INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

2. Mathematical Modeling
Spray constitutes of poly-disperse liquid droplets dispersed in gas medium. A typical
sketch of a pressure-atomized spray breakup and its development is depicted in
Fig. 2.1 [69, 70]. Here poly-disperse means that the properties of the disperse phase
entities can be different for each entity. For example, evaporating sprays have a region
near the nozzle where the liquid jet is not disperse, followed by a region after breakup
of the primary jet that is composed of individual droplets having different properties
such as size, velocity, temperature etc., which are defined as the poly-disperse
droplets [41, 71]. To describe the poly-disperse characteristics of the spray flows, the
mathematical modeling approach of Euler – Lagrangian and Euler – Euler framework
is discussed, and the sub-models for the physical processes of sprays such as evaporation,
forces, coalescence and breakup are elucidated in this chapter. Though the focus
of this work is to model the spray flows using the direct quadrature method of moments
(DQMOM), but the models like quadrature method of moments (QMOM) and
discrete droplet model (DDM), which were used to compare and validate the DQMOM
results, are also presented in this chapter.
2.1 State of the Art
The existing modeling approaches in the area of multiphase flows mainly include, (1)
Lagrangian particle tracking method and (2) Euler – Euler or two continua/fluid meth-
Fig. 2.1: Sketch of a pressure-atomized spray formation [69, 70].