Aircraft Aerodynamics Session delivered by: Mr. Ramjan Pathan 1
Session Objectives At the end of this session students would have understood Basics of Fluid Mechanics Definition of fluid, Fluid flow applications Fluid properties: Compressibility, Viscosity Continuum hypothesis & Perfect gas relations Aircraft Aerodynamics : Lift (wing, tail plane, canard), Drag (types and drag polar) Equilibrium (CG potato, Stability and Trim) 2
Fluids Liquids, gases and their mixtures are fluids. Fluid is capable of flow and easily changes its shape. The air we breathe, the water we drink, the blood circulating in our lungs, fuel of our automobile and cooking, are all fluids. A fluid is a substance that deforms continuously when subjected to shear stress, however small. 3
Fluids Solid has densely spaced molecules with large intermolecular cohesive forces that allow it to maintain its shape, and can not be easily deformed. For gases at normal pressures and temperatures, the spacing is on the order of 10-6 mm and for liquids it is on the order of 10-7 mm The number of molecules per cubic millimeter is on the order of 10 18 for gases and 10 21 for liquids. 4
Fluids Fluid is a substance that deforms continuously when acted upon by any force (shear force) tangential to the area on which it acts. A fluid at rest has no shear force or shear stress existing in it. A solid at rest can resist shear forces and shear forces can cause initial displacement of one layer over the other until a position of stable equilibrium is reached. Whereas fluids cannot resist shear forces and relative motion between layers take place as long as shear forces act on it. A fluid takes shape of the vessel containing it. 5
An Overview of Fluid Mechanics Fluid Mechanics: A physical science dealing with the action of fluids at rest or in motion, and with applications to devices in engineering using fluids. Fluid mechanics is basic to such diverse fields as aeronautics, chemical, civil, and mechanical engineering, meteorology, naval architecture, and oceanography. 6
Fluid Mechanics This is a field of study in which fundamental principles of mechanics are applied to liquids and gases These principles include Conservation of Mass Conservation of Energy Newton s Laws of motion For fluids at rest the study is known as Fluid Statics For fluids in motion the study is known as Fluid Dynamics 7
Significance of Fluid Mechanics Fluids are omnipresent & their applications include Weather & climate Vehicles: automobiles, trains, ships, and planes, etc. Environment Physiology and medicine Sports & recreation Many other examples! 8
Concept of Continuum Fluids are composed of molecules that collide with one another and solid objects. The continuum assumption, however, considers fluidstobe continuous. 9
Concept of continuum In engineering applications, we assume fluids to be a continuous distribution of matter with no empty spaces between them rather than an agglomeration of separate molecules. This assumption enables the fluid properties of velocity, temperature, density etc., to be described as continuous functions in space, for analytical purposes. p This assumption is valid because the number of molecules involved is so vast and the distances between them are so small, thatt fluid properties can be assumed to vary continuously from one point to another in the fluid. 10
Properties of Fluids Density: It is the ratio of the mass of the substance to the volume that it occupies Temperature: Is a thermodynamic state variable that provides a measure of the internal energy of the fluid. 11
Compressibility Compressibility is a measure of change of volume (or density) when it is subjected to a change ofpressure. A fluid may be compressed by the application of pressure thereby reducing its volume and giving rise to a volumetricstrain. t i This property of compressibility of a fluid is expressed by the bulk modulus of elasticity. If by applying a pressure dp, there is a decrease in volume, the bulk modulus of elasticity K is expressed as Liquids are considered to be incompressible, their values of bulk modulus are high. Gases are not usually described with term bulk modulus, since the they are highly compressible. 12
Compressibility If the density change occurs with no heat transported to or from the gas, the process is adiabatic. If in addition, no heat is generated within the gas, the process is called disentropic i process. For this case, the relation is K = and dp = d / dp = p / d dp = K / d dp dp/ p = p p 13
Compressibility Equation of state of an Ideal gas is P = ρ R T dp p R T = = = R T = a 2 d where a is the speed of sound din the medium. Therefore K / = a 2 We can consider a fluid as incompressible if d = dp K <<1 14
Compressibility (Contd) For air, a is about 330 m/s and hence if the velocity of a body in air is 100 m/s or less, we can consider the flow of air as incompressible. We have to use the compressible effects for Mach number ( V/a) of 0.3 and higher. 15
Viscosity Viscosity is the property of fluid to resist its motion. A minimum shear stress across its layers is required to induce motion. du dy is the coefficient of friction or dynamic or absolute viscosity Kinematicviscosityi i i = / / 16
Variation of shear stress in the fluid for varying shearing strain 17
Shear stress and strain variation for different fluids Example for shear thickening is quick sand (sand and water marshy). Example for shear thinning is colloidal and polymer solutions. Bingham plastics behave as solid till a certain shear stress is developed, then they flow. Eg. Toothpaste 18
