46
and Ohnesorge number (Oh)
Oh
l
l
l
= ⋅ ⋅
η
ρ σ
D
(4.2)
with D as the discharge diameter, ρ l is the oil density, σ l is the oil-water interfacial
tension (IFT), η l is the dynamic viscosity of the oil and u l is the oil exit velocity at
the nozzle. In each regime, the breakup of the dispersed oil into drops is governed
by different mechanisms. While the drop diameter is mainly determined by the exit
geometry, buoyancy and interfacial tension between oil and water in regime (0), the
atomization regime is mainly governed by turbulence and the shear forces acting
between oil and water. Since the original work of Ohnesorge, several authors have
sought to specify the borders of these and additional sub-regimes (e.g. Tang 2004;
Hsiang and Faeth 1992; Masutani and Adams 2001; Adams and Socolofsky 2004;
Lefebvre and McDonell 2017), especially with regard to the transition from
Rayleigh instability to full atomization. In a major oil well blowout, it can, however,
be assumed that the discharged liquid will be well beyond the atomization boarder
(Masutani and Adams 2001). In the following therefore only the drop formation
processes in a fully atomized jet will be considered. As it represents the upper limit
of the different approaches for classification of the flow regimes, Tang’s expression
(Tang 2004)
Oh ≥
⋅
−
24 9548
1 0027
.
.
Re
(4.3)
is chosen to mark the transition to full atomization and turbulent breakup.
The breakup of a turbulent jet consists of two phases, the primary and secondary
breakup. In the primary breakup, ligaments form at the edge of the cylindrical jet
due to shear between the continuous phase and the jet, which eventually break up
into drops. The secondary breakup describes the further disintegration of these initial drops into smaller drops due to the ambient flow field. The primary breakup
stage has a major influence on the final droplet size distribution (DSD) and is mainly
controlled by the discharge conditions at the nozzle (Lefebvre and McDonell 2017).
The hydrodynamics taking place at this stage of the jet formation are very complex
and not yet fully understood (Zuzio et al. 2013).
As a result of the turbulent nature of an atomized jet, the formation and size of
individual drops cannot be predicted. The entirety of all drops in an atomized jet
can, however, approximately be described using a characteristic average diameter
and a size distribution function. Depending on the area of application, different
characteristic diameters are used. In oil spill modelling, the median diameters of the
number (d n50 ) or volume distribution (d v50 ) are most commonly used, describing the
50th percentile of all drops by number and total oil volume, respectively. With
regard to mass transfer between the dispersed and the continuous phase, the Sauter
mean diameter (d 32 ) has been established. It describes a drop with the same volume
to surface ratio as the overall oil phase and can be calculated using:
K. Malone et al.
and Ohnesorge number (Oh)
Oh
l
l
l
= ⋅ ⋅
η
ρ σ
D
(4.2)
with D as the discharge diameter, ρ l is the oil density, σ l is the oil-water interfacial
tension (IFT), η l is the dynamic viscosity of the oil and u l is the oil exit velocity at
the nozzle. In each regime, the breakup of the dispersed oil into drops is governed
by different mechanisms. While the drop diameter is mainly determined by the exit
geometry, buoyancy and interfacial tension between oil and water in regime (0), the
atomization regime is mainly governed by turbulence and the shear forces acting
between oil and water. Since the original work of Ohnesorge, several authors have
sought to specify the borders of these and additional sub-regimes (e.g. Tang 2004;
Hsiang and Faeth 1992; Masutani and Adams 2001; Adams and Socolofsky 2004;
Lefebvre and McDonell 2017), especially with regard to the transition from
Rayleigh instability to full atomization. In a major oil well blowout, it can, however,
be assumed that the discharged liquid will be well beyond the atomization boarder
(Masutani and Adams 2001). In the following therefore only the drop formation
processes in a fully atomized jet will be considered. As it represents the upper limit
of the different approaches for classification of the flow regimes, Tang’s expression
(Tang 2004)
Oh ≥
⋅
−
24 9548
1 0027
.
.
Re
(4.3)
is chosen to mark the transition to full atomization and turbulent breakup.
The breakup of a turbulent jet consists of two phases, the primary and secondary
breakup. In the primary breakup, ligaments form at the edge of the cylindrical jet
due to shear between the continuous phase and the jet, which eventually break up
into drops. The secondary breakup describes the further disintegration of these initial drops into smaller drops due to the ambient flow field. The primary breakup
stage has a major influence on the final droplet size distribution (DSD) and is mainly
controlled by the discharge conditions at the nozzle (Lefebvre and McDonell 2017).
The hydrodynamics taking place at this stage of the jet formation are very complex
and not yet fully understood (Zuzio et al. 2013).
As a result of the turbulent nature of an atomized jet, the formation and size of
individual drops cannot be predicted. The entirety of all drops in an atomized jet
can, however, approximately be described using a characteristic average diameter
and a size distribution function. Depending on the area of application, different
characteristic diameters are used. In oil spill modelling, the median diameters of the
number (d n50 ) or volume distribution (d v50 ) are most commonly used, describing the
50th percentile of all drops by number and total oil volume, respectively. With
regard to mass transfer between the dispersed and the continuous phase, the Sauter
mean diameter (d 32 ) has been established. It describes a drop with the same volume
to surface ratio as the overall oil phase and can be calculated using:
K. Malone et al.