Variational Method of Finding Streamlines in Ring Cascades for Creeping Flows

• Autorzy: Tesch K. , Banaszek M.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a new analytical method of finding streamlines for creeping flows in a ring cascade composed of an infinite number of infinitely thin blades. An analytical solution was obtained by minimizing the dissipation functional by means of the variational calculus. The necessary condition for the optimum of the functional yields the Stokes equation after certain additional assumptions are introduced. We considered different variants of fixing of the inlet and outlet of the cascade.

Słowa kluczowe

EN

variational calculus; creeping flow; dissipation

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2011
• Tom: Vol. 15, No 1
• Strony: 71--84
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Tesch K.

autor

Banaszek M.

• Gdańsk University of Technology, Department of Turbomachinery and Fluid Mechanics, Narutowicza 11/12, 80-233 Gdańsk, Poland,

Bibliografia

• [1] Happel J and Brenner H 1981 Low Reynolds Number Hydrodynamics, Springer
• [2] Klonowska-Prosnak M E and Prosnak W J 2001 Acta Mechcmica 146 (1-2) 115
• [3] Tesch K 2008 Fluid Mechanics, Gdańsk Uniwrsity of Technology Publishing, Gdansk (in Polish)
• [4] Puzyrewski R and Tesch K 2010 TASK Quart. 14 (3) 67
• [5] Savage S B 1964 J. Appl. Mech. 31 594
• [6] Helmholtz H 1882 Wissenschaftlichp. Abhandlungen I, Barth J A, Leipzig
• [7] Goursat E 1898 Bulletin de la. S odęte Mathematiąue de France 26 236
• [8] Elsgolc L D 2007 Calculus of Yariations. Dover Publications, Inc., New York
• [9] Glazunov Y 2000 Variational Methods of Solving Differential Equations, Gdansk University of Technology Publishmg. Gdansk (in Polish)