Helicopter airfoil design by solving the generalized inverse problem

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

While aerodynamic design many authors used the inverse problem to improve the profile aerodynamic performance. However, applications based on solving the inverse problem are not widely used for helicopter airfoils for the reason that their aerodynamic design requires simultaneous monitoring of several regimes of plow. For this reason, the general inverse problem with additional constraints on the airfoil pitching moment was formulated at the previous stage of the study. The purpose of the present study was to clarify the applicability of this mathematical model for successive improvements of helicopter airfoils integral aerodynamic criteria.

Based on the generalized inverse problem solving method, the author developed the pressure distribution adjustment procedure for successive improvements of helicopter airfoil performances.

The paper describes the application of the generalized inverse problem concept for aerodynamic design of helicopter airfoils. It considers the following pressure distribution improving variations for NASA series airfoil:

Airfoil pitching moment increase at zero lifting force and small Mach numbers without noticeable losses of maximum lifting force values at small Mach numbers and maximum lift to drag ratio at moderate Mach numbers.

Airfoil maximum lifting force increase at small Mach numbers and practical permanence of the other integral criteria.

Airfoil lift to drag ratio maximum increase moderate Mach numbers and practical permanence of the other integral criteria.

The interactive decrease of wave drag at high Mach number and practical permanence of the other integral criteria.

The results were verified by CFD calculations.

This study established that mathematical model based on the concept of generalized inverse problem and simple physical considerations allow modify pressure distributions successively improving helicopter airfoils performances.

Keywords:

airfoil design, helicopter airfoils, inverse problem

References

1. McFadden G.B. An Artificial Viscosity Method for the Design of Supercritical Airfoils. New York University Report COO-3077-158, 1979.

2. Volpe G. and Melnik, R.E. The Design of Transonic Aerofoils by a Well Posed Inverse Method. Int. J. Numerical Methods in Engineering, Vol. 22, 1986, pp. 341-361.

3. Nikolsky A.A. Some aspects of helicopter airfoil design, Proceedings of the Twenty first European Rotorcraft Forum, Saint- Peterburg, 1995, Paper, no.17,(II), pp. 1-8.

4. Lighthill M.J. A New Method of Two Dimensional Aerodynamic Design, ARC, Rand M 2112, 1945.

5. Nikolsky A.A. Generalized inverse airfoil problem. Tsagi Science Journal, vol. 43, no. 6, 2012, pp.775-786.

6. Bauer F., Garabedian P., Korn D. Supercritical wing sections III. Lecture Notes in Economics and Math. Syst., 1977, N 150.

7. Nikol’skii A.A. Trudy MAI, 2013, no. 66, URL: http://www.mai.ru/science/trudy/published.php?ID=40253