Simulation of the flow through porous layers composed of converging-diverging capillary fissures or tubes

• Autorzy: Walicka A.

Identyfikatory

DOI

10.1515/ijame-2018-0010

• Języki publikacji: EN

Abstrakty

EN

In this paper, a porous medium is modelled by a network of converging-diverging capillaries which may be considered as fissures or tubes. This model makes it necessary to consider flows through capillary fissures or tubes. Therefore an analytical method for deriving the relationships between pressure drops, volumetric flow rates and velocities for the following fluids: Newtonian, polar, power-law, pseudoplastic (DeHaven and Sisko types) and Shulmanian, was developed. Next, considerations on the models of pore network for Newtonian and non-Newtonian fluids were presented. The models, similar to the schemes of central finite differences may provide a good basis for transforming the governing equations of a flow through the porous medium into a set of linear or quasi-linear algebraic equations. It was shown that the some coefficients in these algebraic equations depend on the kind of the capillary convergence.

Słowa kluczowe

EN

laminar flow; symmetrically corrugated capillaries; capillary fissures; capillary tubes; porous layer

PL

przepływ laminarny; warstwa porowata; rurki kapilarne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2018
• Tom: Vol. 23, no. 1
• Strony: 161--185
• Opis fizyczny: Bibliogr. 45 poz., rys., wykr.

Twórcy

autor

Walicka A.

• University of Zielona Góra, Faculty of Mechanical Engineering ul. Szafrana 4, 65-516 Zielona Góra, POLAND

