AE 1001 DISCOVERY COURSE - 123seminarsonly.com Aerodynamics 1 AE 1001 DISCOVERY COURSE Aerodynamics Ref.: Introduction to flight by ... 8/1/2008 Aerodynamics 11 Basic Aerodynamics

8/1/2008 Aerodynamics 1

AE 1001 DISCOVERY COURSE

AerodynamicsRef.: Introduction to flight by

John D. Anderson Ch. 3,4 and 5


Aerospace VehiclesAerospace Vehicles can be divided in two categories, namely, Atmospheric such as airplanes and helicopters and space vehicles such as satellites.Even space vehicles have to encounter atmosphere during blast off and re-entry.Atmospheric properties of interest during flight are pressure, temperature and density. From the two properties, the third can be evaluated using perfect gas relation (p=ρRT).The flight vehicle performance depends on atmospheric properties. Atmospheric properties are obtained both from measurements and mathematical models.


The Standard AtmosphereThe pressure and temperature of the atmosphere depends on altitude, location, time of the day, season etc.Standard atmosphere is a defined atmosphere to relate flight tests, wind tunnel results etc. to a common reference.To a reasonable degree, the standard atmosphere reflects average atmospheric conditions.Geometric height above the sea level is called geometric altitude. The distance from the center of earth is called the absolute altitude. Absolute altitude is important for space flight.


Temperature Distribution in Standard Atmosphere

See appendixof the bookFor T, p and ρVariation withAltitude.


Physical quantities of a flowing gasPressure: Normal force per unit area exerted on a surface. (unit: N/m2)Density: mass of gas per unit volume (Kg/m3)Temperature: a measure of average kinetic energy of the particles in the gas (mean molecular kinetic energy) (K)Velocity: Velocity of an infinitesimally small fluid element as it passes a point.For a steady flow, the fluid element takes a fixed path that is called a streamline.Easy to visualize flow by drawing the streamlines


Flow past an airfoil

Streamlines

Fluid element

Velocity vector


Smoke photograph of a low speed flow


Source of all aerodynamic forcesFlow of air past an object causes object to experience a force.If you put your hand out of a moving car, you would experience a force due to the air flow past your hand.The aerodynamic force exerted on an airplane, missile or any other object arise due to:

1. pressure distribution on the surface.2. shear stress (friction) on the surface.One is a normal force and another is tangential

(due to friction).


Pressure and shear distributions

Pressuredistribution

Shear stressdistribution


Purpose of aerodynamic studiesNo matter how complex the flow field and the shape of the body, aerodynamic forces (such as lift and drag) arise due to the two types of these forces.Prediction of these forces requires the knowledge of complete flow field of the body.This knowledge of flow field can be obtained by experimental and theoretical (including computational aerodynamics) aerodynamic studies.Experimental studies are carried out in wind tunnels. These are ground based facilities to simulate flight conditions in a laboratory environment.


Basic AerodynamicsAerodynamics is the study of forces and the resulting motion of objects through the air.Aerodynamics is the dominant feature that drives the external shape of a flight vehicle.Two basic approaches to the flows are: (i)flow without friction (in-viscid flow) and (ii)flow with friction (viscous flow). All real flows are with friction. The region adjacent to a wall in fluid flow is particularly dominated by viscous effects.The flow adjacent to wall has effect on aerodynamic drag of a body in particular when flow gets separated.


Conservation EquationsInviscid flow analysis is an idealization but is good enough in many cases as the frictional effects are small.For certain flows, influence of friction is dominant and has to be considered.Conservation equations in fluid flows are: (i) Mass is conserved, (ii) momentum equation, and (iii) conservation of energy.Mass is conserved irrespective of flow being with or without friction.The momentum equation for an inviscid flow is Euler’s equation and its simplified form is Bernoulli’s equation.


Continuity equationContinuity equation is basically a mass conservation equation.Consider flow through a stream tube formed by streamlines that go through the circumference of a circle.Mass flow at the inlet of the stream tube is equal to ρ1V1A1 and the mass flow at the exit of stream tube is equal to ρ2V2A2..Accordingly the continuity equation for steady flow is:

ρ1

V1

A1 =

ρ2

V2

A2Note that there can be no flow normal to the stream tube by the definition of streamline.


