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Flows of Sisko Fluid Through Symmetrically Curved Capillary Fissures and Tubes

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a general analytical method for deriving mathematical relationships between pressure losses and the volumetric flow rate for laminar flows of a Sisko fluid. In this paper, only the laminar flow of Sisko type fluids is considered. It was demonstrated that the method can be used to find solutions for other pseudoplastic fluids and for different hapes of fissures and tubes. It can also be a good basis for numerical integration when analytical expressions are hard to obtain due to mathematical complexities. As an example, the following cases of convergent-divergent or divergent-convergent fissures and tubes, namely: parabolic, hyperbolic, hyperbolic cosine and cosine curve were considered. For each example, the formulae for pressure losses, volumetric flow rate and flow velocity were obtained. The most general forms of these formulas can be obtained by introducing hindrance factors.
Rocznik
Strony
27--54
Opis fizyczny
Bibliogr. 46 poz., rys., schem., tab.
Twórcy
autor
  • University of Zielona Góra, Faculty of Mechanical Engineering
autor
  • University of Zielona Góra, Faculty of Mechanical Engineering
autor
  • University of Zielona Góra, Faculty of Mechanical Engineering
Bibliografia
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  • 5. Bear, J. (1972). Dynamics of fluids in porous media.
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  • 7. Gradshteyn, I. S. and Ryzhik, I. M. (2014). Table of integrals, series, and products. Academic press.
  • 8. Greenkorn, R. A. (1983). Flow phenomena in porous media: fundamentals and applications in petroleum, water and food production.
  • 9. Hadim, H. and Vafai, K. (2000a). Overview of current computational studies of heat transfer in porous media and their applications: natural convection and mixed convection. Advances in Numerical Heat Transfer.
  • 10. Hadim, H. and Vafai, K. (2000b). Overview of current computational studies of heat transfer in porous media and their applications-forced convection and multiphase heat transfer. Advances in Numerical Heat Transfer.
  • 11. Harris, S., VASZI, A., FISHER, Q., KARIMI-FARD, M., and Wu, K. (2005). Modelling the effects of faults and fractures on fluid flow in petroleum reservoirs. In Transport Phenomena in Porous Media III, pages 441–476. Elsevier.
  • 12. Held, R. J. and Celia, M.A. (2001). Modeling support of functional relationships between capillary pressure, saturation, interfacial area and common lines. Advances in Water Resources, 24(3-4):325–343.
  • 13. Hilpert, M., Miller, C. T., and Gray, W. G. (2003). Stability of a fluid–fluid interface in a biconical pore segment. Journal of colloid and interfaces cience, 267(2):397– 407.
  • 14. 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. Journal of Hydrology, 486:246–258.
  • 15. Joekar Niasar, V., Hassanizadeh, S., Pyrak-Nolte, L., and Berentsen, C. (2009). Simulating drainage and imbibition experiments in a high-porosity micromodel using an unstructured pore network model. Water resources research, 45(2).
  • 16. Khanafer, K., Bull, J.L., Pop, I., and Berguer, R. (2007). Influence of pulsatile blood flow and heating scheme on the temperature distribution during hyperthermia treatment. International Journal of Heat and Mass Transfer, 50(23-24):4883–4890.
  • 17. Mazaheri, A., Zerai, B., Ahmadi, G., Kadambi, J., Saylor, B., Oliver, M., Bromhal, G., and Smith, D. (2005). Computer simulation of flow through a lattice flow-cell model. Advances in water resources, 28(12):1267–1279.
  • 18. Nield, D. A. and Bejan, A. (1995). Convection in porous media. Springer.
  • 19. 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, 342(12):881–891.
  • 20. Olver, F. W., Lozier, D. W., Boisvert, R.F., and Clark, C.W. (2010). NIST handbook of mathematical functions hardback. Cambridge university press.
  • 21. Pearson, J. and Tardy, P. (2002). Models for flow of non-newtonian and complex fluids through porous media. Journal of Non-Newtonian Fluid Mechanics, 102(2):447–473.
