Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio Γ = 0.50 and Prandtl number Pr = 4.38

2011 ◽  
Vol 676 ◽  
pp. 5-40 ◽  
Author(s):  
STEPHAN WEISS ◽  
GUENTER AHLERS
Keyword(s):  
Nusselt Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
State Transitions ◽  
Small Scale ◽  
Bénard Convection ◽  
Benard Convection ◽  
Run Time ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements of the Nusselt number and properties of the large-scale circulation (LSC) are presented for turbulent Rayleigh–Bénard convection in water-filled cylindrical containers (Prandtl number Pr = 4.38) with aspect ratio Γ = 0.50. They cover the range 2 × 108 ≲ Ra ≲ 1 × 1011 of the Rayleigh number Ra. We confirm the occurrence of a double-roll state (DRS) of the LSC and focus on the statistics of the transitions between the DRS and a single-roll state (SRS). The fraction of the run time when the SRS existed varied continuously from about 0.12 near Ra = 2 × 108 to about 0.8 near Ra = 1011, while the fraction of the run time when the DRS could be detected changed from about 0.4 to about 0.06 over the same range of Ra. We determined separately the Nusselt number of the SRS and the DRS, and found the former to be larger than the latter by about 1.6% (0.9%) at Ra = 1010 (1011). We report a contribution to the dynamics of the SRS from a torsional oscillation similar to that observed for cylindrical samples with Γ = 1.00. Results for a number of statistical properties of the SRS are reported, and some are compared with the cases Γ = 0.50, Pr = 0.67 and Γ = 1.00, Pr = 4.38. We found that genuine cessations of the SRS were extremely rare and occurred only about 0.3 times per day, which is less frequent than for Γ = 1.00; however, the SRS was disrupted frequently by roll-state transitions and other less well-defined events. We show that the time derivative of the LSC plane orientation is a stochastic variable which, at constant LSC amplitude, is Gaussian distributed. Within the context of the LSC model of Brown & Ahlers (Phys. Fluids, vol. 20, 2008b, art. 075101), this demonstrates that the stochastic force due to the small-scale fluctuations that is driving the LSC dynamics has a Gaussian distribution.

Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number

1997 ◽  
Vol 335 ◽  
pp. 111-140 ◽  
Author(s):  
S. CIONI ◽  
S. CILIBERTO ◽  
J. SOMMERIA
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Scaling Laws ◽  
Convective Cell ◽  
Zone Model ◽  
Turbulent Regime ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

An experimental study of Rayleigh–Bénard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, Pr = 0.025), covering a range of Rayleigh numbers 5 × 106 < Ra < 5 × 109, and compare them with results at Pr∼1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra0.26, close to the 2/7 power observed at Pr∼1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra ≃ 2 × 109, with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.

Torsional oscillations of the large-scale circulation in turbulent Rayleigh–Bénard convection

2008 ◽  
Vol 607 ◽  
pp. 119-139 ◽  
Author(s):  
DENIS FUNFSCHILLING ◽  
ERIC BROWN ◽  
GUENTER AHLERS
Keyword(s):  
Rayleigh Number ◽  
Aspect Ratio ◽  
Large Scale ◽  
Small Scale ◽  
Large Scale Circulation ◽  
Number Range ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

Direct Numerical Simulation of a Low Prandtl Number Rayleigh–Bénard Convection in a Square Box

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Ojas Satbhai ◽  
Subhransu Roy ◽  
Sudipto Ghosh
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Dimensionless Temperature ◽  
Bénard Convection ◽  
Benard Convection ◽  
Wide Range ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) are used to study the steady-state Rayleigh–Bénard convection (RB) in a two-dimensional unit aspect ratio box. The steady-state RB convection is characterized by analyzing the time-averaged temperature-field, and flow field for a wide range of Rayleigh number (2.1 × 105 ⩽ Ra ⩽ 2.1 × 108). It is seen that the time-averaged and space-averaged Nusselt number (Nuh¯) at the hot-wall monotonically increases with the increase in Rayleigh number (Ra) and the results show a power law scaling Nuh¯∝Ra0.2593. The current Nusselt number results are compared with the results available in the literature. The complex flow is analyzed by studying the frequency power spectra of the steady-state signal of the vertical velocity at the midpoint of the box for different Ra and probability density function of dimensionless temperature at various locations along the midline of the box.

scholarly journals Numerical simulation of helical-vortex effects in Rayleigh-Bénard convection

2006 ◽  
Vol 13 (2) ◽  
pp. 205-222 ◽  
Author(s):  
G. V. Levina ◽  
I. A. Burylov
Keyword(s):  
Large Scale ◽  
Internal Heat ◽  
Main Idea ◽  
Numerical Approach ◽  
Small Scale ◽  
Forcing Function ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract. A numerical approach is substantiated for searching for the large-scale alpha-like instability in thermoconvective turbulence. The main idea of the search strategy is the application of a forcing function which can have a physical interpretation. The forcing simulates the influence of small-scale helical turbulence generated in a rotating fluid with internal heat sources and is applied to naturally induced fully developed convective flows. The strategy is tested using the Rayleigh-Bénard convection in an extended horizontal layer of incompressible fluid heated from below. The most important finding is an enlargement of the typical horizontal scale of the forming helical convective structures accompanied by a cells merging, an essential increase in the kinetic energy of flows and intensification of heat transfer. The results of modeling allow explaining how the helical feedback can work providing the non-zero mean helicity generation and the mutual intensification of horizontal and vertical circulation, and demonstrate how the energy of the additional helical source can be effectively converted into the energy of intensive large-scale vortex flow.

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