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In recent years, the lattice Boltzmann (LB) method has been widely employed to simulate boiling phenomena [A. Markus and G. Hazi, Phys. Rev. E 83, 046705 (2011); Biferale et al., Phys. Rev. Lett. 108, 104502 (2012); Li et al., Phys. Rev. E 96, 063303 (2017); Wu et al., Int. J. Heat Mass Transfer 126, 773 (2018)]. However, a very important issue still remains open, i.e., how does boiling occur in the LB simulations? For instance, the existing LB studies showed that the boiling on a hydrophobic surface begins at a lower wall superheat than that on a hydrophilic surface, which qualitatively agrees well with experimental studies, but no one has yet explained how this phenomenon appears in the LB simulations and what happened in the simulations after changing the wettability of the heating surface. In this paper, the LB boiling mechanism is revealed by analyzing boiling on a flat surface with mixed wettability and boiling on a structured surface with homogeneous wettability. Through a theoretical analysis, we demonstrate that, when the same wall superheat is applied, in the LB boiling simulations the fluid density near the heating surface decreases faster on a hydrophobic surface than that on a hydrophilic surface. Accordingly, a lower wall superheat can induce the phase transition from liquid to vapor on a hydrophobic surface than that on a hydrophilic surface. Furthermore, a similar theoretical analysis shows that the fluid density decreases fastest at concave corners in the case of a structured surface with homogeneous wettability, which explains why vapor bubbles are nucleated at concave corners in the LB simulations of boiling on structured surfaces.
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When boiling occurs in a liquid flow field, the phenomenon is known as forced-convection boiling. We numerically investigate such a boiling system on a cylinder in a flow at a saturated condition. To deal with the complicated liquid-vapor phase-change phenomenon, we develop a numerical scheme based on the pseudopotential lattice Boltzmann method (LBM). The collision stage is performed in the space of central moments (CMs) to enhance numerical stability for high Reynolds numbers. The adopted forcing scheme, consistent with the CMs-based LBM, leads to a concise yet robust algorithm. Furthermore, additional terms required to ensure thermodynamic consistency are derived in a CMs framework. The effectiveness of the present scheme is successfully tested against a series of boiling processes, including nucleation, growth, and departure of a vapor bubble for Reynolds numbers varying between 30 and 30000. Our CMs-based LBM can reproduce all the boiling regimes, i.e., nucleate boiling, transition boiling, and film boiling, without any artificial input such as initial vapor phase. We find that the typical boiling curve, also known as the Nukiyama curve, appears even though the focused system is not the pool boiling but the forced-convection system. Also, our simulations support experimental observations of intermittent direct solid-liquid contact even in the film-boiling regime. Finally, we provide quantitative comparison with the semi-empirical correlations for the forced-convection film boiling on a cylinder on the Nu-Ja diagram.
We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Benard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of $10^6$ and $10^7$, and Prandtl number of 0.71, where the mesh sizes are up to $257^3$; in Rayleigh-Benard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of $10^6$, $3times 10^6$, and $10^7$, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.
It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments.
Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We develop and investigate a new rectangular central moment LBM based on non-orthogonal moment basis (referred to as RC-LBM). The equilibria to which the central moments relax under collision in this approach are obtained from matching with those corresponding to the continuous Maxwell distribution. A Chapman-Enskog analysis is performed to derive the correction terms to the second order moment equilibria involving the grid aspect ratio and velocity gradients that restores the isotropy of the viscous stress tensor and eliminates the non-Galilean invariant cubic velocity terms of the resulting hydrodynamical equations. A special case of this rectangular formulation involving the raw moments (referred to as the RNR-LBM) is also constructed. The resulting schemes represent a considerable simplification, especially for the transformation matrices and isotropy corrections, and improvement over the existing MRT-LB schemes on rectangular lattice grids that use orthogonal moment basis. Numerical validation study of both the RC-LBM and RNR-LBM for a variety of benchmark flow problems are performed that show good accuracy at various grid aspect ratios. The ability of our proposed schemes to simulate flows using relatively lower grid aspect ratios than considered in prior rectangular LB approaches is demonstrated. Furthermore, simulations reveal the superior stability characteristics of the RC-LBM over RNR-LBM in handling shear flows at lower viscosities and/or higher characteristic velocities. In addition, computational advantages of using our rectangular LB formulation in lieu of that based on the square lattice is shown.
Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third order diagonal moments on the first order moments for standard lattices, and strategies have recently been introduced to restore GI without such errors using a modified collision operator involving either corrections to the relaxation times or to the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that alleviates the numerical stiffness. In the present study, we present a GI formulation of the preconditioned cascaded central moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. Improvements in accuracy and convergence acceleration are demonstrated.
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