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.
  1. 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).