Research Reports and Memoranda

Research Reports and Memoranda 192 AIRCRAFT ENGINEERING July, 1941 single fluid on solid bodies but also with the be­ as a collection of mathematical methods adapted JAPAN haviou r of mixtures such as those which occur in the for the solution of relatively simple problems. TH E AERONAUTICAL RESEARCH petro l engine and in th e atmosphere. In a complete These problems often might require lengthy numeri­ INSTITUTE : TOKYO IMPERIAL stud y of the motion of a fluid attention must be cal calculations or graphical constructions, but paid to reactions between its constituents, evapora­ UNIVERSITY supposedly can be worked out without the use of tion, conduction and radiation of heat, diffusion, advanced methods of mathematical analysis. This (Kôgyô Tosho Kabushiki Kaisha, Tokyo) viscosity and other phenomena. description was perhaps correct some decades ago ; Report No. 203. December, 1940. On the to-da y a large group of scientific workers is engaged I t is uncertain to what extent equations govern­ Mechanism of a New Transformation, and ing the various processes can be derived from a in applying various methods of classical and modern single variational principle as some of the phenom­ analysis to problems in electrical, civil, mechanical, Some Associated New Reactions in the Iron- ena mentioned are known to present difficulties, aeronautical and also chemical engineering. Nickel-Aluminium System. By Syûti Kiuti. bu t the situation may be clarified a little by an I n this paper th e attemp t is made to give a review Fro m X-ray studies of iron-nickel-aluminium examinatio n of th e equations derived from a varia­ of non-linear problems which are of practical interest alloys a new phase a ' was discovered. Although, tional principle of a very general type. an d for whose solution methods have been worked in the surface layers of these alloys an unstable out , or a t least suggested, by mathematicians, physi­ Publication No. 126. Some Mechanical γ-phase is observed in th e early stage of annealing, cists or engineers. The review is not exhaustive, thi s phase disappears entirely with prolonged Tests of Aluminium Alloys 14S-T and 24S-T. bu t it was attempted to include examples of the annealing, the X-ray pattern showing the co­ By W. B. Mechling and S. S. Jack. most typical problems. The question of existence existence of the a- and a'-phases. In the interiors Mechanical tests were conducted on aluminium an d uniqueness of solutions is only superficially of th e specimens th e unstabl e γ-phase is neve r found, alloys 14S-T and 24S-T. The former alloy was in touched ; emphasis is laid on methods for obtaining only diffused X-ray interference lines being observed th e form of a large hand-forged billet and the latter approximat e solutions. there . However, by very long annealing extending in the form of a ¾ by 6-in. rectangular bar. In t o 3,500 hours at 1,000 deg., the writer succeeded additio n to the determination of the usual mechani­ in observing a splitting phenomenon of the X-ray cal properties, tension impact values were also patter n in the interiors of the specimens also. obtaine d for both materials. Care was exercised Thi s new change, a→a+a', has been taken as the t o obtain all test specimens from the same stock and main reaction in the ternary system, instead of the to define the condition of the material by photo­ a→a + γ change as suggested by previous investiga­ micrographs and grain direction. tors . From an X-ray analysis of the Fe-N8-Al I t was found tha t the results obtained compared system, th e a'-phas e ha s been identified as th e solid favourably with the generally accepted mechanical solution of the intermetallic compound NiAl. propertie s of these alloys. Considerable variation Th e ternary equilibria were studied by means of of the mechanical properties with grain direction X-ra y analysis, and Köster's (a+γ)-field was sub­ was found, the magnitude of these variations being divided into phase fields (a+a'), (a'+γ), (a+γ), shown in both tabular and graphical form. an d ( a + a '+ γ ) . The newly found phase boundaries Wherea s the results obtained compare favourably were determined by X-rays. Some associated new wit h the generally accepted physical properties of reactions, viz. a→ ( a + a ') → ( a + a '+ γ ) , a→(a+γ)→ these alloys, these tests present quantitatively the ( a + a '+ γ ) →(a+a'), γ→(γ+a) →(γ+a+a') → variation of these properties with grain direction. ( a + a ') , and γ→(γ+a')→(γ+a'+a)→(a'+a) , were Publication No. 129. Operational Methods also confirmed by dilatometric analysis, from which in the Theory of Airfoils in Non-Uniform result the validity of the new equilibria was ascer­ tained. From th e new ternar y equilibria th e conode Motion. By William R. Sears, Ph.D. line in th e iron-nickel-aluminium magnet alloys was In this paper Heaviside's operators are employed determined , and the mechanism of the splitting t o obtain the following results : phenomeno n of a-crystals due to the new trans­ (1) New integral expressions convenient for formation was thus clarified. numerical calculation are obtained for the lift and circulation of a two-dimensional thin aerofoil follow­ ing a sudden change of its angle of attac k or velocity. U.S.A. (2) Approximate expressions are obtained for the GUGGENHEIM AERONAUTICS initial and final behaviours of these functions. LABORATORY, CALIFORNIA INSTI­ (3) The circulation function is shown to be iden­ TUT E OF TECHNOLOGY, PASADENA tical with the function that expresses the lift of an aerofoil during and following its entrance into a Publication No. 122. The Aerodynamics of sharp-edged vertical gust. Reacting Substances. By H. Bateman. I t appears that in problems concerning the non­ Speaking broadly, the subject of aerodynamics is uniform motion of two dimensional thin airfoils the concerned not only with the forces exerted by a mathematica l analysis is most conveniently carried ou t by th e use of Heaviside's operators. Publication No. 131. The Engineer Grap­ * Under this heading are published, from time to time, abstracts ples with Non-Linear Problems. By Theodore of the Reports on research work undertaken by aeronautical von Kārmān. research institutions and bodies throughout the world so far as these are, in wartime, still being issued and made available. Engineering mathematics is generally considered http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Research Reports and Memoranda

Aircraft Engineering and Aerospace Technology, Volume 13 (7): 1 – Jul 1, 1941

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0002-2667
DOI
10.1108/eb030799
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Abstract

192 AIRCRAFT ENGINEERING July, 1941 single fluid on solid bodies but also with the be­ as a collection of mathematical methods adapted JAPAN haviou r of mixtures such as those which occur in the for the solution of relatively simple problems. TH E AERONAUTICAL RESEARCH petro l engine and in th e atmosphere. In a complete These problems often might require lengthy numeri­ INSTITUTE : TOKYO IMPERIAL stud y of the motion of a fluid attention must be cal calculations or graphical constructions, but paid to reactions between its constituents, evapora­ UNIVERSITY supposedly can be worked out without the use of tion, conduction and radiation of heat, diffusion, advanced methods of mathematical analysis. This (Kôgyô Tosho Kabushiki Kaisha, Tokyo) viscosity and other phenomena. description was perhaps correct some decades ago ; Report No. 203. December, 1940. On the to-da y a large group of scientific workers is engaged I t is uncertain to what extent equations govern­ Mechanism of a New Transformation, and ing the various processes can be derived from a in applying various methods of classical and modern single variational principle as some of the phenom­ analysis to problems in electrical, civil, mechanical, Some Associated New Reactions in the Iron- ena mentioned are known to present difficulties, aeronautical and also chemical engineering. Nickel-Aluminium System. By Syûti Kiuti. bu t the situation may be clarified a little by an I n this paper th e attemp t is made to give a review Fro m X-ray studies of iron-nickel-aluminium examinatio n of th e equations derived from a varia­ of non-linear problems which are of practical interest alloys a new phase a ' was discovered. Although, tional principle of a very general type. an d for whose solution methods have been worked in the surface layers of these alloys an unstable out , or a t least suggested, by mathematicians, physi­ Publication No. 126. Some Mechanical γ-phase is observed in th e early stage of annealing, cists or engineers. The review is not exhaustive, thi s phase disappears entirely with prolonged Tests of Aluminium Alloys 14S-T and 24S-T. bu t it was attempted to include examples of the annealing, the X-ray pattern showing the co­ By W. B. Mechling and S. S. Jack. most typical problems. The question of existence existence of the a- and a'-phases. In the interiors Mechanical tests were conducted on aluminium an d uniqueness of solutions is only superficially of th e specimens th e unstabl e γ-phase is neve r found, alloys 14S-T and 24S-T. The former alloy was in touched ; emphasis is laid on methods for obtaining only diffused X-ray interference lines being observed th e form of a large hand-forged billet and the latter approximat e solutions. there . However, by very long annealing extending in the form of a ¾ by 6-in. rectangular bar. In t o 3,500 hours at 1,000 deg., the writer succeeded additio n to the determination of the usual mechani­ in observing a splitting phenomenon of the X-ray cal properties, tension impact values were also patter n in the interiors of the specimens also. obtaine d for both materials. Care