Stability and heat transfer of rotating cryogens. Part 1. Influence of rotation on the onset of convection in liquid 4 He

Lucas, P.; Pfotenhauer, John M.; Donnelly, Russell J.

doi:10.1017/s0022112083000750

Cited by 38 publications

(21 citation statements)

References 20 publications

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“…In two previous reports, Lucas , Pfotenhauer & Donnelly (1983) (Part 1) and Pfotenhauer, Lucas & Donnelly (1984) (Part 2) we have described the stability and heat transfer of standard Benard convection in a rotating system and have demonstrated that the experimental data generally support existing theories. In one major respect, however, the experimental data revealed some unexpected results which we intend to describe in this report in some detail.…”

Section: Introductionsupporting

confidence: 52%

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Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection

1987

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This report presents data describing convection in a rotating cylindrical Bénard cell filled with He I. In particular, convection modes are observed at Rayleigh numbers substantially below those predicted by linear stability analyses for a horizontally infinite layer. Both the Rayleigh numbers associated with the convective onset and the initial-slope measure of heat transport of these modes are found to depend on the rotation rate Ω and the aspect ratio Γ of the cell. A discussion of the relevant literature reveals that these convective modes are probably the same as those observed by Rossby (1969) and are reasonably well characterized by the recent analysis of Buell & Catton (1983) assuming asymmetric modes.

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Section: Introductionsupporting

confidence: 52%

“…The scatter in Nu in this critical region required in practice that R,/R,, > 1.05 before this distinction could be made. Investigations of this type reveal that the value of 0, for the case when r = 7.81 is less than the value of 200 reported in Lucas et al (1983) and is closer to 52, = 140.…”

Section: Onset Of Convectionmentioning

confidence: 58%

Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection

1987

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“…31 The rotation about a vertical axis introduces Coriolis force as well as centrifugal force 32 in the flow. Rubio, Lopez & Marques 27 showed interesting effects of the centrifugal force even for small values (∼ 10 −2 ) of the Froude number F r, which is a ratio of the centrifugal force to the force of buoyancy.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Pharasi¹,

Kumar²

2013

Physics of Fluids

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We present the results of direct numerical simulations of flow patterns in a lowPrandtl-number (P r = 0.1) fluid above the onset of oscillatory convection in a Rayleigh-Bénard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box (L x ×L y ×1) and a wide range of Taylor numbers (750 ≤ T a ≤ 5000) for the purpose. The horizontal aspect ratio η = L y /L x of the box was varied from 0.5 to 10. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes (0.5 ≤ η < 1 and 1 < η < 2).The flow patterns observed in boxes with η = 1 and η = 2 were different from those with η < 1 and 1 < η < 2. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell (η = 1) for T a < 2700, but observed a set of parallel rolls in the form of standing waves for T a ≥ 2700. The three-dimensional convection was quasiperiodic or chaotic for 750 ≤ T a < 2700, and then bifurcated into a two-dimensional periodic flow for T a ≥ 2700. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle φ = π 2 − arctan (η −1 ) with the straight rolls.

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“…For example, at high rotation rates the first instability of the conductive state is not to a bulk mode as predicted by Chandrasekhar [1] but rather to a traveling-wave state localized near sidewall boundaries. The first evidence for this mode can be seen in heat transport measurements [2,3]; a partial explanation [4] was based on linear stability calculations [5] which predicted a stationary azimuthally periodic wall mode. Flow visualization of rotating convection in a cylindrical convection cell with radiusto-height ratio ⌫ = 1 revealed, however, that the wall mode was a traveling wave [6,7].…”

Section: Introductionmentioning

confidence: 99%

Traveling waves in rotating Rayleigh-Bénard convection

et al. 2004

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A combined analytical, numerical, and experimental study of the traveling-wave wall mode in rotating Rayleigh-Bénard convection is presented. No-slip top and bottom boundary conditions are used for the numerical computation of the linear stability, and the coefficients of the linear complex Ginzburg-Landau equation are then computed for various rotation rates. Numerical results for the no-slip boundary conditions are compared with free-slip calculations and with experimental data, and detailed comparison is made at a dimensionless rotation rate Omega=274. It is found that the inclusion of the more realistic no-slip boundary conditions for the top and bottom surfaces brings the numerical linear stability analysis into better agreement with the experimental data compared with results using free-slip top/bottom boundary conditions. Some remaining discrepancies may be accounted for by the finite conductivity of the sidewall boundaries.

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Stability and heat transfer of rotating cryogens. Part 1. Influence of rotation on the onset of convection in liquid 4 He

Cited by 38 publications

References 20 publications

Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection

Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Traveling waves in rotating Rayleigh-Bénard convection

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