In a biplane aircraft, two wings are placed one above the other. Both provide a portion of the lift, although they are not able to produce twice as much lift as a single wing of similar size and shape because the upper and the lower are working on nearly the same portion of the atmosphere. For example, in a wing of aspect ratio 6, and a wing separation distance of one chord length, the biplane configuration can produce about 20 percent more lift than a single wing of the same planform.In the biplane configuration, the lower wing is often attached to the fuselage, while the upper wing is raised above the fuselage with an arrangement of cabane struts, although other combinations have been used. Almost all biplanes also have a third horizontal surface, the tailplane, to control the pitch, or angle of attack of the aircraft (although there have been a few exceptions). Either or both of the main wings can support flaps or ailerons to assist lateral rotation and speed control; usually the ailerons are mounted on the upper wing, and flaps (if used) on the lower wing. Often there is bracing between the upper and lower wings, in the form of wires (tension members) and slender interplane struts (compression members) positioned symmetrically on either side of the fuselage.Aerodynamic research by NASA found that it was necessary for the two wings to be different in either chord or span otherwise longitudinal oscillation would occur.
At very low Reynolds numbers (<10,000 based on chord length) efficient airfoil sections can look rather peculiar as suggested by the sketch of a dragonfly wing. The thin, highly cambered pigeon wing is similar to Lilienthal's designs. The Eppler 193 is a good section for model airplanes. The Lissaman 7769 was designed for human-powered aircraft.
The Reynolds number Re is a dimensionless numberthat gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. Named after Osborne Reynolds (1842–1912), who popularized its use in 1883. Reynolds numbers frequently arise when performing dimensional analysis of fluid dynamics problems, and as such can be used to determine dynamic similitude between different experimental cases.They are used to characterize different flow regimes, such as laminar or turbulent flow:laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow These definition of Reinclude the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. characteristic dimensionThis dimension is a matter of convention – for example a radius or diameter are equally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes (such as rectangular pipes or non-spherical objects) have an equivalent diameter defined. For fluids of variable density (e.g. compressible gases) or variable viscosity (non-Newtonian fluids) special rules apply.Re= (ρ)(L)(V)/(μ) = (V)(L)/(v)V is the mean velocity of the object relative to the fluid (SI units: m/s)L is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river systems) (m)μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))ν is the kinematic viscosity (ν = μ / ρ) (m²/s)ρ is the density of the fluid (kg/m³)Transition Reynolds numberIn boundary layer flow over a flat plate, experiments can confirm that, after a certain length of flow, a laminar boundary layer will become unstable and become turbulent. This instability occurs across different scales and with different fluids, usually when Rex= 5x105, where x is the distance from the leading edge of the flat plate, and the flow velocity is the freestream velocity of the fluid outside the boundary layer.For flow in a pipe of diameter D, experimental observations show that for 'fully developed' flow (Note:), laminar flow occurs when ReD < 2300 and turbulent flow occurs when ReD > 4000. In the interval between 2300 and 4000, laminar and turbulent flows are possible ('transition' flows), depending on other factors, such as pipe roughness and flow uniformity). This result is generalised to non-circular channels using the hydraulic diameter, allowing a transition Reynolds number to be calculated for other shapes of channel.
NACA:National Advisory Committee for AeronauticsOne can generate a reasonable airfoil section given these parameters. This was done by Eastman Jacobs in the early 1930's to create a family of airfoils known as the NACA Sections.
x/c varies from 0 at the leading edge to 1.0 at the trailing edge. Cpis plotted "upside-down" with negative values (suction), higher on the plot. (This is done so that the upper surface of a conventional lifting airfoil corresponds to the upper curve.) The Cpstarts from about 1.0 at the stagnation point near the leading edge... It rises rapidly (pressure decreases) on both the upper and lower surfaces... ...and finally recovers to a small positive value of near the trailing edge.Upper Surface The upper surface pressure is lower (plotted higher on the usual scale) than the lower surface Cp in this case. But it doesn't have to be. • Lower Surface The lower surface sometimes carries a positive pressure, but at many design conditions is actually pulling the wing downward. In this case, some suction (negative Cp -> downward force on lower surface) is present near the mid-chord. Pressure Recovery This region of the pressure distribution is called the pressure recovery region. The pressure increases from its minimum value to the value at the trailing edge. This area is also known as the region of adverse pressure gradient. As discussed in other sections, the adverse pressure gradient is associated with boundary layer transition and possibly separation, if the gradient is too severe.