  • 22. Peng, X. and Wu, H. (2005). Pore-scale transport phenomena in porous media. In Transport Phenomena in Porous Media III, pages 366–398. Elsevier.
  • 23. Perrin, C. L., Tardy, P. M., Sorbie, K. S., and Crawshaw, J. C. (2006). Experimental and modeling study of newtonian and non-newtonian fluid flow in pore network micromodels. Journal of Colloid and Interface Science, 295(2):542–550.
  • 24. Sisko, A. (1958). The flow of lubricating greases. Industrial & Engineering Chemistry, 50(12):1789–1792.
  • 25. Sisko, A. (1960). Capillary viscometer for non-newtonian liquids. Journal of Colloid Science, 15(2):89–96.
  • 26. Sochi, T. (2010). The flow of newtonian fluids in axisymmetric corrugated tubes. arXiv preprint arXiv:1006.1515.
  • 27. Sochi, T. (2011a). The flow of power-law fluids in axisymmetric corrugated tubes. Journal of Petroleum Science and Engineering, 78(3-4):582–585.
  • 28. Sochi, T. (2011b). Newtonian flow in converging-diverging capillaries. arXiv:1108.0163v1.
  • 29. Sochi, T. (2015). Navier–stokes flow in converging–diverging distensible tubes. Alexandria Engineering Journal, 54(3):713–723.
  • 30. Vafai, K. (1984). Convective flow and heat transfer invariable-porosity media. Journal of Fluid Mechanics, 147:233–259.
  • 31. Vafai, K. (1986). Analysis of the channeling effect in variable porosity media. Journal of energy resources technology, 108(2):131–139.
  • 32. Vafai, K. (2000). Handbook of porous media 1 ed. Crc Press.
  • 33. Vafai, K. (2005). Handbook of porous media 2 ed. Crc Press.
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  • 35. Vossoughi, S. (1999). Flow of non-newtonian fluids in porous media. In Rheology Series, volume 8, pages 1183–1235. Elsevier.
  • 36. Vossoughi, S. and Al-Husaini, O. S. (1994). Rheological characterization of the coal/oil/water slurries and the effect of polymer. Technical report.
  • 37. Walicka, A. (2017). Rheology of fluids in Mechanical Engineering. Oficyna Wydawnicza Uniwersytetu Zielonogórskiego.
  • 38. Walicka, A. (2018a). Flows of Newtonian and power-law fluids in symmetrically corrugated cappilary fissures and tubes. International Journal of Applied Mechanics and Engineering, 23(1):187–211.
  • 39. Walicka, A. (2018b). Simulation of the flow through porous layers composed of converging-diverging capillary fissures or tubes. International Journal of Applied Mechanics and Engineering, 23(1):161–185.
  • 40. Walicka, A. and Walicki, E. (2010). Pressure drops in convergent flows of polymer melts. International Journal of Applied Mechanics and Engineering, 15(4):1273– 1285.
  • 41. Walicki, E. and Walicka, A. (2000a). Conical flows of generalized second grade fluids. Inżynieria Chemiczna i Procesowa, 21:75–85.
  • 42. Walicki, E. and Walicka, A. (2000b). Pressure drops in a wedge flow of generalized second grade fluids of a power-law type and a bingham type. Les Cahiers de rhéologie, 17(1):541–550.
  • 43. Walicki, E. and Walicka, A. (2002). Convergent flows of molten polymers modeled by generalized second-grade fluids of power-law type. Mechanics of composite materials, 38(1):89–94.
  • 44. Walicki, E., Walicka, A., Michalski, D., and Ratajczak, P. (1998). Approximate analysis for conical flow of generalized second grade fluids. Les Cahiers de rhéologie, 16(1):309–316.
  • 45. 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. Journal of contaminant hydrology, 192:101–117.
  • 46. Yeh, W. W. (2015). Optimization methods for groundwater modeling and management. Hydrogeology Journal, 23(6):1051–1065.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-15c04922-2b87-446b-9c0c-64e5b36dddba
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