Abstract
Three-dimensional advective flows in a horizontal cylinder of square section are numerically investigated under thermally insulated lateral boundaries and in the presence of a uniform longitudinal temperature gradient. The flow structure is shown to considerably depend on the Grashof number, the channel length, and the Prandtl number; depending on these parameters, the flow symmetrymode and its temporal behavior may be different. It is established that different cases of transition to oscillatory flow regimes are possible, namely, either with a preliminary violation of the flow symmetry (fork bifurcation) or without a change in the type of symmetry. The parameter range on which only the fork bifurcation is observable, while oscillatory flow patterns do not appear, is also determined.
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References
G.Z. Gershuni, E.M. Zhukhovitskii, and V.M. Myznikov, “Stability of a Plane-Parallel Convective Fluid Flow in a Horizontal Layer,” Zh. Prikl. Mekh. Tekhn. Fiz. No. 1, 95 (1974).
G.Z. Gershuni, E.M. Zhukhovitskii, and V.M. Myznikov, “Stability of a Plane-Parallel Convective Fluid Flow in a Horizontal Layer with Respect to Three-Dimensional Disturbances,” Zh. Prikl. Mekh. Tekhn. Fiz. No. 5, 145 (1974).
G.Z. Gershuni, E.M. Zhukhovitskii, and A.A. Nepomnyashchii, Convective Flow Stability [in Russian], Nauka, Moscow (1989).
H.P. Kuo and S.A. Korpela, “Stability and Finite Amplitude Natural Convection in a Shallow Cavity with Insulated Top and Bottom and Heated from a Side,” Phys. Fluids 31, 33 (1988).
P. Bontoux, C. Smutek, B. Roux, and J.M. Lacroix, “Three-Dimensional Buoyancy-Driven Flows in Cylindrical Cavities with Differentially Heated Endwalls. Part 1. Horizontal Cylinders,” J. Fluid Mech. 169, 211 (1986).
P. Bontoux, B. Roux, G.H. Schiroky, B.L. Markham, and F. Rosenberger, “Convection in the Vertical Midplane of a Horizontal Cylinder. Comparison of Two-Dimensional Approximations with Three-Dimensional Results,” Int. J. Heat Mass Transfer 29, 227 (1986).
S.A. Nikitin, D.S. Pavlovskii, and V.I. Polezhaev, “Stability and Spatial Structure of Convection in an Elongated Horizontal Layer with Lateral Heating,” Fluid Dynamics 31(4), 503 (1996).
N.I. Lobov, D.V. Lyubimov, T.P. Lyubimova, and R.V. Skuridin, “Advective Flows in a Horizontal Channel of Rectangular Section,” in: Fluid Dynamics. Issue 11 [in Russian], Perm Univ. Press, Perm (1988), p. 167.
T.P. Lyubimova, D.V. Lyubimov, V.A. Morozov, R.V. Scuridin, H. Ben Hadid, and D. Henry, “Stability of Convection in a Horizontal Channel Subjected to a Longitudinal Temperature Gradient. Part 1. Effect of Aspect Ratio and Prandtl Number,” J. Fluid Mech. 635, 275 (2009).
T.P. Lyubimova and D.A. Nikitin, “Stability and the Advective Flow in a Horizontal Rectangular Channel with Adiabatic Boundaries,” Fluid Dynamics 46(2), 240 (2011).
W. Dridi, D. Henry, and H. Ben Hadid, “Influence of Acoustic Streaming on the Stability of a Laterally Heated Three-Dimensional Cavity,” Phys. Rev. 77, 046311–1 (2008).
A. Kurganov and D. Levy, “A Third-Order Central Scheme for Conservation Laws and Convection-Diffusion Equations,” SIAM J. Sci. Comput. 22, 1461 (2000).
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Original Russian Text © T.P. Lyubimova, D.A. Nikitin, 2011, published in Vychislitel’nayaMekhanika Sploshnykh Sred, 2011, Vol. 4, No. 2, pp. 72–81.
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Lyubimova, T.P., Nikitin, D.A. Three-dimensional advective flows in a horizontal cylinder of square section with thermally insulated lateral boundaries. Fluid Dyn 46, 975–983 (2011). https://doi.org/10.1134/S0015462811060159
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DOI: https://doi.org/10.1134/S0015462811060159