Session D21: Bubbles: Growth, Heat transfer and Boiling

A more general Force Balance Model to predict Bubble Departure and Lift-off Diameters in flow boiling

Accurate prediction of Bubble Departure and Lift-off Diameters is key for development of closures in two-phase Eulerian CFD simulation of Flow Boiling, owing to its sensitivity in the Heat Flux partitioning approach. Several models ranging from simple correlations to solving complex force balance models have been proposed in literature; however, they rely on data-fitting for specific databases, and have shown to be inapplicable for general flow applications. The aim of this study is to extend the approach by proposing a more consistent and general formulation that accounts for relevant forces acting on the Bubble at the point of Departure and Lift-off. Among the key features of the model, the Bubble Inclination angle is treated as an unknown to be inferred along with the Departure Diameter, and the relative velocity of the bubble sliding on the surface, is modeled to determine the Lift-off Diameter. A novel expression is developed for the bubble growth force in terms of flow quantities, based on extensive data analysis. The model has been validated using 6 different experimental databases with varying flow conditions and 3 fluids. Results show high accuracy of predictions over a broad range, outperforming existing models both in terms of accuracy and generality.   

Counter-current thermocapillary migration of bubbles in self-rewetting liquids.

In this work, we study the counter-current thermocapillary propulsion of a suspended bubble in the fluid flowing inside a channel subject to an axial temperature gradient~when the surface tension~dependence on temperature is non-monotonic. We~use direct numerical simulations to address the two-phase conservation of mass, momentum and energy with a volume-of-fluid method to resolve the deformable interface. Two distinct regimes of counter-current~bubble migration are characterized: i) ``exponential decay'' where the bubble decelerates rapidly until it comes to a halt at the spatial position corresponding to the minimum surface tension and ii) ``sustained oscillations'' where the bubble oscillates about the~point of minimum surface tension. We illustrate how~these sustained oscillations arise at low capillary number O(10$^{\mathrm{-5}})$ and moderate Reynolds~number O(10) and, they are dampened by viscosity at lower Reynolds number. These results are in agreement with~the~experiments~by~Shanahan and Sefiane (Sci. Rep. 4,~2014).   

The effect of flow pattern around a bubble rising near a vertical wall, on the wall to liquid heat transfer.

Two-phase flow is an effective means for heat removal due to the enhanced convective effect caused by bubbly flow and the usually high latent heat of vaporization of the liquid phase. We present a numerical study of the effect of flow patterns around a single bubble rising in shear flow near a vertical wall, on the wall-to-liquid heat transfer. The Navier-Stokes equations are solved in a frame of reference moving with the bubble, by using the front tracking method for interface tracking. Our simulations reveal an enhancement of heat transfer downstream of the bubble, and a less pronounced diminishment of heat transfer upstream of the bubble. We observe that in the range of $5\le Re \le 40$ for Reynolds number based on shear and bubble diameter, heat transfer first increases, attains a maximum and decreases as $Re$ increases. The optimum $Re$ depends on the Archimedes number. The heat transfer enhancement is attributed to flow reversal happening in a confined region of the shear flow, in the presence of a bubble. The analytical solution of $2-D$ inviscid shear flow over a cylinder near a wall is used to identify two parameters of flow reversal namely 'reversal height' and 'reversal width'.These parameters are then used to qualitatively explain what we observe in $3-D$ simulations.   

Simulating Heat Flux and Bubble Nucleation using Molecular Dynamics

Modelling the heat flux in multiphase flow situations must account for nucleation of bubbles, non-linear heat transfer coefficients, complex molecular interaction at the surface, detailed surface textures as well as build up of material on the surface. These complex factors combine to define the well known boiling curve, which characterises the heat flux for a given temperature gradient. Understanding and optimisation of this boiling curve, and its critical heat flux (CHF), is a problem of great importance. Molecular dynamics (MD), by modelling the motion of the individual molecules, can replicate the bubble nucleation and heat flux. Details of the wall-fluid interaction are represented with complex textures and the surface materials can be explicitly reproduced. In this talk, MD simulation results are presented for bubble nucleation and heat flux. The heat flux is matched to experimental results and the process of nucleation explored for both fractal and textured surfaces. The unique insights from the molecular scale are discussed and potential applications including surface design and coupled molecular to continuum simulation are presented.   

