2.1 Power Flow in EGDTPG

A block diagram that describes the energy conversion process can be used to show the power flow of the exhaust gas-driven turbine-powered generator. A turbine is powered by exhaust gases from an internal combustion engine, as seen in Figure 1. A generator transforms this mechanical energy into electrical energy, which can power the vehicle's electrical systems. In addition to providing power for the car's electrical systems, the electricity created lessens the strain on the engine, which increases fuel economy and lowers pollutants. In the end, this approach supports environmental sustainability and fuel conservation.

2.2 Power Requirements of Generator

Under all operating circumstances, the generator must be able to provide the vehicles' current needs. The generator side of the exhaust gas-driven turbine-powered generator was the first to undergo design examination. First, the generator's power needs were established before a turbine study was conducted. The energy required to run the car's electrical systems is represented by this power. Three groups—continuous loads, prolonged loads, and intermittent loads—were created using an inventory of the electrical components utilized in the automobile. The combined electrical load that these components require is roughly 2.07 kW. A 10% safety factor was included to account for design issues, which meant that the vehicle's electrical system would need about (2.07 + 2.07 × 0.1) = 2.27 kW of electricity from the generator. Furthermore, it is projected that 734 W of power are needed at idle speed. The overall power required for the vehicle's electrical systems was taken into account when establishing these two power restrictions.

2.3 Generator Parameters Determination

The generator parameters are crucial for determining its dimensions. These parameters are calculated using the following equations:

The output power of the generator can also be expressed in terms of current and voltage as follows.

2.4 Preliminary Analysis of Turbine Design

The EGDTPG system's turbine, which is powered by exhaust gas energy, is an essential part of the mechanical to electrical energy conversion process. The compact size, excellent efficiency at low mass flow rates, and suitability for automobile exhaust gas circumstances led to the selection of a radial inward-flow turbine. In order to properly size turbine blades, the preliminary turbine design process involved estimating the available exhaust gas power at each engine speed (700, 1500, 2000, 2800, and 3600 rpm), calculating exhaust gas velocity based on mean piston speed and exhaust pipe diameter by applying conservation of mass, and determining the volume flow rate and mass flow rate of exhaust gases at various engine speeds.

Furthermore, the turbine rotor's inducer and exducer dimensions were computed using particular mass flow rates and thermodynamic parameters. According to the design, exhaust gases enter the turbine radially and depart axially. The flow is thought to be isentropic, and there is very little heat loss throughout the turbine. In order to maximize energy extraction while minimizing exhaust backpressure, the turbine blade angles and dimensions were optimized. In the end, the turbine was sized to accommodate the generator's electrical load requirements while continuing to run effectively across the engine's operating speed range. In this section, a preliminary analysis was carried out prior to the design of the turbine and its related components.

2.5 Gas Velocity

The velocity of the exhaust gases in the exhaust pipe is determined using Figure 2.

To determine the relevant parameters, the engine specifications of a specific vehicle model must be considered. The selection of a vehicle model is based on its integration of multiple electrical systems. For this study, the technical specifications of the vehicles are used, and these specifications are outlined in Table 1.

2.5.3 Volume Flow Rate of Exhaust Gas

Volume flow rate refers to the volume of exhaust gas that passes through a given area per unit time. It is determined after calculating the engine cylinder volume, which is calculated as follows.

The compression ratio,

$$$$ {\displaystyle \begin{array}{ll}{\mathrm{r}}_{\mathrm{c}}& =\frac{V_T}{V_C}=15.7\\ {}& \Rightarrow \frac{V_s+{V}_C}{V_C}=15.7\end{array}} $$$$

