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 Contents
Nomenclature 1
1 Introduction 3 1.1 Early History of Motorcycle Aerodynamics ...... 3 1.2 Focus on cornering ...... 4 1.3 Serious Attempts on Wing Use ...... 6
2 Project Overview 8 2.1 Concept ...... 8 2.2 Mechanical aspects ...... 10 2.2.1 Calculations ...... 11 2.2.2 Evaluating the Effect of Interference ...... 12 2.2.3 Anhedral angle effect on Vertical and Horizontal Forces ...... 14 2.2.4 Overall performance ...... 14 2.3 Speed estimation ...... 17 2.3.1 Airfoil Selection: NACA 23015 ...... 18
3 Problem Specification 19 3.1 Identifying Variables - The Buckingham Pi Theorem ...... 19 3.2 Problem Overview ...... 20 3.3 Predicting Near-wall Cell Size ...... 21
4 Numerical Approach 23 4.1 Work Flow ...... 23 4.2 Meshing ...... 24 4.3 Numerical Solver ...... 25
5 Preliminary 2D test-case 26 5.1 Geometrical Setup ...... 26 5.2 Mesh ...... 27 5.3 Solver ...... 28 5.4 Results ...... 29 5.4.1 Airfoil Properties ...... 29 5.4.2 Interpretation of Interfered Airfoil results ...... 30 5.4.3 Interfered Airfoil at α = 0◦ ...... 31 5.4.4 Interfered Airfoil at α = 4◦ ...... 32 5.4.5 Interfered Airfoil at α = 8◦ ...... 34
6 Simple 3D case 38 6.1 Geometrical Setup ...... 38 6.2 Mesh ...... 39 6.3 Solver ...... 40 6.4 Results ...... 41
7 Final Concept 43
1 8 Discussion 45 8.1 Additional Work ...... 45 8.2 Further improvements ...... 45 8.2.1 Higher top speed ...... 45
9 Conclusion 47
Acknowledgments 48
A Appendix: Data 49 A.0.2 Data for 2D cases ...... 49 A.0.3 Data for 3D cases ...... 50
B MotoGP Regulations 2012 52
2 Abstract
A new aerodynamic device, based on flow interference effects, is studied in order to signifi- cantly improve the cornering performance of racing motorcycles in MotoGP. 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 re- sults 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 fl¨odesinterferenser ¨arutv¨arderati syfte att p˚aett noterbart s¨attf¨orb¨attraen roadracing-motorcykels kurtagningsm¨ojligheter. Efter en kort genomg˚angav varf¨ordiverse klassiska “downforce” l¨osningarej ¨arapplicerbara p˚amotorcyklar, presenteras det nya konceptet. Varp˚aen mekanisk analys genomf¨orsi syfte att se ¨over dess till¨ampbarhet.Konceptet bygger p˚aanhedrala vingar som placeras p˚aden fr¨amrek˚apan,d¨arf¨orarenagerar som ett interferensobjekt, och f¨ors¨oker st¨oraut lyftkraften som den ena vingen genererar. Numeriska ber¨akningarbaserade p˚aRANS-ekvationer ¨ar utf¨ordai f¨orenklade statiska 2D och 3D fall. Som ett vidare steg rekommenderas vindtun- neltester. Resultaten visar att fl¨odesinterferenser ¨arytterst m¨arkbaraf¨orvingar och i vissa fall kan lyftkraften reducerats med 70–90%. Detta f¨orst¨aker m¨ojlighetenf¨oren realistisk implementering. Nomenclature
Symbols
2 Aw area of a wing [m ] 2 bw half-span of a wing [m ] Cd, CD drag coefficient for 2D, 3D case [-] Cf friction coefficient [-] CI interference coefficient [-] Cl, CL lift coefficient for 2D, 3D case [-] cr airfoil chord length [m] dc diameter of interference device[m] F~ , F force vector, force [N] 2 g0 sea level gravity constant, 9.81 [m/s ] 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] mr 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[-] ReL Reynolds number for specific lenght[-] −1 Sij mean strain rate tensor [s ] 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] 2 νt turbulence eddy viscosity [m /s] Π dimensionless product [-] Πcount number of dimensionless products [-] ρ density [kg/m3] 2 τw wall shear stress [N/m ] ◦ φwing anhedral angle of wing [ , rad] ◦ ϕlean lean angle of motorcycle [ , rad]
1 Acronyms
CAD Computer Aided Design CFD Computational Fluid Dynamics FIM F´ed´erationInternationale 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.
−2 g0 9.81 [m/s ] 3 ρ∞ 1.225 [kg/m ] µ∞ 1.7894e-05 [kg/(m · s)] T∞ 288.16 [K]
2 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
3 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.
In uence of Lift coe cient during Cornering on a vehicle for unbanked turns
600
2 1 2 mv equation: s ( mg 0 – 2 C L ρ ∞ v Aw ( = 500 rc
values: s = 1 m = 600 kg A = 1.47 m2 CL = –2 400 w
v [km/h]
300 CL = –1
200
CL = 0
100
50 100 150 200 250 300
rc [m]
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]
4 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).
Lateral force Fx component Tilting Wing Wing
F Vertical force Vertical force y component Fy N component N
N N s Front/rear view s Front/rear view
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.
5 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]
6 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.
7 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.
8 While cornering, one is horizontal
Anhedral wings on both sides ...the other one is vertical
Front view Front view, while cornering
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 ow 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.
9 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.
= 300 wing bw r downforce point 1 c3 = 200 w1 c4 = 70
c2 = 800 Fw1 rm rr mass center c1 = 700 mass center motorcycle rider Fm Fr c0 = 600 rw2 Fw2 downforce point 2
N y φlean
s N M0 x
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 F~m is acting on the motorcycle and F~r 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)
2 −v /rc ~ Fm = m0 −g0 (2.1) 0 2 −v /rc ~ Fr = mr −g0 (2.2) 0
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.
10 cos(φ ) 1 w1 F~ = C ρ v2A sin(φ ) (2.3) w1 2 L ∞ w w1 0 cos(φ ) 1 w2 F~ = (1 − C ) C ρ v2A sin(φ ) (2.4) w2 2 I L ∞ w w2 0
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
CL = 1.7 (lift coefficient) bw = 0.3 m (span of one wing-part) cr = 0.2 m (root chord of the wing) 2 Aw = cr · bw = 0.06 m (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.
∆CL CI = = 0 ... 1 CL
The angle for the uninterfered wing φw1 and the interfered wing φw2 is the resulting angle of both the lean angle ϕlean and the anhedral angle of the wings φwing.
1 φ = −ϕ + φ − π (2.5) w1 lean wing 2 3 φ = −ϕ − φ + π (2.6) w2 lean wing 2 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 F~w 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, rcp, in a direction ϕcp.
F~w = f (CI , ϕlean) (2.7)
The problem here is that if the anhedral angle φwing is changed, both the position of the center of pressure rcp will be moved and the angle ϕcp 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 F~0 in 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, F~0 is equal to zero.
11 = 300 wing bw r downforce point 1 c3 = 200 w1 c4 = 70
c2 = 800 Fw1 rm rr mass center c1 = 700 mass center rider rcp motorcycle Fm Fr c0 = 600 φ center of cp pressure rw2 Fw2 downforce point 2
N y φlean Fw = f(CI ,φ lean )
s N M0 x
Figure 2.4: The same model with the use of center of pressure.
