Geodesic
The intensity of convection of fluids with different prandtl number in a vertical cylinder of large aspect ratio
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 1, pp. 70-79.

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We study the free convection in a long vertical cylinder with constant temperature gradient on the side surface. The wall temperature does not change its value in the circumferential direction, the flow is laminar; the fluid is Newtonian; the change in the density from the temperature used in the Boussinesq approximation, the problem is stationary. The movement is simulated by means of CFD in Ansys CFX. Verification of the used model is made. The natural convection of three fluids (water, gas-saturated oil, degassed oil) is studied for aspect ratio (the ratio of height to diameter) of 60, 80, 100, 200. Types of convective motion depending on the Rayleigh number is classified as “immovable” $Ra 3\cdot 10^3$, “spira” $3\cdot 10^3$, “cellular” $1,2\cdot 10^4 Ra$. We define qualitative and quantitative criteria, on which the classification is based. A spiral movement is characterized by a constant average cross-section of vertical velocity. With cellular motion, the average vertical velocity of cross section, experiences a significant change in the height of the cylinder. The intensity of convection is characterized by the vertical speed. The influence of Prandtl number on the intensity of convection is marked. Empirical dependence of the average volume of the vertical speed of the Rayleigh number is received. A single dependence for different fluids is obtained by the use of scale speed $u_{r} = (Q_{0}g/\rho c_{p}\gamma)^{1/3} Q_{0}$ — the average value of the modulus of the heat flow through the side wall, calculated by means of Ansys CFX post-processor; $g$ — acceleration of gravity; $\rho$ — density; $c_p$ — the heat capacity at constant pressure, $\gamma$ — the vertical temperature gradient on the wall. We determine the value of aspect ratio $(h = 60)$ at which the cylinder can be considered infinitely long for the considered problem.
Keywords: convection flow, convection in the vertical cylinder, infinitely long cylinder, modeling in Ansys CFX, antisymmetric flow. 
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     title = {The intensity of convection of fluids with different prandtl number in a vertical cylinder of large aspect ratio},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
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A. S. Khoroshev; V. G. Shakhov. The intensity of convection of fluids with different prandtl number in a vertical cylinder of large aspect ratio. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 1, pp. 70-79. http://geodesic.mathdoc.fr/item/VVGUM_2018_21_1_a7/

[1] G. Z. Gershuni, E. M. Zhukovitskiy, Convective Stability of Incompressible Fluid, Nauka Publ., Moscow, 1972, 392 pp.

[2] G. A. Ostroumov, “Mathematical Theory of Steady Heat Transfer in Round Vertical Borehole due to the Superposition of Forced and Free Laminar Convection”, Zhurnal tekhnicheskoy fiziki, 20:6 (1950), 750–757 | MR

[3] G. A. Ostroumov, Free Convection in Internal Tasks, Gosudarstvennoe izd-vo tekhniko-teoreticheskoy literatury, Moscow, Leningrad, 1952, 286 pp. | MR

[4] A. S. Khoroshev, “The Intensity of Free Convection Flow in a Vertical Cylinder with a Constant Vertical Temperature Gradient on the Side Surface”, Nauchnoe obozrenie, 2014, no. 5, 74–80

[5] A. S. Khoroshev, V. G. Shakhov, “Simulation of laminar Freely Induced Flow in Long Vertical Cylinder”, Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk, 13:4 (2011), 72–76

[6] ANSYS CFX-Solver Theory Guide, ANSYS, Inc., Canonsburg, 2009, 257 pp.

[7] S. P. S. Arya, “Free convection similarity and measurements in flows with and without shear”, Journal of the Atmospheric Sciences, 29 (1972), 877–885 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[8] A. A. Ganguli, A. B. Pandit, J. B. Joshi, “Numerical predictions of flow patterns due to natural convection in a vertical slot”, Chemical Engineering Science, 62 (2007), 4479–4495 | DOI

[9] F. Heslot, B. Castaing, A. Libchaber, “Transitions to turbulence in helium gas”, Physical Review A., 36 (1987), 5870–5873 | DOI

[10] G. Muller, G. Neumann, W. Weber, “Natural convection in vertical Bridgman configurations”, Journal of Crystal Growth, 70 (1974), 78–93 | DOI

[11] S. Schneider, J. Straub, “Laminar natural convection in a cylindrical enclosure with different end temperatures”, Int. J. Heat Mass Transfer, 35 (1992), 545–557 | DOI

[12] I. Rodriguez, J. Castro, C. D. Perez-Segarra, A. Oliva, “Unsteady numerical simulation of the cooling process of vertical storage tanks under laminar natural convection”, International Journal of Thermal Sciences, 48 (2009), 708–721 | DOI