From the above relation, the clearance volume,

$$$$ {V}_C=\frac{{\mathrm{V}}_{\mathrm{s}}}{14.7} $$$$

The swept volume,

$$$$ {\displaystyle \begin{array}{ll}{V}_s& =\frac{\mathrm{E}\mathrm{ngine}\ \mathrm{capacity}}{\mathrm{numbers}\ \mathrm{of}\ \mathrm{cylinders}}=\frac{{\mathrm{E}}_{\mathrm{c}}}{\mathrm{Z}}=5.578\times {10}^{-4}\ {\mathrm{m}}^3\\ {}\to {V}_C& =\frac{{\mathrm{V}}_{\mathrm{s}}}{14.7}=3.794\times {10}^{-5}\ {\mathrm{m}}^3\end{array}} $$$$

The cylinder volume,

$$$$ {V}_T={V}_s+{V}_c=5.957\times {10}^{-4}\ {\mathrm{m}}^3 $$$$

Now, the volume flow rate of exhaust gas at an engine speed of 3600 rpm,

$$$$ {\displaystyle \begin{array}{ll}{\dot{\mathrm{V}}}_{\mathrm{gas}}& =\mathrm{Cylinder}\ \mathrm{volume}\times \mathrm{Engine}\ \mathrm{Speed}=\frac{{\mathrm{V}}_{\mathrm{s}}\times \mathrm{Z}\times {\mathrm{N}}_e}{120}\\ {}& =0.06694\ {\mathrm{m}}^3/\mathrm{s}\end{array}} $$$$

The volume flow rates of exhaust gas at engine speeds of 2000 and 2800 rpm are,

$$$$ {\displaystyle \begin{array}{l}{\dot{\mathrm{V}}}_{\mathrm{gas}}=\frac{{\mathrm{V}}_{\mathrm{s}}\times \mathrm{Z}\times {\mathrm{N}}_e}{120}=0.05206\ {\mathrm{m}}^3/\mathrm{s}\\ {}{\dot{\mathrm{V}}}_{\mathrm{gas}}=\frac{{\mathrm{V}}_{\mathrm{s}}\times \mathrm{Z}\times {\mathrm{N}}_e}{120}=0.03719\ {\mathrm{m}}^3/\mathrm{s}\end{array}} $$$$

The volume flow rate of exhaust gas at engine speed of 1500 rpm,

$$$$ {\dot{\mathrm{V}}}_{\mathrm{gas}}=\frac{{\mathrm{V}}_{\mathrm{s}}\times \mathrm{Z}\times {\mathrm{N}}_e}{120}=0.02789\ {\mathrm{m}}^3/\mathrm{s} $$$$

The engine specifications are used to determine various parameters. This vehicle falls under the category of light-duty vehicles. For the analysis of the required parameters, an engine idle speed of 700 rpm, corresponding to this light-duty vehicle, is utilized.

Now, at engine idle speed of 700 rpm,

$$$$ {\dot{\mathrm{V}}}_{\mathrm{gas}}=\frac{{\mathrm{V}}_{\mathrm{s}}\times \mathrm{Z}\times {\mathrm{N}}_e}{120}=0.01302\ {\mathrm{m}}^3/\mathrm{s} $$$$

The graph in Figure 3 shows the relationship between the volume flow rate of exhaust gas and engine speed. Based on the graph's behavior, the volume flow rate of exhaust gas is directly proportional to engine speed.

The gas velocity at different engine speeds is now calculated using the following formulas. The exhaust gas velocity in the exhaust pipe at maximum engine speed,

$$$$ {\mathrm{V}}_{\mathrm{gas}}=\frac{{\dot{V}}_{gas}}{A_p} $$$$ (9)

where $$$ {A}_p $$$ = area of exhaust gas pipe.

