AE Dept., KFUPM. Dr. Abdullah M. Al-Garni. Fuel Economy. Emissions Maximum Speed Acceleration Directional Stability Stability.

Transcription

1 Aerodynamics: Introduction Aerodynamics deals with the motion of objects in air. These objects can be airplanes, missiles or road vehicles. The Table below summarizes the aspects of vehicle performance directly influenced by aerodynamic design. Fuel Economy Performance Emissions Maximum Speed Acceleration Directional Stability Stability Response to Flow Unsteadiness Crosswind Sensitivity Engine Cooling Transmission Brakes Condenser Comfort Visibility Heating, Ventilation and Air Conditioning Wind Noise Dirt Accumulation Splash and Spray 1

2 Aerodynamics: Aerodynamic Forces When a body moves in the air, a pressure and shear (friction) stresses are produced at every point of the body. The pressure, p, acts normal to the surface and the shear, τ, acts tangential to the surface of the body. The sum of the pressure and shear forces gives the resultant force, R. The aerodynamic forces are mainly due to pressure and shear stress distribution over the body surface. V p τ Airfoil 2

3 Aerodynamics: Aerodynamic Forces The resultant force, R, can be resolved into two components along the wind (freestream) axes: L N R lift = L = component normal to V drag = D = component along V or along the body axes axis: α V M A D chord line normal force = N = component normal to the airfoil chord axial force = A = component along the body chord The point at which the resultant force acts is called the center of pressure. It is convenient sometimes to specify the aerodynamic center which is defined as the point at which the aerodynamic moment, M, is independent of the angle of attack, α. 3

4 Aerodynamics: Aerodynamic Forces In aerodynamics, we usually deal with aerodynamic forces and moments coefficients more than forces and moments. The freestream dynamic pressure, q, ρ is the freestream density and V is the freestream velocity. Pressure Coefficient: P ; P = the freestream pressure Lift Coefficient: Drag Coefficient: Moment Coefficient: C C C C L D M P P = q = = L qs D qs M = qsl 4 q = 1 2 ρ V 2 ; S = the reference area ; l = the characteristic length.

5 Aerodynamics: Aerodynamic Forces From dimensional analysis, the above coefficients depend on some parameters: Mach number, M = V /a where a is the speed of sound. Reynolds number, Re = ρv l /μ where ρ is the air density and μ is the dynamic viscosity of the air. Angle of attack, α. In many practical problems, the lift, drag and moment coefficients are identical for geometrically similar bodies at the same Mach, Reynolds number and angle of attack. 1 2 (C L ) 1 = (C L ) 2 (C D ) 1 = (C D ) 2 5 (C M ) 1 = (C M ) 2

6 Aerodynamics: Airfoil An airfoil is simply a section cut of a wing. It is often called infinite wing. The flow characteristics around an airfoil are significantly different from those around a wing. The flow around the airfoil is two dimensional. higher flow velocity lower pressure V P lower flow velocity higher pressure 6

7 Aerodynamics: Airfoil The pressure and velocity fields around the airfoil are related via the Bernoulli s equation 1 1 P + ρv = P+ ρv The pressure distribution over Joukowski airfoil at α = 10º. The pressure coefficient is negative (means lower than the freestream pressure, P ) over the top surface and positive (higher than the freestream pressure, P ) on the bottom surface of the airfoil. The net imbalance of pressure distribution produces the lift. V P C p higher flow velocity lower pressure lower flow velocity higher pressure x/c

8 Aerodynamics: Wings Often called finite wing The flow around a wing is three dimensional; there is a flow in the spanwise direction. The mechanism for generating lift is the same as that for the airfoil, a higher pressure on the bottom surface and a lower pressure over the top surface. As consequence of the pressure imbalance between the lower and upper surface of the wing, the flow near the wing tips tends to curl around the tips; the flow is forced from the higher pressure region just underneath the wing tips to the lower pressure region on the top of the wing. Flow from higher pressure region (lower surface) to lower pressure region (upper surface) This causes the flow underneath the wing to move along the spanwise direction from the wing root to the tip and the flow on top of the wing to move from the wing tip to the root. 8

9 This flow produced a trailing vortex at both wing tips that trails downstream of the wing. For large airplanes such as the Boeing 747, these vortices are powerful enough to cause light airplanes flying closely behind to go out of control. Aerodynamics: Wings Accidents due to these vortices have occurred and that is one of the reasons for large spacing between aircraft during landing and take-off at airports. Top view Cross section view The vortices draw the air behind the wind thus inducing a downwash (downward flow) in the neighborhood of the wing. 9

10 Aerodynamics: Flow Characteristics for Wings This downwash results in an increase of drag. The additional drag is called induced drag, D i, and is related to the lift by D i L α i D = Lsinα i The downwash also affects the angle of attack. The angle of attack actually seen by the wing is the angle between the chord line and the local relative wind defined as the effective angle of attack, α eff. i α α eff α i V V w Chord line Local relative wind The geometric angle of attack α and the aerodynamic angles of attack α eff and α i is given by α = α α eff i 10

