Vortex lattice method
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The Vortex lattice method, (VML), is a numerical, Computational fluid dynamics, method used mainly in the early stages of aircraft design and in aerodynamic education at university level. The VLM models the lifting surfaces of an aircraft as a infinitely thin sheet of discrete vortices to compute lift and induced drag. The influence of the thickness, viscosity and other things, is neglected.
Background
John DeYoung provides a background history of the VLM in the NASA Langely workshop documentation SP-405[1].
The VLM is the extension of Prandtl lifting line theory [2], were the wing of an aircraft is modeled as a Horseshoe vortex. The name was coined by V.M. Falkner in his aeronautical research council paper of 1946[3]. The method has since then been developed and refined further. Being a numerical method, the VML benefited from the advent of the electronic computer in the 1950's, for the large amounts of computations that are required.
Instead of only one horseshoe vortex per wing, as in the lifting line theory, the VLM utilizes a lattice of horseshoe vortices. The number of vortices used vary with the required pressure distribution resolution, and with required accuracy in the computed aerodynamic coefficients. A typical number of vortices would be around 100 for an entire aircraft wing.
Assumptions
The following assumptions are made regarding the problem in the vortex lattice method:
- The flow field is incompressible,inviscous andirrotational.
- The lifting surfaces are thin.
- The angle of attack is small, small angle approximation.
References
NASA, Vortex-lattice utilization. Nasa SP-405, NASA-Langley, Washington, 1976.
Prandtl. L, Applications of modern hydrodynamics to aeronautics, NACA-TR-116, NASA, 1923.
Falkner. V.M., The Accuracy of Calculations Based on Vortex Lattice Theory, Rep. No. 9621, British A.R.C., 1946.
J. Katz, A. Plotkin, Low-Speed Aerodynamics, 2nd ed., Cambridge University Press, Cambridge, 2001.
J.D. Andreson Jr, Fundamentals of aerodynamics, 2nd ed., McGraw-Hill Inc, 1991.
J.J. Bertin, M.L. Smith, Aerodynamics for Enginners, 3rd ed., Prentice Hall, New Jersey, 1998.
E.L. Houghton, P.W. Carpenter, Aerodynamics for Engineering Students, 4th ed., Edward Arnold, London, 1993.