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Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio. (English) Zbl 1156.80339
Summary: The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10 3 to 3·1×10 4 by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0 to 180 . Flow visualization studies revealed complex three-dimensional patterns. Different thermal-hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.
MSC:
80A20Heat and mass transfer, heat flow
76R10Free convection (fluid mechanics)
References:
[1]Hess, C. F.; Miller, C. W.: Natural convection in a vertical cylinder subject to constant heat flux, Int. J. Heat mass transfer 22, 421-430 (1979)
[2]Lin, Y. S.; Akins, R. G.: Thermal description of pseudo-steady-state natural convection inside a vertical cylinder, Int. J. Heat mass transfer 29, 301-307 (1986)
[3]Ostrach, S.: Natural convection in enclosures, J. heat transfer 110, 1175-1190 (1988)
[4]Varma, M.; Kannan, A.: Enhanced food sterilization through inclination of the container walls and geometry modifications, Int. J. Heat mass transfer 48, 3753-3762 (2005)
[5]Rice, R. G.; Littlefield, M. A.: Dispersion coefficients for ideal bubbly flow in truly vertical bubble columns, Chem. eng. Sci. 42, 2045-2053 (1987)
[6]Baird, M. H. I.; Aravamudan, K.; Rao, N. V. Rama; Chadam, J.; Peirce, A. P.: Unsteady axial mixing by natural convection in a vertical column, Aiche J. 38, 1825-1834 (1992)
[7]Ozoe, H.; Yamamoto, K.; Sayama, H.; Churchill, S. W.: Natural convection in an inclined rectangular channel heated on one side and cooled on the opposing side, Int. J. Heat mass transfer 17, 401-406 (1974) · Zbl 0284.76071 · doi:10.1016/0017-9310(74)90121-5
[8]Arnold, J. N.; Catton, I.; Edwards, D. K.: Experimental investigation of natural convection in inclined rectangular regions of differing aspect ratios, J. heat transfer 98, 67-71 (1976)
[9]Shinkel, W. M. M.: Natural convection in inclined air filled enclosures, (1980)
[10]Soong, C. Y.; Tzeng, P. Y.; Chiang, D. C.; Sheu, T. S.: Numerical study on mode-transition of natural convection in differentially heated inclined enclosures, Int. J. Heat mass transfer 39, 2869-2882 (1996) · Zbl 0964.76544 · doi:10.1016/0017-9310(95)00378-9
[11]Kuyper, R. A.; Van Der Meer, Th. H.; Hoogendoorn, C. J.; Henkes, R. A. W. M.: Numerical study of laminar and turbulent natural convection in an inclined square cavity, Int. J. Heat mass transfer 36, 2899-2911 (1993) · Zbl 0776.76070 · doi:10.1016/0017-9310(93)90109-J
[12]Bontoux, P.; Smutek, C.; Randriamampianina, A.; Roux, B.; Extremet, G. P.; Hurford, A. C.; Rosenberger, F.; De Vahl Davis, G.: Numerical solutions and experimental results for three-dimensional buoyancy driven flows in tilted cylinder, Adv. space res. 6, 155-160 (1986)
[13]A. Heiss, S. Schneider, J. Straub, g-Jitter effects on natural convection in a cylinder: three-dimensional numerical calculations, in: Proceedings of the Sixth European Symposium on Material Sciences under Microgravity Conditions, Bordeaux (ESA SP-256), 1986, pp. 517 – 523.
