INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...

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equations are written in terms of volume fraction of each phase such that the sum of
the volume fractions is unity. When the phases are equally distributed in the domain of
interest with only moderate separation between the phases, the classical Euler – Euler
approach is appropriate.
Euler – Euler methods offer significant advantages over the Euler – Lagrange approach,
e.g. the two-continua method is independent of disperse phase mass loading,
and also the coupling between dispersed and carrier phase does not require averaging
over the parcels unlike in Euler – Lagrangian.
The merits of Euler – Euler methods play an important role when unsteady, turbulent
gas-liquid flows with high dispersed phase mass loading are considered. Additionally,
Euler – Euler methods can outperform the Euler – Lagrange in case of unsteady
spray flows and the computational cost do not depend on the droplet mass loading.
Most of the Euler – Euler methods in the field of spray flows are based on the description
of dispersed phase as a number density function (NDF) and the evolution of
this NDF due to physical processes of spray flows are described by the NDF transport
equation, also known as population balance equation (PBE) [41]. This NDF transport
equation is derived based on the kinetic equation [42] similar to the molecular kinetic
theory, and it is known as general particle-dynamic equation in the field of aerosol
science [43, 44].
There exists several Euler – Euler methods based on the kinetic equation such as
Williams’ spray equation and are categorized mainly as multi-fluid methods [45–47] and
moment based methods [48–54]. In the multi-fluid approach, the distribution function
is discretized using a finite volume technique that yields conservation equations for mass
and momentum of droplets in fixed size intervals called sections or fluids [46]. This
approach has recently been extended to higher order of accuracy [55], but discretization
of droplet size space is still a problem that needs to be addressed. On the contrary,
moment based methods such as quadrature method of moments (QMOM) [51, 52, 56–
58] or direct quadrature method of moments (DQMOM) [53, 54, 59] do not pose this
problem and they are found to be efficient and robust in the poly-disperse multiphase
flow problems.
The scope of this work is modeling and simulation of mono and bi-component evaporating
spray flows in an Euler – Euler framework. The focus is on the description of
the characteristics of the spray flows and spray drying process, and the influence of the
droplet size distribution on the droplet properties. In particular, spray inhomogeneity
associated with the atomization process and its transport in the convective medium is
not well understood. Subtle information is available about the particle formation and
its influence on the properties of the resulting powder in spray drying.
The present study aims to develop a comprehensive spray model, which can be