Here it should be pointed out that in addition to SMD , other
parameters are used to describe the drops, for example,d10 , d20 ,d30 , d43 (Herdan Mean
Diameter or HMD ), etc. \cite{Liu99,Hou06}. SMD is related to the volume-area
ratio and describes the mean size of fuel drops in the fuel spray.
Therefore, this parameter is used in most of the equations related to
the formation of air-fuel mixture and combustion of fuel sprays and
air-fuel mixtures.
Sources \cite{Hir90,Hir89,Hir74} point out several methods for determining the SMD of
drops leaving the injector. The following equations are common for
diesel engines:
\(SMD=4,12d\text{Re}^{0,12}\text{We}^{-0,54}\left(\frac{\mu_{f}}{\mu_{g}}\right)^{0,54}\)(6)
\(SMD=0,38d\text{Re}^{0,25}\text{We}^{-0,32}\left(\frac{\mu_{f}}{\mu_{g}}\right)^{0,37}\left(\frac{\rho_{f}}{\rho_{g}}\right)^{-0,47}\)(7)
\(SMD=8,7\left(\text{Re}_{l}\text{We}_{l}\right)^{-0,28}d_{0}\) (8)
where Re and We are respective Reynolds and Weber numbers,µ – fuel dynamic viscosity (Pa·s), ρ – density (kg/m3),d0 is the diameter of injector’s opening (m).
Index “f “ denotes “fluid” and “g ” denotes “gas”.
In addition to the abovementioned sources there are other authors \cite{Kim09,ORo81,Mar01,Arc97,Mar84}, who
give a theoretical and experimental assessment of SMD in their
work. Results are mostly given as functions of time and distanceSMD = f(t ) and SMD = f(x ) as the sprayed
fuel drops constantly change their size (coalescence, reflexive
separation and stretching separation with satellite drops). TheSMD values of these works remain in the range of 40–100 μm.
- Hybrid breakout model (WAVE)
The size of fuel drops changes continuously after leaving the injector
depending on ambient temperature, drop’s velocity, distance etc. The
size and their change can be described using the WAVE (hybrid breakout)
models. The WAVE models can be used to describe breakout of various
biofuels (HVO, FAME) and the size of their drops in the fuel spray.
The breakout of fuel spray that has left the injector takes place in two
stages. First, the fuel is sprayed into drops (primary breakout). Then,
the drops break out once again due to aerodynamic forces (secondary
breakout) \cite{Gui09,Kek14,Str16,Xia17,Str161}. This dual-stage process can be described according to hybrid
breakout model of drops (Fig. 4).