# Impacts of Micro-Deviations of Aperture on the Characteristics of Collision Atomization Field
## 2 Theoretical Background  
Cavitation indicates the phenomenon of violent vaporization on the liquid surface and inside by curtailing the local liquid pressure to lower than the saturated vapor pressure under constant temperature [25; 26; 27; 28]. With the increase in internal and external pressure distinction and flow velocity, the cavitation flow field in the orifice will present four contrasting states, as shown in Figure 1. When the pressure reaches the critical value of cavitation, bubbles emerge at the inlet of the nozzle, generating the initial stage of cavitation (Cavitation inception, see Figure 1a). When the injection pressure increases, the cavitation domain in the nozzle progressively extends to the nozzle outlet (Cavitation growth, see Figure 1b), until it expands to the orifice outlet and forms super-cavitation (Super cavitation, see Figure 1c). When the pressure increases further, the flow field in the orifice will develop into an advanced state (Hydraulic flip, see Figure 1d). Under the condition of flip flow, the vapor outside the nozzle will pour back into the nozzle, occupying the original cavitation area, with the severe bubble phenomenon disappearing. Instead, a slim membrane of vapor adheres to the inwall of the nozzle separating the liquid, which decreases the passage area in the orifice, and enormously diminishes the flow coefficient (the mass flow rate of the fluid flowing through the orifice in unit time and under constant pressure). A more considerable flow coefficient initiates a narrower pressure loss when the fluid flows through the nozzle, which reflects the nozzle performance more critically.  
The state of cavitation effect determines that of the jet, therefore encountering the critical pressure of cavitation effect and evaluating the state of cavitation effect for the stability and atomization characteristics of direct injection nozzle appear extremely significant. There are two considerable demarcation points for the reversal of cavitation effect state: cavitation inception and hydraulic flip. The critical pressure of these two stages divides the jet into stable and unstable states. When the jet pressure is less than the initial critical pressure of cavitation, there is no cavitation in the orifice with a stable jet. The cavitating flow will conversely develop into a jet which represents instability.  
The parameters characterizing the cavitation effect in the orifice are cavitation coefficient \(K\) and discharge coefficient \(\mathrm{C}_{d}\), which are expressed as  
\[K=\frac{P_{in}-P_{v}}{P_{in}-P_{out}}(P_{in}\
eq P_{out}) \tag{1}\]  
\[\mathrm{C}_{d}=\frac{\dot{m}}{A\sqrt{2\rho_{l}(P_{in}-P_{out})}}(P_{in}\
eq P_ {out}) \tag{2}\]  
where \(P_{in}\), \(P_{out}\) and \(P_{v}\) are the injection pressure, ambient pressure and saturated vapor pressure, respectively (KPa). Moreover, \(\dot{m}\) is the mass flow (g/s) and \(A\) is the cross-sectional area of the orifice (cm\({}^{2}\)).  
The cavitation coefficient reflects the relationship between the internal and external pressure distinction and the saturated vapor pressure and determines the length of the cavitation area. The narrower the cavitation coefficient, the more conducive to cavitation. The bubbles generated by cavitation will occupy the internal capacity of the orifice and narrow the flow channel, affecting the discharge coefficient, which signifies the mass flow of fluid medium through the orifice in a unit time and under constant pressure. The increase in the flow coefficient provokes the decrease in pressure loss when fluid flows through the nozzle, which reveals the performance of the nozzle effectively.