Stream tubes

A1V1ρ1

V2

V1

A1V1ρ1

A2V2ρ2

V.dt


Compressible and Incompressible flowFor compressible flows, density of fluid can change from point to point in the flow field (ρ1≠ρ2)For incompressible flows, density remains constant (ρ1=ρ2).For incompressible flows V1A1 = V2A2 As flow area decreases, flow velocity increases and when flow area increases, flow velocity decreases.In reality no flow can be incompressible.However for low speed air flows (V<100 m/s), flow can be assumed incompressible.


Bernoulli’s EquationBernoulli’s equation is a simplified form of Euler’s equation. It is applicable to only incompressible and inviscid flows in the absence of gravity (neglected for gases).Along a streamline: p+ ρV2 = Const.The above equation relates properties along a streamline. Bernoulli’s equation should not be used for compressible flows.If flow is uniform (all streamlines have same value of p and V) then, the constant is same for all the streamlines. The constant is called total or stagnation pressure.


How lift is produced


Explanation of liftStream tube A is squashed to a smaller cross sectional area is it flows over the upper section of the airfoil sensing obstruction to the flow. Velocity of the flow must increase (from continuity equation) and pressure decrease (from Bernoulli’s equation).Due to the design of airfoil surface, bottom surface presents less of an obstruction and stream tube A is not as much squashed. So the pressure on the lower surface is higher than the upper surface. Lower pressure on upper surface and lower pressure on lower surface causes lift.


Effects of viscosityIn real flows, the flow at the solid surface adheres to the surface due to friction.There is a thin region of retarded flow at the surface called the boundary layer.Flow can be split in two regions, one in the boundary layer and another outside.Flow outside boundary layer is called potential flow and is essentially inviscid.The wall shear stress is equal to the product of the coefficient of viscosity and the velocity gradient at the wall (τw = μ(dV/dy)y=0).


Laminar and turbulent flowLaminar flow: Streamlines are smooth and regular. Fluid element moves smoothly along the streamline.Turbulent flow: Streamlines breakup and fluid element moves in a random, irregular fashion.Shear stress in a turbulent flow is greater than in laminar flow.The Reynold’s number (defined as Re = ρVd/μ

where d is characteristic length) is an important non-dimensional parameter in fluid flow.Transition of flow from laminar to turbulent regime takes place at certain value of Re no.. The transition Re no. depends on the nature of flow.


Boundary layer-Laminar and Turbulent

Boundary layer growth over an airfoil

TurbulentLaminar

BL over flat plate


Flow separationMost of the real flows are viscous and turbulent.Drag arising because of shear stress on the wall is called skin friction drag.In presence of adverse pressure gradient (pressure rising in the direction of flow), the flow may not remain attached to the wall.Another type of drag, called pressure drag arises if the flow separates (stall). There is a drastic fall in lift coefficient and a major rise in drag coefficient when the flow separates over the airfoil surface.


Separated and attached flows

Separated flow

Attached flow

Angle of attack

Lift Coeff.


SummarySkin friction drag arises due to shear stress on the wall. It is more for the turbulent flow than for laminar flow.Drag due to separation is called pressure drag and it’s a magnitude greater than skin friction drag.Separation is more likely in laminar flow than in turbulent flows. One of the reasons for flow separation is the adverse pressure gradient. Flow does not separate on slender bodies (streamlined bodies) like thin airfoil at low angles of attack. Flow will separate past a circular cylinder as it is not a streamlined body.


A wing and airfoil


Airfoil nomenclature


Wing and the airfoilThe cross-sectional shape of an airplane wing at span wise location is an airfoil.Mean camber line of an airfoil is the locus of points mid way between upper and lower surfaces.The most forward and most rear points of the mean camber line are called leading and trailing edges.The camber is the maximum distance between the chord line and the camber line.Camber, shape of mean line and thickness distribution essentially control the lift of the airfoil.


Lift, drag and moments


Pressure distribution on an airfoil


Lift, Drag and the MomentsThe angle between the relative wind and the chord line is the angle of attack.The resultant aerodynamic force (arising out of pressure and shear forces) has two components, namely, Lift (L) and Drag (D)Lift is component perpendicular to relative wind and Drag is parallel to it.In addition there is a moment as the resultant upward force and downward forces may not pass through the same point. The point on the airfoil about which moments are zero is called aerodynamic center. Forces and moments are functions of the angle of attack.


