1、NASA TeelnNicrr TRANSLATION , wk a aD 1 THEORY OH THE LIFTING AlRXRJ!W Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ANNOTATION General During this tr
2、anslators visit to Moscow on the occasion of the USSR-US Aeronautical Symposium in 1973, he had the pleasure of receiving, from Dr. Ye.S. Vozhdayev, a copy of the “justpublishedtt book entitled, Theory of the Lifting Airscrew. A cursory look at the contents seemed to confirm the claim expressed by i
3、ts authors in the Preface that this is a unique publication, not only in the USSR, but in the West as well. A more thorough reading further confirmed that this, indeed, is an exceptional text in the sense that contained within its covers is probably the most thorough exposition of the application of
4、 the vortex theory to rotary- wing aerodynamics. In that respect, one might even regret that this complete reliance on the vortex theory in the presentation of the subject is not, somehow, reflected in the title. Undoubtedly, there are some students and practitioners in the field of rotary wings, an
5、d this translator is one of them, who would believe that in a complete presentation of helicopter aero- dynamics as well as that of other airscrew-type aircraft, there is room for the momentum, and combined blade-element - momentum theories1. However, one should also keep in mind that at the current
6、 state of technology, the vortex theory represents the basis for almost all computer programs related to aeroelastic phenomena of the rotor, as well as for many detailed performance predictions of rotary-wing aircraft. For this reason, the Russian book appeared as a potentially useful source of info
7、rma- tion for the practicing rotary-wing aerodynamicist and/or aero- elastician. It might also serve as a basic text for academic courses. Finally, its value was recognized as a useful reference book and supplementary reading material to be used with other textbooks. This latter aspect was of partic
8、ular interest to this translator in conjunction with the preparation (under a USAAMRDL/NASA contract) of a textbook on fundamentals of rotary- wing aerodynamics. In view of the above-mentioned aspects, the desirability of trans- lating the book into English was discussed; first with Dr. I. Statler,
9、Director of Ames Directorate; and then with Mr. P. Yaggy, Director, and Dr. R. Carlson, Deputy Director of the U.S. Army Air Mobility Research 6 Development Labs (USAAMRDL). They con- curred that the Theory of the Lifting Airscrew should be made available to the English-speaking technical community.
10、 Conse- quently, material contained in this volume was prepared for USAAMRDL by this translator in cooperation with Mrs. Wanda L. Metz, under contract from NASA to Boeing Vertol Company. iii Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Technical C
11、omments Even before starting to study the translated text, the poten- tial reader may ask, “What is new and different in the Soviet approach from that encountered in Western literature, and in what respect does the Soviet school-of-thought appear to vary from that of ours?“ In trying to answer these
12、 questions, one may run the risk of oversimplification and generalization. This is especially true when, as in this case, one is dis- cussing or trying to describe a school-of-thought associated with an active and continuously developing field of technologi- cal and scientific endeavors. Here, one s
13、olitary researcher or small group of investigators thrusting in a new direction might completely change the already established trends. Never- theless, accepting this risk of oversimplification, I will try to indicate what is unique in the Soviet approach to the appli- cation of the vortex theory to
14、 rotary-wing aerodynamics. After following a survey of the field (such as that by Landgrebe and cheney2), one gets the impression that in the West, two periods in the development of rotary-wing aircraft aerodynamics can be distinguished; one, up to the early 60s before the appearance of high-capacit
15、y computers, and from then to the present, where the reliance on computers plays a decisive role. However, before the appearance of high-capacity computers, the development of the vortex theory in the USSR and the West ran along two, separate, but more or less, parallel, courses. At the dawning of t
16、he airscrew vortex theory (in the late teens and early twenties), the Soviet school had a head start with the published works of numerous Russian theoretical aero- and hydro-dynamicists; especially, those of Joukowsky and his students. In this respect, one should realize that Joukowsky, during this
17、period, solved the problem of a stationary airscrew with an in- finite number of blades through the concept of a straight cylin- drical vortex wake. However, because of the lack of exchange of ideas between the USSR and the West, this translator as well as a majority of those engaged in the field of