The relationship between airfoil geometry and airfoil pressure distributions effect of changes in surface curvature For equilibrium we must have a pressure gradient when the flow is curved. In the case shown here, the pressure must increase as we move further from the surface. This means that the surface pressure is lower than the pressures farther away. This is why the Cp is more negative in regions with curvature in this direction. The curvature of the streamlines determines the pressures and hence the net lift.
Reduced camber at aft/rear section pushing the surface downwardSharp nose leads to favourable gradients over 50% of the sectionA thicker section will have a less prominent peak (pressure peak near the nose)Only one line because at zero lift (symmetric upper and lower section with 00 attack), the upper and lower surface pressure coincide. A conventional cambered section. An aft-loaded section, the opposite of a reflexed airfoil carries more lift over the aft part of the airfoil. Supercritical airfoil sections look a bit like this.
Transonic speed is an aeronautics term referring to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.2, i.e. 600-900 mph. This condition depends not only on the travel speed of the craft, but also on the pressure and temperature of the airflow of the vehicle's local environment. It is formally defined as the range of speeds between the critical Mach number, when some parts of the airflow over an air vehicle or air foil are supersonic, and a higher speed, typically near Mach 1.2, when all of the airflow is supersonic. Between these speeds some of the airflow is supersonic, and some is not.Severe instability can occur at transonic speeds. Shock waves move through the air at the speed of sound. When an object such as an aircraft also moves at the speed of sound, these shock waves build up in front of it to form a single, very large shock wave. During transonic flight, the plane must pass through this large shock wave, as well as contending with the instability caused by air moving faster than sound over parts of the wing and slower in other parts.Transonic speeds can also occur at the tips of rotor blades of helicopters and aircraft. However, as this puts severe, unequal stresses on the rotor blade, it is avoided and may lead to dangerous accidents if it occurs. It is one of the limiting factors to the size of rotors, and also to the forward speeds of helicopters (as this speed is added to the forward-sweeping (leading) side of the rotor, thus possibly causing localized transonics).
When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the sonic boom heard as a fast moving aircraft travels overhead. A person inside the aircraft will not hear this. The higher the speed, the more narrow the cone; at just over M=1 it is hardly a cone at all, but closer to a slightly concave plane.At fully supersonic speed, the shock wave starts to take its cone shape and flow is either completely supersonic, or (in case of a blunt object), only a very small subsonic flow area remains between the object's nose and the shock wave it creates ahead of itself. (In the case of a sharp object, there is no air between the nose and the shock wave: the shock wave starts from the nose.)As the Mach number increases, so does the strength of the shock wave and the Mach cone becomes increasingly narrow. As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase. The stronger the shock, the greater the changes. At high enough Mach numbers the temperature increases so much over the shock that ionization and dissociation of gas molecules behind the shock wave begin. Such flows are called hypersonic.It is clear that any object traveling at hypersonic speeds will likewise be exposed to the same extreme temperatures as the gas behind the nose shock wave, and hence choice of heat-resistant materials becomes important.