µsN ~ ~ ~ F0,ref = Fm + Fr + N (2.8) 0 µsN ~ ~ ~ ~ ~ F0,concept = Fm + Fr + Fw1 + Fw2 + N (2.9) 0
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 = ~rm × F~m + ~rr × F~r (2.10) M~ 0,concept = ~rw1 × F~w1 + ~rw2 × F~w2 + ~rm × F~m + ~rr × F~r (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 down- force. 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 µs if 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).
12 Cornering speed over radius of curvature at const. lean angle of 50°
300
250
v [km/h] 200
reference case
CI = 1 (ideal case) 150 CI = 0.9 CI = 0.7 (realistic case)
100 100 200 300 400 500 rc [m]
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.
Cornering speed over lean angle at const. radius of curvature r = 600 m 350
300
250
v [km/h]
200 reference case
CI = 1 (ideal case)
150 CI = 0.9 CI = 0.7 (realistic case)
100
0 10 20 30 40 50 φ [°] 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
13 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.
Vertical force on tires at velocity 65 m/s (234 km/h), r c = 600 m, C I = 0.7
2500
2450
N [N] 2400
reference case 2350 wing = 40° wing = 50° wing = 60° = 70° 2300 wing
0 10 20 30 40 50 [°] φlean
Figure 2.7: A high anhedral angle provides a lower vertical force component
In this case the interference effect CI 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.
14 Horizontal force on tires at velocity 65 m/s (234 km/h), r c = 600 m, C I = 0.7
1700
1650
1600 s N [N]
1550 reference case
wing = 40° = 50° 1500 wing wing = 60° wing = 70° 1450 0 10 20 30 40 50 [°] φlean
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.
Friction coe . for di erent velocities up to maximum lean angle (50°), rc = 300 m, CI = 0.7
1.4
1.2
1.0
s [-]
0.8 reference case
wing = 40° 0.6 wing = 50° wing = 60° = 70° 0.4 wing
140 160 180 200 220 240 v [km/h]
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
15 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.
16 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.
#3:110 km/h 3 TT Circuit Assen #4:195 km/h
2 MotoGP 2012, Qualify, V.Rossi
4 #3:116 km/h 5 6 7 N 1 #2:70 km/h max #4:219 km/h 309 km/h #2:119 km/h max #3:130 km/h 8 291 #4:162 km/h 10 #5:246 km/h km/h 9
21 17 19 max 20 #4:184 km/h #2 :143 km/h 18 240 16 #2:103 km/h km/h
15 #2:111 km/h max #2:106 km/h 11 285 12
km/h
14 #5:227 km/h 13 #3:153 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 – 240 (max speed in section i3) 11 2 111 12 2 106 13 3 153 14 5 227 – 285 (max speed in section i4) 17 4 184 18 2 103 20 2 143
17 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 Recr Comment vc2g 109 30.2 4.13e5 Average 2nd gear corner vc3g 127 35.3 4.84e5 3rd gear corner vc4g 190 52.8 7.23e5 4th gear corner vc5g 237 65.7 8.99e5 5th gear corner
2.3.1 Airfoil Selection: NACA 23015
v ∞
y cr 1 c 4 r x
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 typi- cal 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 Recr km/h m/s Comment vref1 2.6e5 68.4 19.0 ∼1st or 2nd gear corner speed. vref2 6.0e5 157.8 43.8 vref3 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.
18 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 vari- ables 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∞, cr, µ∞, α, dc, xc, yc, R~) = 0 (3.2) Now the new function also depends on the reaction force, thus there is a total of 9 indepen- dent 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.
19 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] dc xc yc CR = f Recr ,M∞, α, , , (3.4) cr cr cr The same procedure can be done for the other coefficients, of lift, drag, moment etc.
dc xc yc CL = f Recr ,M∞, α, , , (3.5) cr cr cr dc xc yc CD = f Recr ,M∞, α, , , (3.6) cr cr cr dc xc yc CM = f Recr ,M∞, α, , , (3.7) cr cr cr 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.
∆CL CI = (3.8) CL
It is defined as the change of lift coefficient ∆CL, divided by the lift coefficient CL of the uninterfered wing. The ∆CL represents 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 equa- tion 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 mo- mentum 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.
20 idea Calculations • Reynolds Number too high • Unsteady problem • No analytical solution
Wind tunnel
Numerical Methods
RANS Fluid Domain • Good for lift estimations • Domain size restrictions • Can not resolve drag correctly • Cell count restrictions
Simpli cations • Focusing only on the principle • Setting up a static problem
Proof of Concept
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 yn and 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.
yn ρ∞uτ yn y+ = = (3.9) l∗ µ∞
Where the uτ is the friction velocity, defined by the wall shear stress, τw. 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. r τw uτ = (3.10) ρ∞
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]
21 1 τ = C ρ v2 (3.11) w 2 f ∞ −0.2 Cf = 0.058ReL (3.12) ρ∞vL ReL = (3.13) µ∞ 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]
22 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 consider- ations. 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)
2D-Mesh (Ansys Mesh) CAD CFD Solver (e.g. Solid-Works/Edge) (Ansys Fluent) 3D-Mesh (Ansys ICEM CFD)
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.
23 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 interfer- ence 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
24 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:
0 0 ui = Ui + ui and p = P + p
∂Ui ∂Ui 1 ∂P ∂ ∂Ui 0 0 + Uj = − + ν − uiuj (4.1) ∂t ∂xj ρ ∂xi ∂xj ∂xj To further simplify the problem one may use Boussinesq expression for the turbulent stress tensor, which is used in Spalart-Allmaras one-equation model. 2 u0 u0 = 2ν S − Kδ (4.2) i j t ij 3 ij
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.
25 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 CI or as it also can be referred to, ∆CL/CL. 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 dimen- sions of the fluid domain are 20 times the size of the airfoil chord, cr in all directions. With a value of cr = 0.2 m, the domain is 4 m in all directions from the center of the airfoil.
ow inlet ) r c 4 m (20·
4 m (20· c ) v r ∞
airfoil 2D cylinder ow outlet ow
y
x
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
26 (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.
Ø = dc
v∞ yc
α
y cr 1 4 cr xc x
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◦ xc/cr 0.5 +0.25 1 yc/cr -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.
27 Inflation first layer height = 1e-5 m max layer = 30 growth rate = 1.15
After this is done, the next step is to let the Fluent solver iterate a few time (see the following section, 5.3). About 50 iterations should do the work and provide some information on how the grid can be adapted. With the obtained results in Fluent a recommended next step is to adapt the velocity gra- dient. Let Fluent calculate the maximum velocity magnitude and then refine the threshold by 0.001. Boundary adaptation is also a good improvement and a distance threshold 0.4 m for airfoil and cylinder is of good use.
Figure 5.3: The mesh improvement after adaptation between the trailing edge of the airfoil and the interference device.
The change of mesh by the use of adaptation brings new complications. Typically the grid size increases and the Orthogonal Quality gets worse. In this case the quality is good enough not to be regarded as unacceptably low by Fluent, but one should keep in mind to be con- servative with the adaptation process. Note that Orthogonal Quality ranges from 0 to 1, where values close to 0 correspond to low quality. A value of 1e-2 is the lowest acceptable value by the solver, here the value for the adapted case is 2.60e-1.