Now, the exhaust gas velocity at an engine speed of 3600 rpm,

$$$$ {V}_{exh}=\frac{{\dot{V}}_{gas}}{A_p}=89.85\ \mathrm{m}/\mathrm{s} $$$$

The exhaust gas velocities at engine speeds of 2000 and 2800 rpm are,

$$$$ {\displaystyle \begin{array}{l}{V}_{exh}=\frac{0.03719}{0.000745}=49.92\ \mathrm{m}/\mathrm{s}\\ {}{V}_{exh}=\frac{0.05206}{0.000745}=69.88\ \mathrm{m}/\mathrm{s}\end{array}} $$$$

The exhaust gas velocity at engine speed of 1500 rpm,

$$$$ {V}_{exh}=\frac{0.02789}{0.000745}=37.44\ \mathrm{m}/\mathrm{s} $$$$

The exhaust gas velocity at engine speed of 700 rpm,

$$$$ {V}_{exh}=\frac{0.01302}{0.000745}=17.48\ \mathrm{m}/\mathrm{s} $$$$

2.6 Mass Flow Rate of Exhaust Gases

The mass flow rate of exhaust gas is analyzed using the principle of conservation of mass. The mass flow rate of gas exiting the combustion chamber is the sum of the mass flow rates of air and fuel entering the combustion chamber. It is calculated using Figure 4.

2.7 Mass Flow Rate of Air

The mass flow rate of air is the amount of air entering the internal combustion engine per unit of time, and it depends on the engine's volumetric efficiency. It is determined as follows.

The volumetric efficiency (η_v) for a turbocharged engine is typically around 110%. This high efficiency occurs because turbocharging increases the amount of air entering the combustion chamber, allowing the engine to take in more air than its displacement volume, thus exceeding 100% efficiency.

2.8 Exhaust Back Pressure

Exhaust backpressure in an internal combustion engine is the pressure created by the engine to overcome the resistance of the exhaust system, allowing the gases to be discharged into the atmosphere. In other words, it is the resistance encountered by exhaust gases as they exit the combustion chamber during the exhaust stroke, flow through the exhaust pipe, and are expelled into the atmosphere.

At 1500 rpm, $$$ {\mathrm{P}}_{\mathrm{back}} $$$ = 0.23 kPa, At 700 rpm, $$$ {\mathrm{P}}_{\mathrm{back}} $$$ = 0.104 kPa

The maximum recommended exhaust backpressure is approximately 20 kPa for engine power levels ranging from 50 to 500 kW. Since the pressure of the exhaust gas is higher than atmospheric pressure, it does not significantly contribute to the formation of backpressure.

2.9 EGDTPG With Turbocharger

The new system, illustrated in Figure 5, operates downstream of the turbocharger. As shown, fresh air enters the compressor, which then forces the air into the engine. The engine expels the burned exhaust gases, which first drive the turbocharger turbine and subsequently flow to the generator turbine. After powering the generator turbine, the exhaust gases are released into the environment.

2.10 Compressor

The compressor is a key component of the turbocharger that compresses fresh air before it enters the engine. It operates through isentropic compression.

2.11 Exhaust Gas Power Calculation

On the left side of the graph, the line indicates a gradual increase in exhaust gas power as the engine speed rises from 700 to 1500 RPM. This trend demonstrates the engine transitioning from an idling condition to a driving condition. Beyond this range, the line shows a rapid increase in exhaust gas power corresponding to the engine speed on the right side of the graph, indicating the engine speed is moving from medium to maximum levels is shown in Figure 6.

2.12 EGDTPG Without Turbocharger

The 2D modeling of the exhaust gas-driven turbine-powered generator system, without a turbocharger, is illustrated in Figure 7. The fresh air enters the engine, which subsequently releases exhaust gas directed toward the generator turbine. The exhaust gas drives the turbine, which then expels the gases into the external environment.

The volumetric efficiency of a naturally aspirated engine is lower than that of a turbocharged engine. As shown in Table 2 the flow rate of gases as well as gas velocity increases with increased engine speed.

2.13 Turbine Design

The turbine is a component of the EGDTPG that converts the energy of exhaust gases into rotational energy. This rotational energy is then used by the generator to produce electricity. As discussed in the literature review, the radial flow turbine, specifically the inward flow radial turbine, is well suited for exhaust gas-driven turbine-powered generators. This system has a lower mass flow rate of gas compared to the mass flow rates found in aircraft and industrial axial turbines. The inward flow radial (IFR) turbine can be classified into two types: the cantilever IFR turbine and the 900 IFR turbine. The 90° IFR turbine is preferred over the cantilever IFR turbine due to its higher structural strength. Overall, the 90° IFR turbine is selected for the design of the EGDTPG.

