Forced Convection inside a Vertical Circular Cylinder with an Inner Coaxial Rectangular Cylinder

Abstract:

In this work, we performed a numerical simulation of laminar forced convection and, in an annular space inside a vertical circular cylinder with an inner coaxial rectangular cylinder having an aspect ratio (height/radius) γ=2, filled with a liquid metal (Pr = 0.0023). Six annular gaps R =0.9, 0.8, 0.7, 0.6, 0.5 and 0.4 were studied. The governing equations are solved using the ANSYS Fluent code which is based on the finite volume method. SIMPLE algorithm is employed for the pressure-velocity coupled momentum equations. Two cases of the rotating parts of the cylinders are investigated and the effect of Reynolds number on the flow are examined. The obtained results of the forced convection show that the increase of the Reynolds number Re affects straightly on the structure of the flow wherever the velocity field are destabilized and the strongest stabilization of the velocity field occurs when the flow generated by the rotating of the circular cylinder and the rectangular cylinder.Keywords: forced convection, annular gap, circular cylinder, rectangular cylinder, co-rotating.

• Periodical: Defect and Diffusion Forum (Volume 406)
• Pages: 25-35
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.406.25
• Online since: January 2021
• Authors: Hamad Ahmed Boughezala*, Said Bouabdallah, Ali Boukhari
• Keywords: Annular Gap, Circular Cylinder, Co-Rotating, Forced Convection, Rectangular Cylinder

References

[1] Batchelor, G.K. Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quart. J. Mech. Appl. Math., 4(1) (1951), 29–41.

DOI: 10.1093/qjmam/4.1.29

[2] Zandbergen, P.J., Dijkstra D. Von Kármán swirling flows. Annu. Rev. Fluid Mech., 19 (2004), 465–491.

DOI: 10.1146/annurev.fl.19.010187.002341

[3] F.C. Li, T. Kunugi, A. Serizawa, MHD Effect on flow structures and heat transfer characteristics of liquid metal - gas annular flow in a vertical pipe, Intl. J. Heat Mass Transf. 48 (2005), 2571–2581.

DOI: 10.1016/j.ijheatmasstransfer.2004.12.041

[4] M. Sankar, M. Venkatachalappa, I.S. Shivakumara, Effect of magnetic field on natural convection in a vertical cylindrical annulus, Internat. J. Engrg. Sci. 44 (2006) 1556–1570.

DOI: 10.1016/j.ijengsci.2006.06.004

[5] M. Venkatachalappa, Y. Do, M. Sankar, Effect of magnetic field on the heat and mass transfer in a vertical annulus, Internat. J. Engrg. Sci. 49 (2011) 262–278.

DOI: 10.1016/j.ijengsci.2010.12.002

[6] S.C. Kakarantzas, L.Th. Benos, I.E. Sarris, B. Knaepen, A.P. Grecos, N.S. Vlachos, MHD liquid metal flow and heat transfer between vertical coaxial cylinders under horizontal magnetic field, Int. J. Heat Fluid Flow 65 (2017) 342–351.

DOI: 10.1016/j.ijheatfluidflow.2017.01.001

[7] A. Bendjaghlouli, B. Mahfoud, D.E. Ameziani. Magnetohydrodynamique flow in a truncated conical enclosure, Journal of Thermal Engineering, Vol. 5, No. 2, Special Issue 9 (2019), pp.77-83, Istanbul, Turkey.

DOI: 10.18186/thermal.532133

[8] E. Van De Sande, B.J.G. Hamer, Steady and transient natural convection in enclosures between horizontal circular cylinders (constant heat flux), Int. J. Heat Mass Transfer 22 (1979) 361–370.

DOI: 10.1016/0017-9310(79)90002-4

[9] Y.T. Tsui, B. Tremblay, On transient natural convection heat transfer in the annulus between concentric, horizontal cylinders with isothermal surfaces, Int. J. Heat Mass Transfer 27 (1984) 103–111.

DOI: 10.1016/0017-9310(84)90242-4

[10] M.Y. Ha, M.J. Jung, Y.S. Kim, Numerical study on transient heat transfer and fluid flow of natural convection in an enclosure with a heat-generating conducting body, Numer. Heat Transfer, Part A: Appl. 35 (1999) 415–433.