Mesh Cells Faces Nodes Min Orth. Quality Max Aspect Ratio Initial 37041 68575 31533 3.94e-1 2.05e2 Adapted 157296 288754 131457 2.60e-1 2.06e2
5.3 Solver
With the use Spalart-Allmaras one-equation model the flow is then solved, using Coupled scheme and Second Order Upwind to solve both the Momentum and Modified Turbulent Viscosity. In the figure below it is very clear that good results can be obtained fairly quickly. Thus it is not necessary to extend the calculation, since even 400 iteration are sufficient enough for an uninterfered wing (see figure 5.4). The situation is a bit different for the interfered cases. It evidently requires more time to solve due to a larger count of cells and more complex geometry. A good approach is to do approximately 200 iterations and to get some preliminary results and then to adapt the grid based on velocity gradient and near wall grid refinement. This will reduce the Orthogonal Quality but will however improve the quality of the result. From figure 5.5 it is also clear
28 ◦ Figure 5.4: Residuals for an undisturbed wing at α = 0 , v∞ = 65 m/s. that the residuals are struggling a bit more to reach low values. For those reasons it is good to do about 2000 iterations to be on the safe side.
◦ Figure 5.5: Residuals for an interfered case. α = 8 , v∞ = 65 m/s, xc/cr = 0.5, yc/cr = 0
5.4 Results
The first step is to verify that the method works by comparing its results with the ones obtained from literature. Next step is then to do calculations for different variable manipu- lations as seen in the table 5.1. To reduce the amount of workload, the idea was to initially only try a very limited amount of positions for the interference device. Initially only 4 posi- tions in vertical directions and only 3 in the horizontal. Since the vertical direction is more interesting this part was then refined for higher airfoil α.
5.4.1 Airfoil Properties The verification of the standard NACA 23015, which is used throughout this thesis, under- went as expected. As seen in table 5.2, some of the values correspond very closely to the reference values obtained from literature [1, pp500-501].
α Cl Cd L/D 0◦ -0.122 (-0.12) 0.0139 (0.006) -8.751 4◦ -0.548 (-0.55) 0.0171 (0.007) -32.10 8◦ -0.952 (-0.97) 0.0178 (0.0085) -53.57 12◦ -1.286 (-1.38) 0.0301 (0.013) -42.79
Table 5.2: Results for NACA 23015. Reference values in parenthesis.
29 It is mainly the lift coefficient Cl, which is very close to the reference case, but only for reasonable angle of attacks, α. As the angle α for the airfoil is increased, the airfoil is getting closer to the stall-angle (which in literature is about 14◦). Even before this angle is reached, a separation bubble is starting to to form on the trailing edge of the airfoil and is noticeable at 12◦. Since the numerical model, which has been used, has a poor ability to resolve vorticity in the wake of the airfoil, the lift at those angles is somewhat under- predicted. It should also be noted that the wake-thickness is significantly larger at α = 12◦ than at 8◦. For the drag coefficient Cd there is a systematic over-prediction which is due to the fact that the Spalart-Allmaras is a one-equation model which lacks the ability to predict transition. The entire flow is treated as turbulent, but in reality about one third of the airfoil should be subjected to laminar flow before the transition occurs. This can actually be visualized with the use of SST, the 4-equation model. However, since only the lift interference coefficient is of interest the one-equation model is good enough for angles α up to 8◦.
◦ Figure 5.6: Pressure over an undisturbed wing at α = 0 , v∞ = 65 m/s
5.4.2 Interpretation of Interfered Airfoil results To better illustrate how the position (of the interference device) affects the interference coefficient, there will be 3 main types of different figures/plots at disposal. At an initial stage only a results at a few selected few points will be obtained to get an idea of what may be o interest. Then some of the more interesting cases will be refined and evaluated to get a better understanding.
Interference coefficient over distance xc/cr This will show the change of interference coefficient as the distance between the airfoil and the interference device is increased. On the x-axis of the plot, is a dimensionless distance variable, xc/cr and on the y-axis is the interference coefficient. Different curves are then showed for different yc/cr positions. The idea is to clearly see what happens to the interfer- ence coefficient as you move away.
Interference coefficient over vertical position yc/cr It is similar to the figure above, with difference that now the vertical position is of main interest. Here the x-axis of the plot is used for plotting the changes of the interference coefficient, while the y-axis shows the vertical position. This type of figure is the one that received most attention, since the changes in vertical positioning has shown some really interesting results.
30 Contour plot for the Interference coefficient Contour plots has 3 axises and here the x and y-axis has been reserved to the x and y position of the interference device. The remaining z-axis shows the interference coefficient by the use of different contour colors.
5.4.3 Interfered Airfoil at α = 0◦ The first case to look into is when the angle of attack of the airfoil is α = 0◦. In these tests the velocity is kept at v∞ = vref3 = 65 m/s, which corresponds to 234 km/h and could be seen as the speed though a 4th or a 5th gear corner. Since the airfoil has a little bit of camber it generates lift even at 0◦. The lift is small however, which means that the resulting interference coefficient is a bit sensitive to changes, as will be seen.
Cl /C l over x c
{ v∞ = 65.00 [m/s], α = 0°, dc /cr = 0.5 } 2
1.5
1
0.5
0
−0.5 l l l C /C C −1
−1.5 yc /cr = −0.10 −2 yc /cr = 0 yc /cr = 0.10 −2.5 yc /cr = 0.20 −3 0.5 0.6 0.7 0.8 0.9 1 xc /cr
Figure 5.7: There is a reduction of interference coefficient as the x-distance increases. Also note the huge interference spread at close distances.
Initially in figure 5.7 one may see the reduction of interference as the x-distance increases. It shows that it does not take much before all of the interference is mostly reduced. Only a half length step in x-direction. This shows that if the rider wants to interfere the wing effectively, he must be positioned close to the airfoil. In the vertical position only a few values has been marked out, to merely give an idea of what is happening. It is clear that to position the interference device below the centerline is to prefer. As mentioned before, at α = 0◦, the interference coefficient is very sensitive in the vertical direction. This results in very high deviations, from -3 to 1.5 for the coefficient. When the interference coefficient has a positive value higher than 1 it shows that there is actually a lift force generated in the opposite direction. This would be very good if it was not for the fact that the airfoil is not generating much lift in the first place. In the contour plot all these values are put together and visualized with the help of different colors. The blue colors show low values for the interference coefficient while the red ones show high. If one would place a interference device somewhere, it should be in the red area.
31 Cl /C l over y c
{ v∞ = 65.00 [m/s], α = 0°, dc /cr = 0.5 } 0.2
xc /cr = 0.50
xc /cr = 0.75 0.15 xc /cr = 1.00
0.1 r
c 0.05 y /c y
0
−0.05
−0.1 −3 −2 −1 0 1 2 Cl /C l
Figure 5.8: The interference coefficient may change rapidly for low α.
Cl /C l contour
{ v∞ = 65.00 [m/s], α = 0°, dc /cr = 0.5 } 0.2
1 0.15 0.5
0.1 0
−0.5 r 0.05 c y /c y −1
0 −1.5
−0.05 −2
−2.5
0.5 0.6 0.7 0.8 0.9 1 xc /cr
Figure 5.9: The red colored area is the optimal place for the interference device.
