Development of a 20-moment Polydisperse and Polykinetic Spray Model Coupled With a Surface Density Approach for the Modelling of the Dense and Disperse Liquid Spray Regimes

A so-called Eulerian-Eulerian spray atomization (EESA) modelling framework is proposed in this thesis for the modelling of both the dense and disperse liquid spray regimes. In this approach, a version of the Sigma-Y quasi-multiphase model is used for modelling of the primary atomization of the liquid jet/sheet in the dense spray regime while the 20-moment Anisotropic Gaussian (AG) moment closure modelling approach is used for the disperse spray regime. Current state-of-art primary atomization modelling approaches used to obtain the droplet probability density function (PDF) are either empirically-based algebraic models or DNS-type approaches with very large computational cost. The Sigma-Y model employs an assumption similar to the Kolmogorov hypothesis which assumes that the large and small-scale flow features are independant for large Reynolds and Weber numbers. The model is compatible with the Reynolds-Averaged Navier-Stokes (RANS) modelling framework and introduces two additional scalar transport equations for the liquid mass fraction and mass-weighted liquid-gas surface density. In this fully Eulerian treatment, spray atomization is modelled through the imposition of source terms in the two transport equations which represent the key physical mechanisms such as primary breakup of the liquid jet/sheet, secondary droplet breakup, as well as droplet collision and coalescence. When the spray determined with this treatment is considered to be sufficiently disperse, the PDF is estimated using the liquid mass fraction and liquid-gas surface density, and is then used as an input to the 20-moment AG moment closure approach as the latter offers advantages for the modelling of drag, droplet collision/coalescence, turbulent dispersion and possible subsequent vaporization and combustion. In the disperse spray regime, the newly developed 20-moment polydisperse, polykinetic AG moment closure approach is used for the modelling of the spray distribution. In this model, statistical spray quantities describing the droplet size/velocity distribution and size-velocity correlations evolve according to a system of first-order hyperbolic equations. The developed model is an extension of the 10-moment monodisperse anisotropic Gaussian closure from kinetic theory, where restrictions on the velocity moments are relaxed to allow them to be functions of a size parameter, S. Functional forms for the resulting size-conditioned moments are proposed based on entropy maximization and polynomial expressions in order to complete the closure of the system of equations. In addition, a second-order, multi-dimensional finite-volume method has been implemented for solution of the 20-moment AG system of equations. Finally, different spray problems are presented for validation of the newly developed 20-moment AG moment closure and EESA modelling approaches. A suite of test problems are presented to demonstrate the ability of the 20-moment AG moment closure to reproduce the effects of droplet drag and evaporation. Lastly, several representative spray problems are used for validation of the EESA model, which include a plain orifice atomizer, turbulent liquid jet in a crossflow and pressure swirl atomizer.

Department dc:contributor.department

Aerospace Science and Engineering

Year dc:date.issued

2025

Author dc:creator

• Leung, Timothy

Advisor dc:contributor.advisor

• Groth, Clinton CPTG

• combustion
• moment closure
• multiphase
• RANS
• spray

Handle dc:identifier.uri

https://hdl.handle.net/1807/145074

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/145074