Advanced Aerodynamics AME 60639
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Date Created: 11/01/15
Panel Methods AME 60639 Spring 2008 Prepared by Lee Neuharth Panel methods are often referred to as vortex panel methods this refers to the cases where each panel or line segment from node to node has an associated vortex 7 at its centerpointi A panel method may be performed with only sources and sinks 4 but this is generally for a non lifting case or a very thick airfoilli When concerned with airfoils though it is necessary to employ the Kutta conditioni According to the methods outlined by Moran2 the Kutta condition may be de ned by assigning a universal value of 7 the same value of 7 is used on each paneli This provides another variable to accompany the extra equation given by the Kutta conditioni Using the de nitions of sources and sinks q and vortices 7 the velocity potential N 48 r V zcosa s1na ilnrii d3 1 lt15 mlt y NYEml 2W 11 J can then be used to nd the velocity everywhere Each source sink and vortex contributes a certain amount to the velocity at each point Through a geometric investigation the velocity components can be used to nd the tangential velocity on each panel and the normal velocity This reduces to N 214139ij AiN1 Y bin 2 13971 The right hand side is the tangent velocity and the Kutta condition is augmented into the matrix at the N lth row and column where N is the number of nodes These two conditions are shown as bi VDo sint9i 7 a 3 and N ZANquj AN1N17 bN1 4 j1 This discussion closely follows the equations and methods presented by Moran a code named PANEL employing the inviscid impermeability and the Kutta conditions is presented in chapter four of this text 1 Katz and A Plotkin Lowespeed Aerodynamics New York Wiley 1984 Chapter 4 2J Moran An Introduction to Theoretiwl and Computational Aerodynamics McGraweHill 1991 Page 317