2.13.1 Design Analysis of Turbine

The overall dimensions of the exhaust gas-driven turbocharged power generator (EGDTPG) are specified as illustrated in Figure 8. The length (l) and height (h) are used to define these dimensions. The cross-sectional area and the radius from the turbine centerline to the centroid of that area are depicted on the turbine housing in Figure 8. Additionally, the dimensions of the inducer (exhaust gas inflow) and exducer (exhaust gas outflow) of the turbine rotor are shown in Figure 9.

According to the specifications from the Holst turbocharger guide, for engine displacements ranging from 1.7 to 2.5 L and horsepower between 150 and 260, the cross-sectional area to radius from the turbine centerline to the centroid of that area (A/R) is 0.67, and the trim is 72.

Trim is a ratio used to describe the turbine wheel dimensions that are based on the inducer and exducer diameters of the turbine.

The turbine wheel trims,

$$$$ {\displaystyle \begin{array}{ll}\mathrm{Trim}& =\frac{Exducer^2}{Inducer^2}\times 100\\ {}& =\frac{Exducer^2}{Inducer^2}\times 100=72\end{array}} $$$$ (26)

The diameter of the inducer can be estimated using the diameter of the exhaust pipe. According to Birmingham Wire Gauge (BWG) standards, the thickness of the exhaust pipe is approximately 0.56 mm. The exhaust pipe surrounds the turbine, and the inducer diameter is determined as follows.

The diameter of inducer,

$$$$ \mathrm{ID}=2\times {D}_p=62\ \mathrm{mm} $$$$

The exducer diameter is calculated based on the inducer diameter using the formula provided above. The calculation is performed as follows.

Diameter of exducer,

$$$$ \mathrm{ED}=\sqrt{\frac{72\times {ID}^2}{100}}=\sqrt{\frac{72\times {62}^2}{100}}=53\mathrm{mm} $$$$

The area to radius,

$$$$ {\displaystyle \begin{array}{l}\mathrm{A}/\mathrm{R}=\frac{\left(\frac{\pi }{4}\right)\times \left({D_o}^2-{D_i}^2\right)}{R}\\ {}=0.67\end{array}} $$$$ (27)

The outer diameter of exhaust pipe,

$$$$ {D}_o=2\times \mathrm{t}+{D}_i=32.12\ \mathrm{mm} $$$$

Now, the radius from turbine centerline to centroid of that area,

$$$$ \mathrm{R}=\frac{\left(\frac{\pi }{4}\right)\times \left({D_o}^2-{D_i}^2\right)}{0.67}=83\ \mathrm{mm} $$$$

A velocity triangle is formed by three different velocities involved in the turbine and gas movement. The nomenclature and velocity triangles are illustrated in Figure 10.

The velocity triangle is constructed based on Figures 11 and 12. The various velocities and associated parameters are determined using the velocity triangle.

Since the inlet angle of the relative velocity ($$$ {\beta}_2 $$$) is 90°, the inlet radial and tangential velocities are equal to the inlet relative and angular velocities, respectively. Similarly, the exit radial and tangential velocities are equal to the exit absolute and angular velocities, as the exit angle of the absolute velocity is also 90°. The parameters at various stages are calculated as follows.

