Boiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to numerous mechanisms, many of which are not understood in quantitative detail. An important component of the overall process is that the buoyancy of the bubble compounds with that of the liquid to give rise to a muchenhanced natural convection. In this article, we focus specifically on this enhancement and present a numerical study of the resulting two-phase Rayleigh-Bénard convection process in a cylindrical cell with a diameter equal to its height. We make no attempt to model other aspects of the boiling process such as bubble nucleation and detachment. The cell base and top are held at temperatures above and below the boiling point of the liquid, respectively. By keeping this difference constant, we study the effect of the liquid superheat in a Rayleigh number range that, in the absence of boiling, would be between 2 × 10 6 and 5 × 10 9. We find a considerable enhancement of the heat transfer and study its dependence on the number of bubbles, the degree of superheat of the hot cell bottom, and the Rayleigh number. The increased buoyancy provided by the bubbles leads to more energetic hot plumes detaching from the cell bottom, and the strength of the circulation in the cell is significantly increased. Our results are in general agreement with recent experiments on boiling Rayleigh-Bénard convection.two-phase convection | latent heat | boundary layers | point bubble model | simulations T he greatly enhanced heat transfer brought about by the boiling process is believed to be due to several interacting components (1-3). With their growth the bubbles cause a microconvective motion on the heating surface, and as they detach by buoyancy, the volume they vacate tends to be replaced by cooler liquid. Especially in subcooled conditions, the liquid in the relatively stagnant microlayer under the bubbles can evaporate and condense on the cooler bubble top. This process provides for the direct transport of latent heat, which is thus able to bypass the low-velocity liquid region adjacent to the heated surface due to the no-slip condition. The bubble growth process itself requires latent heat and, therefore, also removes heat from the heated surface and the neighboring hot liquid. Finally, with their buoyancy, the bubbles enhance the convective motion in the liquid beyond the level caused by the well-known single-phase Rayleigh-Bénard (RB) convection mechanisms (4, 5). This last process is the aspect on which we focus in the present article.In classical single-phase RB convection, the dimensionless heat transport, Nu, the Nusselt number, is defined as the ratio of the total heat transported through the cell to the heat that would be transported by pure conduction with a quiescent fluid. This ratio increases well above 1 as the Rayleigh number Ra = gβΔL 3 νκ is increased due to the onset of convective motion in the cell. Here g is the acceleration of gravity, β the isobaric thermal expansion coefficient, Δ = T h − T c the dif...

. (2011). Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-Bénard convection. Physical Review E, 84(3), 036312-1/7. [036312]. DOI: 10.1103/PhysRevE.84.036312 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

Intermittency effects are numerically studied in turbulent bubbling Rayleigh-Bénard (RB) flow and compared to the standard RB case. The vapour bubbles are modelled with a Euler-Lagrangian scheme and are two-way coupled to the flow and temperature fields, both mechanically and thermally. To quantify the degree of intermittency we use probability density functions, structure functions, extended self-similarity (ESS) and generalized extended self-similarity (GESS) for both temperature and velocity differences. For the standard RB case we reproduce scaling very close to the Obukhov-Corrsin values common for a passive scalar and the corresponding relatively strong intermittency for the temperature fluctuations, which are known to originate from sharp temperature fronts. These sharp fronts are smoothed by the vapour bubbles owing to their heat capacity, leading to much less intermittency in the temperature but also in the velocity field in bubbling thermal convection.

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux j(r) in a cylindrical Rayleigh-Bénard cell with aspect ratio Γ = 1 for Rayleigh numbers Ra between 2 × 10 6 and 2 × 10 9 at a fixed Prandtl number P r = 5.2. The numerical results reveal that the heat flux close to the side wall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, j(r) ∝ Ra γ j (r) . The scaling exponent γj(r) decreases monotonically from 0.43 near the axis (r ≈ 0) to 0.29 close to the side walls (r ≈ D/2). The effective exponents near the axis and the side wall agree well with the measurements of Shang et al. (Phys. Rev. Lett. 100, 244503, 2008) and the predictions of Grossmann and Lohse (Phys . Fluids 16, 1070, 2004). Extrapolating our results to large Rayleigh number would imply a crossover at Ra ≈ 10 15 , where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down, than in the plume depleted regions.

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height R a f is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters R a f (3.96 × 104 ≤ R a f ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [Formula: see text] vs R a f for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nu h increase with the increase in Ste and R a f. There are two distinct RB flow configurations at low R a f independent of Ste. At low and moderate R a f, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [Formula: see text] is always greater than one. However, at higher R a f, the RB convection is turbulent, and [Formula: see text] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

The effect of Prandtl number on the linear stability of a plane thermal plume is analyzed under quasi-parallel approximation. At large Prandtl numbers (P r > 100), we found that there is an additional unstable loop whose size increases with increasing P r. The origin of this new instability mode is shown to be tied to the coupling of the momentum and thermal perturbation equations. Analyses of the perturbation kinetic energy and thermal energy suggest that the buoyancy force is the main source of perturbation energy at high Prandtl numbers that drives this instability.

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Cover Illustration: Boiling of water at 100 o C at 1 atm. pressure in a cylinder heated at bottom and cooled at top with a 0.25 K temperature difference. Instantaneous position of bubbles, and vertical velocity contours (red for up and blue for down moving liquid) are shown.