5.4.4 Interfered Airfoil at α = 4◦ As the angle of attack for the airfoil is increased, the behavior of the interference becomes more predictable. The old rule, that it decreases over horizontal distance remains unchanged as seen in figure 5.10. What becomes more clear, is the shape of the interference coefficient for the vertical positions (figure 5.11). The points at which results has been obtained, are still a bit too scarce to give a full view of the actual behavior. Despite this one may see that there is a clear build up on the lower side of the upside-down airfoil. Naturally it is impossible, with only 4 points
32 Cl /C l over x c
{ v∞ = 65.00 [m/s], α = 4°, dc /cr = 0.5 } 0.8
yc /cr = −0.10 0.7 yc /cr = 0
0.6 yc /cr = 0.10
yc /cr = 0.20 0.5
0.4
0.3 l l l C /C C 0.2
0.1
0
−0.1
−0.2 0.5 0.6 0.7 0.8 0.9 1 xc /cr
Figure 5.10: Now the interference spread becomes lower at close distances. at hand, to estimate where the actual maximums and minimums are, but for now it will do. From previous results it stems that the ideal position to place the interference device is slightly below the airfoil. This statement is based on a low number of points but gives in this case a small overview. In the contour plot this ideal position can be spotted.
Cl /C l over y c
{ v∞ = 65.00 [m/s], α = 4°, dc /cr = 0.5 } 0.2 x/d = 1.00 c x /c = 1.50 c r 0.15 x /c = 2.00 c r
0.1
r 0.05 c y /c y
0
−0.05
−0.1 −0.2 0 0.2 0.4 0.6 0.8
Cl /C l
Figure 5.11: The interference coefficient becomes more predictable.
33 Cl /C l contour
{ v∞ = 65.00 [m/s], α = 4°, dc /cr = 0.5 } 0.2 0.7
0.15 0.6
0.5 0.1 0.4 r 0.3
c 0.05 y /c y
0.2 0 0.1
−0.05 0
−0.1
0.5 0.6 0.7 0.8 0.9 1 xc /cr
Figure 5.12: The ideal position does not change, but becomes more clear.
5.4.5 Interfered Airfoil at α = 8◦ This angle of attack is the most relevant of them all. It is an angle which is high enough to generate significant downforce, yet is not so high that there are separations forming at the trailing edge with a thick wake as a result. This is in fact the most relevant study and has been subject for high refinement.
Cl /C l over x c
{ v∞ = 65.00 [m/s], α = 8°, dc /cr = 0.5 } y /c = −1 1 c r yc /cr = −0.8 y /c = −0.6 0.8 c r yc /cr = −0.4 y /c = −0.2 0.6 c r yc /cr = −0.1 y /c = −0.05 0.4 c r yc /cr = 0 l l l = 0.05 C /C C y /c 0.2 c r yc /cr = 0.075 y /c = 0.1 0 c r yc /cr = 0.2 y /c = 0.4 −0.2 c r yc /cr = 0.6 = 0.8 −0.4 yc /cr 0.5 0.6 0.7 0.8 0.9 1 yc /cr = 1 xc /cr
Figure 5.13: Reduction of interference coefficient over the x-distance offers no surprises.
As before the interference coefficient decreases over horizontal distance as can be seen in figure 5.13. Now when so many points are being investigated in the vertical direction, a
34 more clear idea of the true behavior can be obtained. To fully understand this, the figure 5.14 is presenting very detailed results for when a in- terference device is at different positions behind the upside-down airfoil (which is trying to generate downforce). On the right side of the figure are the contour-plots of the velocity, pointing at specific important results and are trying to illustrate the behavior and interac- tion between the wake of the airfoil and the interference device. There are 4 main positions of interest.
1) Above the airfoil When the interference device is above the airfoil, interference is ac- tually the opposite of what one would hope for. It is the combination of the addition of higher pressure above the airfoil and the fact that the airfoil’s wake seems to be drawn into the wake of the cylindrical interference device, which is being used here. Naturally if the shape of the interference device would have been different, so would the wake interaction. 2) In the wake As the interference device is moved downward, the interference coefficient is increased and reaches a maximum point when the wake of the airfoil is hitting the interference device straight on.
3) Sudden dip Moving the interference device further down will result in a sudden dip in interference coefficient. It is because now, the wake of the airfoil is being curved around the top of interference device and drawn into its wake. 4) Below the airfoil When the interference device is placed further below the airfoil, an- other peak-point is reached. It is due to the interaction of the wakes, but now in the opposite direction and the pressure buildup under the wing.
35 1)
Cl /C l over y c
{ v = 65.00 [m/s], α = 8°, dc /cr = 0.5 } 1
xc /cr = 0.50 0.8 xc /cr = 0.75 0.6 xc /cr = 1.00 2)
36 0.4
0.2 r 0 c y /c y −0.2 3)
−0.4
−0.6
−0.8 4) −1 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Cl /C l
Figure 5.14: The change of interference coefficient and velocity contour plots at each position. This clearly gives more insight into the true nature of interference in the purpose of reducing lift. What can be seen is that it has two main peak points and some unwanted points that can actually do the opposite of what is being attempted to achieve.
Cl /C l contour
{ v∞ = 65.00 [m/s], α = 8°, dc /cr = 0.5 }
1 0.7
0.8 0.6
0.6 0.5
0.4 0.4
0.3 0.2
0.2 r 0 c y /c y 0.1 −0.2
0 −0.4
−0.1 −0.6 −0.2
−0.8 −0.3
−1 0.5 0.6 0.7 0.8 0.9 1 xc /cr
Figure 5.15: This contour plot shows the ideal (red) and less ideal (blue) positions to place the interference device.
To summarize this entire case a contour plot is showing what it looks like when it is all put together. Interesting thing to notice is the clear discontinuity when the wake of the airfoil is trying to hit interference device.
37 Chapter 6
Simple 3D case
After the 2D case is complete the next step is to see if the same theory is valid for a 3D case. The setup is very similar to the one used in the previous chapter, only now the airfoil has turned into a finite wing. With this in mind it will be interesting to see how the interference coefficient will fare with the somewhat changed situation. Typically when a airfoil is turned into a wing, there are losses connected to the wing-tip vortices. The question is how the interference will be affected by this.
6.1 Geometrical Setup
A fluid domain of the same type as the one used for the 2D problem is used. That means a unstructured C-grid with inflow going in the positive x-directions and outflow on the other side.
Stationary Wall (no slip)
Upside-down Wing (NACA-23015)
Interference Device (Flat cigar or rounded cylinder)
y x z
Figure 6.1: The 3D fluid domain with a wing and a semi-infinite flat-cigar.
An important detail here is that nor the wing or the interference device have a span that goes all across the width of the fluid domain which is 2 m. The 3D fluid domain in total is smaller than the 2D domain. About half as long and half as high. The reason for this is that if a properly sized domain would be used, the semi-infinite flat-cigar would be just too
38 long which would complicate the meshing. If one would use full resolution the high number of cells would be inconvenient and if coarsened, the rounded features of the geometry would suffer. The decision is to use a domain that has at least 2 m in all directions from the pivotal point of the wing. The wingspan is 4 dm for the wing and the interference device is just as wide. Other sizing values are kept the same. This small sizing of the fluid domain has evidently a bad effect on the quality of the re- sults. However if one considers other influences which may come in to effect, it is still very manageable. One contributing factor is the low ability to resolve wingtip vortices. Either way, there are 2 different types of interference devices that will be used.
A 3D cylinder which is almost identical to the 2D cylinder, but has completely rounded edges, meaning that the fillet radius is half of the cylinder diameter. The 3D flat-cigar has basically the shape of a horizontally extended cylinder. The flat cigar is semi-infinite to show what kind of effects will be occurring when there is no wake interaction.
