1、4 NASA Contractor Report 4004 A Fundamental Study of Drag and an Assessment of Conventional Drag-Due-to-Lift Reduction Devices John E. Yates and Coleman duP. Donaldson CONTRACT NASI-18065 SEPTEMBER 1986 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,
2、-I NASA Contractor Report 4004 A Fundamental Study of Drag and an Assessment of Conventional Drag-Due-to-Lift Reduction Devices John E. Yates and Coleman duP. Donaldson Aeronautical Research Associates of Princeton, Inc. Princeton, New Jersey Prepared for Langley Research Center under Contract NAS 1
3、- 18065 National Aeronautics and Space Administration Scientific and Technical Information Branch 1986 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I TABLE OF CONTENTS SUMMARY 1 2. FUNDAMENTAL THEORY . 7 2.1 Integral Conservation Laws 7 2.2 Trefft
4、z Plane Representations the of Drag and Lift . . 11 2.3 Drag and Lift in Terms of Vorticity. . 16 2.4 Drag and Lift in Terms of Surface Pressure 25 2.5 A Practical Wing - Drag Formula. . 32 3. AN ASSESSMENT OF CONVENTIONAL DRAG-DUE-TO-LIFT REDUCTION DEVICES AND TECHNIQUES * * * * * - * 36 3.1 Planfo
5、rm Shape (CTOL Wing) 36 3.2 Out of Plane Tip Devices . 38 3.3 Joined Tip Configurations . 43 4. CONCLUSIONS AND RECOMMENDATIONS - * - - * - * * - * * . 46 REFERENCES . 49 PRECEDiNG PAGE BLANK NOT FlLMED iii Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS
6、-,-,-SUMMARY The theory of drag and lift is revisited starting with the integral conservation laws of fluid mechanics. Many representations (some known and some unknown) of drag and lift are derived in terms of far wake properties, intermediate wake properties and surface loading. Although the theor
7、etical results are quite general, these representations are used in the present report primarily to assess the drag efficiency of lifting wings both CTOL and various out-of-plane configurations. The drag-due-to-lift is separated into two major components that reveal themselves quite naturally in the
8、 theory. The first and largest component is the I1inducedf1 drag-due-to-lift that is due to spanwise variations of wing loading. It is a strong function of aspect ratio for a CTOL wing or more generally the projection of the lifting elements on the Trefftz plane. The first component is relatively in
9、dependent of Reynolds number or details of the wing section design or planform. For each lifting configuration there is an optimal load distribution that yields the minimum value of drag-due-to-lift against which the efficiency of a particular design may be assessed. The second and much smaller comp
10、onent of drag-due-to-lift may be called flformlf drag-due-to-lift. It is largely independent of aspect ratio but strongly dependent on the details of the wing section design, planform and Reynolds number. It is a result of wing load variations in the chordwise direction. For well designed high aspec
11、t ratio CTOL wings the two drag components are to lowest order independent with only a weak interaction of the order of the square of the drag coefficient (i.e., a percent or so of wing drag). With modern design technology CTOL wings can be (and usually are) designed with a drag-due-to-lift efficien
12、cy close to unity. Wing tip-devices (winglets, feathers, sails, etc.) that have vertical dimensions of the order of the wing chord can probably improve drag-due-to-lift efficiency by 10 or 15% if they are designed as an integral part of the wing with the proper load on all lifting elements. As add-o
13、n devices for a well designed CTOL wing they can be detrimental. The largest increments of drag-due-to-lift efficiency can be attained with joined tip configurations and vertically separated lifting elements. It is estimated that 25% improvements of wing drag efficiency can be obtained without consi
14、dering additional benefits that might be realized by improved structural efficiency. It is strongly recommended that an integrated aerodynamic/structural approach be taken in the design of or research on future out-of-plane configuration. Provided by IHSNot for ResaleNo reproduction or networking pe
15、rmitted without license from IHS-,-,-1. INTRODUCTION The resistance of bodies moving in a fluid medium (drag) is a subject of considerable interest to the aircraft designer so much so that regular symposia (national and international) are held to discuss the efficiency of modern designs and exchange
16、 ideas on the relative merits of various drag reducing devices (see Ref. 1, e.g.1. For the modern CTOL airplane there is almost equal partition of the total drag into form drag and drag-due-to-lift. Drag research is usually focused on one or the other of these topics. Recent efforts on the developme
