## 4 Results and Discussion
### Steady-State Analysis
#### 4.1.3 Phase 3: Reinstating WG to Control Exhaust Manifold Pressure  
Turbine Size: WG Area Balance Study  
The first part of this phase includes a DoE study for investigating the benefits on the engine's maximum power and energy recovery for a smaller turbine (multipliers less than 1.3) and the WG valve open at different positions (smaller than the original model), as shown in Table 6.  
The results in Figure 16 show that with a 20% larger turbine (rather than 30%) and the WG valve open at half the size as the baseline engine, maximum engine torque can be achieved. The smaller turbine and the open WG reduced the maximum amount of energy harvested at high speeds from 18 down to 12 kW. However, the benefit on the low-speed side of the map was relatively low, as the amount of energy that needs to be provided by the motor at 1600 rpm went from 0.6 down to 0.45 kW. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Case**} & **Turbine Size Compared to the** & **WG Area Compared to the** \\  & **Original Model** & **Original Model** \\ \hline Turb\(\times\)1.1–WG/2 & 10\% larger & 50\% smaller \\ Turb\(\times\)1.1–WG/3 & 10\% larger & 67\% smaller \\ Turb\(\times\)1.2–WG/2 & 20\% larger & 50\% smaller \\ Turb\(\times\)1.2–WG/3 & 20\% larger & 67\% smaller \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Phase 3: DoE analysis for different turbine sizes and WG areas. Figure 14: Phase 2: Motor-generator average energy for the case with original compressor, 30% larger turbine and the WG valve completely shut; negative values indicate energy harvesting; positive values indicate the need for energy provision; the blue line represents the maximum torque line of the baseline engine’s model as provided by the manufacturer (\(\lambda<1\)); the \(\bigotimes\) symbol indicates limit violation; \(\square\) indicates energy provision area. Figure 15: Effect of compressor’s size on average power and torque: (**a**) 1600 rpm; (**b**) 5800 rpm. Smaller Turbine: Increased WG Area Study  
Despite the fact that a large turbine allows energy harvesting within the pre-turbine pressure limit at the high speed and load conditions, it also leads to low speeds and loads' poor performance. This could be theoretically resolved by implementing a small turbine and controlling the pre-turbine pressure limits by increasing the wastewater area. The following DoE study results show the effects of three compressors smaller than the original (multipliers of 0.7 to 0.9) and the WG area open at values 10% to 50% larger (multipliers of 1.1 to 1.5) than in the baseline engine. The results in Figure 17 illustrate that a small turbine can lead to lower energy demands and power generation at low speed/load conditions. However, the smaller the turbine, the higher the pre-turbine pressures, which deteriorate the engine's power output at full load conditions. By increasing the WG area, the pre-turbine pressure drops, and therefore, the full load performance of the engine increases. However, even a 10% increase in the WG area leads to high levels of energy requirements for meeting the baseline engine's power characteristics. Figure 16: Balance study for different turbine sizes and wastegate areas for meeting the baseline engine’s maximum torque. Figure 17: Phase 3: DoE analysis of the motor-generator average energy for different turbine sizes and WG areas; negative values indicate energy harvesting; positive values indicate need for energy provision; blue line represents the maximum torque line of the baseline engine’s model as provided by the manufacturer (\(\lambda<1\)); \(\bigotimes\) symbol indicates limit violation; \(\square\) indicates energy provision area. Smaller Turbine: Increased Pre-Turbine Pressure Study  
The next study in phase 3 focuses on the effects of a smaller turbine with a reduced WG area compared to the baseline engine for benefiting from a good energy balance across the low and high load areas of the engine's speed/load map.