Effect of Gasoline Fuel Additives on Combustion and Engine Performance

2.3.2.2
 
Fuel Temperature 
Temperature is a parameter that affects the droplet size through effects on other 
fuel properties. Increased temperature is known to affect both viscosity and surface 
tension of liquids and for a given injection pressure, a higher temperature fuel will 

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2.3 Spray Characterisation 
56 
result in lower droplet size. Moreover, according to Sazhin et al. [144] increased 
droplet surface temperature reduces the surface tension resulting in increased 
vaporisation speeds and hence smaller droplets. 
2.3.2.3
 
Empirical Relationships 
Several experimental studies have been carried out to establish a relationship 
between different fuel and injection properties and the droplet size. According to 
Lefebvre [7], owing to the complexity of various physical phenomena involved, much 
research into droplet sizing follows empirical methods. Five equations for the Sauter 
Mean Diameter have been displayed in Table 2.3.  
It is clear from the equations that the importance of viscosity compared to 
surface tension on droplet size is much larger. The equations are mainly aimed at 
estimating droplet sizes in diesel sprays and might prove inaccurate when applied to 
other fuels, especially those with higher volatility characteristics. Also, the equations 
do not take into account of the location of the measuring point and try and estimate a 
global droplet size. As will be shown in later chapters, measurement location affects 
the droplet size. Further, the established relationships are derived from a given set of 
experiments and are highly dependent upon achieving same conditions. The effect of 
injection pressure is relatively close between Elkotb and Knight but greatly reduced 
for the case of Hiroyasu and Kodota [143]. 
Moreover, although pressure difference across the nozzle is expected to affect 
the SMD, Araneo et al. [145] found flash boiling to have a significant effect, especially 
at below atmospheric ambient conditions, whereas above 800 kPa ambient pressure 
did not affect SMD further. Wang and Lefebvre [146] found the ambient pressure 
increase above atmospheric to increase the size of droplets to a maximum value 
initially before a decline. This would suggest that the ΔP term in the presented 
equations is limited in its range which, however, is not demonstrated in the equations. 
Lefebvre [7] and Wang and Lefebvre [147] also argue that the liquid sheet 
disintegration at exit from an injector nozzle is in addition to aerodynamic forces 
affected by turbulent or other disruptive forces within the liquid itself and proposed 
Equation 2.11. They acknowledge, however, the difficulty arising from experimental 
difficulties of measuring the liquid film thickness for purposes of the analysis.
It is evident all researches only fit the equation to their specific experiments 
and admit different relationship might be more appropriate compared to other 

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2.3 Spray Characterisation 
57 
researchers. The accuracy/suitability of the relationships presented will be compared 
against the current study in Section 5.1.