[14]Neumann, G.: Three-dimensional numerical simulation of buoyancy driven convection in vertical cylinders heated from below, J. fluid mech. 214, 559-578 (1990) · Zbl 0698.76090 · doi:10.1017/S002211209000026X
[15]Del Arco, E. Crespo; Bontoux, P.; Sani, R. L.; Hardin, G.; Extremet, G. P.: Steady and oscillatory convection in vertical cylinders heated from below, numerical simulation of asymmetric flow regimes, Adv. space res. 8, 281-292 (1988)
[16]Schneider, S.; Straub, J.: Laminar natural convection in a cylindrical enclosure with different end temperatures, Int. J. Heat mass transfer 35, 545-557 (1992)
[17]Muller, G.; Neumann, G.; Weber, W.: Natural convection in vertical bridgman configurations, J. cryst. Growth 70, 78-93 (1984)
[18]Heslot, F.; Castaing, B.; Libchaber, A.: Transitions to turbulence in helium gas, Phys. rev. A 36, 5870-5873 (1987)
[19]He, Y. L.; Tao, W. Q.; Zhao, T. S.; Chen, Z. Q.: Steady natural convection in a tilted long cylindrical envelope with lateral adiabatic surface. Part 2. Heat transfer rate, flow patterns and temperature distributions, Numer. heat transfer A 44, 399-431 (2003)
[20]Cianfrini, C.; Corcione, M.; Dell’omo, P. P.: Natural convection in tilted square cavities with differentially heated opposite walls, Int. J. Therm. sci. 44, 441-451 (2005)
[21]Craig, C. J.; Subramanyan, V.; Valentine, D. T.: On the convection in an enclosed container with unstable side wall temperature distributions, Int. J. Heat mass transfer 41, 2307-2320 (1998) · Zbl 0939.76592 · doi:10.1016/S0017-9310(97)00348-7
[22]D’orazio, M. C.; Cianfrini, C.; Corcione, M.: Rayleigh – Bénard convection in tall rectangular enclosures, Int. J. Therm. sci. 43, 135-144 (2004)
[23]CFX Documentation, CFX Ltd., The Gemini Building, Harwell International Business Centre, Didcort, Oxfordshire OX11 OQR, UK, 2005.
[24]Rhie, C. M.; Chow, W. L.: Numerical study of the turbulent flow past an airfoil with trailing edge separation, Aiaa j 21, 1527-1532 (1983) · Zbl 0528.76044 · doi:10.2514/3.8284
[25]Wang, H.; Hamed, M. S.: Flow mode-transition of natural convection in inclined rectangular enclosures subjected to bidirectional temperature gradients, Int. J. Therm. sci. 45, 782-795 (2006)
[26]Charlson, G. S.; Sani, R. L.: Thermo convective instability in a bounded cylindrical fluid layer, Int. J. Heat mass transfer 13, 1479-1496 (1970) · Zbl 0209.57902 · doi:10.1016/0017-9310(70)90181-X
[27]Charlson, G. S.; Sani, R. L.: On thermo convective instability in a bounded cylindrical fluid layer, Int. J. Heat mass transfer 14, 2157-2160 (1971)
[28]Buell, J. C.; Catton, I.: The effect of wall conduction on the stability of a fluid in a right circular cylinder heated from below, J. heat transfer 105, 255-260 (1983)
[29]Del Arco, E. Crespo; Bontoux, P.: Numerical solution and analysis of asymmetric convection in a vertical cylinder: an effect of Prandtl number, Phys. fluids A 1, 1348-1359 (1989)
[30]Bontoux, P.; Smutek, C.; Roux, B.; Lacroix, J. M.: Three-dimensional buoyancy driven flows in cylindrical cavities with differentially heated end walls. Part 1. Horizontal cylinders, J. fluid mech. 169, 211-227 (1986)
[31]Buscalioni, R. D.; Del Arco, E. Crespo: Flow and heat transfer regimes in inclined differentially heated cavities, Int. J. Heat mass transfer 44, 1947-1962 (2001) · Zbl 1107.76389 · doi:10.1016/S0017-9310(00)00242-8
[32]De Vahl Davis, G.: Laminar natural convection in an enclosed rectangular cavity, Int. J. Heat mass transfer 11, 1675-1693 (1968)
[33]Roux, B.; Grondin, J. C.; Bontoux, P.; Gilly, B.: On a higher-order accurate method for the numerical study of natural convection in a vertical square cavity, Numer. heat transfer 1, 331-349 (1978)