Effect of Gasoline Fuel Additives on Combustion and Engine Performance

2.3.2
 
Droplet Size 
Droplet size is often represented on the basis of a diameter of an equivalent 
sphere [131]. Dependent upon method the equivalence can be based on maximum or 
minimum length, weight, volume, surface area or other properties. However, the 
process of obtaining the diameter of equivalent sphere from non-spherical droplets 
often relies on several assumptions and in case of some optical methods (Section 2.3.3) 
can provide basis for inaccurate analysis. 
The commonly used parameter to characterise the spray is the Sauter Mean 
Diameter (SMD). SMD represents the diameter of a fuel droplet with the same volume 
to surface ratio as the total spray. It is most applicable in cases such as liquid fuel 
sprays where specific surface area, due to its relevance to evaporation rates, is 
important. It follows the form [132]: 
𝐷[3][2] =
Ʃ𝑛𝐷
3
Ʃ𝑛𝐷
2
2.6 
The 
n
term denotes the number of particles of a certain size.
Reduced SMD refers to smaller droplet diameters and increased total droplet 
surface area, meaning higher fuel evaporation rates and improved fuel mixing. 
Enhanced evaporation and mixing characteristics are especially important in the case 
of direct injection where much reduced time periods compared to PFI systems are 
involved. Smaller droplets are expected to occur with increased injection pressures. 
Controversially, Zhang et al. [133] found that while increased fuel injection pressure 
reduced unburned hydrocarbon emissions, CO and NO
x 
emissions increased. It is 
thought CO increase is a resultant of increased fuel-wall impingement with increased 
fuel pressure, while NO
x
increase results from increased amount of fuel being 
available within the cylinder as a result of injection duration being kept constant. A 
more thorough description of emissions will be given in Section 2.4.4 (Page 67). 
Fuel atomisation into a large number of small droplets is important in order to 
create a large surface area on which the fuel can rapidly evaporate. Willauer et al. 
[134] carried out experiments on flammability of aerosols produced by rotary 
atomisers. They found the droplet size to have a profound effect on the flammability 
limit, combustion rate and temperature averages reached during combustion. Reduced 
droplet size was seen to increase the concentration of fuel vapour, thus, enabling easier 

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2.3 Spray Characterisation 
53 
air-fuel mixing and at high fuel flow rates. 75 % decrease in droplet size could increase 
the average temperature of the hot gases and aerosol mixture by nearly 800 %. Larger 
droplets inhibited fuel atomisation and as a result the propagation of pilot flame and 
sustainable burning of fuel was hindered. Similar effect of atomisation quality on 
flammability limit was experienced by Park et al. [130]. The tests on lean burn 
capability of a spray guided direct injection system showed that at 200 bar injection 
pressure φ = 3.0 could be achieved. However, at 100 bar injection pressure the 
flammability limit was reached at only φ = 1.5.
In most cases, the evaporation rate of the fuel follows the D
2
-Law. The size of 
the fuel droplet can be expressed as [135]: 
𝐷
2
= 𝐷
0
2
− 𝜆𝑡
2.7
 
where 
D 
is the final droplet diameter,
D
0
is the droplet initial diameter, 
λ
is the 
evaporation constant and 
t
the evolution time. It is clear from this relationship that 
droplet size decreases over time proportionately to the constant λ. Furthermore,
 λ
is 
expressed in terms of [m
2
/s], indicating clearly its dependence on total droplet surface 
area of the fuel jet and hence the atomisation quality on the evaporation rate.