The absolute velocity of the gas entering the stator (nozzle ring) is determined as follows.

$$$$ {C}_1=\frac{{\dot{V}}_g}{A_p}=89.85\ \mathrm{m}/\mathrm{s} $$$$

Using the steady flow energy equation, the absolute velocity at the inlet of the turbine is calculated as follows.

$$$$ {\displaystyle \begin{array}{ll}\frac{1}{2}\ \left({C_2}^2-{C_1}^2\right)& ={C}_P\left({T}_2-{T}_3\right)\\ {}\to {C}_2& =\sqrt{{C_1}^2+2{C}_P\left({T}_2-{T}_3\right)}\end{array}} $$$$

For isentropic process, $$$ \frac{T_2}{T_3}={\left(\frac{{\mathrm{p}}_2}{{\mathrm{p}}_3}\right)}^{\frac{\gamma -1}{\gamma }} $$$

Then temperature,

$$$$ {T}_3={T}_2{\left(\frac{P_3}{P_2}\right)}^{\frac{\gamma -1}{\gamma }}={786}^{{}^{\circ}}\mathrm{K} $$$$

Now the absolute velocity,

$$$$ {C}_2=\sqrt{89.85^2+2\times 1151\times \left(1073-786\right)}=821\ \mathrm{m}/\mathrm{s} $$$$

The specific work of turbine,

$$$$ {\mathrm{W}}_{\mathrm{t}}=\frac{\mathrm{P}}{\dot{\mathrm{m}}}={{\mathrm{U}}_2}^2 $$$$ (28)

The tangential velocity,

$$$$ {U}_2=\sqrt{\frac{\mathrm{31,500}}{0.10842}}=539\ \mathrm{m}/\mathrm{s} $$$$

The speed of rotation of turbine,

$$$$ {N}_t=\frac{60\times {U}_2}{\pi D}=\mathrm{166,035}\ \mathrm{rpm} $$$$

The angular velocity,

$$$$ {C}_{w2}=\frac{2\pi {N}_t\ }{60}=17,387\ \mathrm{rad}/\mathrm{s} $$$$

Torque produced by turbine,

$$$$ \mathrm{T}=\frac{P}{\omega }=1.812\ \mathrm{Nm} $$$$

Inlet absolute velocity angle,

$$$$ {\alpha}_2={\mathit{\cos}}^{-1}\left(\frac{539}{821}\right)={49}^{{}^{\circ}} $$$$

Inlet radial velocity,

$$$$ {C}_{r2}={C}_2\sin\ {\alpha}_2=620\ \mathrm{m}/\mathrm{s} $$$$

Using the steady flow energy equation, the absolute velocity at the exit of the turbine is calculated as follows.

$$$$ {C}_3=\sqrt{{C_2}^2+2{C}_P\left({T}_3-{T}_4\right)}=1,324\ \mathrm{m}/\mathrm{s} $$$$

The exit tangential velocity,

$$$$ {\mathrm{U}}_3=\frac{\pi DN}{60}=461\ \mathrm{m}/\mathrm{s} $$$$

Exit relative velocity,

$$$$ {\mathrm{V}}_3=\sqrt{{C_3}^2+{U_3}^2}=1,024\ \mathrm{m}/\mathrm{s} $$$$

The exit angle of relative velocity,

$$$$ {\beta}_3={\mathit{\cos}}^{-1}\left(\frac{U_3\ }{V_3\ }\right)={64}^{{}^{\circ}} $$$$

The number of blades should be determined to prevent reversed flow on the pressure side. It is calculated using the following equation.

Number of blades,

$$$$ {\displaystyle \begin{array}{l}\mathrm{Z}=\frac{4\uppi \times \mathrm{U}}{\Delta \mathrm{V}}\\ {}\cong 15\end{array}} $$$$ (29)

2.14 Design of Gearbox

The speed of the generator is significantly lower than that of the turbine. To align the turbine speed with the generator speed, a gearbox is required to reduce the turbine's rotational speed. This reduction is essential to ensure that the turbine operates in harmony with the generator, facilitating smooth and efficient operation of the entire system. By using a gearbox, it is possible to achieve the necessary speed adjustments, which helps optimize performance and prolong the lifespan of both the turbine and the generator, as shown in Figure 13.

