Droplet Heat and Mass Exchange with the Ambient During Dropwise Condensation and Freezing
The distribution of local water vapor in the surrounding air has been shown to be the driving mechanism for several phase change phenomena during dropwise condensation and condensation frosting. This thesis uses reduced-order modeling approaches, which account for the effects of the vapor distribution to predict the droplet growth dynamics during dropwise condensation in systems of many droplets. High-fidelity modeling techniques are used to further probe and quantify the heat and mass transport mechanisms that govern the local interactions between a freezing droplet and its surrounding ambient, including neighboring droplets. The relative significance of these transport mechanisms in the propagation of frost are investigated. A reduced-order analytical method is first developed to calculate the condensation rate of each individual droplet within a group of droplets on a surface by resolving the vapor concentration field in the surrounding air. A point sink superposition method is used to account for the interaction between all droplets without requiring solution of the diffusion equation for a full three-dimensional domain. For a simplified scenario containing two neighboring condensing droplets, the rates of growth are studied as a function of the inter-droplet distance and the relative droplet size. Interactions between the pair of droplets are discussed in terms of changes in the vapor concentration field in the air domain around the droplets. For representative systems of condensing droplets on a surface, the total condensation rates predicted by the reduced-order model match numerical simulations to within 15%. The results show that assuming droplets grow as an equivalent film or in a completely isolated manner can severely overpredict condensation rates.
The point superposition model is then used to predict the condensation rates measured during condensation experiments. The results indicate that it is critical to consider a large number of interacting droplets to accurately predict the condensation behavior. Even though the intensity of the interaction between droplets decreases sharply with their separation distance, droplets located relatively far away from a given droplet must be considered to accurately predict the condensation rate, due to the large aggregate effect of all such far away droplets. By considering an appropriate number of interacting droplets in a system, the point sink superposition method is able to predict experimental condensation rates to within 5%. The model was also capable of predicting the time-varying condensation rates of individual droplets tracked over time. These results confirm that diffusion-based models that neglect the interactions of droplets located far away, or approximate droplet growth as an equivalent film, overpredict condensation rates.
In dropwise condensation from humid air, a full description of the interactions between droplets can be determined by solving the vapor concentration field while neglecting heat transfer across the droplets. In contrast, the latent heat released during condensation freezing processes cause droplet-to-ambient as well as droplet-to-droplet interactions via coupled heat and mas transfer processes that are not well understood, and their relative significance has not been quantified. As a first step in understanding these mechanisms, high-fidelity modeling of the solidification process, along with high-resolution infrared (IR) thermography measurements of the surface of a freezing droplet, are used to quantify the pathways for latent heat dissipation to the ambient surroundings of a droplet. The IR measurements are used to show that the crystallization dynamics are related to the size of the droplet, as the freezing front moves slower in larger droplets. Numerical simulations of the solidification process are performed using the IR temperature data at the contact line of the droplet as a boundary condition. These simulations, which have good agreement with experimentally measured freezing times, reveal that the heat transferred to the substrate through the base contact area of the droplet is best described by a time-dependent temperature boundary condition, contrary to the constant values of base temperature and rates of heat transfer assumed in previous numerical simulations reported in the literature. In further contrast to the highly simplified descriptions of the interaction between a droplet and its surrounding used in previous models, the model developed in the current work accounts for heat conduction, convection, and evaporative cooling at the droplet-air interface. The simulation results indicate that only a small fraction of heat is lost through the droplet-air interface via conduction and evaporative cooling. The heat transfer rate to the substrate of the droplet is shown to be at least one order of magnitude greater than the heat transferred to the ambient air.
Subsequently, the droplet-to-droplet interactions via heat and mass exchange between a freezing droplet and a neighboring droplet, for which asymmetries are observed in the final shape of the frozen droplet, are investigated. Side-view infrared (IR) thermography measurements of the surface temperature for a pair of freezing droplets, along with three-dimensional numerical simulations of the solidification process, are used to quantify the intensity and nature of these interactions. Two droplet-to-droplet interaction mechanisms causing asymmetric freezing are identified: (1) non-uniform evaporative cooling on the surface of the freezing droplet caused by vapor starvation in the air between the droplets; and (2) a non-uniform thermal resistance at the contact area of the freezing droplet caused by the heat conduction within the neighboring droplet. The combined experimental and numerical results show that the size of the freezing droplet relative to its neighbor can significantly impact the intensity of the interaction between the droplets and, therefore, the degree of asymmetry. A small droplet freezing in the presence of a large droplet, which blocks vapor from freely diffusing to the surface of the small droplet, causes substantial asymmetry in the solidification process. The droplet-to-droplet interactions investigated in thesis provide insights into the role of heat dissipation in the evaporation of neighboring droplets and ice bridging, and open new avenues for extending this understanding to a system-level description for the propagation of frost.