Perturbed tangential velocity interpolation procedure for determining its value at an arbitrary point of the vortex wake region

Aeronautical and Space-Rocket Engineering


DOI: 10.34759/vst-2023-2-24-34

Аuthors

Golovnev A. V.*, Danilov S. M.**, Nechaev V. A.

Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia

*e-mail: golovnyev@rambler.ru
**e-mail: dsm2291@gmail.com

Abstract

Vortex wakes studies after various aircraft is of both scientific and practical interest since the other aircraft entering the vortex wake is fraught with catastrophic consequences. The vortex wake is being characterized by the perturbed velocities field, as well as the shape and position in space. Tangential velocities Wτ are of the most interest, as long as their impact on the aircraft, got into the vortex wake, is quintessential.

The article considers approaches to the perturbed tangential speed determining at an arbitrary point in the vortex wake area. That task emerges at the aerodynamic characteristics determining of an aircraft, got into the vortex wake area, by the discrete vortex method, when the perturbed velocities determining is required at the point of the aircraft surface, where the «no-flow» condition is fulfilled and at the node points of the vortex sheet.

The problem of the perturbed tangential velocity computing at the point is being considered in the dimensionless form, i.e. coordinates, velocities and time are dimensionless. The way of the said dimensionless values obtaining is similar to the way employed while setting the problem of the aircraft aerodynamic characteristics determining by the discrete vortex method. The problem solution is being considered in the «frozen» field of the perturbed velocities approximation.

Three types of interpolation are under consideration. They are linear interpolation with mean value calculation of tangential speed at a point close to the given one; linear interpolation for determining the speed differential; non-linear second order interpolation. The authors disclose the advantages and disadvantages, and propose criteria determining selection of this or that interpolation. Finite-difference solution schemes of their differential representation were obtained for each type, and procedures, represented as algorithms and realized in the algorithm for aerodynamic characteristics computing of the aircraft entering the vortex wake by the discrete vortex method were proposed.

A comparative assessment of the computation results with the analytical solution was performed to assess the adequacy of the interpolations. The problem was being solved in a two-dimensional setting. Expressions for a pair of Renkin potential vortices modeling end vortices from the wing was selected as analytical expressions.

The presented work recognized that with the slight gradients of the perturbed tangential velocity changing, the linear interpolation should be used, while with substantial alterations of the velocity gradients and large velocity gradients values the second order nonlinear interpolation procedure should be used.

Keywords:

aircraft aerodynamic characteristics in the vortex wake, flow velocities perturbed by the vortex wake interpolation, discrete vortex method

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