To make it more real the far side of the domain is modeled as a stationary wall with no slip condition, just like the airfoil and the interference device. All walls are meshed with inflation layers.
6.2 Mesh
For the 3D mesh it is preferable to use the Ansys ICEM CFD to have more control over the complex geometry. The surface meshing has been done using All Tri mesh type wich was set to Patch Dependent for all surfaces, excluding the airfoil, interference device and the far wall. Those were set to Autoblock. The volume meshing was done using Tetra/Mixed mesh type with the help of Quick (De- launay) method which uses the TGlib scheme. In the volume mesh there are also inflation layers, or prism layers are they are called in this application. The prism layers were applied to all wall elements.
Inflation growth law = wb-exponential initial height = 5e-6 m height ration = 1.2 number of layers = 30 approx. prism layer thickness = ∼9.1e-3 m Min prism quality = 1e-7
With all the mesh parameters set, both the 3D cylinder and the flat-cigars are meshed. As can be seen in figure 6.2 and 6.3.
Figure 6.2: The finished mesh result for the 3D cylinder
39 Figure 6.3: A similar meshing result for the semi-infinite flat-cigar.
It is worth noticing the level of details on both elements. On the flat-cigar the detail level continues the same way throughout its semi-infinite length. It is not so good from a mesh- size perspective, but the problem is that when one tries to make these smooth reductions as one moves further way, the geometry gets torn. Instead of having smooth edges they now become choppy. It is always a difficult task to decide what may be optimal.
Mesh Cells Faces Nodes Min Orth. Quality Max Aspect Ratio 3D cylinder 1141991 2710274 472205 1.14e-2 8.08e4 Flat-cigar 2687563 6434550 1148948 1.24e-2 9.39e4
As the skewness and quality of the cells was very poor to begin with there was no idea to do further cell adaptations since that usually only make things worse. One solution could be to adapt the mesh and then convert the mesh to Polyhedral. That is a very powerful and reliable way get to get rid of skewness problems.
6.3 Solver
The solution method was identical to the 2D with the exception that no cell adaptations were made and in some cases the pseudo-transient settings were used, with a length-scale manually set to the chord of the airfoil.
Figure 6.4: Residuals for a typical 3D case.
Even when the mesh was not refined and the amount of iterations was only set to 500, it still took 8 hours on the available computer to perform calculations for one case. Despite this it is possible to get residuals close to 1e-7.
40 6.4 Results
As before the fist step is to see what values can be obtained for an uninterfered case. In this case the only way to obtain some realistic values to compare with is to do some calculation both by hand and by the use of some panel method application. The wing has a 2 dm chord and a 4 dm span with no winglets. This makes for a very stocky wing with high amount of wingtip vortices. The Methods used were the application XFLR5, Vortex Lattice Method (VLM) and then obviously Fluent. For the Fluent case one method involved a symmetry plane instead of a vertical wall. This was done to neglect the drag and other influences caused by the wall, so that the comparison would be more real. Obviously the mesh was done a bit differently for the symmetry plane case (no inflation on the vertical wall). [9, pp221-226]
Method CL CD L/D XFLR5 -0.6046 0.0286 -21.14 VLM -0.5762 0.0264 -21.83 Fluent (symmetry) -0.5896 0.0491 -12.01 Fluent (wall) -0.5733 0.5177 -1.107
Table 6.1: Results for a wing (NACA 23015) using different methods for calculation
The results for the uninterfered 3D case show a similar shortcomings as for the 2D case. The lift is close in comparison, but the drag is not. It is worth pointing out that neither the XFLR5 or the VLM have any reliable drag models, so the comparison should be viewed as a basic indication.
CL /C L and C l /C l over y c
{ v = 65.00 [m/s], α = 8°, dc /cr = 0.5 } 1
0.8
0.6
0.4
0.2 r
c 0 y /c y
−0.2
−0.4
3D flat−cigar xc /cr = 0.50 −0.6 3D cylinder xc /cr = 0.75 −0.8 2D cylinder xc /cr = 1.00
−1 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
CL /C L and Cl /C l
Figure 6.5: Close similarities between the 2D and the 3D case are shown. Also the good results for the flat-cigar are unmistakable.
As a final test the 3D cylinder and the flat-cigar has been compared with the 2D cylinder and with each other. This has been done to see the differences when going from 2D to 3D and also to see what happens when the flat-cigar is reducing the wake interaction. It should be mentioned that there is as a difference between the interference coefficient in the 3D and in the 2D environment. The definition for the 2D version is ∆Cl/Cl where the Cl is obviously the 2D case lift coefficient and is defines as the lift force divide by the dynamic pressure and chord. In the 3D case it is the 3D lift coefficient CL that is used, which has
41 wing area as a variable instead of chord. Thus, in the 3D case the interference coefficient is ∆CL/CL. The interesting part is that the interference coefficient is not very different in the 3D case compared with the 2D. Naturally the geometry is slightly different and there is an influence from the wing tip vortices. Overall the results are very similar. As expected the flat-cigar has due to its semi-infinite length obtained the most favorable values for the interference coefficient. It also has much lower dips or fluctuations and is therefor more predictable. The main explanation is that there is no wake behind the semi- infinite flat-cigar in which the flow could get tangle up in and produce unwanted effects. This is very good news, since if the goal is to make a rider interfere a wing with his knee (shaped as a cylinder/sphere), the knee is attached to a leg which is more of a flat-cigar shape. Combining this knowledge will tell us that this method of interference has some real potential in a static case.
42 Chapter 7
Final Concept
Throughout this document the focus has been to see if the interference effect has any poten- tial to make any difference. Preliminary CFD tests in a static environment has shown that there is indeed some promise that the entire concept might work. A lot of work still needs to be done, but as a matter or of interest, let us see what this concept might look like when it is done.
Simple Bi-plane wings Multiple Anhedral wings Anhedral angles
Front view Front view Front view
Figure 7.1: Possible wing geometry for the final concept.
One major problem that might come up is where and how to attach the wings onto the motorcycle fairing. A simple solution would be just to place the wings at some given angle in a position where they could be easily interfered. The problem here is that there is not all that much space to play with. A motorcycle is already about 0.4 to 0.5 m wide and the maximum limit is 0.6 m. This does not give much room for wing placing. From previous initial estimations (in section 2.2) it shows that the wings have to be quite large to make significant changes. A wing with 0.3 m span and 0.2 m chord and a reasonable lift coefficient of 1.7, will produce about 200 to 300 N through a fast 4 or 5th gear corner. This may not seem as much but a MotoGP rider usually weights between 50 to 70 kg. So, this wing will produce almost a half of what this rider produces with his weight – which is to make the bike lean into a corner (also with the help of counter steering), keep that lean angle throughout the corner and to move front and back, so that the front or back wheel are loaded during acceleration or braking. Another solution is to place several wing sections that could be interfered by the use of either one or several body-parts. This way a larger total wing area could be obtained resulting in more downforce. The downside is the higher drag that can be expected. Finally, the idea that may have the greatest potential is the use of curved wings. Here the initial anhedral angle at the wing root could be something in the range of 50◦ and then changing into an anhedral angle closer to 80◦. This way one may take the benefit of multiple anhedral angles (as explained in previous section 2.2.3) and also squeeze in as much wing area as possible into the tight space. Additionally various struts and winglets could be used to strengthen the design or to curve or funnel the flow in desired direction.