DOI: 10.1080/104077899275209

[11] M.Y. Ha, I.-K. Kim, H.S. Yoon, K.S. Yoon, J.R. Lee, S. Balachandar, H.H. Chun, Two-dimensional and unsteady natural convection in a horizontal enclosure with a square body, Numer. Heat Transfer, Part A: Appl. 41 (2002) 183–210.

DOI: 10.1080/104077802317221393

[12] H.-S. Chu, T.-S. Lee, Transient natural convection heat transfer between concentric spheres, Int. J. Heat Mass Transfer 36 (1993) 3159–3170.

DOI: 10.1016/0017-9310(93)90001-m

[13] H.W. Wu, W.C. Tsai, H.-M. Chou, Transient natural convection heat transfer of fluids with variable viscosity between concentric and vertically eccentric spheres, Int. J. Heat Mass Transfer 47 (2004) 1685–1700.

DOI: 10.1016/j.ijheatmasstransfer.2003.10.018

[14] X. Xu, G. Sun, Z. Yu, Y. Hu, L. Fan, K. Cen, Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure, Int. J. Heat Mass Transfer 52 (2009) 3176–3186.

DOI: 10.1016/j.ijheatmasstransfer.2009.01.026

[15] G. de Vahl Davis, R.W. Thomas, Natural convection between concentric vertical cylinders, Physics of Fluids 12 (12) (1969) (II–198–II–207).

DOI: 10.1063/1.1692437

[16] A. Hadjadj, S. Maamir, B. Zeghmati, A new study of laminar natural convection in two concentric vertical cylinders, Heat and Mass Transfer 35 (2) (1999) 113–121.

DOI: 10.1007/s002310050304

[17] A. Hadjadj, M.E. Kyal, Effect of two sinusoidal protuberances on natural convection in a vertical concentric annulus, Numerical Heat Transfer Part A 36 (3) (1999) 273–289.

DOI: 10.1080/104077899274769

[18] M. Charmchi, E.M. Sparrow, Analysis of natural convection in the space between concentric vertical cylinders of different height and diameter, Numerical Heat Transfer Part A 5 (2) (1982) 119–144.

DOI: 10.1080/10407788208913439

[19] E.M. Sparrow, M. Charmchi, Natural convection experiments in an enclosure between eccentric or concentric vertical cylinders of different height and diameter, International Journal of Heat and Mass Transfer 26 (1) (1983) 133–143.

DOI: 10.1016/s0017-9310(83)80015-5

[20] E. Fattahi, M. Farhadi, K. Sedighi, Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus, International Journal of Thermal Sciences 49 (12) (2010) 2353–2362.

DOI: 10.1016/j.ijthermalsci.2010.07.014

[21] J.F. Lafortune, D.A. Meneley, Natural convection in a vertical cylinder: comparison of commix-1a predictions with experiment, International Journal of Heat and Mass Transfer 33 (3) (1990) 435–445.

DOI: 10.1016/0017-9310(90)90179-x

[22] S.C.‏ Dash, N.‏ Singh, Study of axisymmetric nature in 3-D swirling flow in a cylindrical annulus with a top rotating lid under the influence of axial temperature gradient or axial magnetic field, Journal of Thermal Engineering, Vol. 3, No. 6, Special Issue 6, pp (2017). 1588-1606, Istanbul, Turkey.

DOI: 10.18186/journal-of-thermal-engineering.353737

[23] B. Mahfoud, A. Laouari, A. Hadjadj, H. Benhacine, Counter-rotating flow in coaxial cylinders under an axial magnetic field, European Journal of Mechanics / B Fluids 78 (2019) 139–146.

DOI: 10.1016/j.euromechflu.2019.06.009

[24] B. Mahfoud, R. Bessaïh, Magnetohydrodynamic counter-rotating flow in a cylindrical cavity, Int. J. Heat Mass Transfer 93 (2016) 175–185.

DOI: 10.1016/j.ijheatmasstransfer.2015.10.009

[25] R. Bessaïh, A. Boukhari, Ph. Marty, Magnetohydrodynamics stability of a rotating flow with heat transfer, Int. Commun. Heat Mass Transfer 36 (2009) 893–901.

DOI: 10.1016/j.icheatmasstransfer.2009.06.009

[26] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New-York, (1980).

[27] Michelson, J.A, Modeling of laminar incompressible rotating fluid flows,, AFM 86-05, Ph. D. Dissertation. Dept. of Fluid Mechanics, Tech. Univ. of Denmark (1986).