18、 airscrew aerodynamics in the West give the credit for the originality of this approach to Knight and efner (1937). Although the classic works of Lamb, Glauert, Lock, Goldstein, and Betz, as well as all volumes of Durand, etc., were known to the Soviet school, contacts with the West were very limite
19、d until the sixties. Nevertheless there are indications that tech- nical literature in the field of rotary-wing aerodynamics pub- lished in the West had penetrated to the USSR, It may be assumed, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-hence,
20、 that, either directly or indirectly, the Soviet train- of-thought bears some imprint of this influence; while in con- trast, the flow of thoughts in the field of rotary-wing aero- dynamics from the USSR to the West was practically nonexistent until the works of Mil became available through a NASA t
21、ransla- tion in the late sixties4, and other, rather sporadic, transla- tions. It appears that until the sixties, working in that atmosphere of separation, bth the Western and the Soviet schools aimed at the best possible determination of the time-average velocities in- duced in the surrounding medi
22、um by an airscrew in general, and helicopter rotors in particular, in various regimes of flight. Making numerous simplifying assumptions regarding the shape of the wake, attempts were made to obtain solutions for the induced velocities as well as their harmonics under rather simple mathe- matical fo
23、rms. Auxiliary graphs and tables were also made avail- able. Works of Castles and eeeuw, ad well as Heyson and IKatzoff6, etc., can be cited as typical for that period. With the increasirig difficulties encountered in such tasks as the determination of instantaneous induced velocities taking into ac
24、count the time-dependent deformation of the wake, etc., it became more and more difficult to obtain solutions, either explicitly expressed by simple mathematical formulae or with the help of special functions whose tables are generally avail- able. In this respect, a statement by 1liller7, although
25、referring to MIT experience, can probably be quoted as typical of the whole Western approach. “The tests discussed above clearly indicated the need for an analytical too2 for computing blade downwash velocities which would take into account the individual blade wake geometry and also introduce the e
26、ffects of unsteady aero- dynamics. Attempts to obtain a closed form solution to this problem, or one based on tabulated integrals, were not successful and it was evident that extensive computer facili- ties would be required to explore this problem and, hopefulZy, to provide a basis for obtaining si
27、mplified solutions suitable for engineering applications, In 1960, the availability of an IBM 709 computer at the MIT Computation Center and funds from a Carnegie grant permitted initiation of such a program.“ The above statement marked the beginning of the computer- oriented approach toward both ae
28、rodynamic and aeroelastic problems of rotary-wing aircraft in the ?est2. By contrast, as exemplified by this translation, it appears that in the USSR, there remained at least one strong school of thought oriented toward making use of all possible classical mathematics, including the full array of su
29、ch special functions as Bessel and Legendre; elliptic integrals, theory of cylindrical functions ,etc. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-To what extent this trend may be due to the unavailability of a large number of high capacity compu
30、ters, or to what extent it reflects a mastery and love of mathematics, so typical of Russian scientists and engineers, is difficult to answer. It is also possible that their strong attachment to established tradition and patriotism may also have played some role in the development of that particular
31、 school of thought. The reader of the book will probably sense those influences by simply noticing how often the name of Joukowsky, as founder of the vortex theory, and his original solutions and approaches are mentioned with reverence throughout the text. Review of the Text The reader will find tha
32、t material incorporated in the book is briefly reviewed in the Introduction. Using this review as a guide, additional features which should be of particular interest are pointed out. The concept of the flat vortex wake, discussed in Ch. 11, recently generated an interest in the West, as exemplified
33、by the work of 0rmiston8, who indicated that the flat rotor wake concept is applicable down to advance ratios of p w .IS. The Soviet authors establish the limits to the applicabilit of this approach in somewhat different terms of p 2 1.15 9 cy. Ch. IV, dealing with various aspects of aerodynamic int
