## 2 Materials
### 1D Modelling  
The model used for the application is developed using Virtual Engine Model (VEMOD) [47], internal software developed at CMT-Motores Termicos, for visualizing the engine performance. The software groups elements as 0D or 1D elements depending on the spatial dimensions. In 0D elements, all the properties inside the element are constant, while in 1D elements, thermofluid dynamic properties vary with the length of the element. These 1D elements are used as intake and exhaust lines, and when the length-to-diameter ratio is high enough, the flow inside the element is fully developed. So, the most important axis for the flow movement is the X-axis--significantly reducing the calculation time, as the Y and Z axes are not relevant. This led to the proposal of a hyperbolic system of partial differential equations of simplified 1D Euler equations for unsteady compressible non-homentropic flow [47]. The software is assessed for several engine models, and results are compared with experimental data to validate the model. The results for its accurate prediction can be observed in [48]. The engine model, in addition to the pipes, also includes connections, valves, cylinders, and plenums. These elements are used for modeling the novel engine with a 0D-1D approach. The developed model uses design data for its geometry and experimental results to validate engine performance, as will be described in the model validation sub-section. Figure 1 gives information on the major details of the engine. The major parts are the need valve, air pump, exhaust, intake ports, and main engine block consisting of a piston and combustion chamber. The engine block developed in the model assessment uses an opposed two-stroke engine, whose cylinder is considered as a 0D element. The piston position is set by comparing the volume of the combustion chamber with experimental results. Each major element is controlled by a sub-model considering the piston position. These include the air pump volume, and the opening and closing of intake and exhaust ports. Several sensors capture necessary information on mass flow rate, volume, pressure, and temperature inside the cylinder and pipes. The information gathered is then used to develop the sub-systems for control of piston position, air pump volume, port openings and closings, and need valve petal opening. The modeling details of the sub-systems are as follows. A discharge coefficient is used for the intake and exhaust port openings and closings, and is a function of the piston position. The discharge coefficient of the ports is calibrated to attain the instantaneous mass flow rates obtained in the CFD simulations. From Figure 1, it can be seen that the volume of the air pump changes with the piston position. For this reason, the air pump is modeled as a variable volume. The need valve petal is assumed to be a punctual mass concentrated in the petal tip. The lift follows the classical mass-spring-damper model, where the external force depends on the pressure difference upstream and downstream of the valve. The force balance equation is used to deduce the tip lift given by:  
\[\text{F}=\text{m}\ddot{\text{x}}-\text{ b}\ \dot{\text{x}}-\text{ k}\text{x}, \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exhaust Layout** & & **Pipe Details (mm)** & **Speed (rpm)** & **Load** \\ \hline Config 1 & 1. & Exhaust manifold with tapered tailpipe & 2500 & Full Load \\
2. & Long Pipe\(-1\) (380 \(\times\) 33.5) & & & \\
3. & Silencer (180 \(\times\) 35) & & & \\
4. & Long Pipe\(-2\) (650 \(\times\) 33.5) & & & \\ \hline Config 2 & 1. & Exhaust manifold with tapered tailpipe & & \\
2. & Long Pipe\(-1\) (274.5 \(\times\) 35) & & & \\
3. & Silencer (280 \(\times\) 109)\(-2\) units & & & \\
4. & “U” Pipe (213 \(\times\) 35) & & & \\
5. & Long Pipe\(-2\) (385 \(\times\) 35) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Exhaust manifold configuration at different speeds and load conditions.