*4.1. Steady-State Analysis*

### 4.1.1. Phase 1: WG Enthalpy Loss Study (Baseline Engine)

The results in Figure 12 show that the energy loss through the wastegate for the model with the original size of compressor and turbine (Case 9) can reach the amount of 5 kW at high engine speeds and loads. The amount of the potential energy dismissed at medium load and engine speed conditions is of lower magnitude, up to 2 kW. At low loads and speeds, there is no wasted energy, as the WG is completely closed.

**Figure 12.** Phase 1: DoE analysis of the waste-gated enthalpy loss for the different compressor and turbine sizes; the blue line represents the maximum torque line of the baseline engine's model as provided by the manufacturer (λ < 1); the - symbols indicate data points; the # symbol indicates a limit violation at specific points.

Figure 12 highlights the effect of a smaller turbine and compressor on the amount of waste-gated flow and the maximum power of the engine. As can be seen, a smaller compressor (Cases 7 and 8) cannot provide the boosting requirements needed to achieve maximum engine's power at medium and high engine speeds. On the other hand, a smaller turbine (Cases 3 and 6) can slightly increase the amount of waste-gated flow at medium engine speed and load conditions. However, a smaller turbine leads to increased pre-turbine pressure, in some cases violating the maximum limit set, and reduces the maximum torque of the engine.

### 4.1.2. Phase 2: Suppressing WG and Using e-Turbo to Control Boosting

Suppressing the wastegate of an engine leads to extremely high pre-turbine pressures at medium to high loads. Figure 13 presents the pre-turbine pressures and peak engine torques achieved for various turbine sizes and the wastegate valve closed. As shown from the figure, a turbine 30% larger than the original size can provide or even increase the maximum power targets of the baseline engine without violating the pre-turbine pressure limit. A torque deficit occurs at 1000 rpm, but this is mainly due to a poor model convergence at this specific engine speed near the surge line and not the incapacity of the engine to achieve the targeted torque.

**Figure 13.** Engine's performance results for various turbines sizes and the wastegate completely shut: (**a**) pre-turbine pressure; (**b**) engine torque.

The results in Figure 14 show that with this configuration, extremely high amounts of energy, more than 15 kW, can be harvested at high engine speeds and loads. The system can harvest energy up to 10 kW at medium to high engine speeds. However, as can be seen, the larger turbine results in considerable amounts of energy that need to be provided by the motor for meeting, if possible, the targeted maximum torque at low engine speed conditions. This is happening due to the lower pre-turbine pressures and increased turbocharger's inertia at a non-boosting area of the engine's map.

The next stage in this phase was to investigate the potential of reducing the amount of energy needs to be provided by changing the compressor's size. For this reason, five different compressors (multipliers of 0.8 to 1.2) were tested, and the results are presented in Figure 15.

It is clearly shown in Figure 15 that a small compressor could reduce the power level needs to be provided by the motor from 0.6 down to 0.2 kW at 1600 rpm with no effect on the engine's maximum torque. However, a smaller compressor would also reduce the amount of energy that can be harvested (from 18.5 down to 17 kW) at high engine speeds; but foremost, it would struggle to meet the maximum engine's torque demands.

**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 (λ < 1); the # symbol indicates limit violation; Ⴖ indicates energy provision area.

**Figure 15.** Effect of compressor's size on average power and torque: (**a**) 1600 rpm; (**b**) 5800 rpm.

### 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.

**Table 6.** Phase 3: DoE analysis for different turbine sizes and WG areas.


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.

**Figure 16.** Balance study for different turbine sizes and wastegate areas for meeting the baseline engine's maximum torque.

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 wastegate 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 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 (λ < 1); # symbol indicates limit violation; Ⴖ 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. For this study, the WG area is controlled indirectly by setting up a PID controller between the WG valve and the pre-turbine pressure. The targeted value is the pre-turbine pressure, which is set to increased values of 5%, 10% and 15% (multipliers of 1.05 to 1.15) compared to the baseline engine, but always within the set pre-turbine pressure limit.

Figure 18 shows that for a 10% smaller turbine (multiplier of 0.9) than the baseline engine, the e-turbo can harvest energy (up to 4 kW) at most points of the map, except the 1000 rpm speed, where the results are not highly trusted due to non-convergence of the model. Although, the increased pre-turbine pressure leads to increased energy harvesting levels, it also, as expected, reduces the maximum power output of the engine. A 5% pre-turbine pressure increase leads to a 5% penalty on the engine's maximum torque, while for the case with the pre-turbine pressure set at 15% higher, the torque penalty is around 10%.

**Figure 18.** Phase 3: DoE analysis of the motor-generator average energy for different turbine sizes and pre-turbine pressures; 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 (λ < 1); the # symbol indicates limit violation; Ⴖ indicates energy provision area.

Smaller Turbine: Variable Pre-Turbine Pressure Study

The previous study showed that with the right component sizing, energy harvesting could be achieved across most of the speed/load map area of the engine. However, this leads to torque sacrifice at full load conditions. This penalty can be reduced or even eliminated by adjusting the targeted pre-turbine pressure of the engine when running at full load conditions. The present study shows the effects of various pre-turbine targeted values, larger and smaller than the baseline engine, to the maximum power output of the engine and the average power harvested or that needs to be provided by the motor-generator.

As is shown in Figure 19, at full load conditions, the maximum power output of the baseline engine can be met by running the engine at the original pre-turbine pressures or slightly lower. However, this leads to energy provision demands by the e-turbo of up to 2 kW. Higher power outputs, which often work as selling points for automotive manufacturers, can be achieved by running at lower pressures and providing significant amounts of power to the compressor.

**Figure 19.** Effect of pre-turbine pressure % change on: (**a**) engine's torque at full load; (**b**) M/G performance at full load; negative values indicate energy harvesting.
