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.
ESDU 96025 F-2010 history
2010ESDU 96025 F-2010 Drag due to lift for non-planar swept wings up to high angles of attack at subsonic speeds