Variation of dynamic viscosity with temperature 19
Real & Ideal Flows Ideal flow: Inviscid flows are irrotational Inviscid, irrotational and incompressible flow is referred to as Ideal flow Viscous flows are Real flows Vortices are rotating fluid particles created by the viscosity it in the boundary layer, that tgive rise to Circulation around the body. The vortices emanate from a body moving through a fluid giving rise to aerodynamic forces on the body. Viscous flows are always rotational 20
Types of Fluid Flow Uniform and Non Uniform Flow Steady and Unsteady Flow Steady uniform flow Steady non-uniform flow Unsteady uniform flow Unsteady non-uniform flow Compressible and Incompressible flow One,Two and Three Dimensional flows Ideal and Real Fluid flow 21
Types of Fluid Flow Uniform flow: If the flow velocity is the same in magnitude and direction at every point in the fluid it is said to be uniform. Non-uniform: If at agiven instant, t the velocity is not the same at every point the flow is non-uniform. In practice, by this definition, every fluid that flows near a solid boundary will be non-uniform as the fluid at the boundary must take the speed of the boundary, usually zero. However if the size and shape of the of the cross-sectionsection of the stream of fluid is constant the flow can be considered uniform. 22
Types of Fluid Flow Steady: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time. Unsteady: If at any point in the fluid, the conditions change with time, the flow is described as unsteady. In practice there is always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady. 23
Types of Fluid Flow Unsteady uniform flow At a given instant in time the conditions at every point are the same, but will change with time. An example is a pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off. Unsteady non-uniform flow Every condition of the flow may change from point to point and with ihtime at every point. For example waves in a channel. 24
One- Two- and dthree-dimensional i Flows One-dimensional flow is one in which all the flow parameters may be expressed as a function of time and one space co-ordinate only. Two-dimensional flow is one when flow properties may be expressed as a function of two space co-ordinates. In a three dimensional flow, flow properties may be expressed as a function of three space co-ordinates. 25
1D, 2D and 3D flows Y X V=f(y f(y,t) Y X V=f(x,y,t) V=f(x,y,z,t) 26
Laminar Flow Flow moving in layers parallel to axis of the tube..\videos\v8_1.mov..\videos\v9_3.mov 27
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Standard Atmosphere 30
Standard Atmosphere At sea level, the standard condition gives the following properties: pressure = 101,325 N/m2 temperature = 288.16 K viscosity=1.789 10 5m/s acceleration due to gravity = 9.81 m/s2 Various Levels of Atomosphere of interest Troposphere: up to 11 km Tropopause: 11 km Stratosphere: from 20 to 47 km 31
Basics of Fluid Resistance All fluids have some form of viscosity Air has a low viscosity, it sufficient i to account for its effects. However, modeling of flow with viscosity is very complex Initial work was largely based on approximation that air had no viscosity (i.e., inviscid) This simplification gives quick results, but can sometime be completely in-correct Aerodynamic forces of lift and drag are the resultant components of the pressure field around an aircraft. Aircraft designers seek to obtain the maximum possible lift-to-dragt ratio 32
Aerodynamics Aircraft stability and control are the result of harnessing these aerodynamic forces. Aircraft control is applied through modifying these aerodynamic forces by control surfaces Elevator, Rudder, and Aileron. These control surfaces are sized based on the requirements for the full flight envelope without sacrificing safety. 33
Aerodynamics : Forces 2 All objects are subject to gravitational pull : weight For sustained flight, an aircraft requires a lifting surface to oppose the weight The key to lift generation is in the sectional characteristics (i.e., aerofoil) of the lifting surface that serve as wings. We will see how the differential pressure between the upper and lower surfaces of the wing generates Lift. Any motion in air is accompanied by resistance referred to as Drag. For sustained flight we need to overcome Drag. This is accomplished by Thrust produced by the engine 34
Wing cross-section An airfoil has a Leading edge, is the "front" of the airfoil the portion that meets the air first. Trailing edge, is the back of the airfoil the place at which the airflow over the upper surface joins the flow over the lower surface of the airfoil. Chord, of an airfoil is the imaginary straight line drawn through the airfoil from its leading edge to its trailing edge Camber of an airfoil is the curve of its upper and lower surfaces. This curve is measured by how much it departs from the chord of the airfoil. 35
Airfoil NACA Series NACA 5 digit airfoil 23115 implies the following NACA 6 digit airfoil 63 2-212 implies the following 2 36
Airfoils - Nomenclature 37
Airfoils - Nomenclature 38
Forces on the Airfoil Forces act along the entire surface. 39
Net Force Which way does the lifting force actually work? Combining all the forces. 40
Lift Relates to AOA Zero Lift at Zero AOA 41
Published NACA Data NACA 2415 42