January 2011Basics of Aerofoil Rajesh Kumar EDC-Fans Bap Ranipet BHEL 1
History:The serious work on the development of airfoil sections began in the late 1800s.It was known that flat plates would produce lift when set at an angle of incidence, some suspected that shapeswith curvature, that more closely resembled bird wings would produce more lift or do so more efficiently.H.F. Phillips patented a series of airfoil shapes in 1884 after testing them in wind tunnels (artificial currents ofair produced from induction by a steam jet in a wooden conduit)Octave Chanute writes in 1893, "...it seems very desirable that further scientific experiments be made onconcavo-convex surfaces of varying shapes, for it is not impossible that the difference between success and failure ofa proposed flying machine will depend upon the sustaining effect between a plane surface and one properly curvedto get a maximum of lift.”Otto Lilienthal, in 1894, after measuring the shapes of bird wings, tested the airfoils on a 7m diameter"whirling machine". He believed that the key to successful flight was wing curvature or camber. He alsoexperimented with different nose radii and thickness distributions .Wright Brothers aerofoil closely resembled Lilienthals sections: thin and highly cambered. (This was possiblebecause early tests of airfoil sections were done at extremely low Reynolds number, where thin and camberedsections behave better than thicker ones.)Some of the first airplanes (Wright Brothers Flyer) were biplanes reason being erroneous belief that efficientairfoils must be thin and highly cambered. A biplane is a fixed-wing aircraft with two main wings. A biplane wingstructure has a structural advantage, but produces more drag than a similar monoplane wing. It become obsoleteby the late 1930s. 2
A wide range of airfoils developedA family of sections used and tested by the NACA in the early 1920sEastman Jacobs, in 1939, at the NACA in Langley, designed and tested the first laminar flow airfoil sectionhaving extremely low drag and a high lift to drag ratio of about 300.The reasons airfoils looks quite different from one another is that the flow conditions and design goals changesfrom one application to the next. 3
The Reynolds number Re is a dimensionless number which gives a measure of the ratio of inertial forces toviscous forces and quantifies the relative importance of these two types of forces for given flow conditions.It is used to characterize different flow regimes, as laminar or turbulent flow:laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized bysmooth, constant fluid motion while turbulent flow occurs at high Reynolds numbers and is dominated byinertial forces, which tend to produce random, erratic, chaotic eddies, vortices and other flow .At very low Reynolds numbers (<10,000 based on chord length) efficient airfoil sections looks peculiar as thesketch of a dragonfly wing.The Eppler 193 is a good section for model airplanes.The Lissaman 7769 was designed for human-powered aircraft. 4
The various terms related to airfoils are defined below:1. The mean camber line is the locus of points midway between the upper and lower surfaces.2. The chord line is a straight line connecting the leading and trailing edges of the airfoil, at the ends of the mean camber line.3. The chord is the length of the chord line and is the characteristic dimension of the airfoil section.4. The maximum thickness and the location of maximum thickness are expressed as a percentage of the chord.5. For symmetrical airfoils both mean camber line and chord line pass from centre of gravity of the airfoil and they touch at leading and trailing edge of the airfoil.6. The aerodynamic centre is the chord wise length about which the pitching moment is independent of the lift coefficient and the angle of attack.7. The centre of pressure is the chord wise location about which the pitching moment is zero.8. The aspect ratio is defined as the span-to-mean-chord ratio of an airfoil. The aspect ratio of a wing is the length of the wing compared with the breadth (chord) of the wing. A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings. For most wings, the length of the chord varies along the wing so the aspect ratio (AR) is defined as the square of the wingspan divided by the area of the wing platform i.e. AR=b2/S; where, b is the wingspan, and S is the area of the wing platform.9. The solidity ratio is defined as the sum of tip widths divided by the fan circumference. Solidity is Measure of a fan’s pressure capability.10. The stall point is the fan operating condition where the boundary layer of air separates from the airfoil and causes turbulence. 5
Airfoil GeometryAirfoil geometry can be characterized by the coordinates of the upper and lower surface.One can generate a reasonable airfoil section given these parameters: Chord length, maximum thickness, maximum camber, position of max thickness, position of max camber, and nose radius 6
