Tests on a new method for numerical solution to the Navier-Stokes equations. part II: plane unsteady flow around curvilinear contours

• Autorzy: Klonowska-Prosnak, M. E. , Kołodziejczyk, M.
• Języki publikacji: EN

Abstrakty

EN

Similarly as the preceding paper of the authors (Klonowska and Kołodziejczyk, 1999) also the present one deals with the new method (Prosnak and Kosma, 1991) for the determination of unsteady, plane flows of viscous incompressible fluids. The novelty of the method consists in elimination of pressure from the system of the Navier-Stokes equations by means of integration of the "total" differential of pressure. Consequently - the order of the system resulting from such an elimination is not increased in comparison with the original one, and no artificial, non-physical boundary conditions occur. The main difference between the present paper and the previous one consists in geometrical properties of the domain of solution. It is infinite, and bounded by a curvilinear contour. Three contours are considered in the paper: a flat plate, a circle, and the NACA 0012 airfoil. The results prove, that also in these cases the method works properly - at least for rather small values of the Reynolds number. Such a limitation is due to the efficiency of the computers being available at the time, when the calculations were made.

Słowa kluczowe

PL

wytrzymałość materiałów; równanie Naviera-Stokesa; rozciąganie

EN

Navier-Stokes equations; elimination of pressure; conformal mapping; curvilinear grids; doubly connected domains; stretching and compression of subdomains

• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2002
• Tom: Vol. 7, no 2
• Strony: 619-652
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr.

Twórcy

autor

Klonowska-Prosnak, M. E.

• Institute of Oceanology, Polish Academy of Sciences 81-712 Sopot, POLAND,

autor

Kołodziejczyk, M.

• Department of Mechanics, Technical University of Białystok 15-351 Białystok, POLAN

Bibliografia

• [1] Frazer R.A. (1926): On the motion of circular cylinders in a viscous fluid. - Phil. Trans. Roy. Soc., London, vol.A225, pp.93-130.
• [2] Klonowska M.E. and Kołodziejczyk M. (1999): Tests on a new method for numerical solution to the Navier-Stokes equation. Part I: plane unsteady flow in finite, rectangular domains. - Applied Mechanics and Engineering, vol.4, No.2, pp.311-339.
• [3] Klonowska-Prosnak M.E. (1988): Determination of viscous, incompressible flows In multiply connected domains. - Sc. Rep. No.263/1213/88, the Institute of Fluid Flow Machinery, Polish Ac. of Sci., Gdańsk, Poland (in Polish).
• [4] Klonowska M.E. and Prosnak W.J. (1996): On an effective method for conformal mapping of multiply connected domains. - Acta Mechanica, vol. 119, pp.35-52.
• [5] Kołodziejczyk M. (1995): Application of a New Method for Solving the Navier-Stofat Equations to Plane Liquid Motions. - Ph.D. Thesis, the Institute of Fluid Flow Machinery, Polish Ac. of Sci., Gdańsk, Poland (in Polish).
• [6] Prosnak W.J. (1991): On a complex potential suitable for construction of C-type grids. - Acta Mechanica, vol.89, pp. 145-165.
• [7] Prosnak W.J. and Klonowska M.E. (1995): Conformal mapping - procedures ant programs. - Sc. Rep. No.452/1408/95, the Institute of Fluid Flow Machinery, Polish Ac. of Sci., Gdańsk, Poland, (in Polish).
• [8] Prosnak W.J. and Klonowska M.E. (1996): Introduction to Numerical Fluid Mechanic Part B: Conformal Mapping. - Wroclaw: Ossolineum (in Polish).
• [9] Prosnak W.J. and Kosma Z.J. (1991): On a new method for numerical solution of the Navier-Stokes equations. - Acta Mechanica, vol.89, pp.45-63.