Taking into account the features of the flow around the arc-shaped wings at the design stage

DOI: 10.34759/trd-2022-123-06

Аuthors

Egorov I. A.

e-mail: egorov_ff@rambler.ru

Abstract

Currently, arc-shaped wings are widely used for small-sized missiles. Therefore, techniques are needed to determine the aerodynamic characteristics of such wings, primarily the lift coefficient.

1.The peculiarity of the arc-shaped wing flow is reduced to three aspects

Reduction of local angles of attack

2. Reduction of the «useful» component of the local lifting force of the panel

3.The convergence of the wing panels, and the amplification of the mutual influence of the panels.

Consideration of all these aspects is possible when using the discrete vortex method.

The wing is divided into panels with a given pitch in span and chord. In each panel there is a Π-shaped vortex.

When determining the geometric parameters that determine the position of the wing point relative to the vortex, it is necessary to take into account the curvature of the wing.

Two schemes of arc-shaped wings are considered: with an opening angle of 90° and with an opening angle of 135°.

The scheme with an opening angle of 90° is taken as the basis for consideration.

The transition to a scheme with an arbitrary opening angle is reduced to a simple recalculation of coordinates.

The calculation is performed in the following sequence:

1.The coordinates of the wing points in space are calculated.

2.The parameters of discrete vortices in space are determined.

3.A matrix of coefficients of the system of equations is formed.

4.The angles of attack are determined taking into account the spatial orientation of the wing element

5.The circulation values and the value of the wing lift coefficient are determined.

The calculation results for a rectangular wing are presented.

The wing is divided into 24 panels.

Mach number M = 0.8, angle of attack α = 1º.

The conclusion:

1.The discrete vortex method is very convenient for constructing an arc-shaped wing calculation model.

2.Acceptable calculation accuracy can be obtained already with a large grid.

3.The greatest influence on the accuracy of the calculation has an increase in the density of the grid along the span

4.To obtain acceptable accuracy, the curvature of the arched wing must be taken into account at all stages of the calculation

5.An arched wing with an opening angle of 135° has bearing characteristics close to those of a flat wing

Keywords:

lift, wings, arcing, discrete vortices, interference

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