THERMAL SCIENCE

International Scientific Journal

NUMERICAL INVESTIGATION OF INSTABILITY PATTERNS IN TAYLOR-COUETTE FLOW UNDER VARIOUS CONFIGURATIONS

ABSTRACT
This study numerically investigates the onset and evolution of instabilities in a Taylor-Couette system under differential heating. Special emphasis will be placed on characterizing hydrodynamic instabilities for various configurations to determine the optimal setup for effectively controlling the flow regime. The conservation equations and boundary conditions controlling the problem are modeled using the Finite Volume Method with second order of discretization. Our findings reveal that differential rotation significantly impacts the stability of the flow, with distinct instability thresholds observed for different rotational configurations. The results show that the dynamic and thermal field in horizontal ducts depend totally on the azimuthal direction in the mixed convection. In addition, the corotation configuration stands out as the optimal choice for achieving a balance between stability and thermal efficiency for both forced and mixed convection. Although the counter-rotating configuration allows fast conveying and vigorous mixing, it is not suitable for all applications due to potential turbulence.
KEYWORDS
PAPER SUBMITTED: 2025-05-12
PAPER REVISED: 2025-09-19
PAPER ACCEPTED: 2025-10-24
PUBLISHED ONLINE: 2025-12-06
DOI REFERENCE: https://doi.org/10.2298/TSCI250512202R
REFERENCES
[1] Andereck, C. D., et al., Flow regimes in a circular Couette system with independently rotating cylinders, Journal of Fluid Mechanics, 164, (1986), pp. 155-183
[2] Wageningen, C. D., Hoogendoorn, G., Heat transfer in Taylor-Couette flow between independently rotating cylinders, Internationnal Journal of Heat Mass Transfer, 33 (1990), pp. 2071-2085
[3] Balbus, S. A., Hawley, J. F., A powerful local shear instability in weakly magnetized disks, Astrophysics Journal., 376 (1991), pp. 214-233
[4] Couette, M., Study on the friction of liquids, Chim.Phys, 21, (1890), pp. 433-510
[5] Taylor, G., I., Stability of a viscous liquid contained between two rotating cylinders, Philosophical Transaction, 223, (1923), 8, pp. 289-343
[6] Coles, D., Transition in circular Couette flow, Journal of Fluid Mechanics, 21 (1965), pp. 385-425
[7] Andereck, C. D., et al., New flows in a circular Couette system with co-rotating cylinders, Physics of Fluids, 26 (1983), pp. 1395-1401
[8] Grossmann, S., et al., High-Reynolds number Taylor-Couette turbulence, Annual Review of Fluid Mechanics, 48 (2016), 1, pp. 53-80
[9] Dong, S., Direct numerical simulation of turbulent Taylor-Couette flow, Journal of Fluid Mechanics, 587 (2007), pp. 373-393
[10] Godwin, L. E., et al., Transient dynamics in counter-rotating stratified Taylor-Couette flow, Mathematics, 11(2023), 14, pp. 3250-3265
[11] Hamede, M. H., et al., Experimental investigation of turbulent counter-rotating Taylor-Couette flows for radius ratio η = 0.1, Journal of Fluid Mechanics 964 (2023), A36
[12] Ostilla-Mónico, R., et al., Exploring the phase diagram of fully turbulent Taylor-Couette flow, Journal of Fluid Mechanics, 761 (2014), pp. 1-26
[13] Marcus, P. S., Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment, Journal of Fluid Mechanics, 146 (1984), pp. 45-64
[14] Tanaka, R., et al., DNS of Taylor-Couette flow between counter-rotating cylinders at small radius ratio, International Journal of Advances in Engineering Sciences and Applied Mathematics, 10 (2018), 2, pp. 159-170
[15] Jovanović, J., Pashtropanska, M., On the evolution of laminar to turbulent transition and breakdown to turbulence, Thermal Science, 7 (2003), 2, pp. 59-75
[16] Van Gils, D. P. M., et al., Torque scaling in turbulent Taylor-Couette flow with co- and counter-rotating cylinders, Physical Review Letters, 106 (2011), 1024502
[17] Xu, F., et al., Direct numerical simulation of Taylor-Couette flow: regime-dependent role of axial walls, Chemical Engineering Science, 263 (2022), 118075
[18] Xu, F., et al., Direct numerical simulation of Taylor-Couette flow with vertical asymmetric rough walls, Journal of Fluid Mechanics, 975 (2023), A30