was exercised Thi s new change, a→a+a', has been taken as the t o obtain all test specimens from the same stock and main reaction in the ternary system, instead of the to define the condition of the material by photo­ a→a + γ change as suggested by previous investiga­ micrographs and grain direction. tors . From an X-ray analysis of the Fe-N8-Al I t was found tha t the results obtained compared system, th e a'-phas e ha s been identified as th e solid favourably with the generally accepted mechanical solution of the intermetallic compound NiAl. propertie s of these alloys. Considerable variation Th e ternary equilibria were studied by means of of the mechanical properties with grain direction X-ra y analysis, and Köster's (a+γ)-field was sub­ was found, the magnitude of these variations being divided into phase fields (a+a'), (a'+γ), (a+γ), shown in both tabular and graphical form. an d ( a + a '+ γ ) . The newly found phase boundaries Wherea s the results obtained compare favourably were determined by X-rays. Some associated new wit h the generally accepted physical properties of reactions, viz. a→ ( a + a ') → ( a + a '+ γ ) , a→(a+γ)→ these alloys, these tests present quantitatively the ( a + a '+ γ ) →(a+a'), γ→(γ+a) →(γ+a+a') → variation of these properties with grain direction. ( a + a ') , and γ→(γ+a')→(γ+a'+a)→(a'+a) , were Publication No. 129. Operational Methods also confirmed by dilatometric analysis, from which in the Theory of Airfoils in Non-Uniform result the validity of the new equilibria was ascer­ tained. From th e new ternar y equilibria th e conode Motion. By William R. Sears, Ph.D. line in th e iron-nickel-aluminium magnet alloys was In this paper Heaviside's operators are employed determined , and the mechanism of the splitting t o obtain the following results : phenomeno n of a-crystals due to the new trans­ (1) New integral expressions convenient for formation was thus clarified. numerical calculation are obtained for the lift and circulation of a two-dimensional thin aerofoil follow­ ing a sudden change of its angle of attac k or velocity. U.S.A. (2) Approximate expressions are obtained for the GUGGENHEIM AERONAUTICS initial and final behaviours of these functions. LABORATORY, CALIFORNIA INSTI­ (3) The circulation function is shown to be iden­ TUT E OF TECHNOLOGY, PASADENA tical with the function that expresses the lift of an aerofoil during and following its entrance into a Publication No. 122. The Aerodynamics of sharp-edged vertical gust. Reacting Substances. By H. Bateman. I t appears that in problems concerning the non­ Speaking broadly, the subject of aerodynamics is uniform motion of two dimensional thin airfoils the concerned not only with the forces exerted by a mathematica l analysis is most conveniently carried ou t by th e use of Heaviside's operators. Publication No. 131. The Engineer Grap­ * Under this heading are published, from time to time, abstracts ples with Non-Linear Problems. By Theodore of the Reports on research work undertaken by aeronautical von Kārmān. research institutions and bodies throughout the world so far as these are, in wartime, still being issued and made available. Engineering mathematics is generally considered

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Jul 1, 1941

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