## 2 Experiment Setup and Simulation Model
### Simulation Models
#### 2.2.2 Engine Combustion and Flow Model  
There are three kinds of combustion models available for the combustion process simulation, which are non-predictive, semi-predictive, and predictive combustion models. The non-predictive and semi-predictive combustion models do not take into account the physical models in the cylinder, which is not suitable to study the variable affecting the burn rate significantly. In this investigation, the spark timing directly influencing the combustion phase varies to achieve the variable heat/electricity ratio. Therefore, the predictive combustion model and the spark-ignition turbulent flame model must be selected to study the effects of variable spark timing on the flame-propagation burning process within the cylinder. The predictive combustion model takes into account the cylinder's geometry, spark location and timing, air motion, and fuel properties for predicting the burn rate for the homogeneous charge. A two-zone combustion methodology was applied during the combustion process. As shown in Figure 3, the total cylinder volume is divided into two  
Figure 2: Full engine model in GT\(-\)Power. zones, the unburned zone and the burned zone, and is separated by the flame front. The burn rate is governed by the following four equations:  
\[\frac{dM_{e}}{dt}=\rho_{u}A_{e}(S_{T}+S_{L}) \tag{1}\]  
\[\frac{dM_{b}}{dt}=\frac{M_{e}-M_{b}}{\tau} \tag{2}\]  
\[\tau=\frac{\lambda}{S_{L}} \tag{3}\]  
\[\lambda=\frac{C_{\lambda}L_{t}}{\text{Re}_{t}0.5} \tag{4}\]  
where \(M_{e}\) is the entrained mass from the unburned zone into the burned zone through the flame front. \(T\) is the time of combustion. \(P_{u}\) is the density of the unburned mixture. \(A_{e}\) is the entrainment surface area at the edge of the flame front. \(S_{T}\) and \(S_{L}\) are the turbulent and laminar flame speeds, respectively. \(M_{b}\) is the mass of the burned mixture. \(T\) is the time constant. \(\lambda\) is the Taylor microscale length, which represents the dimension of ignition sites within the flame front. Hence, \(\tau\) represents the characteristic time scale for the burnup of a single ignition site. The Taylor microscale is computed from the turbulent integral length scale (\(L_{t}\)) according to Equation (4). \(\text{Re}_{t}\) is the turbulent Reynolds number. \(C_{\lambda}\) is a constant called the Taylor microscale multiplier. As mentioned above, the predicted burn rate is a function of turbulent and laminar flame speed. The laminar flame speed of natural gas is calculated by the following equation:  
\[S_{L}=[B_{m}+B_{\phi}(\phi-\phi_{m})^{2}](\frac{T_{u}}{T_{0}})^{\alpha}(\frac{ P}{p_{ref}})(1-2.06 EGR)^{0.77C_{EGR}} \tag{5}\]  
where \(\phi\) is the equivalence ratio, \(B_{m}\) is the maximum flame speed at equivalence ratio with value \(\phi_{m}\), \(B_{\phi}\) is the laminar speed roll-off value, \(T_{0}\) and \(p_{ref}\) are 298 K and 101,325 Pa, \(T_{u}\) and p are the temperature and the pressure in the combustion chamber, \(\alpha\) and \(\beta\), respectively, are temperature and pressure exponent, and \(C_{EGR}\) is dilution effect multiplier. EGR is the mass fraction of the residual gas, including the internal and external residual gas. The coefficients of natural for calculating the laminar flame speed are shown in Table 2. \begin{table}
\begin{tabular}{l l} \hline \hline
**Fuel** & **Natural Gas** \\ \hline \(B_{m}\) & 0.397 \\ \(B_{\phi}\) & \(-1.649\) \\ \(\phi_{m}\) & 1.061 \\ \(\alpha\) & \(5.75\phi^{2}-12.15\phi+7.98\) \\ \(\beta\) & \(-0.925\phi^{2}+2\phi-1.473\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The coefficients of natural for calculating the laminar flame speed. Figure 3: Two zone combustion methodology schematic diagram.