THERMAL SCIENCE

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Taylor-Couette flow with mixed convection heat transfer and variable properties in a horizontal annular pipe

ABSTRACT
Taylor-Couette flows in a horizontal annular gap between finite coaxial cylinders in rotor-stator configuration are numerically investigated. The inner cylinder (rotor) rotates at a constant angular velocity while the outer cylinder (stator) is at rest. They are limited at their extremities by two fixed walls that prevent axial fluid flow. In addition, a heat transfer is generated by an imposed temperature difference, with the rotor hotter than the stator while the end-walls are adiabatic. The fluid physical properties are temperature dependent. This non-linear physics problem, with a strong coupling of the conservation equations and boundary conditions, is solved by a finite volume method with numerical schemes of second order space and time accuracies. The radius and aspect ratios and the Taylor, Grashof and Prandt numbers are the control parameters. The developed numerical code has been tested for different meshes and perfectly validated. Extensive calculations have been made in large ranges of the Taylor and Grashof numbers to analyze the Taylor-Couette flow in convection modes. The results highlight the dynamic and thermal instabilities generated in the Taylor Couette flow from the appearance of Ekman cells to the Taylor vortex propagation in the entire annulus. The combined effect of these vortices with the secondary flow improves the heat transfer. Furthermore, the influence of the physical properties in the radial direction is more marked in the vicinity of the walls. Finally, we propose an empirical correlation of the Nusselt number in the studied parameter ranges.
KEYWORDS
PAPER SUBMITTED: 2021-02-18
PAPER REVISED: 2021-08-25
PAPER ACCEPTED: 2021-09-01
PUBLISHED ONLINE: 2021-09-18
DOI REFERENCE: https://doi.org/10.2298/TSCI210218271C
REFERENCES
  1. Couette, M., Study on the friction of liquids, Chim.Phys, 21, (1890), pp. 433-510
  2. Taylor, G., I., Stability of a viscous liquid contained between two rotating cylinders, Philosophical Transaction, 223, (1923), 8, pp. 289-343
  3. Childs, P., R., N., Rotating flow, Elsevier Science and Technology Rights, Burlington, USA, 2011
  4. Hopfinger, E. J., Rotating Fluids in Geophysical and Industrial Applications, Springer, France,1992
  5. Di-Prima, R. C., Swinney, H. L., Instabilities and transition in flow between concentric cylinders. In: Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, ed. by Swinney, H. L. and Gollub J. P., Springer-Verlag, 34, (1981),139-180.
  6. Vedantam, S., Joshi, J. B., Annular centrifugal contactors—A Review, Chemical Engineering Research and Design, 84, (2006),7, pp. 522-542.
  7. Andereck, C. D., et al., Flow regimes in a circular Couette system with independently rotating cylinders, Journal of Fluid Mech, 164, (1986), pp. 155-183.
  8. Dutcher, C. S., Muller, S. J., Explicit analytic formulas for Newtonian Taylor-Couette primary instabilities, Physical Review E, 75 (2007), pp. 47301-47305.
  9. Maron, D., M., Cohen, S., Hydrodynamics and heat/mass transfer near rotating surfaces, Advances in Heat Transfer, 21, (1992), pp. 141-183.
  10. Childs, P., R., Long, C., A., A review of forced convective heat transfer in stationary and rotating annuli, Proc. of the Inst. of Mech. Eng., Part C:J.Mech. Eng. Science, 210, (1996),23,pp.123-134.
  11. Fénot, M., et al., A review of heat transfer between concentric rotating cylinders with or without axial flow, International Journal of Thermal Sciences, 50, (2011),7, pp. 1138-1155
  12. Touahri, S., Boufendi, T., Conjugate heat transfer with variable fluid properties in a heated horizontal annulus, Heat Transfer Research, 64, (2015), pp. 1019-1038
  13. Touahri, S., Boufendi, T., Numerical study of the conjugate heat transfer in a horizontal pipe heated by joulean effect, Thermal Sciences, 16, (2012), 1, pp. 53-67
  14. Lei, Y., Bakhtier, F., Three-dimensional mixed convection flows in a horizontal annulus with a heated rotating inner circular cylinder, Int. J. Heat and Mass Transfer,35,(1992), 8, pp.1947-1956
  15. Choi, J. Y., Kim, M., U., Three-dimensional linear stability of mixed convective flow between rotating horizontal concentric cylinders, Int. J. Heat and Mass Transfer, 38, (1995), 2, pp. 27-285
  16. Bouafia, M., et al., Experimental analysis of heat transfer in narrow and grooved annular space with rotating inner cylinder (in french), Int. J. Heat and Mass Transfer, 41, (1998), 10, pp. 1279-1291
  17. Lepiller, V., et al., Hydrothermal instabilities in a vertical cylindrical annular subjected to a strong radial temperature gradient, 18ème C ngrès França s de Mécanique, (2009), Grenoble, France.
  18. Mutabazi I. et al., Flow instabilities in a vertical differentially rotating cylindrical annulus with a radial temperature gradient. EUROMECH Colloquium 525, (2011), pp. 21-23.
  19. Sommerer, Y., Lauriat, G., Numerical study of steady forced convection in a grooved annulus using a design of experiments, Journal of Heat Transfer,123, (2001), pp.837-847
  20. Baehr, H. D., Stephan, K., Heat and Mass Transfer, Berlin, Springer-Verlag, (1998)
  21. Patankar, S. V., Numerical heat transfer and fluid flow, McGraw hill, New York, (1980)
  22. Aït-Moussa, et al., Numerical simulations of co-and counter-Taylor-Couette flows: influence of the cavity radius ratio on the appearance of Taylor vortices, American Journal of Fluid Dynamics, 5(2015),1, pp.17-22