Bibliografia

• [1] Bird R.B., Steward W.F. and Lightfoot E.N. (1960): Transport Phenomena. - New York: Wiley.
• [2] Bird R.B., Armstrong R.C. and Hassager O. (1987a): Dynamics of Polymeric Liquids. - vol.1, Fluid Mechanics, 2nd ed. John Wiley and Sons, New York.
• [3] Bird R.B.: Curtiss C.F., Armstrong R.C. and Hassager O. (1987b): Dynamics of Polymeric Liquids. - vol.2, Kinetic Theory, 2nd ed, John Wiley and Sons, New York.
• [4] Darcy H.P.G. (1856): Les fontaines publiques de la ville de Dijon. - Victor Dalmont, Paris.
• [5] Chen D., Mioshi H., Akai T., Yazawa T. (2005): Colourless transparent fluorescence material: Sintered porous glass containing rare-earth and transition-metal ions. - Applied Physics Letters, vol.86, No.231, pp.908-1-3.
• [6] Bear J. (1972): Dynamics of Fluids in Porous Media. - New York: Elsevier.
• [7] Greenkorn R.A. (1983): Flow Phenomena in Porous Media. - New York: Marcel Dekker Inc.
• [8] Nield D.A., Bejan A. (1995): Convection in Porous Media. - 2nd ed., New York: Springer-Verlag.
• [9] Vafai K. (1984): Convective flow and heat transfer in variable porosity media. - J. Fluid Mech., vol.147, pp.233-259.
• [10] Vafai K. (1986): Analysis of the channelling effect in variable porosity media. - ASME J. Energy Res. Technol., vol.108, 131-139.
• [11] Vafai K. (2000): Handbook of Porous Media. - 1st ed., New York: Marcel Dekker Inc.
• [12] Vafai K. (2005): Handbook of Porous Media. - 2nd ed., New York: Taylor & Francis Group.
• [13] Hadim H. and Vafai K. (2000): Overview of current computational studies of heat transfer in porous media and their applications: forced convection and multiphase transport. - In: Advances in Numerical Heat Transfer. - New York: Taylor & Francis Group.
• [14] Vafai K. and Hadim H. (2000): Overview of current computational studies of heat transfer in porous media and their applications: natural convection and mixed convection. - In: Advances in Numerical Heat Transfer. - New York: Taylor & Francis Group.
• [15] Vafai K. and Tien C.L. (1982): Boundary and inertia effects on convective mass transfer in porous media. - Int. J. Heat Mass Transfer, vol.25, pp.1183-1190.
• [16] Amiri A. and Vafai K. (1998): Transient analysis of incompressible flow through a packed bed. - Int. J. Heat Mass Transfer, vol.41, pp.4259-4279.
• [17] Alazmi B. and Vafai K. (2002): Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions. - Int. J. Heat Mass Transfer, vol.45, pp.3071-3087.
• [18] Khanafer K.M., Bull J.L., Pop I. and Berguer R. (2007): Influence of pulsatile blood flow and heating scheme on the temperature distribution during hyperthermia treatment. - Int. J. Heat Mass Transfer, vol.50, pp.4883-4890.
• [19] Peng X.F. and Wu H.L. (2005): Pore- scale transport phenomena in porous media. - In: Transport Phenomena in Porous Media III, Elsevier, New York, pp.366-398.
• [20] Harris S.D., Fishert Q.J, Karimi-Fard M., Vaszi A.Z. and Wu K. (2005): Modelling the effects of faults and fractures on fluid flow in petroleum reservoirs. - In: Transport Phenomena in Porous Media III, Elsevier, New York, pp.441-476.
• [21] M. Karamouz, A. Ahmadi, M. Akhbari (2001): Groundwater Hydrology: Engineering, Planning, and Management. - CRC Press, New York: Taylor & Francis Group.
• [22] Yeh W.W. (2015): Optimization methods for groundwater modelling and management. - Hydrogeology Journal, vol.23, pp.1051-1065.
• [23] Jivkov A.P., Hollis C., Etiese F., McDonald S.A. and Withers P.J. (2013): A novel architecture for pore network modelling with applications to permeability of porous media. - J. Hydrology, vol.486, pp.246-258.
• [24] Xiong Q., Baychev T.G. and Jivkov A.P. (2016): Review of pore network modelling of porous media: experimental characterisations, network constructions and applications to reactive transport. - J. Contaminant Hydrology, vol.192, pp.101-117.
• [25] Mazaheri A.R., Zerai B., Ahmadi G., Kadambi J.R., Saylor B.Z., Oliver M. And Smith D.H. (2005): Computer simulation of the flow through a lattice flow-cell model. - Advances in Water Resources, vol.28, pp.1267-1279.
• [26] Joekar-Niasar V., Hassanizadeh S.M., Pyrak-Nolte L.J. and Berentsen C. (2009): Simulating drainage and imbibition experiment in a high-porosity micromodel using an unstructured pore network model. - Water Resource Research, vol.45, No.2, DOI: 10.1029/2007WR006641.
• [27] Nsir K. and Schäfer G. (2010): A pore-throat model based on grain-size distribution to quantify gravity-dominated DNAPL instabilities in a water saturated homogeneous porous medium. - Comptes Rendus Geoscience, vol.342, pp.881-891.
• [28] Held R.J. and Celia M.A (2001): Modeling support of functional relationships between capillary pressure, saturation, interfacial area and common lines. - Adv. Water Res., vol.24, pp.325-343.
• [29] Hilpert M., Miller C.T. and Gray W.G. (2003): Stability of a fluid-fluid interface in a biconical pore segment. - J. Call. Interface Sci., vol.267, pp.397-407.
• [30] Acharya R.C., van der Zee S.E.A.T.M. and Leijense A. (2004): Porosity-permeability properties generated with a new 2-parameter 3D hydraulic pore-network model for consolidated and unconsolidated porous media. - Adv. Water Res., vol.27, pp.707-723.
• [31] Chen C.S. (2008): Mechanotransduction - a field pulling together? - J. Cell Sci., vol.121, pp.3285-3292.
• [32] Vossoughi S. (1999): Flow of non-Newtonian fluids in porous media. - In: Advances in the Flow and Rheology of Non- Newtonian Fluids, Elsevier, New York, pp.1183-1235.
• [33] Pearson J.R.A. and Tardy P.M.J. (2002): Models for flow of non-Newtonian and complex fluids through porous media. - J. Non-Newt. Fluid Mech., vol.102, pp.447-473.
• [34] Perrin C.L., Tardy P.M.J., Sorbie K.S. and Crawshaw J.C. (2006): Experimental and modelling study of Newtonian and non-Newtonian fluid flow in pore network micromodels. - J. Colloid. Interface Sci., vol.295, pp.542-550.
• [35] Vossoughi S. and Al-Husaini O.S. (1994): Rheological characterisation of the coal/oil/water slurries and the effect of polymer. - 19th international Technical Conference on Coal Utilization & Fuel Systems, Clearwater, Florida, USA, pp.115-122.
• [36] Walicka A. (2017): Rheology of Fluids in Mechanical Engineering. - Zielona Gora: University Press.
• [37] Rudraiah N., Chandrasekhar B.C., Veerabhadraiah R. and Nagaraj S.T. (1979): Some flow problems in porous media. - PGSAM Ser., vol.2, pp13-16.
• [38] Ostwald W. (1925): The velocity function of viscosity of disperse systems. - Kolloid Z., vol.36, pp.99-117.
• [39] de Waele A. (1923): Viscometry and Plastometry. - Oil Color Chem., Assn. J., vol.6, pp.33-69.
• [40] DeHaven E.S (1953): Control valve design for viscous pseudoplastic fluids. - JEC Equipment and Design, vol.51, No.7, pp.63A-66A.
• [41] DeHaven E.S (1959): Extruder design for pseudoplastic fluids. - Ind. Eng. Chem., vol.51, No.7, pp.813-816.
• [42] Sisko A.W. (1958): The flow of lubricating greases. - Indust. Eng. Chemistry, vol.50, No.12, pp.1789-1792.
• [43] Sisko A.W. (1960): Capillary viscometer for non-Newtonian liquids. - J. Colloid Sci., vol.15, No.1, pp.89-96.
• [44] Luikov A.W. and Shulman Z.P. (1970): Rheophysics and Rheodynamics of Fluidic Systems (in Rusian). - Minsk: Nauka i Miekhanika.
• [45] Shulman Z.P. (1975): Convective Heat Transfer of Rheologically Complex Fluids (in Russian). - Moscow: Energy.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)