1. Fluid Dynamics Around Airfoils - Home UBC Blogs
1. Fluid Dynamics Around AirfoilsTwo-dimensional flow around a streamlined shapeFoces on an airfoilDistribution of pressue coefficient over an airfoilThe variation of the lift coefficient with the angle of attack for a symmetrical and non-symmetrical airfoil1
2. Governing EquationsConservation of mass: This equation describes the time rate of change of the fluid density at a fixed point inspace. 0 Conservation of momentum: Balance of Linear Momentum Momentum balance along the x-axis: Momentum balance along the y-axis: Constitutive laws: For a Newtonian fluid, the viscous stresses are proportional to the velocity gradients:Navier-Stokes Equations:Or in vectorial formUsing vector identities 2 2 ! # # " # # # # " # # '( &'( . '(,&'( - '( # &'( ( % )& '('( . &'( &&'( /'( 0 '() '(. &'( , ' ( / % ' ( "'(- '(1 ( & 2Bernoulli’s Equation: Integrated forms of the simplified versions of the Navier-Stokes Equations, e.g. for unsteadyirrational flows'( . &'(' ( &' ( " ( 0 2 Kelvin’sTheorem: In an incompressible inviscid flow with conservative body forces, the time rate of change of23circulation around a closed curve consisting of the same fluid elements is zero, i.e, 24 02
3. Dimensional Analysis and Control Volume ApproachSome common variables and dimensionless groups in fluid mechanics Control volume for obtaining drag on a two-dimensional body.5 6# 7 # #81 : ; 6 6The decrement of momentum flux is a direct measure of the body drag.3
4. Potential Flow TheoryElementary flows, which can be superimposed to describe the flow around bodies of arbitrary shape.Doublet vortex uniform flow: synthesis of flow around circular cylinder with circulationIrrotational flow around a nonsymetrical airfoilwith zero circulation (zero lift)Actual flow past a nonsymetrical airfoilwith positive circulation (positive lift)The Kutta-Joukowski theorem states that the force experienced by a body in a uniformstream is equal to the product of the fluid density, stream velocity, and circulation and has adirection perpendicular to the stream velocity, ? &@ Γ.4
5. Numerical (Panel) MethodSource panel distribution over the surface of a body of arbitary shape (for non-lifting bodies)Discrete vortex representation of the thin, lifting airfoil model.5
6. Flow over Two-Dimensional Airfoil (Thin-Airfoil Theory)Representation of the mean camber line by a vortex sheetwhose filaments are of variable strength B C 1. The lift slope of a two-dimensional airfoil is 2D.2. The airfoil camber does not change the lift slope and can be viewed as an additional angle of attackeffect.3. The trailing-edge section has a larger influence on the above camber effect. Therefore, if the lift ofthe airfoil needs to be changed without changing its angle of attack, then changing the chordlinegeometry (e.g. by flaps or slats) at the trailing-edge region is more effective than at the leading-edgeregion.4. The effect of the thickness of the airfoil is not treated in a satisfactory manner by this approach.5. The two-dimensional drag coefficient obtained by this model is zero and there is no drag associatedwith the generation of two-dimensional lift. Experimental airfoil data, however, include drag due toviscous boundary layer on the airfoil.6
Schematic description of airfoil camber effect on the lift coefficientEffect of high-lift devices on the lift coefficient of a three-element airfoil (E represents flap deflection)Lift and pitching moment of a NACA 0009 airfoil. The “zero-lift” drag coefficient is close to FG 0.0055.7
6. Flow Over Finite Wings (The Lifting Line Model)Generation of vortex system by finite aspect ratio wingFar field horseshoe model of a finite wingChord and load distribution for a thin elliptic wing.8
1. The wing lift slope ;FI ;J decreases as wing aspect ratio becomes smaller.2. The induced drag of a wing increases as wing aspect ratio decreases.3. Using the results of this theory we must remember that the total drag 5 of a wing includes theinduced drag 5L and the viscous drag 5N .Variation of lift coefficient slope versus aspect ratio for thin elliptic wings.Induced drag for a finite elliptic wing versus FI9
7. Viscous Flow and Boundary Layer TheoryFlow regions in a high Reynolds number flowVelocity profile for the flat-plate laminar boundary layer OPQ 5.477 10TControl volume to derive the momentum integral equation for boundary layer flow.@Displacement thicknessδ 7 "1 @Momentum thicknessN , ;X , , Θ 7"1 ;XXND ρX # Θ ;Θ \ ρX #; Von Karman Momentum Integral: For an accelerating/decelerating boundary layer flow;;X \ δ )X # Θ , X ; ; ρ10
4. Potential Flow Theory Elementary flows, which can be superimposed to describe the flow around bodies of arbitrary shape. Doublet vortex uniform flow: synthesis of flow around circular cylinder with circulation Irrotational flow around a nonsymetrical airfoil with zero circulation (zero lift) Actual flow past a nonsymetrical airfoil
7.4.3 Maximum Lift and Boundary-Layer Separation on Single-Element Airfoils 319 7.4.4 Multielement Airfoils and the Slot Effect 329 7.4.5 Cascades 335 7.4.6 Low-Drag Airfoils with Laminar Flow 338 7.4.7 Low-Reynolds-Number Airfoils 341 7.4.8 Airfoils in Transonic Flow 342 7.4.9 Airfoils in Gro
5.18 The design (dash) airfoils from restarted gappy POD method. . . 74 5.19 The exact Korn (solid) and the design (dash) airfoils from 63 RAE based airfoils in transonic regime. . 76 5.20 The exact Korn (solid) and design (dash) airfoils from new en-semble of snapshots based
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decisions. To that end, wind tunnel aerodynamic tests and aeroacoustic tests have been performed on six airfoils that are candidates for use on small wind turbines. Results are documented in two companion NREL reports: Wind Tunnel Aeroacoustic Tests of Six Airfoils for Use on Small Wind Turbines,
airfoils were designed as part of NASA’s e ort to develop airfoils with high transonic cruise e ciency while obtaining good low-speed characteristics. Two airfoils with the thickness of 10% and 14% are se
Rotor airfoils were designed for each aircraft, and their effects on performance analyzed by CAMRAD II. Airfoil design criteria are discussed for each rotor. Twist and taper optimization are presented in detail for each rotor, with discussions of performance improvements provided by the new airfoils,
