ESDU 96025:2010

INTRODUCTION

This Item describes a method for the prediction of the drag due
to lift for swept wings of straight taper with camber and twist,
alone or in combination with a body under conditions that tend to
induce leading-edge flow separation and a loss of leading-edge
suction at low to moderate values of lift coefficient. It is
applied to wings with mild cranks through the use of an
‘equivalent' straight-tapered wing, a geometric construction that
is described in Addendum A of Item No. 76003 (Derivation 3). The
angle of attack range includes the regime where there may be a full
or partial loss of leading-edge suction and the formation of
leading-edge vortex flow, but widespread flow separation over the
main part of the wing is not addressed. The method applies for
subsonic flow and when the boundary-layer over the whole wing is
fully turbulent. The method is unsuited to hand calculations and
has been programmed as ESDUpac A9625, which operates as a batch
file that runs a number of other programs automatically, writing
their inputs and reading their outputs to produce a final output
file from one input file.

Item No. 95025 (Derivation 10) developed a method for the
prediction of drag due to lift for planar wings. The method invokes
the concept of attainable leading-edge suction to cater for the
effects of wing section geometry (Derivations 17 and 18). For wings
of low aspect ratio the lift associated with the leading-edge
vortex is estimated by extended forms of the Polhamus analogy
(Derivations 13, 15 and 16).

Derivations 20 to 22 and the recapitulation in Reference 43 show
that the calculation of attainable suction for non-planar wings may
be made by using the same equations that apply to planar wings
provided that a reliable estimate can be made of the theoretical
leading-edge suction distribution. They demonstrate that this can
be done by using the theoretical distribution for a planar wing of
identical planform in conjunction with a corrected local angle of
attack. They also show that it is necessary in the calculation of
vortex lift to allow for the migration of the leading-edge vortex
as it travels back over the wing. It is not sufficient to assume
that all the vortex lift acts at the leading edge, and the local
surface slope is of consequence as it determines the direction of
the force. The method of this Item incorporates both these
concepts. The detailed calculation of the corrected angle of attack
follows the technique in Derivations 20 to 22 and Reference 43. The
prediction of the aft migration rate of the leading-edge vortex is
based on the work of Derivation 19, the simplest of the published
options available. As incidence increases the loss of lift due to
the vortex passing over the wing trailing edge or of vortex
breakdown occurring ahead of the wing trailing edge is modified
through a single factor developed from a correlation presented in
Reference 41.

In Derivation 24 the method for estimating attainable suction
was improved over the earlier versions in Derivations 17, 18 and
21. A final modification was reported in Reference 43. The
programmed method takes account of all these changes. Full details
of the development of the method are not given because the basic
philosophy of the technique remains as summarised in Section 3.2 of
Item No. 95025. Moreover, Derivation 24 provides a comprehensive
description of the development of the whole method for attainable
suction and does not simply confine itself to the improvements
made. It is therefore an ideal reference for users who wish to know
more of the intricacies involved.

The overall model for a wing is detailed in Section 3. Section 4
indicates a simple extension to include wing-body configurations.
Section 5 discusses accuracy and applicability. Section 6 lists the
Derivation and References and Section 7 describes the input and
output for the programmed version of the method, with examples. In
the input file (see Section 7.3), after the free-stream conditions
and configuration geometry have been specified, some entries allow
the user to alter a number of the program default settings and so
examine the influence of certain parameters or calibrate prediction
against known experimental data.

Appendix A sets out the formulae for the calculation of
leading-edge suction. Appendix B discusses the estimation of
lift-dependent viscous drag, which forms a secondary component of
the overall drag polar. Appendix C addresses leading-edge vortex
migration and breakdown.