The investigator will develop and study a new computational approach for the simulation of turbulent droplet-laden flows rooted in the probabilistic-based description of particle transport. This requires the determination of the evolution of the particle-density function in space and time, coupled with the turbulent flow of the carrier phase (gas or liquid). Knowledge of this function enables consistent coupling with the flow through mass, momentum, and energy sources in the governing equations of the carrier gas flow. The main mathematical difficulty that has prevented this approach from progressing in the past is the high dimensionality of the space of independent variables of the distribution function, which renders traditional computational techniques ineffective with current or foreseeable computational resources. The main idea of the research is the use of a new non-linear global basis function projection approach that condenses several of the extra dimensions of the problem. The transformative nature of the proposal is in (i) devising a methodology for integrating the transport equation for the distribution function that is computationally amenable, (ii) implementing the numerical methodology in an efficient predictive and modular tool, and (iii) extending the knowledge of the currently inaccessible aspects of the microphysics interaction with the carrier gas in atmospheric cloud simulations. Furthermore, collaboration with a team at Max-Planck Institute for Meteorology will ensure the effective transfer and dissemination of the technology that is proposed to the area of physical meteorology.
The prediction of multi-phase flows, particularly solid or liquid particles dispersed in a host-gas, is challenging and computationally onerous. These flows arise in natural phenomena; encompassing cloud dynamics, dust storms and grassland fires; and industrial applications such as food and chemical processing as well as chemical synthesis and propulsion. The interactions between a highly turbulent flow and the extremely large number of particles (millions-to-billions and beyond) of different shape and size, moving in different directions with different velocities, that undergo phase transformation and/or chemical reactions, lead to a complex mathematical problem. The proposed research will make a significant impact in the understanding of a wide range of science and engineering phenomena involving flows with dispersed particles that are currently inaccessible. The research will enable high-fidelity computations that incorporate phenomena at the small and large scales consistently. Enhancement in the prediction of these flows has numerous scientific and societal benefits; e.g., because atmospheric flows are critical to improve weather prediction and to better understand the global energy balance of our planet.