34、eractions within a two-rotor system, contains much useful information from the practical design engineering and performance estimate point of view for axial, tandem and side-by-side configurations. Here, one will also find valuable considerations of the aerodynamic influence of a lifting rotor on th
35、e tail rotor, including such problems as the significance of the vertical location of the tail rotor as far as its power requirements in various regimes of for- ward flight is concerned. As to the influence of the wake structure in general, one should notice that, similar to the Western trend2, it a
36、ppears as the core of all considerations, beginning with Ch. VI. This was done with an increasing sophistication: The lifting-line approach evolved into the lifting-surface concept. Simple linear treat- ment of the flow problem, with its associated rigid wake, was replaced by the nonlinear, time-dep
37、endent interactions between the field of induced velocities and vortex filaments. Finally, considerations of both viscosity and compressibility were in- corporated. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In the treatment of axial flow, the a
38、ssumption is made that elements of free (trailing) vortices move along straight lines. This obviously means that, similar to many studies in the West during the late 50s and early 60s, contraction of the wake is not considered. However, the material pre- sented may be quite useful for those cases wh
39、ere airscrews in axial translation (ascent) can be modeled by a noncontracting wake. The readily available influence coefficients should greatly reduce the time of computation. Attention is also called to Ch. VIII, dealing with the concept of representing a rotor blade through a lifting surface. Thi
40、s approach considerably improves the understanding of flow in the tip region of regular blades as well as over the complete span of low-aspect ratio blades. Ch. IX may be of particular interest, since it represents an original application of the vortex theory concept to vertical descent - the regime
41、 of flight recognized as rather elusive for pure analytical treatment. The Soviet authors attacked this problem by postulating a physico-mathematical model based on the following concept: Trailing vortices are distributed along a conical surface, while the axial pitch of the helical vortices is appr
42、oximately constant. This leads to the establish- ment of relationships for instantaneous and time-average in- duced velocities, while tables of coefficients appearing in these expressions reduce the mathematical procedureto ele- mentary operations. In the bulk of tasks associated with the skewed flo
43、w (Chs. X- XV), ideal fluid is assumed. However, in one case, the influ- ence of compressibility on a stationary field of induced veloc- ities is briefly considered (end of Ch. X). Here, the applica- tion of the Biot-Savart law, modified for a compressible medium, indicates that steady-state fields
44、of induced velocities are affected only by the Mach number (M E V/al of the uniform flow directed along the axis of the skewed vortex wake, and do not depend on Mach number related to the tip speed (Mu Rw/a). Diffusion of vortices due to the viscosity effects is also discussed (Ch. XV.3), and the Bi
45、ot-Savart law is obtained for velocities induced by the diffused vortices. Considerations of the motion of vortex filaments within the vortex surface, which lead to ways of describing movements of the entire wake, may be of particular interest (Ch. XV.6). This approach, when adapted to simple forms
46、of vortex surfaces, can contribute to the solution of such various problems as, (a) vortex sheet roll-up behind the blade, (b) determination of the shape of the wake (including the roll-up of the vortex surface downstream) in vertical ascent as well as hovering in- and out-of-ground effect, etc. vii
47、 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In the development of relationships for induced velocities (both time-average and instantaneous) and especially, their harmonic components, wide use is made of Bessel functions, Legendre polynomials an
48、d functions, etc. In addition, to facilitate actual computations, tables and graphs are pro- vided in the text. Flost of the material presented in Chs, X-XV is based on the linear theory which leads to the movement of free vortices along the straight lines forming generatrices of skewed cylinders. H
49、owever, application of the nonlinear theory to the determination of the rotor vortex system in an oblique flow is also demonstrated (Ch. XV.9). This approach, when applied to the deformation of tip vortices at various p values (from = -07 to p = .2) leads to results which may be compared with those of Sadlerg (also see Ref. 2). Discussion of vortices in a compressible medium (Ch. X
