## 3 Case Study
### Assessment of the Emissions Abatement at the Cold Start  
The behavior and the potential of the curved POCS application as a pre-catalyst are investigated through an assessment of its performances under simplified cold start conditions. The proposed structure was designed to be suitable for the application of an electrical circuit, so that an EHC-POCS could be obtained. In particular, two different materials were employed: steel for the inner and outer pipes and silicon carbide for the struts. As such, the characteristic behavior of a light bulb is achieved; and the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Species** & **C3H6** & **C3H8** & **CO2** & **H2O** & **N2** & **O2** & **CO** & **H2** & **NO** \\ \hline - & 0.0039 & 0.0020 & 0.1635 & 0.0718 & 0.7170 & 0.0320 & 0.0082 & 0.0007 & 0.0009 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Exhaust gases species concentrations: Mass fractions. difference in terms of the electrical conductivity of the two materials (\(10^{7}\) and \(10^{2}\) S/m, respectively) is such that the electrical current flows through the whole length of the inner pipe (connected to the power supply), and then it starts to propagate through the POCS struts. As briefly addressed in the previous section, the inner pipe is extended towards the outside of the duct, while insulating material is interposed between the inner pipe and the exhaust manifold to avoid gas leaks and to preserve the integrity of the electrical circuit. To verify the effects of the electrical current on the POCS temperature, a sensitivity analysis on the applied potential difference (1, 10, 20, 30 and 38 V) was carried out for a total of five seconds. The upper limit is set to be representative of the maximum potential difference that is available from the common battery of a traditional vehicle for the application under investigation. The CFD framework is applied and the performed simulations consist only of the two different solid regions, duct and struts, respectively. The employed mesh is created similarly to the reference computational grid (B-curved version, whose details are presented in Table 2) and were employed for the pressure difference investigation. Once the effects of Joule heating were verified, simplified cold start conditions were considered. The assessment was carried out on an exhaust line equipped with two different catalysts. Four different domains were included in the multi-region simulation framework, whose details were reported in Table 4.  
A schematization of the considered exhaust line is reported in Figure 6. The fluid region describes the exhaust gas flow, the two three-way catalysts account for the presence of the two different catalytic converters while the solid region describes the solid walls of the line. The time-varying boundary conditions for a total of twenty seconds are assigned at the inlet of the exhaust manifolds, imposing the values of the exhaust gas mass flow rates and temperatures. The imposed profiles are constructed to replicate the engine behavior at cold start, where the cranking phase influences the exhaust gases' features. After an initial period of approximately ten seconds, the engine is supposed to reach a steady-state condition of approximately 130 kg/h of exhaust gases with a temperature equal to 1273.5 K.  
The imposed profiles at the inlet of each exhaust manifold, in terms of temperature and mass flow rate, are reported in Figure 7. The imposed chemical species concentrations are kept constant and equal to the values reported in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Region** & **Fluid** & **CAT1** & **CAT2** & **Solid** \\ \hline Cells number & \(17.65\cdot 10^{6}\) & \(0.42\cdot 10^{6}\) & \(0.57\cdot 10^{6}\) & \(6.28\cdot 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Assessment of the emissions’ abatement at the cold start: computational domain details. Figure 6: Assessment of the emissions abatement at the cold start: exhaust line schematization. Four different simulations are considered.