2.15 Design of Shaft

A shaft is a rotating machine element used to transmit power from one location to another. It transfers power from the exhaust gas-driven turbine to the generator for the production of electric power in electrical systems. When the system begins to operate, the shaft experiences a twisting moment as it facilitates power transfer. The diameter of the shaft is determined using the torsion equation. The power transmitted by shaft,

The diameter of the shaft can be determined using the two torque relations: T = $$$ \frac{\pi }{16}\times \tau \times {\mathrm{d}}^3 $$$ and $$$ \frac{60\times P}{2\times \pi \times N} $$$ as follows. The diameter of shaft,

3.1 Modeling and Simulation Using MATLAB/Simulink

The generator model illustrated in Figure 14 has been developed using the blocks from the Simulink library in MATLAB. These blocks are interconnected to create a comprehensive model of the generator.

The three generator parameter values—voltage, frequency, and power are—entered by selecting the three-phase parallel RLC load, as depicted in Figure 15.

The number of phases, rotor type, and mechanical input are determined in Figure 16 by selecting the permanent magnet generator block.

The modeling and simulation of the exhaust gas-driven turbine-powered generator system have been conducted using MATLAB/Simulink, allowing for a thorough comparison of the simulation results with the calculated outcomes. In this setup, the system model is constructed by integrating the turbine with a gearbox and a generator, as illustrated in Figure 17. This configuration enables the examination of the interactions between the components, ensuring a comprehensive understanding of their performance dynamics. Once the modeling has been completed, the system undergoes simulation to generate graphical representations of the desired parameters, providing valuable insights into the operational characteristics and efficiency of the exhaust gas-driven turbine-powered generator and facilitating analysis and optimization of the system.

The sinusoidal waveform of the voltage, depicted in Figure 18, reaches its peak value and maintains this level as the engine operates. This sustained maximum voltage indicates a consistent power output generated by the system during its functioning. As the engine runs, the voltage fluctuations remain within the established limits, demonstrating the stability of the electrical output. This behavior is crucial for ensuring that the connected electrical systems can operate efficiently without experiencing voltage spikes or drops, which could affect performance and reliability.

As illustrated in Figure 19, it takes approximately 0.8 s for the system to reach its maximum value. This duration signifies that, during this initial 0.8 s, all electrical systems will remain non-operational. This delay could impact system performance and efficiency, as it prevents any electrical operations from occurring until the maximum value is achieved. Understanding this lag is crucial for optimizing the system's response and ensuring that all components are synchronized for optimal functionality.

The output current waveform, illustrated in Figure 20, achieves its peak value during the electricity production phase, which corresponds to the operational conditions of the engine. This maximum current output signifies that the generator is effectively converting mechanical energy into electrical energy, ensuring optimal performance of the system. As the engine operates under various driving conditions, the waveform reflects the dynamic nature of current generation, capturing the fluctuations associated with different loads and demands. The consistency in reaching this maximum value is essential for maintaining a reliable power supply, indicating that the generator can meet the energy requirements of vehicle electrical systems without compromising performance.

Similar to Figure 21, the output current waveform takes approximately 0.8 s to reach its maximum value. This delay in achieving peak current indicates that the system requires this initial period before full operational capacity is attained. Understanding this response time is essential for effective system performance analysis and for ensuring that all electrical components function harmoniously.

The results indicate that the current and voltage values obtained were a little bit lower than the numerical values calculated in the analysis section. This discrepancy can be attributed to certain parameters present in the Simulink models that were not accounted for in the analytical calculations. These parameters may include specific system losses, component efficiencies, or environmental factors that influence performance but were excluded from the initial analysis. Consequently, this highlights the importance of integrating comprehensive system characteristics into both modeling and analysis to ensure a more accurate representation of the generator's operational performance. Understanding these differences is useful for refining models and enhancing the reliability of predictions in future simulations.

