In case of stretching separation the KEseparationand PEcoalescence can be presented as follows:
\begin{equation}
text{KE}_{\text{separation}}=\frac{1}{2}\rho\left(v_{1}+v_{2}\right)^{2}V_{2}\left\{\frac{\Delta^{3}}{\left(1+\Delta^{3}\right)^{2}}\left[\left(1+\Delta^{3}\right)-\left(1-B^{2}\right)\left(\varphi_{1}+\Delta^{3}\varphi_{2}\right)\right]\right\}\nonumber \\
\end{equation}(32)
\(\text{PE}_{\text{coalescence}}=\sigma\left[2\pi V_{2}D_{2}\lambda\left(\Delta^{3}\varphi_{1}+\varphi_{2}\right)\right]^{\frac{1}{2}}\)(33)
V2 in equations 32 and 33 marks the volume of the
second drop before the collision.
Taking into account the separation volume coefficient in equation (29)
and the values of φ1 in equation (23) andφ2 in equation (24), the diametersdc of the drops after the collision can be
calculated as follows:
\(d_{c1}=\left(1-C_{v}\varphi_{1}\right)^{\frac{1}{3}}d_{1}\) (34)
\(d_{c2}=\left(1-C_{v}\varphi_{2}\right)^{\frac{1}{3}}d_{2}\) (35)
where d1 and d2 are the
respective diameters of the first and second drop before the collision,dc1 and dc2 are the
respective diameters of the first and second drop after the collision.
Fig. 10 shows the relative diameters of drops for different impact
parameters. This illustrates the change of the size of the drops
breaking out and colliding. Calculations have been performed for four
fuel types. In case of the relation Δ1 = 0.5, the
ratio of the sizes of the formed drop and the collided drop changes.
This means that in case of a small impact parameter, the size of the
drop formed after the collision is a smaller percentage of the drop size
before collision in comparison to the values of greater impact
parameters. In simpler terms this means that the small values of the
impact parameter result in smaller drops after the collision than
compared to greater values of the impact parameter. It is important
about the relation of dc /d for various
fuels that the ratio of change of the drop size does not change
significantly for the value Δ1 . Here we can
conclude that the injection of fuels with different physical and
chemical properties into the engine cylinder does not result in a
significant difference of the quality of the air-fuel mixture.
In a situation where Δ2 = 1, the influence of the
impact parameter on the relative drop diameter in the fuel spray changes
significantly. It can be seen from the figure that at the impact
parameter’s values B = 0–0.15 the drop size ratio increases as
the impact parameter increases. At the values B = 0.15-1 the relative
diameter of the drops increases as the value of the impact parameter
increases. It can be further seen from the graph that at the impact
diameter value of B = 0.22, the fuel properties have an influence
on the drop size. For example, at the value of B = 0.15 the drop
of gasoline after breakout is ~2.5% smaller than
compared to the HVO fuel. The comparison of FAME fuel and diesel fuel
does not reveal a significant change in drop size ratio. The drop size
ratio of diesel fuel remains on the same level as gasoline and FAME
fuel.