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Dec 2005

Volume 17, Issue 12, Articles (12xxxx)

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back to top Instability and Transition

Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side

D. J. Ma, D. Henry, and H. Ben Hadid

Phys. Fluids 17, 124101 (2005); http://dx.doi.org/10.1063/1.2141430 (12 pages) | Cited 6 times

Online Publication Date: 9 December 2005

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Three-dimensional steady and oscillatory flows are simulated in a vertical cylinder partially heated from the side. The vertical wall is heated in a zone at midheight and is insulated above and below this middle zone, while both ends of the cylinder are cooled. The cylinder aspect ratio (A = height/radius) ranges from 2 to 8, whereas a fixed Prandtl number, Pr = 0.021, is considered as well as a fixed length of the heated zone, equal to the cylinder radius. Three-dimensional steady and unsteady simulations as well as mode decomposition techniques and energy transfer analyses are used to characterize the flows and their transitions. The flows that develop from the steady toroidal pattern beyond the first instability threshold break the axisymmetry. At small A (2 ⩽ A ⩽ 2.5), the flow corresponds to a two-roll rotating pattern, which is triggered by a k = 2 azimuthal mode as a result of a hydrodynamic instability. At large A (3 ⩽ A ⩽ 8), the flow is steady and corresponds to a main one-roll pattern in the upper part of the cylinder. The flow is triggered by a k = 1 mode as a result of buoyancy effects affecting this unstably stratified upper part (Rayleigh-Bénard instability), but shear effects are involved in the instability for the smaller values of A. These steady flows then transit at a higher threshold to a standing-wave oscillatory one-roll pattern associated with the breaking of symmetry of the previous steady pattern. For intermediate values of A (2.7 ⩽ A ⩽ 2.9), the transition is toward an oscillatory pattern, but hysteresis phenomena with multiplicity of steady and oscillatory states have been found. Comparisons with experiments performed at aspect ratios A = 4 and 8 are then considered and discussed.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Hd Stratified flows
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Splitting and merging of Görtler vortices

H. Mitsudharmadi, S. H. Winoto, and D. A. Shah

Phys. Fluids 17, 124102 (2005); http://dx.doi.org/10.1063/1.2151227 (12 pages) | Cited 2 times

Online Publication Date: 27 December 2005

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The splitting and merging of Görtler vortices are experimentally studied by varying the spacings of vertical wires located 10 mm upstream of a concave surface leading edge of 2.0 m radius of curvature subjected to a free-stream velocity of 3.0 m/s. The splitting and merging as the result of the linear instability of the vortices with respect to spanwise perturbation (Eckhaus instability), occurred when the wire spacing was set to respectively twice and half of the dominant or most amplified wavelength of Görtler vortices. These show the susceptibility of Görtler vortices to wavelengths greater and smaller than the most amplified wavelength of the vortices. The spectral study shows that the values of the dimensionless frequency parameter for the wire spacings of 7.5, 15.0, and 30.0 mm are nearly constant (of about 0.5) for the streamwise locations where the mushroom-like structures dominate the flow. It is also found that the dimensionless wavelength parameter is more sensitive than the Reynolds number of the vertical wires as a threshold identification of transition from one pair to two pairs of vortex configurations.
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47.32.C- Vortex dynamics
47.20.Lz Secondary instabilities
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