caa a22 4500 469081511 CHVBK 20180323132951.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01170808 doi (NATIONALLICENCE)springer-10.1007/BF01170808 Liu G. Laboratory of Turbomachinery Aerodynamics, Shanghai Institute of Mechanical Engineering, 516 Jun-Gong Road, 200 093, Shanghai, People's Republic of China aut Variational principles and generalized variational principles for fully 3-D transonic flow with shocks in a turbo-rotor Part I. Potential flow [Elektronische Daten] [G. Liu] Summary: In this article three families of variational principles (VPs) for the direct problem of 3-D transonic steady potential (Part I) and rotational (Part II) flows with embedded shocks in a turbomachine impeller of axial-, radial- or mixed-flow type are developed. Their special features are to take full advantage of natural boundary conditions, functional variations with variable domain and "artificial interfaces” [31] and to account for mass suction/blowing along the walls, so as to facilitate the handling of various complex boundary conditions. Moreover, it is also shown that by taking variations of the position of unknown flow discontinuities (such as shocks, free trailing vortex sheets) all matching conditions across these discontinuities, including the well-known Rankine-Hugoniot shock relation, can be derived from the VPs as natural interface-conditions. This article is intended primarily to provide, incorporating a new special finite element (FE) with self-adjusting internal discontinuities [14], a theoretical basis for developing a novel computational method for capturing automatically all flow discontinuities. The VPs presented herein are extensions of Bateman's principle [23] to rotor flow. The numerical FE solutions [29], [32] based on this theory show good agreement with the measured data. In the Appendix I, a new analogy between functional variations with variable domain and the Reynolds' transport theorem is pointed out and used as a basis for deriving a general formula for such variations. Springer-Verlag, 1992 Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 117-130 0001-5970 95:1-4<117 1992 95 707 https://doi.org/10.1007/BF01170808 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01170808 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Liu G. Laboratory of Turbomachinery Aerodynamics, Shanghai Institute of Mechanical Engineering, 516 Jun-Gong Road, 200 093, Shanghai, People's Republic of China aut NATIONALLICENCE 773 0- Acta Mechanica Springer-Verlag 95/1-4(1992-03-01), 117-130 0001-5970 95:1-4<117 1992 95 707 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 469081511 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer