c_r 0.5 +0.25 1

y_c/c_r -0.2 +0.1, (+0.05) 0.4

Table 5.1: Variable Manipulation

5.2 Mesh

As stated before, the 2D meshing is done using Ansys Mesh and is accessed through Work- bench. The Mesh-method is set to Triangles since an unstructured mesh will be used. It is also important to set all of the general mesh parameters:

Relevance center = Fine Smoothing = high Min.Size = 1e-4

Next step is to define the Edge Sizing for the airfoil and the cylinder. For the top and bottom side of the airfoil, the element size is set to 8e-4 m. There is also a Bias Factor, which is set to 10 and a Bias Type that is specified so that the smallest cell-spacing is at the leading and trailing edge of the airfoil. Since the airfoil has a blunt trailing edge it worked best just to set the Number of Divisions for that part to 8 with no bias. For the cylinder a Edge Sizing of 1e-3 is sufficient.

For both the airfoil and the cylinder, following Inflation settings yield.

Motorcycle Cornering Improvement: An Aerodynamical Approach based on Flow Interference