*3.1. Steady-State Simulations*

The steady state analysis of the model was performed in the area of three axes, compressor and turbine size and WG area, as shown in Figure 8. The purpose of the study was to understand the effects of the compressor and turbine sizing on the amount of energy that needs to be provided/harvested by the motor/generator and to identify any regions where the e-turbo can replace the wastegate for load control.

**Figure 8.** Area of investigation for the steady-state simulations.

The steady-state simulations are divided into three phases based on the type of investigation.


### 3.1.1. Phase 1: WG Enthalpy Loss Study

The first phase of the study was performed to calculate the amount of energy that is lost through the wastegate of a modern 2.0 L turbocharged gasoline engine. The amount of power loss was calculated using the equation:

$$Q = m \times c\_{\mathbb{P}} \times \Delta T\_{\prime} \tag{2}$$

where *Q* is the amount of heat to the system (power), *m* is the mass flow rate through the wastegate, *c*p is the specific heat of the gas and Δ*T* is the temperature difference.

A Design of Experiment (DoE) analysis was performed to evaluate the effects of the compressor and turbine's size on the amount of enthalpy loss, combustion limiting parameters and maximum engine power. The nine cases studied are described in Table 4.

**Table 4.** Phase 1: Design of Experiment (DoE) analysis for different compressor and turbine sizes.


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

Phase 2 of the steady-state simulations section involves the application of a motor/generator, which is directly linked to the shaft of the turbocharger. The purpose of the motor/generator is to provide or harvest energy, as needed, to/by the compressor for achieving the boosting demands of the engine. For this phase, the WG has been completely suppressed and the model run once with the original size of the compressor and turbine. However due, to the shut off of the WG valve, extremely high pre-turbine pressures violating the limits at high loads were noticed.

A sweep study was performed for five different turbine sizes (10% to 50% larger) to evaluate the optimum turbine size for the model without a WG valve. Then, the optimum turbine was tested for different compressor sizes (20% smaller to 20% larger) to evaluate its effect on the energy harvesting/provision requirements.

3.1.3. Phase 3: Reinstating WG to Control Exhaust Manifold Pressure

Phase 3 of the steady-state simulations involves the reinstatement of the WG valve for reducing the required size of the turbine and enhancing the energy performance across the low speeds area of the engine's speed/load map. This section is divided into four studies, as shown below:

