Yuan Tian

Capturing the highly nonlinear, transient temporal dynamics of nucleate boiling heat flux imposes severe computational burdens, particularly when involving complex inhomogeneous surfaces where intense liquid–vapor interactions induce chaotic thermal fluctuations. To deeply reveal these underlying phase-change mechanisms, this study establishes a coupled framework integrating the hybrid pseudopotential lattice Boltzmann method with deep learning architectures. Systematic analysis reveals that the transient surface heat flux exhibits pronounced high-frequency oscillations, which are fundamentally driven by the periodic physical cycles of vapor blanketing, bubble departure, and rapid surface rewetting. While conventional neural networks (such as multilayer perceptrons and convolutional neural networks) structurally disrupt the temporal continuity of this thermal history, the recurrent neural network (RNN) uniquely aligns with the physical periodicity of the boiling cycle. The internal memory cells of the RNN function analogously to the thermal inertia of the heating wall, successfully capturing the cyclic destruction and reconstruction of the thermal boundary layer and yielding superior predictive accuracy. Furthermore, on inhomogeneous surfaces with isosceles trapezoidal microstructures, the fundamental periodicity of boiling is physically disrupted. Intense contact line pinning and premature lateral bubble coalescence drastically prolong localized vapor blanketing, shifting the multiphase heat transfer from a stable cyclic process to a highly chaotic, nonlinear dynamic regime. The proposed framework effectively tracks these complex transitions, proving that structural micro-confinement profoundly modulates the localized thermal fluctuations.

Enhancing pool boiling heat transfer within porous media remains a formidable challenge, primarily due to the intricate coupling between complex structural parameters and multiphase transport phenomena. To bridge the gap between pore-scale hydrodynamics and macroscopic performance, this study employs an advanced cascaded lattice Boltzmann method to rigorously investigate pool boiling on heater surfaces with discrete geometric topologies. Departing from conventional studies focused on homogenized uniform or gradient foams, we elucidate the distinct regulatory mechanisms governing boiling crises at the element level, specifically driven by shape-induced nucleation, vorticity evolution, and capillary-modulated rewetting. Our results demonstrate that triangular topologies induce the highest Nusselt number, where sharp corner singularities accelerate nucleation and promote vigorous bubble departure. Conversely, circular geometries, owing to their symmetry, foster uniform nucleation and stable bubble ascent, offering dynamic stability at the cost of peak heat transfer rates. Trapezoidal structures, however, exhibit disordered phase distribution due to asymmetry, precipitating premature film boiling and suboptimal performance. Furthermore, a critical dimensionless spacing regime (0.65–0.86 capillary lengths) is identified. This regime represents an optimal equilibrium that maximizes beneficial inter-bubble coalescence while sustaining liquid rewetting pathways; deviations lead to either vapor blanketing (narrow spacing) or insufficient flow agitation (wide spacing). Ultimately, this work reveals that performance divergence is fundamentally governed by the synergistic modulation of heat flux concentration, flow confinement, and phase-change thermodynamics, providing vital theoretical guidelines for the topological design of next-generation boiling surfaces.

In this paper, a novel method is proposed for heat flux calculation of cylindrical boiling, which exploits circular symmetry to implement quadrant-wise Newton/Lagrange interpolation. In comparison to alternative conventional solution schemes, the novel method demonstrates sufficient precision near the boundary as well as inside the solid. The accuracy is further verified by comparison with the theoretical solutions for cylindrical film boiling. Additionally, this method is also applied to evaluate different curved boundary schemes. The findings suggest that the heat flux on the cylindrical surface exhibits abnormally high values for the linear interpolation and Zhao–Yong schemes. Analyses indicate that this phenomenon arises from large spurious velocities generated by these two schemes, which in turn affect the temperature field. Specifically, these two schemes have limited applicability in simulating complex phase-change scenarios and require further consideration and testing.

Boiling heat transfer, a pivotal mechanism in energy and high-tech sectors, demands innovative approaches for efficient heat flux prediction. A novel coupling approach is introduced in the current study, which integrates machine learning with the lattice Boltzmann method (LBM). The coupling approach involves training a recurrent neural network (RNN) using datasets generated from a hybrid pseudopotential LBM model, followed by employing the RNN to predict heat flux densities under various wall superheat conditions. In the implementation of the RNN model, feature engineering is utilized to significantly reduce the input dimensionality, reducing the need for numerous known parameters required by the traditional LBM. This simplification maintains accuracy while streamlining the computational requirements. The RNN architecture, employing rectified linear unit activation functions, establishes a robust nonlinear mapping between simplified parameters and heat flux dynamics. Compared to pure LBM simulations, this approach increases computational efficiency by at least 73.6%. The model is validated, demonstrating outstanding performance: the coefficient of determination exceeds 0.999, and the root mean square error is less than 0.000 05. Notably, the model does not require structural adjustments to accommodate different conditions, exhibiting unparalleled generalization capability, making it more advantageous than conventional RNN models, which often need to be reconfigured for different scenarios. Furthermore, the model predictions are accurate even on completely independent test datasets. By integrating LBM simulations with data-driven learning, the current research pioneers a bidirectional “mechanism-to-data-driven” paradigm, extending the forefront of multiphase flow analysis and enabling scalable and efficient heat transfer predictions within complex phase-change systems.

