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Current Work


A long outstanding problem in fluid mechanics is the development of mathematical models that can predict the mean effects of turbulent flows. Through bypassing the requirement for resolving instantaneous features, such models are expected to much cheaper for a computer program than high-fidelity simulations. A key factor hindering such advancements is the difficulty of deriving the correct mathematical model form for transport under turbulence. As a result, researchers often rely on physical intuition, and heuristic arguments to justify assuming certain model forms. The subsequent tuning process, through which the model coefficients are determined, often mask the problems with choice of model form, because it is often possible to tune the coefficients so that a model performs well in one class of turbulence problems, while lacking in wide range of other problems. To address these challenges, our group has recently developed the Macroscopic Forcing Method (MFM), which is a statistical technique that can be used for quantitative assessment of turbulence model form. More broadly, MFM reveals the differential operators acting upon the mean fields of quantities transported by underlying fluctuating flows. Our current research heavily involves application of MFM for model development and model assessment for mass and momentum transport by turbulence. Primary areas of engagement include aerodynamic flows with specific focus flow separation phenomena on curved surfaces, environmental flows, and mass transport in material mixing applications.  

Two-Phase Flows

Two-phase flows are subject to significant interest because of their wide range of natural and industrial applications such as rain formation, spread of contagious disease, breaking waves, spray atomization and bubbly flows. Numerical simulations are particularly useful for studying realistic two-phase flow problems due to the limited scope of theoretical results and the difficulties associated with experimental techniques in two-phase environments.  Our group has been working on the development of accurate, physically consistent and cost-effective numerical methods for modeling two-phase flows with the goal of simulating practical problems of interest in industrial and natural settings. Specifically, using a diffuse-interface method technique, we have developed the first two-phase flow method that allows simultaneous numerical conservation of mass, momentum, and kinetic energy. This methodology has recently been extended to compressible flow regimes, allowing simultaneous simulations of shocks, acoustic waves, and phase interfaces. Our ongoing work focuses on extension of this methodology to mass and heat transfer problems hence paving the way for highly robust, accurate, and scalable simulations of multiphysics problems involving material interfaces. 

Our recent studies involving physics of two-phase flows involve analysis of turbulence interactions with superhydrophobic surfaces, analysis of turbulent hydraulic jumps, a comprehensive study revealing evolution of thin gas films under liquid-liquid impact events and microbubble generation.


Many electrochemical and microfluidic systems involve voltage-driven transport of ions in fluids in confined and unconfined structures. These systems involve the interplay between fluid flow, mass transport, and electrostatic effects. Our group is focuses on the theoretical and computational modeling of such phenomena in different settings including applications in ion separation, desalination, microfluidic settings, and membrane processes. 

In a recent work, we have developed the first direct numerical simulation of chaotic electroconvection, which is a phenomenon common in electrodialysis desalination. These simulations revealed a multiscale structure in electroconvection with remarkable similarity to turbulent flows despite their low Reynolds number, and provided quantitative evidence explaining the gap between experimental measurements and prior reduced-order models neglecting electroconvection effects. Current research activity on this topic focuses on physics of electroconvection, electrokinetic effects in plasma-based systems, catalytic conversion in membrane / gas diffusion electrode assemblies.

Past Work

Particle Laden Flow

Flows laden by particles are found in many applications including soot formation in internal combustion engines and rain droplets in clouds. Recent work conducted under the Predictive Science Academic Alliance Program 2 (PSAAP2), a multi-institutional collaboration involving Stanford and the universities of Colorado, Texas, Stony Brook, and Minnesota, has considered particle-turbulence-radiation interaction in a solar receiver where particles lend themselves to volumetric heating of the gas which can improve system efficiency. Considerable attention has focused on quantifying particle preferential concentration, turbulence modification, and heat transfer modification in a variety of canonical environments. There has been an additional focus on developing next-generation particle-laden flow modelling capabilities, especially in the context of Euler-Lagrange simulation.