43 Figure 7.2: A concept using curved wings with multiple anhedral angles. The CFD per- formed here is very approximative.
Figure 7.3: Front view of he motorcycle with the curved wings.
44 Chapter 8
Discussion
Despite showing a lot of promise thus far, this new concept still has a long way to go before reaching a final concept stage. The positive surprise has been that the interference effect is there and shows a significant contribution. However the problem of the concept implementation is still an unsolved case.
8.1 Additional Work
The next step on the the way to reach a working prototype, is to verify that all of these results that has been presented here are valid. This means testing all of the simplified concepts in a wind tunnel and then compare them with the CFD results in this thesis. A severe limitation of the calculations performed here, is that in reality, it is mainly a dynamical problem since the body of the rider is moving into the position of the ideal interference. This can give hysteresis effects. Basically a case when a previous position has an influence on the current position. How to deal with this and what to expect can be complex problem to solve. In many ways due to the very complex geometry of the motorcycle, it may be severely difficult to do a simplified case test of this.
8.2 Further improvements
When it comes to the actual design there are many complications that may be difficult to overcome. One them is the placement of the wings and adapting the fairing so that the oncoming air comes in as smoothly as possible (see figure 8.1). The problem is that when a motorcycle is cornering the air moves around the motorcycle in a curved way. If the fairing of the motorcycle is too narrow one may have separations on the outer side of the bike. This means that the fairings have to be designed in such way that the air is smoothly directed at the wings. Another problem with the curved flow during cornering, is that the inner wing (which the rider is trying to block) is actually experiencing higher angle of attack (if the anhedral angle is very high), thus being more effective. So, the outer wing does not only suffer from possible separation bubbles disturbing the flow, but also has a lower angle of attack. None of these details work in favor for the concept.
8.2.1 Higher top speed One problem that all wings are having is the high lift-induced drag they create. A problem most noticeable when the vehicle is trying to reach the top speed. This problem has however been reduced by Mercedes in Formula 1 and could be applicable for wing configurations in MotoGP (figure 8.2). It works with the help of static pressure, which typically increases when the speed does. At a specific moment the static pressure becomes so large, that with the help of clever channeling, a separation occurs and the wing is rid of lift-induced drag. This is obviously at the cost of high separation drag, but nevertheless the total drag is smaller.[8] The best part is that it is legal by the (current) MotoGP regulations of 2012.
45 Figure 8.1: The relatively wide cooler does not simplify the wing implementation. This could however be resolved with some redesigning. The question is at what consequences. [12]
Figure 8.2: The Mercedes-Horn is using static pressure to stall the wing at high speeds to reduce drag. This type of device is legal by the MotoGP regulations (2012).[8]
46 Chapter 9
Conclusion
A concept has been suggested which has the capacity to significantly improve the corner- ing abilities of road racing motorcycles. This idea is also compliant with the road racing regulations of MotoGP 2012. This concept suggest the use of highly anhedral wings for use during cornering, where one of the wings would have its lift generations reduced, as the rider is leaning of the bike in the corners. The ideal result would be that the other wing alone would generate all of the necessary downforce and make the bike perform better than the existing ones. After doing simplified numerical calculations, only focusing on the basic principles in static cases, it has shown the the principle of interference effect is existing and is a very significant one. The search for an optimal positioning of an interference device, also shows a complex behavior where several peak points can be identified, as well as positions that have a very undesired effect. Even with these initial positive results there are still many issues that need to be addressed. The main one is how this interference effect will actually behave in a wind tunnel test and if the results will be the same. Then there is the question of what will happen in reality where the problem is highly dynamical and there is a great risk of unwanted hysteresis effects. Even when all this is dealt with the question is how all this can be applied on a real motorcycle with a real rider trying to set the best lap of the race. Despite all of these unresolved concerns, the fact remains that this concept has a lot of promise, with ideas that can surely deepen the understanding of other fields in aerodynamics.
47 Acknowledgments
An early idea of this concept came to the author’s mind when taking a course in vehi- cle aerodynamics. This idea was then told, in its very basic form to the course lecturer, Alessandro Talamelli. This sparked a discussion which evolved this basic idea into a full theory, described in this thesis. Without the help and support from Alessandro, this idea would likely never been anything more than a sketch on a piece of jagged paper, forgotten deep down in a drawer. Thus, it is fully in order to express sincere gratitude to Alessandro Talamelli for his time, effort and ideas which moved the work forward. As the thesis was underway Stefan Wallin was the one who provided support and help for the CFD tools. His help was very appreciated and brought forward some great results. Also the author would like to thank the “Department of Mechanics” and “Department of Aeronautical and Vehicle Engineering” at KTH for all their help an support, making this thesis possible. Finally the author would like to thank Michal Sedlak for bringing up ideas and thoughts regarding the work and what could be improved.
48 Appendix A
Appendix: Data
A.0.2 Data for 2D cases Details of these cases are explained in Chapter 5.
Table A.1: Uninterfered Reference Case for NACA-23015 in 2D
v∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl 65.00 0◦ 7.22 -63.16 0 -- -0.122 0.014 -8.751 - 65.00 4◦ 8.83 -283.42 0 -- -0.548 0.017 -32.095 - 65.00 8◦ 9.20 -493.10 0 -- -0.953 0.018 -53.573 - 65.00 12◦ 15.56 -665.72 0 -- -1.286 0.030 -42.794 -
Table A.2: Interference Case for NACA-23015 and a Cylinder (dc/cr = 0.5)
v∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl 65.00 0◦ 106.24 34.76 0 0.5 -0.1 0.067 0.205 0.327 1.550 65.00 0◦ 105.57 -9.10 0 0.5 0 -0.018 0.204 -0.086 0.856 65.00 0◦ 106.10 -112.67 0 0.5 0.1 -0.218 0.205 -1.062 -0.784 65.00 0◦ 106.75 -236.62 0 0.5 0.2 -0.457 0.206 -2.217 -2.746 65.00 0◦ 108.71 -0.05 0 0.75 -0.1 0.000 0.210 -0.001 0.999 65.00 0◦ 109.77 -54.64 0 0.75 0 -0.106 0.212 -0.498 0.135 65.00 0◦ 108.24 -101.75 0 0.75 0.1 -0.197 0.209 -0.940 -0.611 65.00 0◦ 109.67 -148.23 0 0.75 0.2 -0.286 0.212 -1.352 -1.347 65.00 0◦ 110.40 -24.03 0 1 -0.1 -0.046 0.213 -0.218 0.619 65.00 0◦ 112.45 -63.48 0 1 0 -0.123 0.217 -0.565 -0.005 65.00 0◦ 110.11 -85.71 0 1 0.1 -0.166 0.213 -0.778 -0.357 65.00 0◦ 111.80 -113.26 0 1 0.2 -0.219 0.216 -1.013 -0.793 65.00 4◦ 107.01 -64.37 0 0.5 -0.1 -0.124 0.207 -0.602 0.773 65.00 4◦ 107.00 -84.95 0 0.5 0 -0.164 0.207 -0.794 0.700 65.00 4◦ 102.48 -197.71 0 0.5 0.1 -0.382 0.198 -1.929 0.302 65.00 4◦ 103.87 -328.78 0 0.5 0.2 -0.635 0.201 -3.165 -0.160 65.00 4◦ 111.24 -162.73 0 0.75 -0.1 -0.314 0.215 -1.463 0.426 65.00 4◦ 106.18 -183.05 0 0.75 0 -0.354 0.205 -1.724 0.354 65.00 4◦ 107.75 -249.00 0 0.75 0.1 -0.481 0.208 -2.311 0.121 65.00 4◦ 109.71 -302.08 0 0.75 0.2 -0.584 0.212 -2.754 -0.066 65.00 4◦ 113.51 -211.17 0 1 -0.1 -0.408 0.219 -1.860 0.255 65.00 4◦ 110.20 -230.44 0 1 0 -0.445 0.213 -2.091 0.187 65.00 4◦ 112.47 -250.33 0 1 0.1 -0.484 0.217 -2.226 0.117 65.00 4◦ 111.71 -297.49 0 1 0.2 -0.575 0.216 -2.663 -0.050 65.00 8◦ 126.50 -319.34 0 0.5 -1 -0.617 0.244 -2.524 0.352 65.00 8◦ 127.17 -270.13 0 0.5 -0.8 -0.522 0.246 -2.124 0.452 65.00 8◦ 118.26 -216.38 0 0.5 -0.6 -0.418 0.228 -1.830 0.561 65.00 8◦ 112.37 -160.02 0 0.5 -0.4 -0.309 0.217 -1.424 0.675 Continued on Next Page. . .
