The possibility of using nonlinear lift functions of attack angle in the lifting line theory

Аuthors

Nikolsky A. A.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

e-mail: anikolskii@mail.ru

Abstract

Purpose — Many authors considered direct problem of obtaining wing-lift coefficient dependence on incidence angle, using a well-known airfoil dependence based on modified theory of lifting line. The first purpose of the study was to clarify the limits of applicability of this mathematical model in case of nonlinear lift dependencies. The second purpose was to develop methods for solving inverse problem of determining the aerodynamic characteristics of the airfoils based on the results of wing model tests in wind tunnels, taking into account the nonlinear dependence of the lift on the angle of attack.

Design / methodology / approach — Based on the modified theory of lifting line we developed a two-step iterative algorithm for solving direct problem for rectangular wing of finite span. To verify it an alternative optimization method was developed based on the genetic algorithm, which allows determining the global optimum. Extensive computational studies led to the conclusion of the modified theory of the lifting line approximate nature, in contrast to the classical Prandtl theory.

Findings — Introduced is the concept of acceptance criterion, which allows satisfying the hypothesis of flat sections with a reasonable accuracy and finding the approximate solution of the direct problem. The limits of applicability of the modified theory are discussed. On the basis of an algorithm for solving the direct problem, an optimization algorithm for solving inverse problem was developed in trust region of wing angles of attack.

Practical applications — The results of this study will be used in recalculations of wings test data.

Originality / value — This study establishes that for mathematical model based on modified lifting line theory, the trust region of wing attack angles is limited by a near vicinity of critical angle of attack.

The paper describes a straightforward procedure to recalculate wing aerodynamic characteristics to get airfoil characteristics for later use in the calculation of the main/tail rotor.

Keywords:

airfoil, wing box, lifting line

References

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