airfoil - Airfoil Aerodynamics Using Panel Methods,...

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Airfoil Aerodynamics Using Panel Methods Accepted for publication in The Mathematica Journal . Richard L. Fearn Potential flow over an airfoil plays an important historical role in the theory of flight. The governing equation for potential flow is Laplace's equation, a widely studied linear partial differential equation. One of Green's identities can be used to write a solution to Laplace's equation as a boundary integral. Numerical models based on this approach are known as panel methods in the aerodynamics community. This paper announces the availability of a collection of computational tools for constructing numerical models for potential flow over an airfoil based on panel methods. Use of the software is illustrated by implementing a specific model using vortex panels of linearly varying strength to compute the flow over a member of the NACA four-digit family of airfoils. Introduction Fluid dynamics is a branch of mechanics concerned with the motion of a fluid continuum under the action of applied forces. The motion and general behavior of a fluid is governed by the fundamental laws of classical mechanics and thermodynam- ics, and plays an important role in such diverse fields as biology, meteorology, chemical engineering and aerospace engineer- ing. A introductory text on fluid mechanics, such as Sabersky, Acosta, Hauptmann and Gates (1) surveys the basic concepts of fluid dynamics and the various mathematical models used to describe fluid flow under different restrictive assumptions. Advances in computational power and in modeling algorithms during the past few decades have enabled industry to use increasingly realistic models to solve problems of practical geometric complexity. Alternatively, these advances make it feasible to adapt some of the older, simpler models to inexpensive desktop computers. Aerodynamics is a branch of fluid dynamics concerned primarily with the design of vehicles moving through air. In the not-so-distant past, a collection of relatively simple numerical models, know as panel methods, were the primary computa- tional tool for estimating some of the aerodynamic characteristics of airplanes and their components for cruise conditions. For example, Hess (2) commented in 1990 that at Douglas Aircraft Company, a major design calculation was performed using panel methods approximately ten times per day. Panel methods are numerical models based on simplifying assumptions about the physics and properties of the flow of air over an aircraft. The viscosity of air in the flow field is neglected, and the net effect of viscosity on a wing is summarized by requiring that the flow leave the sharp trailing edge of the wing smoothly. The compressibility of air is neglected, and the curl of the velocity field is assumed to be zero (no vorticity in the flow field). Under these assumptions, the vector velocity describing the flow-field can be represented as the gradient of a scalar velocity potential, Q A =“f , and the resulting flow is
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airfoil - Airfoil Aerodynamics Using Panel Methods,...

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