3.2 Numerical Result Analysis

The performance of the exhaust gas-driven turbine-powered generator is investigated through a numerical study that considers various parameters, including engine speed, exhaust gas power, volumetric flow rate of the exhaust gas, and overall system efficiency. The engine speed is categorized into distinct ranges: 700 rpm representing low speed, 1500, 2000, and 2800 rpm representing medium speeds, and 3600 rpm representing high speed. This study meticulously examines how variations in engine speed impact these critical performance parameters. By analyzing the relationship between engine speed and performance metrics, valuable insights can be gained regarding the efficiency and effectiveness of the generator system across different operational conditions. This analysis not only enhances our understanding of the system's behavior but also provides a foundation for optimizing design and operational strategies in exhaust gas-driven turbine systems.

A comparison of EGDTPG system with previous studies reveals notable improvements. For instance, Gürbüz et al. demonstrated that a latent heat thermal energy storage system for exhaust gases in SI engines recovered approximately 8.5% of the waste heat energy [22]. Similarly, Gürbüz et al. (2022, J. Energy Storage) reported that integrating a phase change material system achieved approximately 9% energy recovery efficiency [23]. In our study, the exhaust gas-driven turbine-powered generator achieved a system efficiency of up to 66.8% for naturally aspirated engines (Table 3), representing a significant improvement compared to the 8%–9% reported in the previous studies. Furthermore, Gürbüz et al. highlighted an integrated TEG-thermal energy storage system that reached around 10% recovery efficiency [24], while the EGDTPG system demonstrated higher efficiency. Additionally, Gürbüz et al. (2022, Applied Thermal Engineering) developed a TEG system that achieved a maximum recovery efficiency of approximately 12% [25], while our system again surpassed this by approximately 54%.

3.3 Influence of Engine Speed on Exhaust Gas Power Before Turbocharger

The Figure 22 provides a graphical representation of the exhaust gas power generated by turbocharged and naturally aspirated engines. The exhaust gas power of a turbocharged engine is significantly higher than that of the naturally aspirated engine. This increase in power can be attributed to the superior volumetric efficiency of the turbocharged engine, which results from compressed air being forced into the combustion chamber. This enhanced airflow allows for a more efficient combustion process, leading to greater power output.

3.4 Influence of Engine Speed on Exhaust Gas Power After Turbocharger

The influence of engine speed on exhaust gas power is illustrated in Figure 23, which provides a graphical comparison for both turbocharged and naturally aspirated engines. As shown in Figure 23, the exhaust gas power produced by naturally aspirated engines is greater than that generated by turbocharged engines. This phenomenon can be attributed to the power consumption associated with the turbocharger in turbocharged engines. The turbocharger requires a portion of the engine's output power to function effectively, leading to a reduction in the available exhaust gas power. Consequently, while turbocharged engines are designed to enhance overall performance and efficiency, the inherent energy demands of the turbocharger result in lower exhaust gas power compared to their naturally aspirated counterparts.

Figure 24 illustrates exhaust gas power using a bar chart, highlighting the peak power at three different engine speeds for both naturally aspirated and turbocharged engines. This visual representation allows for easy comparison of the power output between the two engine types across the specified speeds.

3.5 Influence of Engine Speed on System Efficiency

The influence of engine speed on system efficiency is depicted in Figure 25, which presents the graphical characteristics of system efficiency across various engine speeds. System efficiency is defined as the combined efficiency of the turbine, gearbox, and generator, reflecting the overall effectiveness of the power generation process. As illustrated in Figure 25, system efficiencies for both turbocharged and naturally aspirated engines tend to improve as engine speed increases. However, it is noteworthy that the system efficiency of turbocharged engines remains lower than that of naturally aspirated engines. This difference arises because the exhaust gas power reaching the turbine in naturally aspirated engines is greater than that in turbocharged engines. The turbocharger's operational demands consume some of the available exhaust gas power, thereby reducing the power available for the generator turbine.

The output power of the generator and system efficiency for both engine types are presented in Table 3. As shown in Table 3, both output power and system efficiency decrease with lower engine speeds for each engine type. Notably, the values for naturally aspirated engines in both parameters (output power and system efficiency) are higher than those for turbocharged engines. This difference can be attributed to the exhaust gas power consumed by the turbocharger, as previously explained.

