Numerical simulation of single bubble growth in microgravity

Nucleate boiling is a highly efficient heat transfer process due to the high latent heat of vaporization that is transferred from the liquid to the vapor bubbles. It remains a topic of ongoing research due to the great complexity of the length and time scales involved. A valuable technique for attaining a more comprehensive understanding is the use of validated numerical simulations through the means of computational fluid dynamics (CFD). The coupled conservation of mass, momentum and energy as well as the dynamics of the liquid-vapor interface require not only sophisticated models, but also a substantial amount of computational power. For the scientific examination of nucleate boiling, the Multiscale Boiling Experiment (RUBI) has been conducted on the International Space Station (ISS). The research focuses on the growth of single bubbles within subcooled boiling, which involves simultaneous evaporation near the bubble foot and condensation near the bubble top. The interplay between this experiment and the numerical study in this work is twofold. Initially, the experiment serves to validate the numerical models and the numerical solver. In return, the numerical solution delivers insights that are not accessible by today's experimental measurement techniques. Consequently, the aim of this work is the development and application of a numerical solver for the simulation of single bubble growth in microgravity. Therefore, specific cases from the RUBI experiment with variable subcooling, heater heat flux and preheating time are selected for both the validation and detailed analysis. The framework of choice is a custom single-component, multiphase and multiregion solver using the Volume-of-Fluid (VOF) method in OpenFOAM. This solver has been extended with the incorporation of new and significantly enhanced models, primarily concerning conjugate heat transfer and a subgrid model for contact line evaporation. It is demonstrated that the default conjugate heat transfer between the solid and the fluid with the VOF method is non-physical for bubble growth. This is due to the fact that in the cells which contain the liquid-vapor interface and are coupled to the solid wall, the properties of the liquid and vapor are averaged. Thus, the heat transfer properties artificially deteriorate. A physical model for the conjugate heat transfer in interface cells is presented, which only performs the conjugate heat transfer between the liquid and the solid and respects the liquid filling of each interface cell. Thereby, the heat transfer in the interface cells is significantly enhanced. The result is a larger bubble growth rate than with the default approach, which facilitates the validation against bubble growth experiments. Still, with common mesh sizes in CFD simulations, the heat and mass transfer close to the contact line is not resolved because of the very small length scale. Therefore, the micro region model is utilized, which is a semi-analytical model for the comprehensive description of the heat and mass transfer process near the contact line. An improved approach for the numerical solution process of the micro region model is proposed, which addresses a significant error source, especially for small contact angles. The integrated heat flux and the dynamic contact angle obtained from the micro region model are embedded as a subgrid model within the CFD simulations. In previous implementations, the micro region model was not implemented as an actual subgrid model. Rather, it was employed as a calculation method for the complete contact line cell, which resulted a.o. in a temperature discontinuity between the solid and the fluid. The new implementation is embedded into the CFD simulation as an actual subgrid model and thoroughly couples the conjugate heat transfer and the phase change. This results in a more implicit embedding in the CFD simulation, which leads to a higher solution quality. Each model development is verified and validated, either against analytical results or experimental data from a reference case. In addition to the numerical models, considerable attention is put on the numerical setup. The tremendous sensitivity of bubble growth simulations to input quantities, such as the saturation temperature or the boundary conditions of the numerical domain, is demonstrated. The actual saturation temperature in the experiment is determined by a comparison of the bubble growth in a selected experiment case to an analytical bubble growth solution. The outcome is an effective saturation temperature which is significantly smaller (1.7 K) than the official value. The mesh independence of the results is ensured by conducting a mesh study, after which a mesh size is selected which balances resolution and computational effort. The preheating phase and the laser energy required for bubble nucleation in the experiment are implemented and validated. The impact of employing an axisymmetric domain to represent the actual 3D geometry of the experiment is thoroughly analyzed through the use of both 3D and axisymmetric simulations. The partitioning of the heater heat flux into the solid and fluid region is analyzed in detail. For the given setup, the vast majority of the heat flux enters the solid region and only a minor portion actually reaches the fluid region. The initial validation attempt of the numerical solver for the bubble growth simulations reveals that the bubble growth is significantly smaller than in the reference case from the RUBI experiment. This is an unexpected result, given that each particular model and setup has been validated or verified. It is reasonable to conclude that the presence of non-condensable gases is the most probable explanation. During the evaporation near the bubble foot, these gases are added to the vapor bubble. Together with the vapor, they flow towards the bubble top, where the pure vapor condenses due to the subcooling. There, they accumulate over time and hinder further condensation, resulting in stronger bubble growth. In the absence of multi-component capabilities of the solver, a workaround for the condensing phase change by a local modification of the saturation temperature is introduced, which significantly enhances the agreement between the simulation results and the experiment. Additionally, it allows the estimation of the amount of non-condensable gases in the experiment. Ultimately, the numerical simulations of the selected RUBI cases are discussed. It is made transparent that the initial agreement is rather mediocre and case-specific modifications in the local saturation temperature for condensation are required for a satisfying agreement. Now, the heat transfer paths from the heated solid towards the subcooled liquid through the vapor bubble are analyzed in detail. The exact partition of the heat flow from the heater into the solid region, into the vapor, through contact line evaporation and into the superheated liquid layer around the vapor bubble is determined and its variability with the influence parameters subcooling, heater heat flux and preheating time is discussed. The share of contact line evaporation of the total phase change is in the order of 10 %, while the remaining 90 % is attributed to the balance of evaporation and condensation at the free interface. In addition, the heat flux trajectories from the heater and the flow field are analyzed. The expected high share of the heat transfer through the superheated liquid layer towards the liquid-vapor interface is observed. It is noteworthy that also in the vapor the majority of the heat flow from the solid is directed towards the liquid-vapor interface, where it facilitates evaporation. The flow field in the bubble illustrates that the flow from the evaporating section towards the condensing section is primarily driven by the enhanced phase change in the region around the contact line. This finding underscores the significant role of the evaporated mass near the contact line. In order to assess the heat removal efficiency of a bubble growth configuration, a dimensionless quantity is introduced. This quantity compares the total transferred heat through the bubble growth to the input heat. It is observed that in general comparably small bubble growth is more efficient than comparably large bubble growth, referenced to the occupied area at the wall. This finding is translated to both recommendations on the design of technical devices in microgravity utilizing a boiling process and on the discussion on the most efficient configuration in the contact line evaporation regime near the contact line. The analysis suggests that the generation of a multitude of smaller bubbles is more advantageous than the generation of a smaller number of larger bubbles, due to the fact that the process of generating conditions conducive to comparably strong bubble growth decreases the heat removal efficiency.