Non dimensional parametersL = q∞

x S x cl

D = q∞

x S x cd

M = q∞

x S x c x cm

Cp

= (p-p∞

)/ q∞q∞

= ½

ρ.V2 (dynamic head)S = Wing areacl

= lift coefficient {f1

(α, M, Re)}cd

= drag coefficient {f2

(α, M, Re)}cm

= moment coefficient {f3

(α, M, Re)}

Cp = pressure coefficient


Pressure Distribution on an airfoil

Area between The two curvesIs the lift coefficient


Lift Curve of symmetrical airfoil

Lift increases with angle of attack till stall occurs

--------stall


High lift devices (used during take off and landing)


Increase in lift coefficient with flap


Typical lift coefficient values for high lift devices


Slats (increase lift coefficient)


Effect of finite wingThe flow field about a finite wing is three dimensional.The non dimensional coefficients of a finite wing are different from those of an infinite wing.All real airplane wings are finite.Aspect ratio is important in determining the three dimensional effects.Higher aspect ratio wings have lower induced drag (drag induced in generating lift).From structural and internal volume consideration, lower aspect ratio has some beneficial effects.


Finite Wing

Aspect ratio= AR = S/b2

S-wing area

Wing span


Wing tip vortices


Wing let (used to reduce tip losses)


Winglets on B 747-400


Energy EquationEquation of state p=ρRT relates pressure, density and temperature at a point.The first law of thermodynamics states that the change in internal energy of a system is equal to work done and the heat added to the system.An adiabatic process is one in which no heat is added or removed from the system.A reversible process is one in which no frictional or dissipative effects occur.An isentropic process is one which is both adiabatic and reversible.


ContinuedFor an isentropic flow:

(p2/ p1) = (T2/ T1)(γ/γ-1)

The above equation is relevant for compressible flow only.Energy can not be created or destroyed. It can only change form.CpT+1/2V2 = const. is energy equation along a

streamline. If all streamlines emanate from a uniform flow, the constant is same for all streamlines. The above equations replace the Bernoulli’s equation for compressible flows.


Speed of SoundSound waves travel in air at a definite speed called the speed of sound.The speed of sound in a perfect gas depends only on the temperature of the gas. a = (γRT)1/2 where γ is the ratio of specific

heats, R is gas constant and T is the absolute temperature.M = V/a is called the Mach number (V is flow velocity).If M<1, the flow is subsonic, M=1, the flow is sonic and for M>1 the flow is supersonic.


Critical Mach number


Flow over an airfoil at high speedsWhile airplane may be flying at subsonic velocity, the flow over the wing can be supersonic in some regions.The flow accelerates and expands over the suction surface of an airfoil, therefore, Mach number locally in some regions would be greater than free stream Mach number.The value of free stream Mach number at which the sonic flow (M=1) is obtained is called the critical Mach number.For free stream Mach numbers greater than critical, airfoil would experience a dramatic increase in drag. This drag arises because of local supersonic flow over the airfoil.


Drag Divergence

Wave drag is a magnitude greater than profile drag

Profile drag

W a

v e

Mainly wave drag

CD

M∞


Effect of Airfoil shape on critical Mach number

Thicker airfoilshave lowerCritical M nos.


Supercritical airfoilAn airfoil shape for efficient flight at supercritical Mach number was proposed by Whitcomb (1965) working for NASA.All modern civilian jets are designed with supercritical wings.In supercritical airfoil, the shape of the airfoil is designed with relatively flat top surface.The local Mach number on a supercritical airfoil is less than conventional airfoil when the free stream mach number exceeds the critical value. Drag divergence mach number therefore increases compared to a conventional airfoil.


Wind TunnelsLift and drag of an aerodynamic body are same whether the air moves over the body or body moves through the stagnant air. This concept is foundation of wind tunnel testing.Wind tunnels are used for force and moment measurements, flow visualization, detailed velocity and pressure measurements etc.The wind tunnels can be open circuit or closed circuit. Open circuit wind tunnels are easy to build and cheap. Mostly wind tunnels are closed circuit to reduce energy losses.Wind tunnels can be continuous running or blow down.There are many types of specialized wind tunnels


Open Circuit Wind Tunnel


Closed Circuit Wind Tunnel

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AE 1001 DISCOVERY COURSE - 123seminarsonly.com Aerodynamics 1 AE 1001 DISCOVERY COURSE Aerodynamics Ref.: Introduction to flight by ... 8/1/2008 Aerodynamics 11 Basic Aerodynamics