17、nt of laminar flow airfoils (Ref. 1, papers of Saric or Braslow and Fischer) and riblets (Ref. 1, paper by Bushnell) to reduce turbulent skin friction are primarily concerned with the reduction of form drag. We will see herein that a reduction of form drag (at least on a lifting surface) also has a
18、secondary benefit of reducing the drag-due-to-lift. Research efforts on drag-due-to-lift have focused primarily on improved wing efficiency. Planform optimization (in particular the tip design) has held the center of attention (Ref. 2) since the advent of the Whitcomb winglet (Ref. 3). Many devices
19、both active and inactive have been proposed (Refs. 4,5,6 i.e., variation of the load in the cross stream direction with the production of strong axial vorticity. With a more unified viewpoint the emphasis on wing tip design can perhaps be put into better perspective as Only one component of a totall
20、y integrated design both aerodynamic and structural. The biggest payoff in the future may well be in the design of 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I configurations that eliminate all unnecessary cross stream load variations (a stron
21、g case for the flying wing and joined tip configuration) in particular if there are structural benefits to be realized. In this study we have deliberately omitted any detailed considerations or evaluation of active devices such as tip blowing, propellers, etc. The lifting configurations of this stud
22、y do not exchange mass, momentum or energy at their boundary so that drag efficiency can be measured in terms of entropy production of the airframe for a required amount of lift. If part of the powerplant energy or auxiliary energy is used to alter the flow over the lifting elements then the drag be
23、comes difficult if not impossible to separate from the powered thrust. Efficiency must then be measured in terms of total power requirements (including all auxiliary blowing) for a given lift. While this can and must be done to evaluate active devices we have concentrated on the efficiency of inacti
24、ve lifting elements herein. A natural and worthwhile follow on to the present study would be to revise the basic formulation of Section 2 to include mass, momentum and energy exchange at all surfaces and so integrate the powerplant and auxiliary blowing devices into the aerodynamic e Val ua t i on.
25、I 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NOMENCLATURE A b2/S, aspect ratio (Or angular momentum in half Control volume) b wing span c(y) cd(y) section drag distribution chord distribution of wing planform average wing section drag coeffici
26、ent flat plate skin friction coefficient section lift curve slope D/S-q, drag coefficient based on area S of lifting surface drag associated with wake cross flow kinetic energy (induced drag-due-to-lift) see (2.3.28) cas Cf CRa CD CD C drag in absence of lift DO L/S*q, lift coefficient cL total lift
27、 curve slope io?, drag, see (2.1.4) and (2.1.6) + cLa D e energy/unit mass (or wing efficient factor, see (2.3.31) E total energy in control volume see (2.1.1) f(x,y) wing thickness distribution, see (2.4.3) it resultant force, see (2.1.4) g(x,y) wing camber and twist distribution, see (2.4.3) H h+v
28、L/2, total enthalpy k section drag-due-to-lift factor, see (2.4.17 and 2.4.18) K wing total drag-due-to-lift factor, see (2.4.15 and 2.4.16) form drag-due-to-lift factor, see (4.2.) induced drag-due-to-lift factor, see (4.2) Kf Ki L lift, see (2.1.4 and 2.1.5) 4 Provided by IHSNot for ResaleNo repro
29、duction or networking permitted without license from IHS-,-,-IO IS M Mm P P R Re *.Y S S t T T1 /2 n + V V Wav t - Y ci 6 integral scale of wake vorticity, see (2.3.27) fraction of wing leading edge that is separated, see (2.5.5) total mass in control volume see (2.1 .I) Mach number at infinity stat
30、ic fluid pressure p+p vL/2, total head pressure total momentum in control volume, see (2.1.1) heat flux vector gas constant, see (2.2.1) Reynolds number entropy/uni t mass total entropy in control volume, see (2.1.) reference area of wing time Trefftz plane (or temperature) half Trefftz plane free s
31、tream velocity in x-direction, see Figure 2.1 normal component of velocity on a surface with normal n (u,v,w) velocity components magnitude of velocity in the Trefftz plane average circulation velocity, see (2.4.24) (x,y,z) Cartesian coordinates, see Figure 2.1 vortex span, see (2.3.4) angle of atta
32、ck (geometric) measure of wing max camber or twist wake displacement thickness, see (2.5.9) 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A As E Y rO P Pm lJ + + T + w difference pressure coefficient or load, see (2.4.5) s- 5, measure of wing max
