# An Electric Load Simulator for Engine
## 3 Load Characteristics of the Exhaust Valve
### 3D Numerical Simulation  
The 3D engine model was established for numerical simulation, which included the cylinder, piston, exhaust valve, and exhaust port, as shown in Figure 5a. The specific technical parameters of the engine are shown in Table 4.  
The intake port was always closed because only the exhaust stroke of the engine was considered. In the process of dividing the grid, the exhaust valve and piston were set to move to simulate the actual exhaust stroke of camless valvetrains. The refined regions of the moving parts are shown in Figure 5b. The operating mode of the engine had four strokes, which included the work stroke, exhaust stroke, intake stroke, and compression stroke. The displacement curve of the piston is shown in Figure 6. The exhaust stroke of the 3D engine model was simulated to obtain the gas force characteristics of the exhaust valve. The piston moved from the bottom dead center to the top dead center. In the camless engine model, the valve and valve actuator were coupled to each other. The valve actuator drove the valve to move. By controlling the movement of the valve actuator, it is possible to control the displacement curve of the valve. In order to improve the division accuracy and solution speed of the moving mesh, the displacement curve was simplified. The actual curve and simplified curve of the valve actuator during the exhaust stroke are shown in Figure 7. The maximum displacement of the valve was set to 8 mm, and the transition time was 5.76 ms when the exhaust valve was fully open. The exhaust stroke piston moves for 25 ms in Figure 6. The process from closing to full opening of the exhaust valve was 5.76 ms. We mainly studied the gas physical force during the process from opening to full opening of the valve, during which the gas physical force will constantly change due to the change of displacement, which is our research content. \begin{table}
\begin{tabular}{c c} \hline
**Type** & **Single Cylinder, Four-Stroke** \\ \hline Bore & 80 mm \\ \hline Stroke & 70 mm \\ Cylinder volume & 352 mL \\ Compression ratio & 10.63:1 \\ Valve lift & 8 mm \\ \hline \end{tabular}
\end{table} 
Table 4: Technical parameters of the engine. Figure 5: 3D model of the engine in the exhaust stroke. (**a**): The 3D engine model; (**b**): The refined regions of the moving parts. In the process of setting solution conditions, the fluid properties were set to air. The transport equation for the standard \(k-\varepsilon\) wall function was set as Equations (3)-(4) to optimize the laminar flow area. \[\frac{\partial}{\partial t}(\rho k)+\frac{\partial}{\partial x_{i}}(\rho ku_{i} )=\frac{\partial}{\partial x_{j}}[(\mu+\frac{\mu_{i}}{\sigma_{k}})\frac{ \partial k}{\partial x_{j}}]+G_{k}+G_{b}-\rho\varepsilon-Y_{M}+S_{K} \tag{3}\]  
\[\frac{\partial}{\partial t}(\rho\varepsilon)+\frac{\partial}{\partial x_{i}}( \rho\varepsilon u_{i})=\frac{\partial}{\partial x_{j}}[(\mu+\frac{\mu_{i}}{ \sigma_{\varepsilon}})\frac{\partial\varepsilon}{\partial x_{j}}]+C_{1 \varepsilon}\frac{\varepsilon}{k}(G_{k}+C_{3\varepsilon}G_{b})-C_{2 \varepsilon}\rho\frac{\varepsilon^{2}}{k}+S_{\varepsilon} \tag{4}\]  
where \(k\) is turbulent kinetic energy; \(\varepsilon\) is the dissipation rate; \(G_{k}\) is turbulent kinetic energy generated by the average velocity gradient; \(G_{b}\) is turbulent kinetic energy generated by buoyancy; \(Y_{M}\) is the expansion dissipation rate; \(C_{1\varepsilon}\), \(C_{2\varepsilon}\), and \(C_{3\varepsilon}\) are constants; \(\sigma_{k}\), \(\sigma_{\varepsilon}\) are the turbulent Prandtl number of \(k\) and of \(\varepsilon\); \(S_{K}\), \(S_{\varepsilon}\) are user-defined source terms. Figure 6: Four-stroke operation mode of the engine. Figure 7: Displacement curve of the exhaust valve. Set the turbulent and turbulent energy lengths of the system according to Equations (5)-(7). \[\text{Turb.kin.energy}=1.5*(u^{2}) \tag{5}\]  
\[\text{Turb.length.scale}=H/2 \tag{6}\]  
\[u=1.4*h*(n/60) \tag{7}\]  
where \(n\) is engine speed; \(H\) is the maximum valve lift; \(h\) is the piston stroke.