3.6 Influence of Engine Speed on Current

The graph of current versus engine speed presented in Figure 26 features two lines representing naturally aspirated and turbocharged engines. The production of current increases with engine speed for both types of engines. Notably, the output current generated by the naturally aspirated engine is higher than that of the turbocharged engine. This difference can be attributed to the turbocharger, which utilizes a portion of the exhaust gas power in turbocharged engines. Consequently, this consumption reduces the overall output current of the generator in turbocharged systems.

3.7 Influence of Engine Speed on Output Power

The influence of engine speed on output power is illustrated graphically in Figure 27, which shows the generator's output power at various engine speeds. The output power increases as engine speed rises, reaching a peak at medium speeds during driving conditions. Once this maximum required value is attained, the output power remains constant, even as the engine speed continues to increase beyond the medium range. This behavior is attributed to the vehicle's electrical system requirements, which dictate that the output power reaches a maximum value necessary to meet the system's demands.

3.8 Graphical Behavior of Output Power With System Efficiency

The graph of output power versus system efficiency, shown in Figure 28, demonstrates that system efficiency increases with the generator's output power until it reaches a constant level. This plateau indicates that the power required by the electrical systems during driving, from the lowest to the maximum engine speed, remains constant throughout operation.

3.9 Overall Analysis of EGDTPG With Turbocharger and Without Turbocharger

The parameters, including exhaust gas power, volumetric flow rate of exhaust gas, turbine efficiency, and others, are presented in Tables 4 and 5. These tables summarize the numerical results of the exhaust gas-driven turbine-powered generator for vehicles equipped with both turbocharged and naturally aspirated engines.

Table 4 presents various parameters of the exhaust gas-driven turbine-powered generator (EGDTPG) for turbocharged engines at different engine speeds. It is evident that the values of all parameters decrease as engine speeds decline. Due to the presence of the turbocharger, the parameters for turbocharged engines, such as exhaust gas pressure, exhaust gas power, and turbine efficiency, are lower than those of naturally aspirated engines. This reduction can be attributed to the decrease in exhaust gas energy, which is consumed by the turbocharger during operation. However, the mass flow rates of exhaust gas for turbocharged engines are higher than those for naturally aspirated engines, as the turbocharger effectively boosts more air into the combustion chamber.

Table 5 presents various parameters of the EGDTPG for naturally aspirated engines (without a turbocharger) at different engine speeds. The values of these parameters increase with higher engine speeds, indicating improved performance under these conditions. However, it is important to note that the mass flow rates of exhaust gas for naturally aspirated engines are lower than those for turbocharged engines. This difference is primarily due to the lack of a turbocharger, which in turbocharged engines enhances the intake of air into the combustion chamber, resulting in greater exhaust gas flow.

3.10 Comparison of Power Recovery Methods

The Figure 29 illustrates the comparison of EGDTPG with TEG and the Rankine Cycle, highlighting these differences in power recovery capabilities visually. The comparison of power recovery methods in internal combustion engines reveals significant differences in efficiency. The Rankine Cycle, with a minimum power recovery of 5 kW and a maximum of 25 kW, shows remarkable potential for harnessing waste heat from exhaust gases, surpassing both TEGs and Exhaust Gas Driven Turbine-Powered Generators (EGDTPGs) in terms of power output. However, its implementation in vehicles faces significant challenges, such as complexity, weight, and space requirements. The need for large heat exchangers and additional components can complicate integration into compact automotive designs, making it less feasible for lightweight vehicles or those with stringent space constraints. In contrast, while TEGs recover less power (1–5 kW), their compactness and simplicity make them more suitable for smaller vehicles, and EGDTPGs offer a good balance with a recovery range of 1.03–21.04 kW. Thus, while the Rankine Cycle holds great promise for large-scale waste heat recovery, its practical limitations often hinder widespread adoption in the automotive sector.