33、 thickness ratio of specific heats, see (2.2.1) circulation distribution in wake total vorticity (circulation) in half Trefftz plane see (2.3.3) see (2.5.4) fluid viscosity mass density free stream density mean pressure coefficient, see (2.4.4) viscous stress tensor stream function, see (2.3.13) cur
34、l 3, vorticity 6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2. FUNDAMENTAL THEORY I 2.1 Integral Conservation Laws Consider a lifting body (airplane) fixed in a fluid that moves in the positive x direction at speed u, as shown in Figure2.l. We f
35、urther consider a cylindrical control volume V that encloses the body and is bounded by an upstream y-z plane T, and a downstream (Trefftz) plane T at an arbitrary location x. The cylinpical boundary is denoted by C and the surface of the airplane by S. Also n is the unit normal on the outer boundar
36、y (positive out of VI and on S (positive into VI. We consider the conservation of mass, linear and angular momentum, energy and entropy (also total head) and their relation to the resultant force that acts on the airplane: M = /pdV V Mass Linear Momentum V A= I + 1 ex x pfdV Angular Momentum (Half C
37、ontrol Volume) 112 V cy? = J psdV V Ener g y Entropy The compressible viscous equations of fluid motion are: (2.1.1) aP + at - + div pv = 0 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- 0 fs: 4- I f I i b i2 4 0 3 d 0 k u k 1 bL I 4 N a, k 1 8 P
38、rovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-+ -z+ (2.1.2) a 2 at - p(e+v /2) + div p;(e+v2/2) + pv - IOV + 41 = 0 We compute the time rate of change of each of the global quantities defined in (2.1.1) and assume that in steady state operation the
39、time average rate of change is zero. The time average of all subsequent equations is implied although we have omitted any explicit notation to indicate averages. We assume that the velocitv and heat flux through S are zero. Also we assume that the Reynolds number is very large so that contributions
40、of viscous stresses on the outer control boundary may sensibly be neglected. The conservation of mass leads to the following integral equation for the outflow through C and T, a result that is used in all subsequent equations. The conservation of linear momentum leads to the following representation
41、 of the resultant force on S: $E- / (pR-!*;)dS Result ant Force S (2.1.4) + =?D+t with 1.2 = 0 where D is the total drag due to pressure and viscous stresses and by definition is the projection of the result+ant force on the free stream direction. The transverse force is denoted by L and if the x-z
42、plane is a plane of symmetry, then L = kjL where L is the lift. We assume a plane of symmetry in the following development. The Trefftz plane representations of the lift and drag are given by 9 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Lift whi
43、le the surface definitions of lift and drag are given by (2.1.5) j (2.1.6) , (2.1.7) (2.1.8) The conservation of angular momentum in one half of the control volume leads to an expression for the root bending moment; i.e., T1/2 y=o Sgmme t ry plane while M is defined in terms of surface forces by (2.
44、1.9) (2.1.10) where the subscript (1/2) denotes one half of the wing, the Trefftz plane or control volume bounded by the symmetry plane y = 0. The conservation of total energy combined with the assumption of an adiabatic surface S leads to the conclusion that the total enthalpy deficit in the Trefft
45、z plane is zero; i.e., Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(2.1.11) where (Total Enthalpy) (2.1.12) 2 H = h+v /2 Conservation of entropy combined with Fouriers law of internal heat conduction leads to the following result for entropy flux
46、 through the Trefftz plane: /pu(s-s.)dS = p(:y;: :). k (Ti2 dV 2 0 (2.1.13) T We remark that if the fluid is incompressible the last statement can be rewritten as a flux of total head loss; i.e., T V where (Total Head) 2 P = p + pv /2 + and o = curl? is the vorticity. 2.2 Trefftz Plane Representatio
47、ns of the Drag and Lift (2.1.14) (2.1.15) The objective of this section is to use the global conservation laws in conjunction with other principles of wing theory, Betz type wake roll-up theory, etc. to derive a variety of representations of the drag and lift from which solid conclusions can be draw
48、n and which can be used to assess proposed methods for reducing drag, in particular drag-due-to-lift of conventional take off and land (CTOL) aircraft. 11 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-First we consider the fundamental Trefftz plane relation for the drag (2.1.6) and introduce the following perfect gas relations: (2.2.1) and assume that total enthalply is conserved on every streamline through the Trefftz