Got Lift? Flaps Flaps increase the wing s camber. Some also increase the wing area (fowler flap). Almost all jet transports also have leading edge flaps. 43
High Lift Devices High-lift devices are small aerofoil-like elements that are fitted at TE of the wing as a flap or at the LE as a slat In typical cruise conditions, the flaps and slats are retracted within the contour of the aerofoil. Flaps and slats can be used independently or in combination. At low speed, they are deflected about a hinge line, rendering the aerofoil more curved as if it had more camber. 44
Flow field with Flaps 45
Flaps Flaps increase the wing s camber. Some also increase the wing area (fowler flap). Almost all jet transports also have leading edge flaps. 46 46
Drag: Total Drag (Power Required) Curve 1,400 1,200 1,000 800 max. lift/drag best glide Induced drag due to Lift parasite drag - resistance 600 400 total drag Drag (lbs s) 200 50 100 150 200 Indicated Airspeed (knots) 47
Airfoil : Desired characteristics Designers look for the following qualities in the characteristics of a 2D aerofoil: The lift should be as high as possible; this is assessed by the C L max of the test results. The stalling characteristics should be gradual ie the aerofoil should able to maintain some lift past C Lmax. However, desired stall characteristics depend on the application. For a Trainer airplane it is better to have forgiving, gentle stalling characteristics. Combat airplane designers can trade-off for better performance. 48
Airfoil : Desired characteristics There should be a rapid rise in lift; that is, a better lift curve slope given by dc L /dα. There should be low drag using a drag bucket, retaining flow laminarization as much as possible at the design C L (i.e., angle of incidence). C m characteristics should give nose-down moments for a positively cambered aerofoil. It is preferable to have low C m to minimize trim drag. 49
Airflow Around a Wing AOA 0 3 8 Circulation Pattern Bound Vortex Notice that: Air on top arrives well before air below. accelerated (stretched in the diagram) Air below decelerated (arrives after free stream ) (compressed in the diagram) 50
Wing : 3D effects A 3D finite wing produces vortex flow as a result of tip effects (shown in next slide) The high pressure from the lower surface rolls up at the free end of the finite wing, creating the tip vortex. This vortex flow generates a downwash, which is distributed spanwise at varying strengths. Lift is a reaction force to this downwash Energy lost in the downwash appears as lift dependent induced drag, D i and its minimization is a goal of aircraft designers. 51
Wing : 3D effects Downwash decreases for large span wings : aspect ratio For large AR, flow can be approximated by 2D flow...\videos\v9_1_shuttle_landing.mov..\videos\v4_2_vortex generated in Smoke.mov 52
Typical values for δα max The wing tip effect delays the stall by a few degrees because the outer-wing flow distortion reduces the local angle of attack it is shown as δα max. is the shift of CL max ; this value of δα max is determined experimentally. Typical empirical relationship δα max = 2 deg, for AR > 5 to 12, δα max = 1 deg, for AR > 12 to 20, δα max = 0 deg, for AR > 20. 53
Effect of 3D effects 54
Wing Planform 55
Wing Definition Sweep Angle aspect ratio, AR = (b b)/(b c) ) = (b 2 )/(SW) 56
Wing Definition 2 Wing Sweep Angle, The wing quarter-chord line is the locus of one fourth of the chord of the reference wing planform area measured from the LE, as shown in Figure. The wing sweep is measured by the angle of the quarter-chord line extended from the line perpendicular to the centerline. Wing Root (croot) and Tip (ctip) Chord These are the aerofoil chords parallel to the aircraft at the centerline and the tip, respectively, of the trapezoidal reference area. 57
Wing Definition Wing Taper Ratio, λ This is dfi definedd as the ratio of the wing tip chord to the wing root chord (ctip/croot). Range is from 0.3 to 0.6. The taper ratio improves the wing efficiency by giving a higher Oswald s efficiency factor Wing Twist The wing can be twisted by making the wing tip nose down relative to the wing root This causes the wing root to stall earlier (to retain aileron effectiveness). Typically, y, a1-to2-deg twist is sufficient 58
Typical values : Ref Kundu A W is aircraft wetted, S W is wing plan form area area, b is span 59
Aerodynamics Design Drivers Minimizing the drag of an aircraft is one of the main obligations of aerodynamicists. Viscosity contributes to approximately two-thirds of the total subsonic aircraft drag. The effect of viscosity is apparent in the wake of an aircraft as disturbed airflow behind the body. Its thickness and intensity are indications of the extent of drag and can be measured. One way to reduce aircraft drag is to shape the body such that it will result in a thinner wake. 60
Flow over a circle 61
Streamlining General approach is to shape the body as a tear drop aft end narrower and sloping gradually Supersonic flow is different but it is still preferable for the aft to be smaller. The smooth contouring of is called streamlining follows the natural airflow lines around the aircraft body aircraft have attractive smooth contour lines. Streamlining is synonymous y with speed and its influence in shaping is revealed in many objects Boats, automobiles, cycling helmets etc. 62
Streamlining i The body has an elongated shape in the rear part to produce a gradual increase in pressure. The optimum contour for a streamlined body is one in which form drag is minimum (smallest wake zone). Early flow separation results in a larger wake. 63
