Abstract
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 introduces the availability of a computational tool for constructing numerical modelfor potential flow over an airfoil based on panel methods. Use of the software is illustrated by implementing a specific model using Hess and Smith panel method to compute the flow over a member of the NACA four-digit airfoils.
Highlights
Aerodynamics is a branch of fluid dynamics concerned primarily with the design of vehicles moving through air
Panel methods are numerical models based on simplifying assumptions about the physics and properties of the air flow over an aircraft
The vector velocity describing the flow field can be represented as the gradient of a scalar potentialvelocity, V = V0 and the resulting flow is referred to as potential flow
Summary
Aerodynamics is a branch of fluid dynamics concerned primarily with the design of vehicles moving through air. A linear combination of relatively simple singular solutions is a solution to the differential equation This superposition of simple solutions provides the complexity needed for satisfying boundary conditions for flow over objects o f complex geometry. The tangent-flow boundary condition is required to be satisfied at a discrete number of points called collocation points This process leads to a system of linear algebraic equations to be solved for the unknown singularity-strength parameters. The potentials created by the distribution of sources/sinks and vortices are given by: Notice that in these formulae, the integration is to be carried out along the complete surface of the airfoil. Knowing the tangential velocity component, we can compute the pressure coefficient at the midpoint of each panel according to the following formula c p fa ,y )= i - From this equation (15) the force coefficientscan be computed. In this paper we use a computational tool (MATLAB code)to compute the geometry of NACA 0012 airfoil and constructing the numerical models to compute aerodynamics characteristic o f airfoil with variation of angle of attack a =10, 20, 30, 40, 50
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