Numerical Simulation of Bubble Formation in a Microchannel Using a Micro-Pillar

A three dimensional numerical simulation of bubble formation in a microchannel with a micro-pillar is investigated. Simulation results are validated against experimental data, where the working fluids are water and nitrogen. The gas enters the microchannel through a single slit located at 0\textdegree , along the pillar's depth. The bubble formation process has two main regimes, namely discrete bubble and attached ligament. The transformation from one regime to another is dictated by the capillary number Ca and the volumetric flow ratio Q. An analysis is performed to evaluate the critical values at which the transformation takes place. In addition, for the discrete bubble regime, the simulation results provide a proportional correlation between Q and the size of bubbles, and an inversely proportional relationship between Q and formation time, for each Ca. The computations are performed in the range of 10$^{\mathrm{-4}}$ \textless Ca \textless 10$^{\mathrm{-2}}$ and 0.5 \textless Q \textless 10$^{\mathrm{-2}}$.   

Gas depletion through single gas bubble diffusive growth and its effect on subsequent bubbles

In weakly supersaturated mixtures, bubbles are known to grow quasi-statically as diffusion-driven mass transfer governs the process. In the final stage of the evolution, before detachment, there is an enhancement of mass transfer, which changes from diffusion to natural convection [O.R. Enr\'iquez et al., The quasi-static growth of CO2 bubbles, \textit{Journal of Fluid Mechanics} \textbf{741}, R1 (2014)]. Once the bubble detaches, it leaves behind a gas-depleted area. The diffusive mass transfer towards that region cannot compensate for the amount of gas which is taken away by the bubble. Consequently, the consecutive bubble will grow in an environment which contains less gas than for the previous one. This reduces the local supersaturation of the mixture around the nucleation site, leading to a reduced bubble growth rate. We present quantitative experimental data on this effect and the theoretical model for depletion during the bubble growth rate.   

Mass transfer effects on the transmission of bubble screens

In this work we investigate, theoretically and numerically, the reflection and transmission properties of bubble screens excited by pressure wave pulses. We use modified expressions for the bubble resonance frequency and the damping factor in order to capture the influence of mass transfer on the reflection-transmission coefficients. In addition to the influence of variables such as the bubble radius and the averaged inter-bubble distance, the analysis reveals that in conditions close to the saturation line there exists a regime where the heat transport surrounding the bubble plays an important role on the bubble's response also influencing the reflection properties of the bubble screen. The linear analysis allows us to predict the critical vapor content beyond which liquid heat's transport controls the dynamic response of the bubbles. Numerical simulations show that these effects become especially relevant in the nonlinear regime.   

Parametric study of cross shaped hydrophobic dot for pool boiling

In this work we applied the shape of hydrophobic dots as a new variable of pool boiling with patterned wettability. We investigated the effect of dot shapes on heat transfer rate and buoyancy of bubbles. The shape of dot is set to be cross-shaped with the aspect ratios of the branches were varied in four cases: 0.173, 0.444, 1.074, and 2.000. In this research, multiphase single component lattice Boltzmann model was used for the simulation. The shapes of contact lines were similar to the shape of boarder lines of hydrophobic dots, but the surface tension to make the contact line in circular shape also existed. For dots with larger aspect ratio, the shape of contact line was too distorted. Therefore large portion of the contact line invaded to the hydrophilic surface via surface tension. The fluid near contact line on the hydrophilic surface has shown large buoyancy force by capillary flow toward contact line. This overall large buoyancy force caused the quick departure of the bubble. Therefore, with large aspect ratio, the heat transfer dropping period was reduced, while heat transfer rate increased in total nucleation cycle.   

Transition process leading to microbubble emission boiling on horizontal circular heated surface in subcooled pool

Microbubble emission boiling (MEB) produces a higher heat flux than critical heat flux (CHF) and therefore has been investigated in terms of its heat transfer characteristics as well as the conditions under which MEB occurs. Its physical mechanism, however, is not yet clearly understood. We carried out a series of experiments to examine boiling on horizontal circular heated surfaces of $5$ mm and of $10$ mm in diameter, in a subcooled pool, paying close attention to the transition process to MEB. High-speed observation results show that, in the MEB regime, the growth, condensation, and collapse of the vapor bubbles occur within a very short time. In addition, a number of fine bubbles are emitted from the collapse of the vapor bubbles. By tracking these tiny bubbles, we clearly visualize that the collapse of the vapor bubbles drives the liquid near the bubbles towards the heated surface, such that the convection field around the vapor bubbles under MEB significantly differs from that under nucleate boiling. Moreover, the axial temperature gradient in a heated block (quasi-heat flux) indicates a clear difference between nucleate boiling and MEB. A combination of quasi-heat flux and the measurement of the behavior of the vapor bubbles allows us to discuss the transition to MEB.