Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows

Scheel, Janet; Schumacher, Jörg

doi:10.1103/physrevfluids.2.123501

Cited by 66 publications

(132 citation statements)

References 52 publications

(104 reference statements)

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“…The data is plotted over Ra in figure 8 and we find Nu (0.12 ± 0.04)Ra 0.27±0.02 . It agrees excellently with measurements by Cioni et al [10] in mercury (Pr = 0.025) and matches the numerical results by Scheel and Schumacher [27] of Nu (0.13 ± 0.04)Ra 0.27±0.01 for Pr = 0.021 with only a small shift. The results by Takeshita et al [9] in mercury (Pr = 0.024) agree with respect to the scaling exponent, but give a somewhat higher Nusselt number magnitude with Nu 0.155Ra 0.27±0.02 .…”

Section: A Heat Transportsupporting

confidence: 92%

“…The scaling exponent of Re centre (Ra) agrees very well with the result of DNS by Scheel and Schumacher [27] (open circles in figure 9(a)). In the numerical simulations, the Reynolds number was calculated from the rms-velocity over the whole cell for Pr = 0.021 and gave a scaling of Re (6.5 ± 0.6)Ra 0.45±0.01 .…”

Section: B Momentum Transportsupporting

confidence: 86%

“…Furthermore, the angles oscillate in anti-phase, which is a clear indication of the torsion mode. The LSC flow is thus characterized by a torsion in agreement with DNS at similar Pr by Scheel and Schumacher [26,27] and experiments in liquid sodium [13, Pr = 0.008]. We come back to this point in section III B.…”

Section: Large-scale Flow Dynamicssupporting

confidence: 79%

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Combined measurement of velocity and temperature in liquid metal convection

et al. 2019

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Combined measurements of velocity components and temperature in a turbulent Rayleigh-Bénard convection flow at a low Prandtl number of Pr = 0.029 and Rayleigh numbers between 10 6 ≤ Ra ≤ 6×10 7 are conducted in a series of experiments with durations of more than a thousand free-fall time units. Multiple crossing ultrasound beam lines and an array of thermocouples at mid-height allow for a detailed analysis and characterization of the complex three-dimensional dynamics of the single large-scale circulation (LSC) roll in the cylindrical convection cell of unit aspect ratio which is filled with the liquid metal alloy GaInSn. We measure the internal temporal correlations of the complex large-scale flow and distinguish between short-term oscillations associated with a sloshing motion in the mid-plane with varying orientation angles of the velocity close to the top/bottom plates and the slow azimuthal drift of the mean orientation of the roll as a whole that proceeds on a hundred times slower time scale. The coherent LSC drives a vigorous turbulence in the whole cell that is quantified by direct Reynolds number measurements at different locations in the cell. The velocity increment statistics in the bulk of the cell displays characteristic properties of intermittent small-scale fluid turbulence. We also show that the impact of the symmetry-breaking large-scale flow persists to small-scale velocity fluctuations thus preventing the establishment of isotropic turbulence in the cell centre. Reynolds number amplitudes depend sensitively on beam line position in the cell such that different definitions have to be compared. The global momentum and heat transfer scalings with Rayleigh number are found to agree with those of direct numerical simulations and other laboratory experiments.arXiv:1907.03472v1 [physics.flu-dyn]

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Section: A Heat Transportsupporting

confidence: 92%

Section: B Momentum Transportsupporting

confidence: 86%

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Combined measurement of velocity and temperature in liquid metal convection

et al. 2019

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“…merical simulation results obtained in a cylindrical RB cell filled with liquid mercury or liquid gallium2,12,40,41 , where Nu ∝ Ra 0.25∼0.27 , while the momentum scaling exponent from the present two-dimensional simulation is larger than that in previous three-dimensional simulations12,41 , where Re ∝ Ra 0.44∼0 45. .…”

contrasting

confidence: 52%

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Shi

2019

Physics of Fluids

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We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution twodimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 10 6 ≤ Ra ≤ 10 7 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra 0.25 and Re = 6.11Ra 0.50 , respectively, indicating that the scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relative lower Ra, while they approach the Gaussian profile at relative higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re. a a) This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Xu et al., Phys. Fluids 31, 125101 (2019) and may be found at

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“…Rather, the goal was to have convection cells over as wide as an area possible for the thermal imaging to yield significant temperature statistics, both temporally and spatially. The criteria was then for a large diameter to thickness ratio of the apparatus (225 mm / 7 mm) that yielded a stable convection cell pattern at least or greater than 150 mm in diameter and stable for as long as the power is applied [64][65][66] . To the best of our knowledge, this has not been done before.…”

Section: Experimental Methodologymentioning

confidence: 99%

Coexisting Ordered States, Local Equilibrium-like Domains, and Broken Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state

Chatterjee

Yadati

Mears

et al. 2019

Sci Rep

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A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-Bénard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system’s temperature manifold.

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Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows

Cited by 66 publications

References 52 publications

Combined measurement of velocity and temperature in liquid metal convection

Combined measurement of velocity and temperature in liquid metal convection

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Coexisting Ordered States, Local Equilibrium-like Domains, and Broken Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state

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