Effect of inertia in Rayleigh-Bénard convection

Breuer, M.; Wessling, Stefan; Schmalzl, J.; Hansen, Ulrich

doi:10.1103/physreve.69.026302

Cited by 85 publications

(140 citation statements)

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“…Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14)(15)(16)(17)(18). These simulations turn out to become very demanding if the small-scale structure of turbulence is to be studied, even for moderate Rayleigh number Ra, the parameter that quantifies the thermal driving in turbulent convection (19,20). Whereas heat transport is reduced in low-Pr convection, the production of vorticity and shear are enhanced significantly, which amplifies the small-scale intermittency in these flows.…”

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confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large-and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. T urbulent convection depends strongly on the material properties of the working fluid that are quantified by the Prandtl number, the ratio of kinematic viscosity of the fluid to thermal diffusivity of the temperature, Pr = ν=κ. Compared with the vast number of investigations at Pr ≥ 1 (1, 2), the very-low-Pr regime appears almost as a "terra incognita" despite many applications. Turbulent convection in the Sun is present at Prandtl numbers Pr < 10 −3 (3-5). The Prandtl number in the liquid metal core of the Earth is Pr ∼ 10 −2 (6). Convection in material processing (7), nuclear engineering (8), or liquid metal batteries (9) has Prandtl numbers between 3 × 10 −2 and 10 −3 . Rayleigh-Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10-12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals. Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14-18). These simulations turn out to become very demanding if the...

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mentioning

confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…Three-dimensional direct simulations of high-P r flows still face considerable problems. To our knowledge, the full three-dimensional problem in a cell confined by solid walls has been solved for P r > 10 only by Hansen [12].…”

Section: Physical and Numerical Setup 21 Introductionmentioning

confidence: 99%

“…Only a few of them ( [12], [77]) mimic a set-up similar to experiments, thus allowing a proper comparison of the results. A smaller number of studies concerns very high-P r regimes.…”

Section: Introductionmentioning

confidence: 99%

“…In [12] a wider range of P r numbers is explored (10 −3 ≤ P r ≤ 10 2 ), but only at fixed Ra = 10 6 .…”

Section: Introductionmentioning

confidence: 99%

“…Some numerical studies deal with varying P r numbers ( [17], [12], [65], [41], [77]). Only a few of them ( [12], [77]) mimic a set-up similar to experiments, thus allowing a proper comparison of the results.…”

Section: Introductionmentioning

confidence: 99%

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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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2012

Rotating Thermal Flows in Natural and Industrial Processes

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Effect of inertia in Rayleigh-Bénard convection

Cited by 85 publications

References 25 publications

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Numerical Simulations of Thermal Convection at High Prandtl Numbers

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