Skip to main content
SpringerLink
Log in

Mathematical Simulation of the Swirling Flow of a Thermoviscous, Pseudoplastic Sisco Fluid in a Cylindrical Channel

  • TRANSFER PROCESSES IN RHEOLOGICAL MEDIA
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The swirling flow of a thermoviscous, pseudoplastic Sisco fluid in a cylindrical channel was investigated. It was established that, in the case of irrotational flow of a pseudoplastic fluid in such a channel, the effective viscosity of the fluid in the neighborhood of the channel axis is substantially increased. A swirling of this flow leads to an increase in the rate of shear deformation of the fluid in the axial region of the flow and to a decrease in its effective viscosity. As the swirling of the flow in the channel increases, the fluid near the channel walls and the fluid at the boundary of the recirculation zone are subjected to a dissipative heating leading to a decrease in their effective viscosity. The intensity heating of the fluid in the channel increases with increase in the rate of swirling (the Rossby number) of its flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. M. Kutepov, L. D. Polyanin, Z. D. Zapryanov, A. V. Vyaz’min, and D. A. Kazenin, Chemical Hydrodynamics, Reference Book [in Russian], Byuro Kvantum, Moscow (1996).

    Google Scholar 

  2. C. S. Brazel and S. L. Rosen, Fundamental Principles of Polymeric Materials, John Wiley & Sons (2012).

  3. R. I. Tanner, Engineering Rheology, Oxford University Press, New York (2000).

    MATH  Google Scholar 

  4. L. S. Leibenzon, Collection of Works, Vol. III. Oilfield Mechanics [in Russian], Izd. AN SSSR, Moscow (1955).

  5. B. S. Petukhov and V. N. Popov, Theoretical calculation of the heat exchange and the friction resistance in the turbulent flow of an incompressible fluid with variable physical properties, Teplofiz. Vys. Temp., 1, No. 1, 85–101 (1963).

    Google Scholar 

  6. B. S. Petukhov, L. G. Genin, S. A. Kovalev, and S. L. Solov’ev, Heat Exchange in Nuclear Power Plants [in Russian], Izd. MÉI, Moscow (2003).

    Google Scholar 

  7. D. N. Popov, O. I. Varfolomeeva, and D. A. Khvorenkov, Features of nonisothermic fluid flows with variable rheological properties in channels with local resistances, Vestn. IzgGTU im. M. T. Kalashnikova, No. 1 (57), 146–149 (2013).

  8. S. F. Khizbullina, Numerical investigation of the influence of the temperature dependence of the viscosity of a fluid on the structure of its Couette flow, Tr. Inst. Mekh. R. R. Mavlyutova UNTs RAN, 11, No. 2, 188–192 (2016).

    Google Scholar 

  9. S. F. Khizbullina and S. F. Urmancheev, Oscillation regimes of dynamic parameters changing in Couette flow of anomalous thermoviscous liquids, Procedia IUTAM, 8, 153–1602 (2013).

    Article  Google Scholar 

  10. S. F. Khizbullina, Mathematical model of the Couette flow of an anomalously thermoviscous non-Newtonian fluid, Tepl. Protsessy Tekh., No. 7, 290–294 (2015).

  11. S. F. Urmancheev and V. N. Kireev, Steady-state fluid flow with a temperature anomalous viscosity, Dokl. Akad. Nauk, 396, No. 2, 204–207 (2004).

    Google Scholar 

  12. V. N. Kireev, S. F. Khizbullina, and S. F. Urmancheev, Simulation of flow of a liquid sulphur layer in a heat-exchange channel, Neftegaz. Delo, 3, 333–338 (2005).

    Google Scholar 

  13. A. G. Merzhanov and A. M. Stolin, Hydrodynamic analog of the ignition and extinction effects, Prikl. Mekh. Tekh. Fiz., No. 1, 65–74 (1974).

  14. S. A. Bostandziyan, A. G. Merzhanov, and S. I. Khudyaev, On hydrodynamic thermal explosion, Dokl. AN SSSR, 163, No. 1, 133–136 (1965).

    Google Scholar 

  15. S. A. Bostandziyan and S. M. Chernyaeva, On hydrodynamic thermal explosion of a non-Newtonian fluid, Dokl. AN SSSR, 170, No. 2, 301–304 (1966).

    Google Scholar 

  16. S. A. Kaganov, On steady-state laminar flow of an incompressible fluid in a plane channel and in a round cylindrical pipe with a friction heat and a temperature-dependent viscosity, Prikl. Mekh. Tekh. Fiz., No. 3, 96–99 (1962).

  17. E. I. Borzenko and G. R. Shrager, Steady-state nonisothermal flow of a power-law fluid in an axisymmetric plane channel, Vestn. Tomsk. Gos. Univ., Mat. Mekh., No. 42, 41–52 (2018).

  18. O. V. Matvienko, V. P. Bazuev, and N. K. Uzhanova, Mathematical simulation of a twisted pseudoplastic fluid flow in a cylindrical channel, J. Eng. Phys. Thermophys., 84, No. 3, 589–593 (2011).

    Article  Google Scholar 

  19. O. V. Matvienko, V. P. Bazuev, and N. K. Uzhanova, Mathematical simulation of the swirling flow of a dilatant liquid in a cylindrical channel, J. Eng. Phys. Thermophys., 87, No. 1, 200–207 (2014).

    Article  Google Scholar 

  20. O. V. Matvienko, V. P. Bazuev, and N. K. Dul′zon, Mathematical simulation of a swirling viscoelastic fluid flow in a cylindrical channel, J. Eng. Phys. Thermophys., 87, No. 5, 1177–1185 (2014).

