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Stability Regimes of Flow in a Channel between Coaxial Cylinders

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Abstract

The stability of spiral flow occurring in the simultaneous presence of a pressure difference in the channel between two coaxial cylinders and rotation of one of the cylinders is studied. It is shown that depending on the azimuthal Reynolds number the modes with different azimuthal wavenumbers can be most unstable. The data of calculations are in good agreement with the available experimental data. It is shown that certain experimental results correspond to the earlier unknown regime of the zeroth azimuthal mode instability. The stability characteristics of spiral flow of a nanofluid based on water with zirconium oxide particles are studied. In all the cases considered the nanofluid is less stable than the baseline fluid. The degree of nanofluid flow destabilization increases with increase in the particle concentration and a decrease in their dimensions.

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References

  1. J. E. Mott and D.D. Joseph, “Stability of Parallel Flow between Concentric Cylinders,” Phys. Fluids 11 (10), 2065 (1968).

    Article  ADS  MATH  Google Scholar 

  2. D. I. Cotrell and A. J. Pearlstrein, “Linear Stability of Spiral and Annular Poiseuille Flow for Small Radius Ratio,” J. Fluid Mech. 547, 1 (2006).

    Article  ADS  MATH  Google Scholar 

  3. E. M. Sparrow, W. D. Munro, and V. K. Jonsson, “Instability of the Flow between Rotating Cylinders: The Wide–Gap Problem,” J. Fluid Mech. 21 (1), 35 (1964).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. D. Coles, “Transition in Circular Couette Flow,” J. FluidMech. 21 (3), 385 (1965).

    Article  ADS  MATH  Google Scholar 

  5. R. C. DiPrima, P. M. Eagles, and B. S. Ng, “The Effect of Radius Ratio on the Stability of Couette Flow and Taylor Vortex Flow,” Phys. Fluids 27 (10), 2403 (1984).

    Article  ADS  MATH  Google Scholar 

  6. V. V. Kolesov and A. G. Khoperskii, “Simple Regimes of Fluid Motion in the Neighborhood of the Intersection of Bifurcations Initiating Nonisothermal Taylor Vortices and Azimuthal Waves,” Fluid Dynamics 37 (2), 257 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. C. D. Andereck, S. S. Liu, and H. L. Swinney, “Flow Regimes in a Circular Couette System with Independently Rotating Cylinders,” J. FluidMech. 164, 155 (1986).

    Article  ADS  Google Scholar 

  8. M. A. Gol’dshtik and V. A. Sapozhnikov, “Flow Stability in an Annular Channel,” Fluid Dynamics 6 (4), 639 (1971).

    Article  ADS  Google Scholar 

  9. T. A. Vil’gel’mi, M. A. Gol’dshtik, and V. A. Sapozhnikov, “Stability of a Flow in a Circular Tube,” Fluid Dynamics 8 (1), 16 (1973).

    Article  ADS  Google Scholar 

  10. T. A. Vil’gel’mi and V. N. Shtern, “Stability of Spiral Flow in an Annulus,” Fluid Dynamics 9 (3), 360 (1974).

    Article  ADS  Google Scholar 

  11. M. A. Gol’dshtik and V. N. Shtern, Hydrodynamic Stability (Nauka, Novosibirsk, 1977) [in Russian].

    Google Scholar 

  12. D. I. Takeuchi and D. F. Jankowski, “A Numerical and Experimental Investigation of the Stability of Spiral Poiseuille Flow,” J. FluidMech. 102, 101 (1981).

    Article  ADS  Google Scholar 

  13. B. S. Ng and E. R. Turner, “On the Linear Stability of Spiral Flow between Rotating Cylinders,” Proc. Roy. Soc. London A 382, 83 (1982).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. A. Meseguer and F. Marques, “On the Competition between Centrifugal and Shear Instability in Spiral Couette Flow,” J. FluidMech. 402, 33 (2000).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. A. Meseguer and F. Marques, “On the Competition between Centrifugal and Shear Instability in Spiral Poiseuille Flow,” J. FluidMech. 455, 129 (2002).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. J. M. Nouri and J. H. Whitelaw, “Flow of Newtonian and Non–Newtonian Fluids in an Eccentric Annulus with Rotation of the Inner Cylinder,” Int. J. Heat Fluid Flow 18 (2), 236 (1997).

    Article  Google Scholar 

  17. M.P. Escudier, I. W. Gouldson, and D.M. Jones, “Flow of Shear–Thinning Fluids in a Concentric Annulus,” Experiments Fluids 18 (4), 225 (1995).

    Article  ADS  Google Scholar 

  18. E. V. Podryabinkin and V. Ya. Rudyak, “Moment and Forces Exerted on the Inner Cylinder in Eccentric Annular Flow,” J. Engineering Thermophysics 20 (3), 320 (2011).

    Article  Google Scholar 

  19. E. V. Podryabinkin and V. Ya. Rudyak, “Modeling Flows of Non–Newtonian Fluids in an eccentric cylindrical Gap with Rotation of the Inner Cylinder,” Dokl. Ross. Akad. Nauk Vyssh. Shkoly 19 (2), 112 (2012).