49 Table A.2 – Continued v∞ α Nx Ny Nz xc/cr yc/cr Cl Cd L/D ∆Cl/Cl 65.00 8◦ 107.43 -149.98 0 0.5 -0.2 -0.290 0.208 -1.396 0.696 65.00 8◦ 105.78 -183.53 0 0.5 -0.1 -0.355 0.204 -1.735 0.628 65.00 8◦ 104.61 -197.83 0 0.5 -0.05 -0.382 0.202 -1.891 0.599 65.00 8◦ 100.91 -163.90 0 0.5 0 -0.317 0.195 -1.624 0.668 65.00 8◦ 102.02 -147.27 0 0.5 0.05 -0.285 0.197 -1.444 0.701 65.00 8◦ 102.44 -132.91 0 0.5 0.075 -0.257 0.198 -1.298 0.730 65.00 8◦ 96.51 -195.34 0 0.5 0.1 -0.377 0.186 -2.024 0.604 65.00 8◦ 98.74 -355.30 0 0.5 0.2 -0.686 0.191 -3.598 0.279 65.00 8◦ 103.08 -590.79 0 0.5 0.4 -1.141 0.199 -5.731 -0.198 65.00 8◦ 102.46 -672.26 0 0.5 0.6 -1.299 0.198 -6.561 -0.363 65.00 8◦ 102.60 -672.91 0 0.5 0.8 -1.300 0.198 -6.558 -0.365 65.00 8◦ 103.23 -651.74 0 0.5 1 -1.259 0.199 -6.313 -0.322 65.00 8◦ 124.19 -340.18 0 0.75 -1 -0.657 0.240 -2.739 0.310 65.00 8◦ 121.51 -313.62 0 0.75 -0.8 -0.606 0.235 -2.581 0.364 65.00 8◦ 118.21 -289.07 0 0.75 -0.6 -0.558 0.228 -2.445 0.414 65.00 8◦ 115.01 -276.38 0 0.75 -0.4 -0.534 0.222 -2.403 0.439 65.00 8◦ 111.85 -290.46 0 0.75 -0.2 -0.561 0.216 -2.597 0.411 65.00 8◦ 109.96 -307.60 0 0.75 -0.1 -0.594 0.212 -2.797 0.376 65.00 8◦ 110.50 -317.49 0 0.75 -0.05 -0.613 0.213 -2.873 0.356 65.00 8◦ 107.52 -324.93 0 0.75 0 -0.628 0.208 -3.022 0.341 65.00 8◦ 103.59 -319.49 0 0.75 0.05 -0.617 0.200 -3.084 0.352 65.00 8◦ 101.93 -320.89 0 0.75 0.075 -0.620 0.197 -3.148 0.349 65.00 8◦ 102.87 -361.46 0 0.75 0.1 -0.698 0.199 -3.514 0.267 65.00 8◦ 98.30 -418.24 0 0.75 0.2 -0.808 0.190 -4.255 0.152 65.00 8◦ 107.14 -500.15 0 0.75 0.4 -0.966 0.207 -4.668 -0.014 65.00 8◦ 106.71 -566.94 0 0.75 0.6 -1.095 0.206 -5.313 -0.150 65.00 8◦ 106.50 -594.78 0 0.75 0.8 -1.149 0.206 -5.585 -0.206 65.00 8◦ 106.41 -599.69 0 0.75 1 -1.159 0.206 -5.636 -0.216 65.00 8◦ 122.42 -365.16 0 1 -1 -0.705 0.237 -2.983 0.259 65.00 8◦ 120.58 -351.70 0 1 -0.8 -0.679 0.233 -2.917 0.287 65.00 8◦ 118.52 -343.13 0 1 -0.6 -0.663 0.229 -2.895 0.304 65.00 8◦ 116.29 -344.82 0 1 -0.4 -0.666 0.225 -2.965 0.301 65.00 8◦ 113.81 -358.58 0 1 -0.2 -0.693 0.220 -3.151 0.273 65.00 8◦ 112.27 -370.25 0 1 -0.1 -0.715 0.217 -3.298 0.249 65.00 8◦ 106.98 -376.09 0 1 -0.05 -0.727 0.207 -3.516 0.237 65.00 8◦ 110.16 -384.59 0 1 0 -0.743 0.213 -3.491 0.220 65.00 8◦ 108.52 -391.66 0 1 0.05 -0.757 0.210 -3.609 0.206 65.00 8◦ 99.34 -369.46 0 1 0.075 -0.714 0.192 -3.719 0.251 65.00 8◦ 100.79 -400.71 0 1 0.1 -0.774 0.195 -3.976 0.187 65.00 8◦ 98.77 -461.33 0 1 0.2 -0.891 0.191 -4.671 0.064 65.00 8◦ 109.21 -482.49 0 1 0.4 -0.932 0.211 -4.418 0.022 65.00 8◦ 109.18 -522.24 0 1 0.6 -1.009 0.211 -4.783 -0.059 65.00 8◦ 109.18 -548.25 0 1 0.8 -1.059 0.211 -5.021 -0.112 65.00 8◦ 108.73 -561.08 0 1 1 -1.084 0.210 -5.160 -0.138
A.0.3 Data for 3D cases Details of these cases are explained in Chapter 6.
