# Equivalent Simulation Study of Delta-Rotor Engine
## 4 Establishment and Verification of Equivalent Model  
This study used MATLAB R2016b to build various mathematical models, GT-SUITE V7.5 to build equivalent simulation models, and CONVERGE 3.0 to build three-dimensional simulation models. The running environment of these software were Win10, and the workstation configuration was as follows: Intel C621 series chipset; Intel Xeon Gold 6145 processor, 40 cores and 80 threads, a main frequency of 2.0 GHz, a maximum turbo frequency of 3.7 GHz; 128 GB of memory, NVIDIA GT1030, and two GB graphics card. In this study, a single-cylinder gasoline rotary engine was used for research and verification. The structural parameters of the rotary engine are listed in Table 1. This is a small rotary engine that uses gasoline as fuel, premixed with an intake port and ignited by a single spark plug. It is generally used as a power unit for long endurance unmanned aerial vehicles and cruise missiles, with an output power of 12.3 kw and a working speed of 8000 revolutions per minute. To verify the correctness and accuracy of the equivalent one-dimensional simulation model proposed in this study, CONVERGE was used to establish a three-dimensional simulation model in combination with the relevant boundary conditions, and the curves of the cylinder volume, temperature, pressure, and mass were extracted to verify the equivalent one-dimensional simulation model. The solid and computational fluid domain models established based on these parameters are shown in Figure 7. Based on the previous two sections, the equivalent simulation model established in combination with engine-related parameters is shown in Figure 8 ([PERSON] et al., 2023; [PERSON] et al., 2024; [PERSON] et al., 2021) [26; 27; 28]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Creation radius (mm) & 60 \\ Eccentricity (mm) & 10 \\ Rotor width (mm) & 42 \\ Translational distance (mm) & 1.45 \\ Speed (r/min) & 8000 \\ Single cylinder volume (cc) & 133 \\ Compression ratio & 10 \\ Ignition advance angle & 30\({}^{\circ}\) BTDC \\ Ignition source & Single spark plug \\ Fuel type & Gasoline \\ Jet strategy & Premixed intake duct \\ Air–fuel ratio & 1 \\ Ignition diameter (mm) & 8 \\ Ignition energy (J) & 0.08 \\ Engine power (kw) & 12.3 \\ Torque (N.m) & 15.66 \\ Oil consumption (g/kw.h) & 402.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rotor engine structure parameters. Figure 7: 3D model. Figure 9: Comparison of cylinder volume. Figure 10: Comparison of cylinder pressure. Figure 11: Comparison of cylinder temperature. Figure 12: Comparison of cylinder mass. To further verify the accuracy of the one-dimensional equivalent simulation model established in this study, the cylinder volume, pressure, and temperature curves of the one-dimensional equivalent simulation model and three-dimensional simulation model as well as the average deviation, maximum deviation, maximum relative error, and average relative error of the main working stages of the in-cylinder mass curve from \(5^{\circ}\) CA before ignition to exhaust port opening (\(-35^{\circ}\) CA to \(135^{\circ}\) CA) were calculated. The results are summarised in Table 2; the error of the equivalent model mainly occurs in the intake and exhaust stages (\(135^{\circ}\) CA to \(540^{\circ}\) CA), the deviation in the main working stage (\(-35^{\circ}\) CA to \(135^{\circ}\) CA) is small, and the maximum relative error is below 10%. The maximum deviation of the in-cylinder pressure is 0.1503 MPa (9.0314%), which occurs at \(-35^{\circ}\) CA. the maximum deviation of the in-cylinder temperature is 68.3762 K (9.7714%), which occurs at \(-35^{\circ}\) CA. The deviation of the maximum pressure in the cylinder is 0.0136 MPa (0.4572%), and the deviation of the crankshaft angle at the maximum pressure in the cylinder is 1.4004\({}^{\circ}\) CA. The average relative errors of the cylinder volume, cylinder pressure, cylinder temperature, and cylinder mass are less than 6%.