Abstract
Simulation of the flow of a non-Newtonian fluid with the free surface that is realized on the filling of planar channels in the gravity field has been carried out. Mathematical statement of the problem with the use of the Shwedow-Bingham rheological model has been formulated. A numerical algorithm for solving the problem on the basis of finite difference methods has been constructed. Parametric investigations of major features of the process in relation to values of governing parameters have been made. Flows have been studied, and various filling regimes for two different orientations of the flow direction relative to action of gravitational forces have been identified. Evolution of quasi-solid nuclei for various values of yield stress has been demonstrated.
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References
Rudert, A. and Schwarze, R., Experimental and Numerical Investigation of a Viscoplastic Carbopol Gel Injected into a Prototype 3D Mold Cavity, J. Non-Newtonian Fluid Mech., 2009, vol. 161, nos. 1–3, p. 60.
Kim, J.M., Ahn, K.H., Lee, S.J., and Lee, S.J., Numerical Simulation of Moving Free Surface Problems in Polymer Processing Using Volume of Fluid Method, Polym. Eng. Sci., 2001, vol. 41, no. 5, p. 858.
Borzenko, E.I., Shrager, G.R., and Yakutenok, V.A., Filling of Channels by a Non-Newtonian Fluid in the Gravitational Field, Izv. Akad. Nauk, Mekh. Zhidk. Gaza, 2009, no. 6, p. 40.
Chekhonin, K.A. and Sukhinin, P.A., Motion of a Nonlinearly Viscoplastic Fluid with a Free Surface Filling an Axisymmetric Space, Mat. Model., 2001, vol. 13, no. 3, p. 89.
Al’es, M.Yu. and Konstantinov, Yu.N., Numerical Simulation of High-Viscosity Non-Newtonian Fluids with Heat Transfer, Gidrogazodinam. Tekh. Teplomassoobm., 1990, no. 4, p. 136.
Mitsoulis, E. and Matsoukas, A., Free Surface Effects in Squeeze Flow of Bingham Plastics, J. Non-Newtonian Fluid Mech., 2005, vol. 129, no. 3, p. 182.
Mitsoulis, E., Annular Extrudate Swell of Pseudoplastic and Viscoplastic Fluids, J. Non-Newtonian Fluid Mech., 2007, vol. 141, nos. 2–3, p. 138.
Smol’skii, B.M., Shul’man, Z.P., and Gorislavets, V.M., Reodinamika i teploobmen nelineino-vyazkoplastichnykh materialov (Rheodynamics and Heat Transfer Properties of Nonlinearly Viscoplastic Materials), Minsk: Nauka i Tekhnika, 1970.
Shrager, G.R., Kozlobrodov, A.N., and Yakutenok, V.A., Modelirovanie gidromekhanicheskikh protsessov v tekhnologii pererabotki polimernykh materialov (Simulation of Hydromechanical Processes in Polymer Processing), Tomsk: Tomsk. Gos. Univ., 1999.
Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Washington, DC: Hemisphere, 1980.
Borzenko, E.I. and Yakutenok, V.A., Free Surface Evolution in the Filling of Plane Channels by a Viscous Fluid, Izv. Akad. Nauk, Mekh. Zhidk. Gaza, 2008, no. 1, p. 24.
Borzenko, E.I. and Yakutenok, V.A., Numerical Simulation of a Flowing Viscous Incompressible Fluid with a Free Surface Using the SIMPLE Method, Mat. Model., 2007, vol. 19, no. 3, p. 52.
Gramberg, H.J.J., van Vroonhoven, J.C.W., and van de Ven, A.A.F., Flow Patterns behind the Free Flow Front for a Newtonian Fluid Injected between Two Infinite Parallel Plates, Eur. J. Mech., 2004, vol. 23, p. 571.
Rose, W., Fluid-Fluid Interfaces in Steady Motion, Nature, 1961, vol. 191, p. 242.
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Original Russian Text © E.I. Borzenko, G.R. Shrager, V.A. Yakutenok, 2011, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2011, Vol. 45, No. 2, pp. 187–193.
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Borzenko, E.I., Shrager, G.R. & Yakutenok, V.A. Simulation of the process of the filling of planar channels with viscoplastic fluid. Theor Found Chem Eng 45, 173–179 (2011). https://doi.org/10.1134/S0040579511020059
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DOI: https://doi.org/10.1134/S0040579511020059