11 Aerodynamics: Lift on Airfoil At small angles of attack the lift coefficient varies linearly with the angle of attack for both symmetric and cambered airfoils. C l Cambered airfoil Symmetric airfoil at high α The mathematical analysis shows that for a symmetric airfoil Cl = 2πα α L=0 < 0 dcl ηo = dα Symmetric airfoil at small α α for a cambered airfoil : α L=0 =0 Cl = 2 π ( α α L = 0) The slopes of the lift coefficient for symmetric and cambered airfoils are the same. η = dc / dα = 2π o l 11

12 Aerodynamics: Lift on Airfoil As the angle of attack increases, an adverse pressure gradient starts to develop over the top surface of the airfoil which will cause the boundary layer to separate. C l Cambered airfoil Symmetric airfoil at high α At a certain angle of attack, this adverse pressure becomes strong enough to cause flow separation over the top surface of the airfoil. α L=0 < 0 dcl ηo = dα Symmetric airfoil at small α Once the flow separates the lift coefficient drop drastically and as a consequence stall occurs as shown in Figure 9. α L=0 =0 α 12

13 Aerodynamics: Lift on Wing The lift curve for a wing has smaller slope than the corresponding lift curve for an airfoil with the same airfoil cross section. The relationship between the two slopes is given by dcl dα = η = ηo ηo 1 + (1 + τ ) π R where η is the slope of a wing, ηo is the slope of the airfoil, is the aspect ratio, τ is a correction factor. R=b 2 / S The aspect ration is defined as where b is the span and S is the area of the wing. 13

14 Aerodynamics: Lift and Circulation The lift per unit span of an airfoil can be related to the intensity of the circulatory flow or circulation, Γ, via Kutta-Joukowski Theorem L' = V Γ ρ where the L is the lift per unit span of the wing. This relation shows that the lift per unit span is directly proportional to circulation. It is a pivotal relation in ideal incompressible flow theory often called potential flow theory. Thus, a major propel of the potential flow theory is to calculate circulation. 14

15 Aerodynamics: Lift and Circulation Example of this relation: flow over a circular cylinder The flow around non-lifting circular cylinder is symmetric Hence one would expect that the pressure distribution over the top and bottom surfaces of the cylinder is also symmetric. This results in zero lift for the cylinder. Flow over Non-lifting circular cylinder L = 0 Flow over lifting circular cylinder L > 0 However, if the cylinder rotates about its axis, then the flow field is not symmetric any more. 15

16 Aerodynamics: Lift and Circulation Why do we have a lift when the cylinder rotates?. When the cylinder rotates, this will increase the flow velocity over the top surface and decrease it on the bottom of the cylinder. Flow over lifting circular cylinder L > 0 As a result, the pressure on the top surface decreases and the pressure on the bottom surface increases (Bernoulli s equation). 1 1 P + ρv = P+ ρv 2 2 This net imbalance of pressure will produce a finite lift as sketched in Figure. This is often called Magnus effect V High speed flow Low pressure L ω Low speed flow High Pressure

17 Aerodynamics: Lift and Circulation Another Example of this relation: flow over a airfoil with a leading-edge rotating cylinder Leading-edge cylinder is off [α = 0] a) U c /U = 0 L = Uc/U=0 Uc/U=1 Uc/U=2 Uc/U=3 Uc/U=4 1.2 C L Leading-edge cylinder rotates b) U c /U = 1 L > α o 17

18 Aerodynamics: Lift and Circulation a) Uc/U = 0 e) Uc/U = 4 α = 20 b) Uc/U = 1 18

19 Aerodynamics: High Lift Devices The lifting properties of a given airfoil can be enhanced by using high lift devices as shown in the Figure 13. Wing with a trailing-edge flap The most common of these devices is the simple flap at the trailing edge of the wing. C L δ Wing with a leading-edge slat When the flap is deflected downward, the camber of the airfoil is increased. d increases Wing without flap and slat This increase is associated with a dramatic increase in the maximum lift coefficient, C L,max and a shift of the zero-lift angle of attack to a more negative value for the wing. α 19

20 Aerodynamics: High Lift Devices In some airplanes, the flap is designed not only to deflect downward but also to translate rearward which increases the wing area and hence increase the lift. The flap can increase the maximum lift coefficient by about 200%. Wing with a trailing-edge flap C L δ Wing with a leading-edge slat High lift devices can also be applied to the leading edge of the wing with the most common is the leading-edge slat. d increases Wing without flap and slat The leading edge slat can alter the pressure distribution over the wing, reduce the pressure on the top and increase the pressure on the bottom surface. As a result, a more lift is generated on the wing. Another advantage of the leading-edge slat is the delay of flow separation over the top surface of the wing to higher angles of attack and consequently delays stall of the wing. In modern aircraft a combination of leading-edge slat and trailing-flaps is common. 20 α

