On Drag Minimization of Lifting Non-Circular Aircraft Forebody at Supersonic Flight Speeds

Аuthors

Mitin A. L.

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

e-mail: alexmitin03@gmail.com

Abstract

The forebody drag can contribute significantly to the overall aircraft drag at supersonic speeds, thus its minimization is of high practical importance. In the current situation, this subject was developed especially profoundly for the axisymmetric forebodies, which are most widely employed in the aerodynamic design. For them, the drag minimization problem was successfully solved in various formulations for the wide range of Mach numbers.

For the 3D forebodies with noncircular cross-section, which find increasingly widespread application on the current and advanced supersonic aircraft, the problem under consideration becomes more complicated due to higher complexity of the relationship between the surface shape and the pressure distribution. Nevertheless, the optimal shapes of noncircular bodies have been successfully determined within the local interaction laws framework. Further development of the subject associated with transition to the more complex physical models, such as Euler or Navier–Stokes equations, was achieved due to the application of automatic optimization algorithms, combined with computational fluid dynamics.

The presented article studies the issue to what extent the results of the drag minimization of lifting noncircular forebody by the direct method are consistent with the results of its drag minimization, which is realized with the supersonic equivalence rule. In order to do this, the pressure drag of an optimal noncircular lifting forebodies family is compared to their equivalent bodies of revolution. Then the axisymmetric body shape with minimum wave drag is determined by optimization. After this, the wave drag is compared with the equivalent bodies of revolution of the original forebodies.

The study was performed at the Mach number value of M = 1.5 and zero angle-of-attack and angle-of-sideslip within the conditions of inviscid supersonic flow of the ideal gas. The drag of noncircular forebodies and their equivalent bodies of revolution was estimated by the numerical solution of Euler equations using the Godunov-type finite volume method. The search for the optimum axisymmetric shape with the minimum wave drag was performed by the line search method.

As a result, it was found that lifting non-circular forebodies of a given aspect ratio being optimal in terms of drag have a unitary shape of the equivalent body of revolution, which does not depend on lifting properties and is close to the one of a body of revolution of minimal wave drag. Based on the obtained results, the conclusion was made that the noncircular lifting noncircular forebody shape, which is close to the optimal one in terms of the drag value, can be designed based on the supersonic equivalence rule, despite the inherent errors of the former when estimating the drag of lifting bodies.

Keywords:

aircraft forebody, supersonic flow-around, equivalence rule, drag minimization

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