Airfoil Aerodynamics Using Panel Methods

Richard Fearn
2008 The Mathematica Journal  
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 article introduces the availability of a collection of computational tools for
more » ... tional 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. 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 leaves the sharp trailing edge of the wing smoothly. 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 = " f, and the resulting flow is referred to as potential flow. A statement of conservation of mass in the flow field leads to Laplace's equation as the governing equation for the velocity potential, " 2 f = 0. Laplace's The Mathematica Journal 10:4
doi:10.3888/tmj.10.4-6 fatcat:6qrc7rd2rbdvva4wip5vdp7g7y