Modeling Multivariate Spray Characteristics with Gaussian Mixture Models

With the increasing demand for efficient and accurate numerical simulations of spray combustion in jet engines, the necessity for robust models to enhance the capabilities of spray models has become imperative. Existing approaches often rely on ad hoc determinations or simplifications, resulting in information loss and potentially inaccurate predictions for critical spray characteristics, such as droplet diameters, velocities, and positions, especially under extreme operating conditions or temporal fluctuations. In this study, we introduce a novel approach to modeling multivariate spray characteristics using Gaussian mixture models (GMM). By applying this approach to spray data obtained from numerical simulations of the primary atomization in air-blast atomizers, we demonstrate that GMMs effectively capture the spray characteristics across a wide range of operating conditions. Importantly, our investigation reveals that GMMs can handle complex non-linear dependencies by increasing the number of components, thereby enabling the modeling of more complex spray statistics. This adaptability makes GMMs a versatile tool for accurately representing spray characteristics even under extreme operating conditions. The presented approach holds promise for enhancing the accuracy of spray combustion modeling, offering an improved injection model that accurately captures the underlying droplet distribution. Additionally, GMMs can serve as a foundation for constructing meta models, striking a balance between the efficiency of low-order approaches and the accuracy of high-fidelity simulations.