Numerical and analytical calculations of the free surface flow between two semi-infinite straights

• Autorzy: Chedala Fatma Zohra , Amara Abdelkader , Meflah Mabrouk

Identyfikatory

DOI

10.17512/jamcm.2020.4.02

• Języki publikacji: EN

Abstrakty

EN

The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated.

Słowa kluczowe

EN

free surface; flow; surface tension; free streamline theory; exact solution; series truncation; Weber number

PL

numer Webera; napięcie powierzchniowe; dokładne rozwiązanie; przepływ swobodny

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 4
• Strony: 21--32
• Opis fizyczny: Bibliogr. 22 poz., rys., tab.

Twórcy

autor

Chedala Fatma Zohra

• Department of Mathematics, Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla 30000, Algeria

autor

Amara Abdelkader

• Department of Mathematics, Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla 30000, Algeria

autor

Meflah Mabrouk

• Department of Mathematics, Laboratory of Applied Mathematics, University of Kasdi Merbah Ouargla 30000, Algeria

Bibliografia

• [1] Laiadi, A., & Merzougui, A. (2020). Numerical solution of a cavity problem under surface tension effect. Math. Meth. Appl. Sci., 2020, 1-9.
• [2] Panda, S. (2016). A study on inviscid flow with a free surface over an undulating bottom. J. Appl. Fluid Mech., 9(3), 1089-1096.
• [3] Panda, S., Martha, S.C., & Chakrabarti, A. (2016). An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography. Appl. Math. Comput., 273, 165-177.
• [4] Panda, S., Martha, S.C., &Chakrabarti, A. (2015). Three-layer fluid flow over a small obstruction on the bottom of a channel. The ANZIAM Journal, 56(3), 248-274.
• [5] Stokes, T.E., Hocking, G.C., & Forbes, L.K. (2012). Steady free surface flow induced by a submerged ring source or sink. J. Fluid Mech., 694, 352-370.
• [6] Chen, M.J., & Forbes, L.K. (2011).Waves in two-layer shear flow for viscous and inviscid fluids. Eur. J. Mech. B Fluids, 30, 387-404.
• [7] Vanden Broeck, J.M., & Keller, J.B. (1986). Pouring flows. Phys. Fluids, 29, 3958-3961.
• [8] Merzougui, A., Mekias, H., & Guechi, F. (2007). A waveless two-dimensional flow in a channel against an inclined wall with surface tension effect. J. Phys. A: Math. Theor., 40, 14317-14328.
• [9] Guechi, F., & Dahel, M. (2012). Free surface flow modeling between two plates. I. Elec. J. Pure. Appl. Math., 4, 179-184.
• [10] Guechi, F., & Khermache, M. (2012). Free streamline for flow over step. I. J. Pure. Appl. Math., 74, 367-372.
• [11] Chapman, S.J., & Vanden Broeck, J.M. (2002). Exponential asymptotics and capillary waves. Siam J. Appl. Math., 62, 1872-1898.
• [12] Choi, J.W. (2002). Free surface waves over a depression. Bull. Austral. Math. Soc., 65, 329-335.
• [13] Dias, F., & Vanden Broeck, J.M. (1989). Open channel flows with submerged obstructions. J. Fluid Mech., 206, 155-170.
• [14] Dias, F., & Vanden Broeck, J.M. (1991). Nonlinear free-surface flow past a submerged inclined flat plate. Phys. Fluids., A3, 2995-3000.
• [15] Forbes, L.K., & Schwartz, L.W. (1982). Free-surface flow over a semicircular obstruction. J. Fluid Mech., 114, 299-314.
• [16] Gasmi, A., & Amara, A. (2018). Free-surface profile of a jet flow in U-shaped channel without gravity effects. Adv. Stud. Contemp. Math. (Kyungshang), 28, 393-400.
• [17] Gasmi, A. (2014). Two-dimensional cavitating flow past an oblique plate in a channel. J. Comput. Appl. Math., 259, 828-834.
• [18] Ockendon, J.R., Howison, S.D., Lacey, A.A., & Movichan, A.B. (2003). Applied Partial Differential Equations. Revised Edition Oxford University Press.
• [19] Tuck, E.O. (1965). The effect of nonlinearity at the free surface on flow past a submerged cylinder. J. Fluid Mech., 22, 401-414.
• [20] Vanden Broeck, J.M. (1984). Bubbles rising in a tube and jets falling from a nozzle. Phys. Fluids, 27, 1090-1093.
• [21] Vanden Broeck, J.M. (1987). Free surface flow over a semi-circular obstruction in a channel. Phys. Fluids, 30, 2315-2317.
• [22] Vanden Broeck, J.M. (2010). Gravity-Capillary Free Surface Flows. Cambridge: Cambridge University Press.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).