Effect of Gasoline Fuel Additives on Combustion and Engine Performance

Table 2.2: Secondary droplet break-up mechanisms based on Weber number 

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2.3 Spray Characterisation 
48 
Figure 2.2: Schematics of fuel spray and key parameters
An additional dimensionless relationship to relate the viscous and surface 
tension effects is the Ohnesorge number, Oh: 
𝑂ℎ =
√𝑊𝑒
𝑙
𝑅𝑒
=
𝜇
√𝜌
𝑙
𝜎
𝑙
𝐷
2.5
 
Due to the Ohnesorge number completely disregarding the gas phase 
properties, it is assumed that 
µ
g
<< 
µ
l
[117]. Van Romunde [116] proposes additionally 
using gas phase Weber number or liquid to gas density ratio to obtain improved 
understanding of spray characteristics. 
The fuel is introduced into the combustion chamber or intake manifold through 
one or several nozzle holes. Figure 2.2 displays a typical fuel spray through a high 
pressure injector and lists the key parameters associated with the spray development. 
As the liquid fuel leaves the injector nozzle it is rapidly accelerated to high 
velocities due to the high pressure difference to the ambient conditions and becomes 
turbulent. Fuel jet leaving the injector nozzle entrains ambient gases and spreads out 
and small drops will start developing along the outer edges of the jet.
The liquid fuel leaving the injector will for a given geometry and pressure 
conditions disintegrate as a result of turbulence and air entrainment at a finite distance 

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2.3 Spray Characterisation 
49 
from the injector nozzle. This is called the spray 
break-up length
. Break-up in sprays 
relates to the phenomena where intact fuel jet breaks up into ligaments and droplets. 
Lin and Reitz [120] conclude that spray properties depend on a large number of 
parameters including nozzle internal flow effects resulting from cavitation, jet velocity 
profile, turbulence at the nozzle exit and the physical and thermodynamic states of the 
liquid and the ambient gases. Although particularly important in high-speed break-up 
regimes, nozzle internal flow effects have only been incorporated into break-up 
theories empirically. Break-up phenomena in liquid jets has been divided into 5 
distinguishable groups, as shown in Figure 2.3.