## 3 Results and Discussion  
### Steady State (Low-End Torque)  
This study focuses on the VGO impact on the low-end torque, using the developed and validated engine-TC model. Simulations are performed at 1000 and 1500 RPM in this section. The methodology followed consists of performing iso-boundary and iso-AFR (Air to Fuel Ratio) calculations; hence, the differences arising would be solely attributed to compressor performance differences. The VGT is imposed to follow a sequence of steps, with sufficient time between each step, to guarantee stabilization. Each stage corresponds to another 1% VGT closure. Consequently, it would be possible to identify within a 1% VGT resolution the variables that imply the boost limitation and the corresponding performance. Figure 10A represents the procedure explained for the VGT management, and the resulting boost pressure sequence is plotted in Figure 10B.  
Following this line of investigation, thermomechanical limitations are identified for each compressor configuration and engine speed. In the example of 1500 RPM and TC\(-\)1 (in both configurations), it is shown that TC speed limitation (see Figure 10C) and turbine inlet pressure (see Figure 10D) were under safe operation. Furthermore, at 1500 RPM, the  
Figure 10: VGT management for extended boost study and resulting boost pressure. Cases dealing with TC\(-\)1, 1500 RPM, closed and open configuration: VGT actuator (**A**), Boost pressure (**B**), Turb-bocharger Speed (**C**), Turbine inlet pressure (**D**), Compressor outlet temperature (**E**), and BMEP (**F**).  
surge margin was far from being reached. The compressor outlet temperature was the unique limitation for both configurations, as observed in Figure 10E, where both series approach the thermo-mechanical constraint (dashed string). Having reached the value of 205 \({}^{\circ}\)C, the boost achieved by the open configuration is about 2.9, while the closed is about 2.87. BMEP figures are 27.75 and 27.32 bar, respectively.  
In this case, the limitation for TC\(-1\) is the same as in the experiments: the compressor outlet temperature. However, at this point, the differences are only motivated by the compressor configuration and not by the boundary conditions, which are assumed to be the same for both simulations. These differences originated from the compressor efficiency maps. At the selected \"maximum performance points\", the open configuration provides 0.35% higher efficiency, which is the reason why a slight boost is achieved for the same T2 limitation.  
The same analysis is repeated for 1000 RPM; however, in this case, the limitation is the surge phenomena, which appears sooner for the open configuration, imposing a more restrictive boost (1.44 bar) compared to the closed setup maximum boost (1.53 bar). In BMEP terms, the expected improvement is about 0.94 bar (from 13.05 bar to 13.99 bar). A summary of the best performance and the limitation for each configuration is included in Table 5. Compared to the experimental differences in Figure 3, differences are slightly more significant here than in the experiments, due to the iso-boundary conditions, which do not favor the open configuration, unlike in the experiments (where a cooler environment occurred).  
Similar conclusions are identified for the TC\(-2\) but with slightly different absolute results, which gives an idea of the robustness of the findings achieved for TC\(-1\). A summary of the results for TC\(-2\) is included in Table 6. To sum up, in the TC\(-2\), at 1000 rpm, 0.72 bar BMEP improvement in the closed configuration is found, whereas a decline of 0.37 bar BMEP is found at 1500 RPM.  
This all shows that a potential benefit of 0.94 bar can be expected, but only at low engine speeds. It would be interesting to identify the transition from closed to open configuration in the engine map since, at some point, it may represent a decline. This would be expected to happen between 1000 and 1500 RPM.