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Keywords:
solvability; boundary value problems; non-viscous; irrotational, subsonic flows; cascades of profiles; layer of variable thickness; classical solution; variational formulation; weak solution; existence; uniqueness; monotone operator theory
solvability; boundary value problems; non-viscous; irrotational, subsonic flows; cascades of profiles; layer of variable thickness; classical solution; variational formulation; weak solution; existence; uniqueness; monotone operator theory
Summary:
The paper is devoted to the study of solvability of boundary value problems for the stream function, describing non-viscous, irrotional, subsonic flowes through cascades of profiles in a layer of variable thickness. From the definition of a classical solution the variational formulation is derive and the concept of a weak solution is introduced. The proof of the existence and uniqueness of the weak solution is based on the monotone operator theory.
References:
[1] И. Г. Белехова: Учет пространственное потока обтекающего рабочее колесо турбомашины. Вестник ЛГУ, № 1, 1958. Zbl 0995.62501
[2] R. W. Carrol: Abstract Methods in Partial Differential Equations. Harper, Row Publishers, New York, 1968. MR 0433480
[3] J. Cea: Optimisation, Théorie et Algorithmes. Dunod, Paris, 1971. MR 0298892 | Zbl 0211.17402
[4] T. Czibere: Über die Berechnung der Schaufelprofile von Strömungsmaschinen mit halbaxialer Durchströmung. Acta Technica, Hungary, 4, 1963.
[5] M. Feistauer: Mathematical study of three-dimensional axially symmetric stream fields of an ideal fluid. In: Methoden und Verfahren der mathematischen Physik, Band 21, 45 - 61, Verlag P. D. Lang, Frankfurt am Main, 1980. MR 0714155
[6] M. Feistauer: Numerical solution of non-viscous axially symmetric channel flows. In: Methoden und Verfahren der mathematischen Physik, Band 24, 65 -78, Verlag P. D. Lang, Frankfurt am Main, 1982. Zbl 0513.76013
[7] M. Feistauer: Mathematical study of rotational incompressible non-viscous flows through multiply connected domains. Apl. mat. 26 (1981), No. 5, 345-364. MR 0631753 | Zbl 0486.76025
[8] M. Feistauer: On non-viscous flows in cascades of blades. ZAMM, Band 64, (1984), T186-T188.
[9] M. Feistauer: Solution of some nonlinear problems in mechanics of non-viscous fluids. Proceedings of the 5th Summer School "Software and Algorithms of Numerical Mathematics 83", Faculty of Math. and Phys., Charles University, Prague, 1984 (in Czech).
[10] M. Feistauer J. Římánek: Subsonic irrotational flow of compressible fluid in axially symmetric channels. Apl. mat. 20 (1975), No. 4, 253 - 265. MR 0378560
[11] M. Feistauer J. Polášek Z. Vlášek: Flow through cascades of blades in a layer of variable thickness. Research report No. SVÚSS 82-04012, State Inst. for Machine Design, Prague, 1982 (in Czech).
[12] M. Feistauer J. Felcman Z. Vlášek: Calculation of irrotational flows through cascades of blades in a layer of variable thickness. Research report, ŠKODA Plzeň, 1983 (in Czech).
[13] S. Fučík A. Kufner: Nonlinear Differential Equations. Studies in Applied Mechanics 2, Elsevier, Amsterdam-Oxford-New York, 1980. MR 0558764
[14] M. Hoffmeister: Ein Beitrag zur Berechnung der inkompressiblen reibungsfreien Strömung durch ein unendlich dünnes Schaufelgitter in einem Rotationsrohrraum. Maschinenbautechnik, Band 10, No. 8, 1961.
[15] K. Jacob: Berechnung der inkompressiblen Potentialströmung für Einzel- und Gitterprofile nach einer Variante des Martensens-Verfahrens. Bericht 63 RO 2 der Aerodynamischen Versuchsanstalt Göttingen, 1963.
[16] Z. Kazimierski: Plane flow in axial blade row of stream machine. Arch. budowy maszyn, XIII, 1966, No. 2 (in Polish).
[17] К. А. Киселев: Профилирование лопастей рабочего колеса радиально-осевой турбины методом особенностей. Вестник ЛГУ, № 1, 1958. Zbl 0995.62501
[18] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[19] J. L. Lions: Quelques Methodes de Résolution des problèmes aux Limites non Linéaires. Dunod, Paris, 1969. MR 0259693 | Zbl 0189.40603
[20] Л. A. Люсгперник В.И. Соболев: Елементы функционального анализа. Наука, Москва, 1965. Zbl 1225.00032
[21] R. Mani A. J. Acosta: Quasi two-dimensional flows through a cascade. Transactions of the ASME, Journ. of Eng. for Power, Vol. 90, Series A, No. 2, April 1968.
[22] E. Martensen: Berechnung der Druckverteilung an Gitterprofilen in ebener Potentialströmung mit einer Fredholmschen Integralgleichung. Arch. Rat. Mech. Anal. 3 (1959), 253-270. DOI 10.1007/BF00284179 | MR 0114431 | Zbl 0204.25603
[23] J. Nečas: Über Grenzwerte von Funktionen, welche ein endliches Dirichletsches Integral haben. Apl. mat. 5 (1960), No. 3, 202-209. MR 0118782
[24] J. Nečas: Les Méthodes Directes en Théorie des Équations Elliptiques. Academia, Prague, 1967. MR 0227584
[25] J. Polášek Z. Vlášek: Berechnung der ebenen Potentialströmung von rotierenden radialen Profilgittern. Apl. mat. 17 (1972), 295-308. MR 0312808
[26] Б. С. Раухман: Прямая задача обтекания двухмерной решетки профилей. Труды ЦКТ 1, Вып. 61, 1965. Zbl 1099.01519
[27] Б. С. Раухман: Расчет обтекания несжимаемой жидкостью решетки профилей на осесимметричной поверхности тока в слое переменной толщины. Изв. АН СССР, МЖГ, 1971, № 1, 83-89. Zbl 1170.92344
[28] K. Rektorys: Variační metody. SNTL Praha, 1974. English translation: Variational Methods. Reidel Co., Dordrecht-Boston, 1977. Zbl 0371.35001
[29] В. И. Смирнов: Курс высшей математики. Том. 5. ГИФМЛ, Москва, 1960. Zbl 1004.90500
[30] J. D. Stanitz: Some theoretical aerodynamic investigation of impellers in radial- and mixed-flow centrifugal compressors. Transactions of the ASME, 74, No. 4, 1952.
[31] M. M. Вайнберг: Вариационный метод и метод монотонных операторов. Наука, Москва, 1972. Zbl 1156.34335
[32] С. В. Валландер: Протекание жидкости в турбине. ДАН СССР, Том 84, № 4, 673-676, 1952. Zbl 1145.11324
[33] Z. Vlášek: Plane potential flows past groups of profiles and cascades of profiles. Ph. D. Thesis, Faculty of Math. and Phys., Charles University, Prague, 1973 (in Czech).
[34] M. B. Wilson R. Mani A. J. Acosta: A note on the influence of axial velocity ratio on cascade performance. Proceedings of the symp. "Theoretical Prediction of Two- and Three-Dimensional Flows in Turbomachinery" held at Pennsylvania State University, 1974, NASA-SP-304, 1974, Session I, Part I.
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