Fuselage : Area - ruling This is implemented for high speed (Trans and supersonic) combat airplanes. However, for transport or cargo airplanes, we need a uniform c/s fuselage. 64
The Boundary Layer Newtonian fluid model: Viscous stress is proportional to Rate of strain Velocity at a solid surface relative to the surface is zero (no-slip condition) There is no discontinuity of velocity in the fluid Consequently close to the surface, there is a region where velocity increases rapidly from zero and approaches the velocity of the main stream. This region is known as the boundary layer. 65
The Boundary Layer The increase of velocity from the solid surface indicates that shear stresses are present. Since this layer is thin, it indicates that thevelocity gradient is high. h In 1904, Ludwig Prandtl suggested that any external flow past a body can be considered in two parts: A boundary layer where shear stresses are of prime importance and Beyond the boundary layer where the velocity gradients are small and theeffects of viscosity are negligible. 66
Boundary Layer 1. Consider a flow past a flat plate parallel to the direction of the oncoming fluid. There is no other solid surface and the pressure of the flow is uniform. 2. The viscosity action near the surface of the plate gives rise to a velocity gradient. The flow is retarded in the neighborhood of the surface; and the boundary layer begins at the leading edge of the plate. 67
Boundary Layer 68
Boundary Layer Control Drag on a body depends on: Whether boundary layer is laminar or turbulent Position at which separation occurs Reduction of drag is of prime importance in aircraft design. Skin friction drag can be reduced by delaying transition from laminar to turbulent boundary layer and also by delaying boundary layer separation. 69
Boundary Layer Control Separation of flow can be prevented by accelerating the flow in the direction of flow. This is achieved by the following: extract slow moving fluid by suction through slots or through a porous surface Inject fluid at high velocity from small rearward facing slots at the boundary surface Slotted wing 70
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Boundary Layer Control Mechanism of Wall Suction: Fluid particles close to the wall lose their kinetic energy near the separation point. Separation can be prevented or at least delayed by removing these retarded fluid particles and replacing them by fluid particles with higher kinetic energy. This is possible by sucking the flow particles through a porous wall. Particles of higher kinetic energy in the upper layer now move close to the wall and prevent separation of the boundary layer. Suction also delays transition from laminar to turbulent flow in the boundary layer, and so reduces skin-friction drag. 72
Control by tangential blowing 73
Boundary Layer Control Mechanism of tangential blowing Injection of air through a porous wall can also control boundary layer separation. This is generally accomplished by blowing high energy air tangentially from a rearward facing perforation. Injection of air promotes turbulence in the boundary layer and thereby increases skin friction. However, form drag is reduced considerably due to delayed flow separation (reduction of wake). 74
Relaminarization Boundary Layer Control It has been observed that there are methods that can ensure reversal of turbulent flow to laminar flow. One can employ some special means, such as buoyancy and magnetic fields, whereby turbulent flow can be changed to laminar flow. 75
Boundary Layer Control Relaminarization There are three different classes of mechanisms that are responsible for re-laminarization. In the first case, turbulent energy is dissipated through the action of a molecular transport property, such as, viscosity and the governing parameter turns out to be the Reynolds number. Consider a flow in aduct having a small expansion angle of 1 o or 2 o.. The duct Reynolds number far downstream drops gradually until turbulent flow can no longer be sustained. Example : screens in a wind tunnel. The turbulence intensity decreases downstream direction. 76
Relaminarization ( contd.) In the second case, turbulent energy is destroyed or absorbed by work done against an external energy like buoyancy force or curvatures of the geometry. In such flows, the typical parameter which governs laminarization is the Richardson number Ri. It is a measure of stratification (positive for stable stratification). 77
Relaminarization ( contd.) The third category of reversion of flow is exemplified by a turbulent boundary layer subjected to severe acceleration. Consider a highly accelerating flow through a nozzle. flow at the entrance of the nozzle is turbulent. Downstream, a two layer zone is observed. The In the outer layer, turbulence is rapidly removed forcing the inner viscous layer near the wall to respond and bi bring about re-laminarization. 78
Control by Boundary layer fences 79
Control by Vortex generators 80
Session Summary Following topics were covered in this session: Basics of Fluid Mechanics Definition of fluid, Fluid flow applications Fluid properties: Compressibility, Viscosity Continuum hupothesis & Perfect gas relations Aircraft Aerodynamics : Lift (wing, tail plane, canard), Drag (types and drag polar) Equilibrium (CG potato, Stability and Trim) 81
Thank you! 82