A Theoretical, Experimental, and Computational Framework for Droplet Collision Modeling in Lagrangian-Eulerian Simulation of Sprays

Description

Two-phase flows of liquid droplets dispersed in gaseous environments (simply called sprays hereinafter) are ubiquitous in natural and industrial processes. A long-lasting scientific problem arisen from understanding and applications of sprays is to develop quantitative simulation capability for predicting the time-evolving properties of dispersed droplets (e.g. size, velocity, and temperature) and their two-way coupling with gaseous environments (e.g. through phase change, heat and mass transfer, chemical reactions). Among various approaches to spray simulation, this proposal concerns the Lagrangian-Eulerian (denoted by L-E for short hereinafter) approach, in which the dispersed droplets are treated as noncontinuous particle-like entities in a Lagrangian framework, and gas flow is described by continuous field equations in a Eulerian framework. This proposal is particularly interested in using particle method to solve spray equation, which statistically describes the evolution of droplet distribution function (denoted by DDF for short hereinafter) in a high-dimensional phase space. Furthermore, the emphasis of the proposed study is on modelling droplet collision from a physically clear and mathematically rigorous perspective and by use of multiple-scale analysis. The proposed study aims to establish an improved theoretical, experimental, and computational framework for dealing with droplet collision in L-E simulation of sprays. The proposed study consists of three major components. Theoretically, the proposer will derive a spray equation by using the Liouville approach that is well known in statistical physics, with focus on modelling droplet collision source term based on the two-droplet statistics. Experimentally, the proposer will improve and parametrize the regime nomogram in theWe – B - Δ – ohparameter space for modelling the droplet collision transition probability function, which is required for model closure of droplet collision source term. Computationally, the proposer will establish a computational algorithm of the derived spray equation by using discrete DDF and implement it in the famous open-source code KIVA. The advantages of the proposed framework are that physical and mathematical approximations can be separated from each other, that modelling and computational parameters can be differentiated from each other, and that various existing models can be reinterpreted, compared, and improved.