Development of an advanced hybrid model based on the direct quadrature method of moments and validation in complex polydisperse sprays

Due to increasing fuel prices and stronger emissions regulations, combustion has emerged as one of the most economically important applications of technical sprays. In combustion processes involving a liquid fuel, the mixing of oxidizer and fuel vapor and, consequently, the combustion efficiency are strongly influenced by the spray character of the fuel injection. Therefore, the current demand for efficient and robust numerical methods to accurately describe the full complexity of unsteady spray systems, and optimize the spray behavior in modern engines, is significant. A major challenge for the simulation of spray systems is the accurate description of strongly coupled phenomena, such as liquid atomization and secondary droplet breakup, droplet-droplet and droplet-gas interactions, turbulent dispersion and evaporation, while maintaining the computational cost practicable. Due to high computational cost, a detailed description of technical sprays on a microscopic level is still prohibitive. Therefore, most numerical tools for the spray simulation are based on a statistical description given in terms of a probability density function; a so-called mesoscopic level of description. The time and spacial evolution of this probability density function is accurately described by a kinetic Boltzmann type equation, known as the Williams spray equation, which is able to account for the principal phenomena governing the spray system. There are two main approaches to solve the Williams equation: the stochastic Lagrangian and the Eulerian moment methods. The stochastic Lagrangian methods allow a straightforward and accurate description of the occurring physical phenomena. However, the computational cost of Lagrangian methods is high, and an optimal parallelization of the solver is hardly possible. An efficient coupling between the Lagrangian description of the disperse phase and the Eulerian formulation of the continuous phase is also challenging. Regarding massively parallelized simulations as well as the efficient coupling between disperse and continuous phases, Eulerian moment methods are promising alternatives to the Lagrangian approach. In this work, a novel hybrid approach for the numerical modeling of polydisperse sprays, which combines the Direct Quadrature Method of Moments (DQMOM) with a Sectional Method, is proposed. This method, referred to as the Direct Quadrature based Sectional Method of Moments (DQbSMOM), includes some of the most advanced methods for the description of spray processes within an Eulerian framework, such as the Eulerian Multi-Size Moment (EMSM) model for spray evaporation. The main goal is an accurate description of the principal physical effects governing the evolution of a dilute spray system, while the stability of the solver is ensured. A new DQMOM based algorithm for calculating droplet coalescence is introduced. In order to validate the proposed method, three complex spray configurations were numerically investigated. Its accuracy with regard to spray evaporation, droplet coalescence and convective transport in physical space was assessed, while its robustness and stability was demonstrated.