# Equivalent Simulation Study of Delta-Rotor Engine
## 3 Combustion Process Equivalence  
In conventional engine simulation modelling, to simplify the combustion model, the EngCyclCyclCombDIWebe (direct injection diesel engine Wiebe model), or the EngCyclCombSIWebe (spark plug Wiebe combustion model), the Wiebe probability density function is often used to define the in-cylinder combustion process. The former is mainly used for simulating the combustion heat release rate of direct injection compression ignition engines, while the latter is mainly used for simulating the combustion heat release rate of intake of premixed ignition engines. This combustion model assumes that the mixed gas in the cylinder is burned as a percentage and that its heat release rate generally behaves as a uniform change curve, as shown in Figure 3a. However, triangular rotor engines are limited by their combustion chamber structure, and it is difficult to achieve uniform combustion. Figure 4 shows the flame distribution cloud diagram of the cylinder for different eccentric shaft rotation angles ([PERSON] et al., 2020) [24]. It can be seen from the figure that after ignition starts, the fire core was formed from the ignition cavity and continued to develop into the combustion chamber, eventually forming a stable combustion flame surface. The flame spread slowly during the early development of the fire core. As the flame spread area increased, the flame spread speed also increased significantly. Because of the unidirectional flow field in the cylinder, it was difficult for the flame to propagate to the rear end of the combustion chamber, which resulted in an unburned area at the rear end. This combustion mode generated the typical heat release rate curve of a triangular rotor engine, as shown in Figure 3b. The heat release rate curve shows a decreasing trend at the end of combustion. The difference in the combustion process is the main reason for the inconsistency between the equivalent model and actual engine performance parameters, such as the cylinder temperature. To improve the simulation accuracy, the in-cylinder working process of a rotary engine was equated to two uniform combusions instead of one combustion. The heat release rate distributions of the two combustion processes were based on the three-parameter Weibull function shown in Equation (11). In the equation, \(p_{n}\) is the shape parameter of the nth combustion, which determines the offset direction of the heat release rate distribution; \(\gamma_{n}\) is the position parameter of the nth combustion, which determines the centre position of the heat release rate distribution; \(\beta_{n}\) is the scale parameter of the nth combustion, which determines the steepness of the heat release rate distribution. The two combusions were independent of each other, and the total heat release rate in the cylinder was the sum of the heat release rates of the two combusions. Figure 5 shows the combustion heat release rate used in this study. It can be seen from the figure that the heat release rate curve is consistent with the common heat release rate curve trend of the rotary engine shown in Figure 3b. Suppose that the total heat releases of the two combustions are \(HR_{1}\) and \(HR_{2}\). Combined with relevant research and analysis, the \(\frac{HR_{1}}{HR_{2}}\) of the triangular rotor engine under different working conditions is between 6.5 and 7.5, and the difference between the centre positions of the heat release rate distribution of the two combustions is between 65\({}^{\circ}\) CA and 90\({}^{\circ}\) CA. Figure 6 shows the calculation flowchart of equivalent heat release rate. \[f_{n}(\alpha,p_{n},\beta_{n},\gamma_{n})=\frac{p_{n}}{\beta_{n}}\left(\frac{ \alpha-\gamma_{n}}{\beta_{n}}\right)^{(p_{n}-1)}e^{-(\frac{\alpha-\gamma_{n}} {\beta_{n}})^{p_{n}}}n=1,2. \tag{11}\]  
Figure 4: Cloud map of flame distribution inside the cylinder. Figure 5: Heat release rate of combustion model. Figure 3: Heat release rate curve. (**a**) Heat release rate for Wiebe combustion model. (**b**) Typical heat release rates for rotary engines.