lectures-chapter7

lectures-chapter7 - 650:460 Aerodynamics Chapter 7 Prof....

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Unformatted text preview: 650:460 Aerodynamics Chapter 7 Prof. Doyle Knight Tel: 732 445 4464, Email: doyleknight@gmail.com Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 General Comments Chordwise pressure distribution Spanwise pressure distribution Effective lift distribution Effect of finite span Fig. 7.1 2 General Comments Air on lower surface flows outboard Air on upper surface flows inboard Tip vortices form at wingtips Vortices rotate in opposite directoins Fig. 7.2 3 General Comments Fig. 7-2 4 General Comments Fig. 7.3 5 General Comments Fig. 7.4 6 Lifting Line Theory Local lift per unit span l = U ( y ) Idealize the vortex system as a collection of horseshoe vortices Helmholtzs Law requires a vortex to be shed downstream ( i.e. , a vortex cannot end in the fluid) Fig. 7.4 7 Lifting Line Theory The strength of the vortex shed between y and y + dy is = d dy dy Each shed vortex induces a flow in the vicinity of the airfoil Fig. 7.4 8 Lifting Line Theory The induced velocity due to a shed vortex is dw = 1 2 2 (distance) where distance is the spanwise distance between the vortex and the point of interest Fig. 7.4 9 Trailing Vortices and Downwash Induced velocity at y 1 due to vortex at y w ( y 1 ) = 1 2 bracketleftbigg d dy dy 1 2 ( y- y 1 ) bracketrightbigg Resultant induced velocity at y 1 w ( y 1 ) = + 1 4 integraldisplay + s s d / dy y- y 1 dy Fig. 7.5 10 Trailing Vortices and Downwash Induced velocity generates downwash = tan 1- w ( y 1 ) U - w ( y 1 ) U Downwash changes the angle of attack e = - Fig. 7.6 11 Trailing Vortices and Downwash Local lift is perpendicular to local resultant velocity Total lift is perpendicular to freestream velocity vector U Thus, a component of drag is generated due to change in effective angle of attack Fig. 7.6 12 Trailing Vortices and Downwash Kutta-Joukowski theorem l = U ( y ) Vortex (induced) drag d =- w ( y )( y ) Fig. 7.6 13 Trailing Vortices and Downwash Total lift L = integraldisplay + s s U ( y ) dy Total vortex (induced) drag D =- integraldisplay + s s w ( y )( y ) dy Fig. 7.6 14 Elliptic Lift Distribution Elliptic lift ( y ) = o radicalbigg 1- parenleftBig y s parenrightBig 2 Fig. 7.7 Induced velocity w ( y 1 ) =- o 4 s integraldisplay + s s y radicalbig s 2- y 2 ( y- y 1 ) dy =- o 4 s See derivation in text 15 Elliptic Lift Distribution Total lift on wing L = integraldisplay + s s U ( y ) dy = integraldisplay + s s U o radicalbigg 1- parenleftBig...
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lectures-chapter7 - 650:460 Aerodynamics Chapter 7 Prof....

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