21 Aerodynamics: Drag The drag is an important subject in aerodynamics. A reduction in drag can lead to a reduction in fuel consumption and better performance for a vehicle. The drag coefficient varies from one object to another depending on the particular geometry of that object. For streamlined body such as wing and airfoil, the drag coefficient is low compared to bluff body such as circular cylinder, sphere or road vehicle. 21

22 Aerodynamics: Drag Normal Plate V d C D = 2.0 Circular Cylinder V d C D = 1.2 at Re = 10 5 C D = 0.6 at Re = 10 7 Streamlined body V d C D = 0.12 Half Cylinder V d C D = 1.2 Half Cylinder V d C D = 1.7 Equilateral triangle V d C D = 1.6 Pickup truck Z X C D = Piper PA-16 Clipper C D = Boeing 747 C D =

23 Aerodynamics: Drag for Airfoil vs. Wing It is important to note that there is a difference between the drag of an airfoil and that of a wing. The drag acting on an airfoil section is the sum of the skin friction drag, D f, and the pressure drag, D p, which is due to flow separation. That is, C d = D f + D qs The sum of the skin friction drag and the pressure drag is called profile drag. On the other hand, the total drag of a subsonic finite wing in a real case is the sum of the induced drag, D i, and the profile drag, p C D Di = Cd + qs where the subscript D represents the drag of the wing and the subscript d represent the drag of the airfoil. 23

24 Aerodynamics: Drag for Airfoil vs. Wing Using the lifting line theory it can be shown that for a general wing 2 where is the induced drag coefficient and e is the span efficiency factor. For elliptical wing, e = 1 and for other platforms, e < 1. Therefore, the induced drag is minimum for an elliptical platform. In the past, several aircraft have been designed with elliptical wings. However, elliptical wings are more expensive to manufacture than other simple platform such as rectangular wings. The rectangular wing is considered far from optimum. A compromise between the elliptical wing (manufacturing difficulty) and rectangular wing (poor efficiency) is the tapered wing. C Di, CL = π er 24 Elliptic wing Rectangular wing Tapered wing

25 Aerodynamics: Laminar and Turbulent Flows The drag coefficient of a body depends on the flow around the body whether it is laminar or turbulent. When the streamlines are smooth and regular and a fluid element moves smoothly along a streamline the flow is called laminar. On the other hand, when the streamlines break up and a fluid element moves in a random, irregular, and tortuous fashion the flow is called turbulent. Laminar flow Most of real flows are turbulent flows. In turbulent flow, the higher energy fluid elements from the outer regions of the flow are pumped close to the surface. Hence, the average flow velocity near a solid surface is larger for a turbulent flow in comparison with laminar flow. Figure 15 shows the velocity profile for laminar and turbulent boundary layers. Turbulent flow 25

26 Aerodynamics: Laminar and Turbulent Flows In turbulent flow, the higher energy fluid elements from the outer regions of the flow are pumped close to the surface. Hence, the average flow velocity near a solid surface is larger for a turbulent flow in comparison with laminar flow. Since the shear stress is proportional to the velocity gradient along the y-direction τ u / y then the shear stress (friction) as well as aerodynamic heating at the wall surface is higher for turbulent flow than laminar flow. y Laminar Turbulent u 26

27 Aerodynamics: Streamlined vs. Bluff body Airfoils, flat plate and wings are considered to be streamlined bodies. On the other hand, cylinder, sphere, trucks are bluff bodies. The flow around streamlined and bluff bodies is significantly different. Streamlined body- small wake The flow over streamlined body is usually smooth and the wake behind the body is small. The flow over bluff body, however, exhibits a large wake downstream the body. This wake is caused by separating flow from the body surface with a low-energy recirculating flow inside the wake as shown in the figure below. Bluff body- large wake 27

28 Aerodynamics: Streamlined vs. Bluff body The skin friction drag is due to the shear forces acting on the body and the pressure drag is due to flow separation from the body surface. Therefore, if the body is streamlined, the flow separation is minimal and one would expect that the friction drag is much greater than the pressure drag. Since skin friction drag is smaller for laminar than for turbulent flow, laminar flow is desirable for streamlined bodies. On the other hand, the pressure drag which is due to flow separation is much greater for bluff body than skin friction drag. In this case, the turbulent flow is desirable because the pressure drag for turbulent flow is smaller than for laminar flow. 28 D f D Laminar flow is desirable D p D Turbulent flow is desirable p f

29 Bluff body: Square Back (SB) Model Wind Tunnel View Model Top View Y X Model Side View Z X Z Y Cab Back 29

30 PIV Results U = 30 m/s Mean velocity and vorticity Fields Streamlines of the mean velocity field y (mm) y (mm) x (mm) x (mm) 30