    Article  Google Scholar 

  21. O. V. Matvienko, Numerical investigation of flow of non-Newtonian fluids in cylindrical channels, Izv. Vyssh. Uchebn. Zaved., Fiz., 57, No. 8 (2), 183–189 (2014).

  22. O. V. Matvienko, V. P. Bazuev, and A. E. Aseeva, Mathematical modeling of swirling Herschel–Balkley pseudoplastic fluid flow in a cylindrical channel, J. Eng. Phys. Thermophys., 92, No. 1, 208–218 (2019).

    Article  Google Scholar 

  23. O. V. Matvienko, V. P. Bazuev, and A. E. Aseeva, Mathematical modeling of the swirling flow of a dilatant Herschel–Balkley fluid in a in a cylindrical channel, J. Eng. Phys. Thermophys., 92, No. 6, 2641–2651 (2019).

    Article  Google Scholar 

  24. O. V. Matvienko, F. G. Unger, and V. P. Bazuev, Mathematical Models of Production Processes of Preparation of Bituminous Dispersions [in Russian], Izd. Tomskogo Gos. Arkh.-Stroit. Univ., Tomsk (2015).

    Google Scholar 

  25. W. L. Wilkinson, Non-Newtonian Fluids [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  26. G. M. Ostrovskii, Applied Mechanics of Inhomogeneous Media [in Russian], Nauka, St. Petersburg (2000).

    Google Scholar 

  27. A. Ya. Malkin and A. I. Isaev, Rheology: Concepts, Methods, Applications [in Russian], Professiya, St. Petersburg (2007).

  28. M. Patel, J. Patel, and M. G. Timol, Laminar boundary layer flow of Sisko fluid, Applic. Appl. Math. Int. J., 10, Issue 2, 909–918 (2015).

    MathSciNet  MATH  Google Scholar 

  29. N. Moallemi, I. Shafieenejad, and A. B. Novinzadeh, Exact solutions for flow of a Sisko fluid in pipe, Special Issue Bulletin Iranian Math. Soc., 37, No. 2, Part 1, 49–60 (2011).

  30. R. S. Armstrong and H. H. Winter, Heat transfer in Newtonian fluids, in: Manual on Heat Exchangers [Russian translation], Énergoatomizdat, Moscow (1987), Vol. 1, pp. 327–336.

  31. S. V. Nemilov, Thermodynamic and Kinetic Aspects of the Vitreous State, CRC Press, London–Tokyo (1995).

    Google Scholar 

  32. M. L. Williams, R. F. Landel, and J. D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, J. Am. Chem. Soc., 77, 3701–3707 (1955).

    Article  Google Scholar 

  33. J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley & Sons, New York (1980).

    Google Scholar 

  34. M. Rütten and O. Wünsch, Heat transfer dependent vortex shedding of thermo-viscous shear-thinning fluids, Int. J. Mech. Mechatron. Eng., 11, No. 6, 1236–1245 (2017).

    Google Scholar 

  35. O. V. Matvienko, Investigation of steady-state flow of a pseudoplastic fluid defined by the Sisco model in a cylindrical pipe, Vestn. Tomsk. Gos. Univ., Mat. Mekh., No. 55, 99–112 (2018).

  36. S. V. Patankar, Numerical Methods of Solving Problems on Heat and Mass Exchange and Fluid Dynamics [Russian translation], Énergoatomizdat, Moscow (1983).

    Google Scholar 

  37. B. Van Leer, Towards the ultimate conservative differencing scheme. IV. A new approach to numerical convection, J. Comput. Phys., 23, 276–299 (1977).

    Article  Google Scholar 

  38. J. P. Van Doormal and G. D. Raithby, Enhancements of the SIMPLE method for predicting incompressible fluid flows, Numer. Heat Transf., 7, 147–163 (1984).

    MATH  Google Scholar 

  39. O. V. Matvienko, V. P. Bazuev, N. R. Sabylina, A. E. Aseeva, and A. A. Surtaeva, Investigation of steady-state flow of a viscoplastic bituminous binder defined by the Shvedov–Bingham model in a cylindrical pipe, Vestn. Tomsk. Gos. Arkh.-Stroit. Univ., 21, No. 3, 158–177 (2019).

    Google Scholar 

  40. O. V. Matvienko, V. P. Bazuev, I. S. Cherkasov, and A. E. Litvinova, Investigation of flow of a bituminous binder defined by the Ostwald–de Waele model in a cylindrical pipe, Vestn. Tomsk. Gos. Arkh.-Stroit. Univ., 22, No. 1, 171–192 (2020).

    Google Scholar 

  41. A. A. Khalatov, Theory and Practice of Swirling Flows [in Russian], Naukova Dumka, Kiev (1989).

Download references

Author information

Authors and Affiliations

  1. National Research Tomsk State University, 36 Lenin Ave, Tomsk, 634050, Russia

    O. V. Matvienko & A. E. Aseeva

  2. Tomsk State University of Architecture and Civil Engineering, 2 Solyanaya Sq, Tomsk, 634003, Russia

    O. V. Matvienko

Authors
  1. O. V. Matvienko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. E. Aseeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. V. Matvienko.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 4, pp. 857–869, July–August, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matvienko, O.V., Aseeva, A.E. Mathematical Simulation of the Swirling Flow of a Thermoviscous, Pseudoplastic Sisco Fluid in a Cylindrical Channel. J Eng Phys Thermophy 93, 827–838 (2020). https://doi.org/10.1007/s10891-020-02185-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-020-02185-6

Keywords

Search

Navigation