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A numerical method for the calculation of nonlinear, unsteady lifting potential flow problems

1969; American Institute of Aeronautics and Astronautics; Volume: 7; Issue: 10 Linguagem: Inglês

10.2514/3.5494

1533-385X

R. HARIJONO DJOJODIHARDJO, Sheila E. Widnall,

Fluid Dynamics and Vibration Analysis

A numerical method is developed for attacking lifting problems of a general three-dimensional wing executing an arbitrary motion in a potential flow. The formulation of the problem is exact in the sense that the boundary conditions are satisfied on the surface of the wing and the geometry of the time-dependent wake is predicted. The problem is then governed by a Fredholm integral equation of the first kind which relates the velocity potential doublet distribution to the normal velocity on the surface of the wing, subject to the Kutta condition of smooth flow off the trailing edge and the condition that the wake cannot sustain any pressure difference. The solution of the integral equation is obtained in a step-by-step fashion, and the appearing surface integrals are evaluated by employing a discrete set of approximate surface elements and an assumption of the doublet distribution over the element which is based on a formal expansion of the velocity influence coefficient. Verification of the method is made by comparison with solutions of classical problems. To demonstrate its utility, the method is applied to obtain the airloads due to transient motion of wings with simple planforms. The nonlinear effects due to the wake, aspect ratio, and thickness are discussed. Results of these calculations indicate that the present method can be applied to treat more complicated geometries and motion to obtain accurate and efficient prediction of the airloads.