    Google Scholar 

  20. E. V. Podryabinkin and V. Ya. Rudyak, “Modeling Turbulent Flows in an Eccentric Cylindrical Gap with Rotation of the Inner Cylinder,” Vestn. Novosibirsk. Univ. Fizika 7 (4), 79 (2012).

    Google Scholar 

  21. V. Ya. Rudyak and A. V. Minakov, Topical Problems of Microfluidics and Nanofluidics (Nauka, Novosibirsk, (2016) [in Russian].

    Google Scholar 

  22. V. Ya. Rudyak, A. V. Minakov, D. V. Guzei, V. A. Zhigarev, and M. I. Pryazhnikov, “On Laminar–Turbulent Transition in Nanofluid Flows,” Thermophysics Aeromechanics 23 (5), 773 (2016).

    Article  ADS  Google Scholar 

  23. V. Ya. Rudyak and E. G. Bord, “On the Stability of Plane and Cylindrical Poiseuille Flows of Nanofluids,” J. Appl.Mech. Technical Phys. 58 (6), 45 (2017).

    Article  MathSciNet  Google Scholar 

  24. L. G. Loytsyanskii, Mechanics of Liquids and Gases (Pergamon Press, Oxford, 1966).

    Google Scholar 

  25. V. Ya. Rudyak, E. B. Isakov, and E. G. Bord, “Instability of Antisymmetric Disturbances of the Poiseuille Flow of Inhomogeneous Fluid,” Thermophysics Aeromechanics 3 (1), 51 (1996).

    Google Scholar 

  26. V. Rudyak, E. Isakov, and E. Bord, “Hydrodynamic Stability of the Poiseuille Flow of the Dispersed Fluid,” J. Aerosol Sci. 28 (1), 53 (1997).

    Article  ADS  Google Scholar 

  27. E. G. Bord, E. B. Isakov, and V. Ya. Rudyak, “Stability of Laminar Flows of Rarefied Disperse Media,” Fluid Dynamics 32 (4) (1997).

    Google Scholar 

  28. V. Ya. Rudyak, E. B. Isakov, and E. G. Bord, “Stability of Two–Phase Flows,” ThermophysicsAeromechanics 5 (1), 51 (1998).

    Google Scholar 

  29. V. V. Kozlov, I. D. Zverkov, B. Yu. Zanin, A. V. Dovgal, V. Ya. Rudyak, E. G. Bord, and D. F. Kranchev, “Experimental and Theoretical Investigation of Boundary Layer Perturbation Development on a Low–Aspect–Ratio Wing,” Thermophysics Aeromechanics 13 (4), 507 (2006).

    Article  ADS  Google Scholar 

  30. H. Schlichting, Boundary Layer Theory (McGraw–Hill, New York, 1968).

    MATH  Google Scholar 

  31. R. Betchov and V. Criminale, Stability of Parallel Flows (Acad. Press, New York, 1967).

    MATH  Google Scholar 

  32. S. Sh. Hosseini, A. Shahrjerdi, and Y. Vazifeshenas, “A Review of Relations for Physical Properties of Nanofluids,” Australian J. Basic Appl. Sci. 5 (10), 417 (2011).

    Google Scholar 

  33. I. M. Mahbubul, R. Saidur, and M. A. Amalina, “Latest Developments on the Viscosity of Nanofluids,” Int. J. HeatMass Transfer 55, 874 (2012).

    Article  Google Scholar 

  34. V. Ya. Rudyak, S. V. Dimov, V. V. Kuznetsov, and S. P. Bardakhanov, “Measuring the Viscosity Coefficient of a Nanofluid Based on Ethylene Glicol with Silicon Dioxide Particles,” Doklady Phys. 58 (5), 173 (2013).

    Article  ADS  Google Scholar 

  35. V. Ya. Rudyak and S. I. Krasnolutskii, “Dependence of the Viscosity of Nanofluids on Nanoparticle Size and Material,” Phys. Lett. A 378, 1845 (2014).

    Article  ADS  Google Scholar 

  36. S. M. S. Mursheda and P. Estelléb, “A State of the Art Review on Viscosity of Nanofluids,” Renewable and Sustainable Energy Reviews 76, 1134 (2017).

    Article  Google Scholar 

  37. V. Ya. Rudyak, A. V. Minakov, and M. I. Pryazhnikov, “Thermal Properties of Nanofluids and Their Similarity Criteria,” Tech. Phys. Letters 48 (1) 23 (2017).

    Google Scholar 

  38. D. V. Guzei, A. V. Minakov, and V. Ya. Rudyak, “Investigation of Heat Transfer of Nanofluids in Turbulent Flow in a Cylindrical Channel,” Fluid Dynamics 51 (2), 189 (2016).

    Article  MATH  Google Scholar 

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Correspondence to E. G. Bord.

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Original Russian Text © E.G. Bord, V.Ya. Rudyak, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2018, No. 6, pp. 9–18.

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Bord, E.G., Rudyak, V.Y. Stability Regimes of Flow in a Channel between Coaxial Cylinders. Fluid Dyn 53, 729–737 (2018). https://doi.org/10.1134/S0015462818060162

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