## 2 Materials and Methods
### Numerical Procedure
#### 2.2.2 Governing Equation  
In the computational fluid domain of a typical heated surface in the fishing vessel's engine room, the whole calculation process follows the basic equations of mass conservation, momentum conservation, and energy conservation. According to the law of mass conservation, the mass increment of the fluid in the computational domain should be equal to the difference between the mass of inflow and the mass of outflow. Based on this, the integral form of fluid flow continuity equation is deduced as Equation (1). The first term on the left of Equation (1) represents the increment of mass inside the control body, and the second term represents the net flux from control surface into the control body. \[\frac{\partial}{\partial t}\iiint_{\mathrm{V}}\rho\mathrm{d}x\mathrm{d}y \mathrm{d}z+\iint_{\mathrm{A}}\rho v\cdot\mathrm{ndA}=0 \tag{1}\]  
where V is the control body, m\({}^{3}\): A is the control surface, m\({}^{2}\); \(\rho\) is the density, kg/m\({}^{3}\); \(v\) is the flow velocity of the leaking marine oil, m/s; \(t\) is the time, s.  
The motion equation involved in the process of igniting marine oil on the heated surface in the fishing vessel's engine room is the momentum conservation equation, which represents that the time rate of change of momentum in the system is equal to the sum of the external forces acting on it, as shown in Equation (2). \[ \begin{cases}\rho\frac{\mathrm{d}u}{\mathrm{d}t}=\rho F_{bx}+\frac{\partial p _{xx}}{\partial x}+\frac{\partial p_{yx}}{\partial y}+\frac{\partial p_{xx}}{ \partial z}\\ \rho\frac{\mathrm{d}v}{\mathrm{d}t}=\rho F_{yy}+\frac{\partial p_{xx}}{ \partial x}+\frac{\partial p_{yy}}{\partial y}+\frac{\partial p_{yy}}{ \partial z}\\ \rho\frac{\mathrm{d}w}{\mathrm{d}t}=\rho F_{bz}+\frac{\partial p_{xz}}{ \partial x}+\frac{\partial p_{yx}}{\partial y}+\frac{\partial p_{zz}}{ \partial z}\end{cases}  \tag{2}\]  
where \(F\) is the component of mass force per unit mass on fluid in three directions, N/kg; \(p\) is the component of the internal stress tensor of fluid. The fluid motion of leaking marine oil on a heated surface follows the first law of thermodynamics, so its energy equation can be shown in Equation (3). As defined by the turbulence model used in the numerical calculation, \(J_{\mathrm{f}^{\prime}}\) is the diffusion flow of component \(j\). \(S_{\mathrm{h}}\) covers the chemical reaction heat and other customized volumetric heat source  
Figure 2: Geometrical modeling of fishing vessel’s engine room by CFD-based tool. terms. The first three terms on the right of Equation (3) describe energy transport by heat conduction, component diffusion, and viscous dissipation, respectively. \[\frac{\partial}{\partial t}(\rho E)+\frac{\partial}{\partial x_{i}}(u_{i}(\rho E +p))=\frac{\partial}{\partial x_{i}}\left(k_{\text{eff}}\frac{\partial T}{ \partial x_{i}}-\sum_{j}h_{j}J_{j}+\ u_{j}\big{(}\tau_{ij}\big{)}_{\text{eff} }\right)+\ S_{\text{h}} \tag{3}\]  
\[E=h-\frac{p}{\rho}+\frac{u_{i}^{2}}{2} \tag{4}\]  
where \(k_{\text{eff}}\) is the effective heat transfer coefficient; \(k_{\text{t}}\) is the turbulent heat transfer coefficient, W/m\({}^{2}\cdot\)K.  
The leaked marine oil in the fishing vessel's engine room absorbs the heat transferred by the high-temperature heated surface after being converted from liquid to vapor, during which a phase transition occurs. The model computed the numerical simulation of the phase transition processes, following the principles below. * Regarding the evaporation process of leaked marine oil (\(T_{l}\geq T_{\text{sat}}\)), the mass transfer rate of phase transition is shown in Equation (5). \[\dot{m}_{\text{lv}}=coeff\cdot\alpha_{\text{l}}\rho_{\text{l}}\frac{(T_{\text{ l}}-T_{\text{sat}})}{T_{\text{sat}}}\] (5)
* Regarding the condensation process of leaked oil (\(T_{\text{v}}<T_{\text{sat}}\)), the mass transfer rate of phase transition is shown in Equation (6).