Numerical study of heat-transfer in two-and quasi-two-dimensional Rayleigh–Bénard convection

A detailed comparative numerical study between the two-dimensional(2 D) and quasi-two-dimensional(quasi-2 D)turbulent Rayleigh–B′enard(RB) convection on flow state, heat transfer, and thermal dissipation rate(TDR) is made. The Rayleigh number(Ra) in our simulations ranges up to 5×10~(10) and Prandtl number(Pr) is fixed to be 0.7. Our simulations are conducted on the Tianhe-2 supercomputer. We use an in-house code with high parallelization efficiency, based on the extended PDM–DNS scheme. The comparison shows that after a certain Ra, plumes with round shape, which is called the temperature islands, develop and gradually dominate the flow field in the 2 D case. On the other hand, in quasi-2 D cases, plumes remain mushroom-like. This difference in morphology becomes more significant as Ra increases, as with the motion of plumes near the top and bottom plates. The exponents of the power-law relation between the Nusselt number(Nu) and Ra are 0.3 for both two cases, and the fitting pre-factors are 0.099 and 0.133 for 2 D and quasi-2 D respectively,indicating a clear difference in magnitude of the heat transfer rate between two cases. To understand this difference in the magnitude of Nu, we compare the vertical profile of the horizontally averaged TDR for both two cases. It is found that the profiles of both cases are nearly the same in the bulk, but they vary near boundaries. Comparing the bifurcation height zb with the thermal boundary layer thickness dq, it shows that zb δ_θ(3 D) δ_θ(2 D) and all three heights obey a universal power-law relation z ~Ra~(-0.30). In order to quantify the difference further, we separate the domain by zb, i.e., define the area between two zb(near top and bottom plates respectively) as the mid region and the rest as the side region, and integrate TDR in corresponding regions. By comparing the integral it is found that most of the difference in TDR between two cases, which is connected to the heat transfer rate, occurs within the thermal boundary layers. We also compare the ratio of contributions to total heat transfer in BL–bulk separation and side–mid separation.     

Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection

Journal of Visualization -  To enrich the three-dimensional experimental details of vortex structures in rotating Rayleigh–Bénard convection, we established a technique...     

Large scale structures in Rayleigh-Bénard convection at high Rayleigh numbers

Direct numerical simulations of Rayleigh-Bénard convection in a plane layer with periodic boundary conditions at Rayleigh numbers up to 10(7) show that flow structures can be objectively classified as large or small scale structures because of a gap in spatial spectra. The typical size of the large scale structures does not always vary monotonically as a function of the Rayleigh number but broadly increases with increasing Rayleigh number. A mean flow (whose average over horizontal planes differs from zero) is also excited but is weak in comparison with the large scale structures. The large scale circulation observed in experiments should therefore be a manifestation of the large scale structures identified here.     

Onset of coherent oscillations in turbulent Rayleigh-Bénard convection

We report temperature cross correlation and velocity profile measurements in the aspect-ratio-one convection cell filled with water. A sharp transition from a random chaotic state to a correlated turbulent state of finite coherence time is found when the Rayleigh number becomes larger than a critical value Ra(c) approximately equal to 5 x 10(7). The experiment reveals a unique mechanism for the onset of coherent oscillations in turbulent Rayleigh-Bénard convection.     

Identification and visualization of coherent structures in rayleigh-bénard convection with a time-dependent RANS

A time-dependent Reynolds-average-Navier-Stokes (TRANS) method is applied to capture and analyze the large-scale coherent structure in Rayleigh-Bénard (RB) convection over a flat and wavy bottom wall at a range of Rayleigh numbers. The method can be regarded as a Very Large Eddy Simulation (VLES) in which the unresolved random motion is modelled using a low-Re-number $k - \varepsilon - \bar \theta ^2 $ algebraic stress/flux single-point closure model. The large scale motion, which is the major mode of heat and momentum transfer in the bulk central region, is fully resolved by the time solution. In contrast to LES, the contribution of both modes to the turbulent fluctuations are of the same order of magnitude. The approach was assessed by comparison with the Direct Numerical Simulations (DNS) and experimental data using several criteria: visual observation of the large structure morphology, different structure identification criteria, and long-term averaged mean flow and turbulence properties. A visible similarity with large structures in DNS was observed, confirming the suitability of TRANS approach to reproduce the flows dominated by large coherent motions.     

Evidence for slow velocity relaxation in front propagation in Rayleigh–Bénard convection

Recent theoretical work has shown that so-called pulled fronts propagating into an unstable state always converge very slowly to their asymptotic speed and shape. In the light of these predictions, we reanalyze earlier experiments by Fineberg and Steinberg on front propagation in a Rayleigh–Bénard cell. In contrast to the original interpretation, we argue that in the experiments the observed front velocities were some 15% below the asymptotic front speed and that this is in rough agreement with the predicted slow relaxation of the front speed for the time scales probed in the experiments. We also discuss the possible origin of the unusually large variation of the wavelength of the pattern generated by the front as a function of the dimensionless control parameter.     

Rotating turbulent Rayleigh–Bénard convection subject to harmonically forced flow reversals

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = 10⁹ and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/Ro^* = 1 while various modulation frequencies 0.1 ≤ Ro_ω ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.     

Side wall effects in Rayleigh Bénard experiments

In Rayleigh Bénard experiments, the side wall conductivity is traditionally taken into account by subtracting the empty cell heat conductivity from the measured one. We present a model showing that the correction to apply could be considerably larger. We compare to experiments and find good agreement. One of the consequences is that the Nusselt behavior for Ra < 10¹⁰ could be closer to Nu∝Ra ^1/3 than currently assumed. Also, the wall effect can appear as a continuous change in the γ exponent Nu∝Ra ^γ. Received 26 April and Received in final form 1st October 2001     

Rayleigh-Bénard convection in large-aspect-ratio domains

The coarsening and wave number selection of striped states growing from random initial conditions are studied in a nonrelaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as t0.12, the orientational correlation length scales as t0.54, and the density of defects scale as t(-0.45). The final pattern evolves toward the wave number where isolated dislocations become motionless, suggesting a possible wave number selection mechanism for large-aspect-ratio convection.     

Dislocation dynamics in Rayleigh-Bénard convection

Theoretical results on the dynamics of dislocations in Rayleigh-Bénard convection are reported both for a Swift-Hohenberg model and the Oberbeck-Boussinesq equations. For intermediate Prandtl numbers the motion of dislocations is found to be driven by the superposition of two independent contributions: (i) the Peach-Koehler force and (ii) an advection force on the dislocation core by its self-generated mean flow. Their competition allows to explain the experimentally observed bound dislocation pairs.     

Efficiency of heat transfer in turbulent Rayleigh-Bénard convection

We present an experimental study of turbulent Rayleigh-Bénard convection (RBC) in a cylindrical cell of height 0.3 m, diameter 0.3 m. It is designed to minimize the influence of its structure on the convective flow of cryogenic (4)He gas of Prandtl number Pr≈1, with the aim of resolving existing contradictions in Nusselt (Nu) versus Rayleigh number (Ra) scaling. For 7.2×10(6)≤Ra≤10(11) our data agree with suitably corrected data from similar cryogenic experiments and are consistent with Nu∝Ra(2/7). On approaching Ra≈10(11) our data display a crossover to Nu∝Ra(1/3) that approximately holds up to Ra=4.6×10(13); there is no sign of a transition to the ultimate Kraichnan regime. Differences in Nu(Ra) scaling observed in similar RBC experiments for Ra≥10(11) cannot be explained due to the difference in Pr, but seem to depend also on experimental details.