Table A.3: Uninterfered Reference Case for NACA-23015 in 3D
v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL 65.00 8◦ 107.19 -118.69 -140.08 -- -0.573 0.518 -1.107 -
50 Table A.4: Interference Case for NACA-23015 and a 3D Cylinder (dc/cr = 0.5) v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL 65.00 8◦ 143.49 -49.42 -144.67 0.5 -0.4 -0.239 0.693 -0.344 0.584 65.00 8◦ 141.53 -39.85 -146.26 0.5 -0.1 -0.192 0.684 -0.282 0.664 65.00 8◦ 143.50 -34.11 -150.99 0.5 0 -0.165 0.693 -0.238 0.713 65.00 8◦ 139.36 -41.70 -144.40 0.5 0.05 -0.201 0.673 -0.299 0.649 65.00 8◦ 142.84 -37.54 -144.08 0.5 0.1 -0.181 0.690 -0.263 0.684 65.00 8◦ 143.69 -98.76 -150.47 0.5 0.2 -0.477 0.694 -0.687 0.168
Table A.5: Interference Case for NACA-23015 and a Flat-Cigar (dc/cr = 0.5, length is semi-infinite) v∞ α Nx Ny Nz xc/cr yc/cr CL CD L/D ∆CL/CL 65.00 8◦ 119.85 -14.88 -337.95 0.5 -0.4 -0.072 0.579 -0.124 0.875 65.00 8◦ 120.05 -11.87 -336.85 0.5 -0.3 -0.057 0.580 -0.099 0.900 65.00 8◦ 119.40 -10.14 -337.87 0.5 -0.2 -0.049 0.577 -0.085 0.915 65.00 8◦ 119.94 -9.20 -342.43 0.5 -0.1 -0.044 0.579 -0.077 0.922 65.00 8◦ 120.30 -9.00 -338.55 0.5 -0.05 -0.043 0.581 -0.075 0.924 65.00 8◦ 120.43 -9.06 -338.94 0.5 0 -0.044 0.582 -0.075 0.924 65.00 8◦ 120.05 -8.38 -336.58 0.5 0.05 -0.040 0.580 -0.070 0.929 65.00 8◦ 115.47 -9.77 -322.70 0.5 0.1 -0.047 0.558 -0.085 0.918 65.00 8◦ 121.56 -16.01 -338.01 0.5 0.2 -0.077 0.587 -0.132 0.865 65.00 8◦ 121.96 -26.14 -338.11 0.5 0.3 -0.126 0.589 -0.214 0.780 65.00 8◦ 123.99 -37.66 -339.85 0.5 0.4 -0.182 0.599 -0.304 0.683
51 Appendix B
MotoGP Regulations 2012
Since the aim of this work is to provide a viable concept, which can be used for motorcycle road racing (e.g Grand Prix), it is of interest to know the specific limitations and options. Only the relevant rules are presented here and the ones of extra interest are emphasized. [4]
2.7.7 Bodywork 2.7.7.1 The windscreen edge and the edges of all other exposed parts of the streamlining must be rounded. 2.7.7.2 The maximum width of bodywork must not exceed 600mm. The width of the seat or anything to its rear shall not be more than 450mm (exhaust pipes excepted). 2.7.7.3 Bodywork must not extend beyond a line drawn vertically at the leading edge of the front tyre and a line drawn vertically at the rearward edge of the rear tyre. The suspension should be fully extended when the measurement is taken. 2.7.7.4 When viewed from the side, it must be possible to see: a. At least 180 degrees of the rear wheel rim. b. The whole of the front rim, other than the part obscured by the mudguard, forks, brake parts or removable air-intake. c. The rider, seated in a normal position with the exception of the forearms. Notes: No transparent material may be used to circumvent the above rules. Covers for brake parts or wheels are not considered to be bodywork obstructing the view of wheel rims in regard to the above rules. 2.7.7.5 No part of the motorcycle may be behind a line drawn vertically at the edge of the rear tyre. 2.7.7.6 The seat unit shall have a maximum height of the (approximately) vertical section behind the riders seating position of 150mm. The measurement will be taken at a 90 angle to the upper surface of the flat base at the riders seating position, excluding any seat pad or covering. Any on-board camera/antenna mounted on the seat unit is not included in this measurement. 2.7.7.7 Mudguards are not compulsory. When fitted, front mudguards must not extend: a. In front of a line drawn upwards and forwards at 45 degrees from a horizontal line through the front wheel spindle. b. Below a line drawn horizontally and to the rear of the front wheel spindle. The mudguard mounts/brackets and fork-leg covers, close to the suspension leg and wheel spindle, and brake disc covers are not considered part of the mudguard. 2.7.7.8 Wings may be fitted provided they are an integral part of the fairing or seat and do not exceed the width of the fairing or seat or the height of the handlebars. Any sharp edges must be rounded. Moving aerodynamic devices are prohibited.
52 2.7.7.9 The lower fairing has to be constructed to hold, in case of an engine breakdown, at least half of the total oil and engine coolant capacity used in the engine (minimum 5 litres for MotoGP and Moto2, minimum 2.5 litres for Moto3). The lower fairing should incorporate a maximum of two holes of 25mm. These holes must remain closed in dry conditions and must be only opened in wet race conditions, as declared by the Race Director. 2.7.8 Clearances 2.7.8.1 The motorcycle, unloaded, must be capable of being leaned at an angle of 50 degrees from the vertical without touching the ground, other than with the tyre. 2.7.8.2 There must be a clearance of at least 15mm around the circumference of the tyre at all positions of the motorcycle suspension and all positions of the rear wheel ad- justment.
53 References
[1] I. H. Abbott and A. E. V. Doenhoff. Theory of Wing Sections. Dover Publications, inc., dover edition, 1958.
[2] J. Beeler. First shots of valentino rossi on the ducati. http://www.asphaltandrubber. com/news/valentino-rossi-ducati-valencia-test/. 2010–11–09, visited 2012–09– 18. [3] J. Black. Aprilia’s max biaggi wins the double to extend his world superbike lead as carlos checa crashes. http://www.foxsports.com.au/motor-sports/ superbikes/aprilias-max-biaggi-wins-race-one-at-misano-from-carlos -checa-to-extend-his-world-superbike-lead/story-fn5k3gtw-1226390545446. 11th June 2012, visited 2012–09–18. [4] F. I. de Motocyclisme. FIM Road Racing World Championship Grand Prix Regulations. 2012 1st edition. [5] T. Foale. Motorcycle Handling and Chassis Design, the art and science. Tony Foale Designs, 2011. [6] A. Johansson. Turbulence - SG2218, Lecture notes. KTH Mechanics, 2011. [7] J. John D. Anderson. Fundamentals of Aerodynamics. McGraw-Hill, Inc., 2nd edition, 1991.
[8] D. Madier. The F1-Forecast.com Technical Files - Aerodynamical & Mechanical Updates 2010. F1-Forecast, 12 2010. [9] A. Rizzi. Aerodynamic Design, a Computational Approach. KTH Aeronautical & Ve- hicle Engineering, 2002.
[10] T. Stevenson. Rodger freeths aerofoil viko tz750a. http://www.motorcycletrader.co. nz/View/Article/Rodger-Freeths-Aerofoil-Viko-TZ750A/236.aspx?Ne=145&N= 4294967266&No=135, http://www.classicyams.com/special-yamaha-bikes/ special-yamaha-bikes/yamaha-tz750a-aerofoil.html. visited 2012–07–16. [11] various. The magnificent seven - british racing legend barry sheene. https://theselvedgeyard.wordpress.com/2010/12/20/the-magnificent-seven -british-racing-legend-barry-sheene/. December 20, 2010, visited 2012–09–18. [12] various. Pit lane sportbike news (fastdates.com): Ducati’s monocoque design dilemma. http://www.fastdates.com/PitLaneNews2012.01.03.HTM. Bologna, Italy, Dec 15th, visited 2012–09–18.
[13] various. ANSYS Help - Fluent. SAS IP, Inc., 2011. [14] various. Introduction to ANSYS FLUENT 14.0. ANSYS, inc., 2012, January 25. [15] various. Introduction to ANSYS ICEM CFD 14.0. ANSYS, inc., 2012, March 21.
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