NACA aerofoil (Eastman Jacobs)The NACA 4 digit and 5 digit airfoils were created by superimposing a simple mean line shape with a thicknessdistribution that was obtained by fitting a couple of popular airfoils of the time: y = (t/0.2) * (.2969*x0.5 - .126*x - .3537*x2 + .2843*x3 - .1015*x4)The camber line of 4-digit sections was defined as a parabola from the leading edge to the position of maximumcamber, then another parabola back to the trailing edge. 4 4 12 Max camber in % chord Position of maximum Maximum thickness in % of chord camber in 1/10 of chord NACA 4412 2 30 12 Approx Max camber in Position of maximum Maximum thickness in % of % chord camber in 2/100 of chord chord NACA 23012NACA 5 – digit sections had the same thickness distribution, but used a camber line with more curvature nearthe nose. 7
The 6-series of NACA airfoil sections were generated1. from a more or less prescribed pressure distribution and2. were meant to achieve some laminar flow. 6 3 2 2 12 Six series Location of minimum Half width of low drag Ideal CL in Max thickness in Cp in 1/10 of chord bucket in 1/10 of CL tenths % of chordAfter the six-series sections, 1. airfoil design became much more specialized 2. particular application specific 3. these sections form basis of several airfoil sections and then the entire geometry is modified based on its 3-D characteristics. 8
Airfoil Pressure Distributions and PerformanceThe aerodynamic performance depends on the distribution of pressure over the airfoil.This distribution is expressed in terms of the pressure coefficient which is the difference between local staticpressure and free stream static pressure, non-dimensionalized by the free stream dynamic pressure. Cp = (P-P∞)/(1/2 ρU2∞)Plot Cp vs. x/c:x/c varies from 0 at the leading edge to 1.0 at the trailing edge.1. Stagnation Point : The stagnation point occurs near the leading edge. It is the place at which V = 0, In incompressible flow Cp = 1.0, In compressible flow it may be somewhat larger.2. The upper surface pressure is lower than the lower surface in this case. But it doesnt have to be always.3. The lower surface sometimes carries a positive pressure, and pulls the wing downward (near the mid-chord). 9
4. The region of the pressure distribution is called the pressure recovery region or region of adverse pressure gradient. The pressure increases from its minimum value to the value at the trailing edge.5. Adverse pressure gradient is associated with boundary layer transition and separation, if the gradient is too severe.6. The pressure at the trailing edge is related to the airfoil thickness and shape near the trailing edge. For infinitely thin sections Cp = 0 at the trailing edge.7. Large positive values of Cp at the trailing edge imply more severe adverse pressure gradients. severity of the adverse pressure gradient. 10
Effect of pressure on flow:• For equilibrium we must have a pressure gradient when the flow is curved• The pressure must increase as we move further from the surface (negative Cp)• Depends on angle of attack and aerofoil shape 11
Effects of changes in camber, leading edge radius, trailing edge angle, and local distortions in the airfoil surface. Cp vs. x/c plots 2 1 4 3 5 1. Reduced camber at aft/rear section pushing the surface downward 2. Sharp nose leads to favourable gradients over 50% of the section 3. A thicker section will have a less prominent peak (pressure peak near the nose) 4. Only one line because at zero lift (symmetric upper 6 and lower section with 00 attack), the upper and lower surface pressure coincide. 5. A conventional cambered section. 6. An aft-loaded section, the opposite of a reflexed airfoil carries more lift over the aft part of the airfoil. Supercritical airfoil sections look like this. 12
Airfoil DesignAirfoils may be designed to produce1. low drag without generating any lift2. low drag while producing a given amount of lift3. very high lift to drag ratio4. maximum lift and drag doesnt really matterTo achieve any of these, constraints may apply on1. thickness, or2. stagger angle, or3. pitching moment, or4. off-design performance, or5. stall characteristics, etc. 1. pitch chord ratio/ solidity, or 2. blade spacing, orDesign Approach1. Design by authority2. Use of an already designed airfoil3. Works well if the goals of a particular design problem matches with the goals of the original airfoil design4. The availability of the test data ensures, with the available tools now airfoil section can be designed with accurate predictability without testing 13
Methods for airfoil design Direct design Inverse designDirect Methods involve A specified section geometry (such as a NACA airfoil) Ready calculation methods for pressures and performance Evaluation based on given shape Identifying the problems in the performance characteristics Modification of the shape to improve the performanceThe two main problems of direct methods are 1. The identification of the problems in performance 2. Shape optimization for improved performanceInverse Design Methods involve The objective function as the target pressure distribution or the least squares difference between the actual and target Cp Changing the airfoil shape to improve the performance. This may be done in several ways: 1. By hand, using knowledge of the effects of geometry changes on Cp and Cp changes on performance. 2. By numerical optimization, using shape functions to represent the airfoil geometry and letting the computer decide on the sequence of modifications needed to improve the design. 14
