lec20 - Aerodynamics Lecture 20 Aerodynamic Interference...

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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.1 Lecture 20 Aerodynamics Method of Images, Kelvin’s Circulation Theorem AE311 Aerodynamics Manoj T. Nair IIST
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.2 Agenda 1 Aerodynamic Interference: Method of Images 2 Kelvin’s Circulation Theorem
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.3 Aerodynamic Interference: Method of Images I Till now we dealt with flow about single bodies in an infinite fluid In many practical problems there are many bodies and there is mutual interference depending on the proximity and size of the bodies Examples are the effect of proximity of ground, flow fields of other aircrafts, effect of wind tunnel boundaries, etc The method of images in one form or other is used to determine the magnitude of these interferences The streamlines representing solid surfaces can be generated in a systematic fashion The approach takes advantage of the fact that there can be no flow across lines of symmetry separating identical flows
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.4 Aerodynamic Interference: Method of Images II Source near a wall Consider the distortion of the flow generated by a source at y = a in the presence of a wall at y = 0 A boundary condition is imposed at the wall: v = 0 at y = 0 The effect of the wall is identical with that of an image source of equal strength y = - a
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.5 Aerodynamic Interference: Method of Images III The velocity field is superposition of the two sources The velocity is tangent everywhere to the wall at y = 0 The stream function is ψ = Λ 2 π tan - 1 y - a x + tan - 1 y + a x
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.6 Aerodynamic Interference: Method of Images IV The potential for the source near a wall is given by φ = Λ 2 π ln q x 2 + ( y - a ) 2 + ln q x 2 + ( y + a ) 2 Both the sources will move away if no external constraints are put on the sources
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Aerodynamics Aerodynamic Interference: Method of Images Kelvin’s Circulation Theorem 20.7
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