Confined turbulent convection

Niemela, Joseph; Sreenivasan, Katepalli R.

doi:10.1017/s0022112003004087

Cited by 187 publications

(248 citation statements)

References 43 publications

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“…These results show a slightly decrease of N u with increasing P r, in agreement with the Grossmann and Lohse predictions [33]. However, a slightly different behavior of Nusselt number in the cell of Γ = 1 with respect to the cell of Γ = 1/2 was already found in the dependence of N u versus Ra [52].…”

Section: Nusselt Number Versus Ra and P Rsupporting

confidence: 89%

“…The exponent −0.7 was also found in [52], where the trend of Re versus P r is plotted for a wide interval of P r (0.02 P r 200).…”

Section: Reynolds and Peclet Numbersmentioning

confidence: 52%

“…On the other hand, the Re decreases with P r ( [52], [46]). Then at high P r and moderate Ra the flow is expected not to be really turbulent, and a laminar flow usually needs less resolution to be correctly solved.…”

Section: Physical and Numerical Setupmentioning

confidence: 98%

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Numerical Simulations of Thermal Convection at High Prandtl Numbers

Silano

Sreenivasan

Verzicco

2010

Direct and Large-Eddy Simulation VII

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In this thesis we present the results of an extensive campaign of direct numerical simulations of Rayleigh-Bénard convection at high Prandtl numbers (10 −1 ≤ P r ≤ 10 4 ) and moderate Rayleigh numbers (10 5 ≤ P r ≤ 10 9 ). The computational domain is a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1/2, with the no-slip condition imposed to the boundaries.By scaling the results, we find a 1/ √ P r correction to apply to the free-fall velocity, obtaining a more appropriate representation of the large scale velocity at high P r. We investigate the Nusselt and the Reynolds number dependence on Ra and P r, comparing the results to previous numerical and experimental work. At high P r the scaling behavior of the Nusselt number with respect to Ra is generally consistent with the power-law exponent 0.309.The Nusselt number is independent of P r, even at the highest Ra simulated. The Reynolds number scales as Re ∼ √ Ra/P r, neglecting logarithmic corrections. We analyze the global and local features of viscous and thermal boundary layers and their scaling behavior with respect to Rayleigh and Prandtl numbers, and with respect to Reynolds and Peclet numbers.We find that the flow approaches a saturation regime when Reynolds number decreases below the critical value Re s ≃ 40. The thermal boundary layer thickness turns out to increase slightly even when the Peclet number increases. We explain this behavior as a combined effect of the Peclet number and the viscous boundary layer influences.The range of Ra and P r simulated contains steady, periodic and turbulent solutions.A rough estimate of the transition from steady to unsteady flow is obtained by monitoring the time-evolution of the system until it reaches stationary solutions (Ra U ≃ 7.5 × 10 6 at P r = 10 3 ). We find multiple solutions as long-term phenomena at Ra = 10 8 and P r = 10 3 which, however, do not result in significantly different Nusselt number. One of these multiple solutions, even if stable for a long time interval, shows a break in the mid-plane symmetry of the temperature profile. The result is similar to that of some non-Boussinesq effects. We analyze the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. We also describe how the behavior of the flow structures changes for increasing P r. A wide variety of large-scale circulations and plumes structures are found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other solutions, at lower P r, the mean flow generally consists of two opposite toroidal structures; at higher P r, the flow is organized in multi-cell structures extending mostly in the vertical direction. At high P r, plumes detach from sheet-like structures. The different large-scale-structure signatures are generally reflected in the data trends with rei spect to Ra, but not in those with respect to P r. In particular, the Nusselt number is independent of P r, even when the flow structures appear strongly diffe...

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Section: Nusselt Number Versus Ra and P Rsupporting

confidence: 89%

“…The exponent −0.7 was also found in [52], where the trend of Re versus P r is plotted for a wide interval of P r (0.02 P r 200).…”

Section: Reynolds and Peclet Numbersmentioning

confidence: 52%

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Numerical Simulations of Thermal Convection at High Prandtl Numbers

Silano

Sreenivasan

Verzicco

2010

Direct and Large-Eddy Simulation VII

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“…The influence of finite wall conductivity (Ahlers 2000;Roche et al 2001;Verzicco 2002;Niemela & Sreenivasan 2003) was negligible, except for the small cell where a correction of order 1% was applied. These experiments are described in detail by Brown et al (2005).…”

Section: Nob Effects On Nu and Rementioning

confidence: 99%

“…In helium gas beyond Ra ≈ 10 11 Chavanne et al (1997Chavanne et al ( , 2001) found a steeper increase in the logarithmic slope of the Nu(Ra) curve than Niemela et al (2000Niemela et al ( , 2001 and they associated this finding with the ultimate Kraichnan regime. However, there is a major controversy about whether these and other large-Ra data are 'contaminated' by NOB effects (Chavanne et al 1997(Chavanne et al , 2001Roche et al 2001Roche et al , 2002Niemela et al 2000Niemela et al , 2001Niemela & Sreenivasan 2003;Ashkenazi & Steinberg 1999).…”

Section: Introductionmentioning

confidence: 99%

Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection

et al. 2006

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Non-Oberbeck-Boussinesq (NOB) effects on the Nusselt number Nu and Reynolds number Re in strongly turbulent Rayleigh-Bénard (RB) convection in liquids were investigated both experimentally and theoretically. In the experiments the heat current, the temperature difference, and the temperature at the horizontal midplane were measured. Three cells of different heights L, all filled with water and all with aspect ratio Γ close to 1, were used. For each L, about 1.5 decades in Ra were covered, together spanning the range 10 8 6 Ra 6 10 11 . For the largest temperature difference between the bottom and top plates, ∆ = 40 K, the kinematic viscosity and the thermal expansion coefficient, owing to their temperature dependence, varied by more than a factor of 2. The Oberbeck-Boussinesq (OB) approximation of temperature-independent material parameters thus was no longer valid. The ratio χ of the temperature drops across the bottom and top thermal boundary layers became as small as χ = 0.83, which may be compared with the ratio χ = 1 in the OB case. Nevertheless, the Nusselt number Nu was found to be only slightly smaller (by at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus Nu and Re are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of Nu with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference ∆. The net effects on Nu are proportional to ∆ 2 and thus increase only slowly and still remain minor despite drastic materialparameter changes. We then extend the Prandtl-Blasius boundary-layer theory to NOB Rayleigh-Bénard flow with temperature-dependent viscosity and thermal diffusivity. This allows calculation of the shift in the bulk temperature, the temperature drops across the boundary layers, and the ratio χ without the introduction of any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within the experimental resolution, the theory also gives the measured small Nusselt-number reduction for the NOB case. In addition, it predicts an increase by about 0.5%

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Aspects of Hydrodynamic Turbulence in Classical and Quantum Systems

Niemela

2009

Astrophysics and Space Science Proceedings

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Confined turbulent convection

Cited by 187 publications

References 43 publications

Numerical Simulations of Thermal Convection at High Prandtl Numbers

Numerical Simulations of Thermal Convection at High Prandtl Numbers

Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection

Aspects of Hydrodynamic Turbulence in Classical and Quantum Systems

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