Typical Problems1. Thick Airfoil DesignThe minimum pressure decreases due to thicknessA more severe adverse pressure gradient and the need to start recovery soonerThe section with maximum thickness must recover pressure with almost steepest possible gradientThis problem addressed by Liebeck in connection with maximum liftThe thickest possible section has a boundary layer just on the verge of separation throughout the recovery2. High Lift Airfoil DesignRequires large negative pressures on the upper surface of the airfoil. The limit to this suction is associated withi. compressibility effects, andii. the boundary layer to be capable enough of negotiating the resulting adverse pressure recovery.For maximum lift, it is best to keep the boundary layer on the verge of separationFor maximum airfoil lift, the best recovery location is chosen and the airfoil is made very thin so that the lowersurface produces maximum lift as well. (Since the upper surface Cp is specified, increasing thickness only reducesthe lower surface pressures.)3. Laminar AirfoilUseful for reducing skin friction drag, increasing maximum lift, or reducing heat transfer.At low Reynolds numbers it is achieved by maintaining a smooth surface and using an airfoil with a favourablepressure gradient. 15
Typical Problems4. Transonic Airfoil DesignSevere instability can occur at transonic speeds. Shock waves move through the air at the speed of sound. When an object also moves at the speed of sound, these shock waves build up in front of it to form a single, very large shock wave. During transonic flight, the body must pass through this large shock wave, as well as cope up with the instability caused by air moving faster than sound over parts of the wing and slower in other parts.Objective is to limit shock drag losses at a given transonic speed.Since both lift and thickness reduce (increase in magnitude) the minimum Cp, the transonic design problem is to create an airfoil section with high lift and/or thickness without causing strong shock wave.Supercritical airfoil are designed to operate efficiently with substantial regions of supersonic flow. But the maximum local Mach numbers should not exceed about 1.2 to 1.3 on a well-designed supercritical airfoil. 16
Mach number, MaIt is the speed of an object moving through air, or any other fluid media, divided by the speed of sound in thatmedium at that particular condition of temperature and pressure. Ma=V/Vswhere, Ma is the Mach numberV is the relative velocity of the source to the medium andVs is the speed of sound in the mediumAt Standard Sea Level conditions (150C temperature), the speed of sound is 340.3 m/s in the Earths atmosphere.High-speed flow around objects High- Regime Subsonic Transonic Sonic Supersonic Hypersonic hypersonic Mach No, Ma <1.0 0.8–1.2 1.0 1.2–5.0 5.0–10.0 >10.0When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of theaircraft, called a shock wave. This spreads backward and outward from the aircraft in a cone shape (called as aMach cone). It causes the sonic boom as heard when fast moving aircraft travels overhead. 17
Mach number, Ma High- Regime Subsonic Transonic Sonic Supersonic Hypersonic hypersonic Mach No, Ma <1.0 0.8–1.2 1.0 1.2–5.0 5.0–10.0 >10.0 in a subsonic compressible flow in a supersonic compressible flow where, M is Mach number is impact pressure and P is static pressure and γ is the ratio of specific heat of a gas at a constant pressure to that at constant volume (1.4 for air) 18
Typical Problems5. Low Reynolds Number Airfoil DesignToo much laminar flowRestricted severe pressure gradients and maximum lift capabilityThe boundary layer is much less capable of handling an adverse pressure gradient without separationLaminar separation bubbles are common can lead to excessive drag and low maximum lift6. Multiple Design Point AirfoilsOne of the difficulties in designing a good airfoil is the requirement for acceptable off-design performance.Low drag section must perform well without separation at an angle of attack slightly away from its designpoint.Airfoils with high lift capability may perform poorly at lower angles of attack.To overcome these one can design the upper and lower surface of the section to satisfy separate design pointoperation. Often it is clear that the upper surface will be critical at one of the points and we can design the uppersurface at this condition. The lower surface can then be designed to make the section behave properly at thesecond point.Variable geometry can be employed (at some expense) as in the case of high lift systems. 19