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282964 The Growth of a Vapor Bubble On a Heated Surface Using the Lattice Boltzmann Calculation: Flow, Heat Transfer and Phase Change

Nucleate boiling is a very attractive method for cooling down a hot surface because, due to typically large latent heats, evaporation of a small amount of liquid can absorb a large amount of heat from the solid. The danger, however, is that the solid surface can even temporarily dry out, and the consequent hiatus in cooling could be catastrophic. One would therefore like to understand the physics of nucleate boiling well enough to prevent dryout.

Previously we reported conduction-only calculations for this problem that, surprisingly, yielded results that agreed with a large amount of phenomenology and experimental observations for these systems. These calculations showed, however, that nearly all of the evaporation takes place at the three-phase contact line (CL). Moreover the poorly-understood motion of the CL is critical to the evolution of vapor bubbles as gravity deforms them and drives them toward detachment from the solid surface, processes that determine which boiling regimes the system is in and that are clearly central to system’s deciding whether dryout will occur. Since CL motion with bubble growth is an input to a traditional continuum calculation, and since, even in the absence of phase change, is a subject of much disagreement in the literature, we seek to employ a method that obviates the need for ad hoc assumption about CL motion.

As such, we employ and extend the lattice Boltzmann equation (LBE) method, one of a class of methods known as diffuse interface methods, to include heat transfer, fluid flow and phase transition phenomena and implement it in two dimensions. The advantage of this method is that it considers the liquid and the vapor as a single phase of variable density. As such, the liquid-vapor interface is in the fluid domain and, in particular, the CL is part of its solid-fluid boundary, and their positions are outputs of the calculation, rather than input to it. The price that one pays for this approach is that the interface no longer remains nanoscopic, but rather is resolved over 3-5 gridpoints. The way that we employ this method is by using phase field theory to determine the transport properties of the multiphase flow such as pressure tensor and chemical potential from the Helmholtz free energy. This uses a known LBE formulation for the flow field. For the temperature field, we derive a LBE that, via Chapman-Enskog expansion techniques, can recover the correct energy equation (in an entropy formulation that allows a straightforward incorporation of the latent heat) from thermodynamic theory by ignoring the viscous dissipation term. We verify the accuracy of these calculations by comparison with problems having known analytic (e.g., similarity) solutions, such as Laplace’s law, Stephan problem and Scriven’s growth of a single bubble in an infinite fluid.

We look at the growth of a vapor bubble on an infinitely thin heated solid surface. Since we require the solid surface to be isothermal, it fixes the CL temperature as the surface temperature, unlike our earlier conduction-only calculation that included the solid and set the CL temperature equal to the saturation temperature. We calculate the temperature and flow fields and the motion of the CL at various time points up to and beyond bubble detachment and compare with (3D) data in the literature. We consider the size of the escaping bubble and of the vapor residue and its fate, including the descent and impingement of colder fluid that replaces the escaping detached bubble. Time permitting, we consider the case with a finite thickness solid as well and how issues of finite interface thickness play out in the solutions.

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