Numerical solution of the inverse airfoil problem using the PGT technique


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

The purpose of the presented work consists in creating an effective method for the viscous inverse problem numerical solution based on a substantiated airfoil geometry corrector, PGT (Parent function Generating function Transformation) technique developed earlier and the concept of effective non-viscous circulation for the airfoil viscous flow-around. The possibility of this method application for the integral aerodynamic characteristics improving of the multi-mode profiles was studied additionally.

Universal model, allowing developing arbitrary profile, consisted of the functions generating the aerodynamic airfoil contour based on the universal parental function and two parameters, was developed earlier based on the PGT method for the aerodynamic design tasks. The PGT method distinctive feature is the fact that generating functions increase monotonically from 0 to 1 on the [0, 1] segment. The presented work employs this universal model for mathematical representation of the velocity circulation distribution around the airfoil contour. The model allowed solution efficiency increasing of a well-posed inverse problem for the full potential equation. The same model was employed for setting and solving the inverse problem for the profile in a viscous flow as well. Verification of the viscous inverse problem solution was performed on the example of the NACA-23012 profile. The examples of the profile contour resurrection by the pressure distribution in it for several flow-around modes were presented.

The article presents demonstration example, which reveals the possibility of the multi-mode airfoil aerodynamic characteristics improving based on the inverse viscous problem solution.

The author shows that well-posed non-viscous inverse problem solving method application as a corrector allows realizing pressure distribution along the upper contour of the airfoil practically coinciding with the target one.

The presented study revealed that the original mathematical model based on the PGT method and application of the concept of effective non-viscous circulation allows creating an effective method for a viscous inverse problem solving and efficiency improving of the method for the well-posed non-viscous inverse problem solving.

Keywords:

PGT technique, aerodynamic design, airfoil, inverse problem, pressure distribution

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