[19] Berghout, P., et al., Direct numerical simulations of spiral Taylor-Couette turbulence, Journal of Fluid Mechanics., 887 (2020), pp. A18 (1-16)
[20] Berghout, P., et al., Characterizing the turbulent drag properties of rough surfaces with a Taylor-Couette set-up, Journal of Fluid Mechanics, 919 (2021), pp. 411-444
[21] Avila, K., Hof, B., Second-order phase transition in counter-rotating Taylor-Couette flow experiment, Entropy, 23 (2020), 1, pp. 1-58
[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
[23] Ali, M., Weidman, P. D., On the stability of circular Couette flow with radial heating, Journal of Fluid Mechanics., 220 (1990), pp. 53-84
[24] Bahloul, A., et al., Codimension 2 points in the flow inside a cylindrical annulus with a radial temperature gradient, The European Physical Journal Applied Physics., 9 (2000), 3, pp. 253-264
[25] Eckhardt, B., et al., Torque scaling in turbulent Taylor-Couette flow between independently rotating cylinders, Journal of Fluid Mechanics., 581 (2007), pp. 221-250
[26] Eckert, E. R. G., Carlson, W. O., Natural convection in an air layer enclosed between two vertical plates with different temperatures, Internationnal Journal of Heat Mass Transfer, 2 (1961), 2, pp. 106-120
[27] Batchelor, G. K., Heat transfer by free convection across a closed cavity between vertical boundaries at different temperature, Quarterly of Applied Mathematics, 12 (1954), 3,pp. 209-233
[28] Snyder, H. A., Karlsson, S. K. F., Experiments on the stability of Couette motion with a radial thermal gradient, Phys. Fluids, 7 (1964), 10, pp. 1696-1706
[29] Birikh, R.V., et al., Stability of the steady convective motion of a fluid with a longitudinal temperature gradient, Journal of Applied Mathematical Mechanics., 33 (1969), 6, pp. 937-947
[30] Ball, K. S., Farouk, B., A flow visualization study of the effects of buoyancy on Taylor vortices, Physics of Fluids. A: Fluid Dynamics., 1 (1989), 9, pp. 1502-1507
[31] Polasanapalli, S. R. G., Anupindi, K., Mixed convection heat transfer in a two-dimensional annular cavity using an off-lattice Boltzmann method, Internationnal Journal of Thermal Science., 179 (2022), 3, pp. 107-677
[32] Kang, X., et al., Numerical simulation of circular Couette flow under a radial thermo-electric body force, Physics of Fluids, 29 (2017), 11, pp. 105-114
[33] Vyas, P., Srivastava, N., Radiative magnetohydrodynamic compressible Couette flow in a parallel channel with naturally permeable wall, Thermal Science, 18 (2014), Suppl. 2, pp. S573-S585
[34] Wang, F.-H., et al., Effect of circumferential wave number on stability of suspension flow, Thermal Science, 18 (2014), 5, pp. 1517-1523
[35] Wan, Z.-H., et al., Dynamic stability of non-dilute fiber shear suspensions, Thermal Science, 16 (2012), 5, pp. 1551-1555
[36] Zhao, Q., et al., Flow and heat transfer characteristics of high pressure natural gas in the gaps of high-speed motors with a high radius ratio, Thermal Science, 28 (2024), 5A, pp. 3725-3736
[37] Redjaimia, I., et al., Numerical approach of the first instability appearance in inclined Taylor-Couette system, Journal of Thermophysics and Heat Transfer, 38 (2024), 4, pp. 1-10
[38] Chaieb, I., et al., Taylor-Couette flow with mixed convection heat transfer and variable properties in a horizontal annular pipe, Thermal Science, 26 (2022), 1A, pp. 287-298
[39] Viazzo, S., Poncet, S., Numerical simulation of the flow stability in a high aspect ratio Taylor-Couette system submitted to a radial temperature gradient, Computers and Fluids, 101 (2014), pp. 15-26
[40] Dubrulle, B., et al., Stability and turbulent transport in Taylor-Couette flow from analysis of experimental data, Physics of Fluids, 17 (2005), 9, pp. 095103(1-19)
[41] Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Pub. Co., McGraw-Hill, New York, (1980), pp. 120-129
[42] Nonino, C., Giudice, S. D., Finite element analysis of laminar mixed convection in the entrance region of horizontal annular ducts, Numerical Heat Transfer, Part A: Applications, 29 (1996), 3, pp. 313-330
[43] Islam, N., et al., Mixed convection heat transfer in the entrance region of horizontal annuli, International Journal of Heat and Mass Transfer, 44 (2001), 11, pp. 2107-2120

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence