CAREER: Consistent Continuum Formulation and Robust Numerical Modeling of Non-Isothermal Phase Changing Multiphase Flows

Numerical modeling of phase change problems is crucial to understanding many natural and engineering processes. For example, ice formation and additive manufacturing. A major challenge arises from the coupling of heat transfer and fluid dynamics equations. Water, polymers, and metals all exhibit changes during processes like melting or evaporation that must also be considered in the model. Although several advances have been made in modeling some phase change processes, the modeling of three phase gas-liquid-solid flows with simultaneous melting, solidification, evaporation, and condensation (MSEC) remains an unsolved problem. In this project, the researchers will formulate a robust numerical scheme for simulating three-phase gas-liquid-solid flows that can undergo simultaneous MSEC and volume shrinkage/expansion. This method would permit realistic simulations and optimization of emerging manufacturing technologies like additive manufacturing and thin film deposition, where all four modes of phase change occur simultaneously. Additionally, the project provides significant educational activities, including training students in scientific and high-performance computing, outreach activities, and sharing of research codes through open-source software. This project will develop governing equations for multi-phase gas-liquid-solid flows with phase change that are consistent both at the continuous and discrete levels. The project focuses on ensuring the stability of the numerical scheme when all four modes of phase change are present. It is especially critical for flows with significant volumetric changes and with high-density contrast. Analytical and experimental validation are also part of this project. To validate that the numerical scheme captures the density/volume change during phase transition, a novel analytical model is proposed. The framework will be further validated with experimental data from the National Institute of Standards and Technology (NIST) on metal solidification and evaporation. This project will result in an experimentally validated framework that will assist in simulating and understanding metal additive manufacturing processes such as selective laser melting and powder bed fusion. Advanced computer simulations will allow the manufacturing industry to optimize process parameters, such as laser scan speed and gas flow rates, to ensure high-quality and defect-free printed parts. The numerical methods of this project will be made open source with user-friendly documentation via IBAMR software. In order to increase student participation in computing, the researcher will offer: (1) a new project-based course on Applied Scientific Computing; (2) organize summer workshops on high-performance computing (HPC) in partnership with the San Diego-based HPC industry; and (3) work with SDSU programs to recruit students from local high schools and community colleges to provide summer internship opportunities. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.