The droplet nucleation and sweeping dynamics critically govern the condensation and self-cleaning functionality of superhydrophobic surfaces, yet their synergistic regulation remains underexplored. Four wedge-shaped micropillar architectures (5/10 μm heights) were investigated via combined condensation experiments and multiphase flow simulations. Geometric asymmetry-induced capillary force gradients were found to simultaneously enhance nucleation density and sweeping efficiency. The 10 μm flower-like surface achieved 26.67 × 108 droplets/m2 nucleation density (592% higher than conventional surfaces) with 563% faster nucleation, while enabling removal of 24 droplets per sweeping event and a 378.8% increase in frequency, resolving the historical nucleation-sweeping trade-off. Mechanistically, increased pillar height enhances nucleation by extending three-phase contact lines and reducing critical film rupture thickness, while intensified capillary gradients during coalescence drive nonlinear sweeping improvements via amplified energy conversion. Simulations confirm superior post-coalescence X-direction velocity (0.0317 m/s) and angular velocity (300.22 rad/s) on optimized surfaces, directly linking performance to capillary gradients. Design strategies for engineering superhydrophobic surfaces that synergistically integrate high-flux condensation and ultrafast self-cleaning are established in this work.

The pseudopotential multi-relaxation time phase-change lattice Boltzmann model is employed in the current work to simulate pool boiling on surfaces with various base geometries, including triangular, square-column, and trapezoidal structures. The dynamic processes of bubble nucleation, growth, coalescence, and detachment as well as heat flux on these surfaces are systematically analyzed with conjugate heat transfer and continuous wetting conditions. The results show that for protruding structures, bubbles nucleate at the concave corners of the base, where larger concave angles promote easier detachment and higher heat flux. In concave structures, earlier boiling onset and higher local solid temperatures lead to a shorter bubble growth and detachment cycle, enabling rapid and continuous bubble release, which enhances heat flux. The analysis of various structures and wettability settings reveals that concave structures achieve slightly higher average heat flux during boiling compared to convex surfaces under identical superheat conditions. Concave structures slightly hinder bubble detachment, their faster bubble growth and detachment rates result in improved heat flux compared to protruding structures. At the dimensionless time t* = 8700, the triangular structure, with its largest concave angles, demonstrates the most efficient bubble detachment and achieves the highest heat flux.

The lattice Boltzmann method (LBM) has a natural advantage in dealing with complex solid boundaries. However, it proves to be challenging in LBM to deal with contact angles in an intricate curved surface for multiphase flows. Applying traditional curved boundary schemes could produce relatively accurate results near complex geometric boundaries, but they often lead to issues such as mass leakage. As a result, in the current study, two improved curved boundary schemes are proposed to cope with flow problems with intricate geometric boundaries by introducing non-ideal force into the linear interpolation scheme and the Zhao–Yong scheme, followed by mass compensation for interpolation errors. The accuracy and mass conservation of the two proposed boundary schemes have been thoroughly validated through a series of numerical tests involving static droplet and dynamic multiphase flow. Meanwhile, the two curved schemes with central linear interpolation and multireflection schemes are also utilized to successfully achieve the different wettability of curved walls. It is found that mass correction and non-ideal force are not required for such schemes when simulating the wetting phenomenon of triple-point contact angles at curves. In addition, the accuracy of simulations is affected by different wettability schemes, and therefore, the contact angles for various wall wettability models have also been investigated in the present study. It is demonstrated that the improved virtual-density scheme does not result in unphysical layers and has smaller spurious currents as well. These advantages do not occur in other schemes, such as fluid–solid interaction, improved fluid–solid interaction, and virtual-density schemes.

An improved U-net accelerated coupling model, tailored for multi-relaxation-time lattice Boltzmann method (MRT-LBM), is proposed in the current paper. The coupling model is employed to analyze the natural convection process with a protruded triangular thermal conductivity boundary on high-temperature wall in a square cavity. The acceleration effect of the coupling model is analyzed and compared under different arrangements of the thermal conductivity triangle at several positions (Lc), varying hypotenuse lengths (Lb), and different Rayleigh number (Ra), leading to the following significant findings: The application of the coupling model with different Lc results in significant improvements in convergence iteration steps and computation time, achieving the maximum efficiencies improvement of 16.77% and 19.03%, respectively. Then, the coupling model demonstrates an enhanced efficiency of up to 19.31% and 27.33% in terms of convergence iteration steps and computation time, respectively, when considering Lb variations; When the coupling model is applied in different Ra conditions, the efficiency of converging number and computation time is improved by 25.9% and 25.44%, respectively. Additionally, the maximum relative error of the average Nu numbers under different Lc, Lb, and Ra conditions is 0.66%, 0.89%, and 0.77%, respectively (all less than 1%), which indicates that the model has high generalization performance and accuracy and provides an effective reference for the acceleration of MRT-LBM.

An interface accurate numerical method for phase-change processes is developed, and the velocity decomposition is introduced into the front-tracking framework. The method decomposes the velocity field into a potential part associated with phase change and a rotational part. The two parts are solved separately, which decouples the numerical errors in the potential and rotational parts during the advancement of the liquid–gas interface. The results of the present method are compared with the existing method at various density ratios, demonstrating more accurate representation of the interface and robust using the present method. Additionally, by explicitly tracking the interface, the method reduces the number of Poisson equations solved compared to the interface capturing framework, improving the computational efficiency during the interface advection process. The proposed method is validated through a series of benchmark tests, including the one-dimensional (1D) Stefan problem, the one-dimensional (1D) sucking problem, and two-dimensional (2D) droplet evaporation at both saturation and sub-saturation temperatures. Additionally, the method is tested by simulating one or two evaporating droplets falling under gravity in both two- and three-dimensional cases, further demonstrating its accuracy and robustness.