Study on the Effect of Exhaust Gas Recirculation Coupled Variable Geometry Turbocharger and Fuel Quantity Control on Transient Performance of Turbocharged Diesel Engine

Abstract

With increasingly stringent emissions regulations, there are growing demands for the transient performance of diesel engines. This study conducted a transient bench test on a two-stage turbocharged heavy-duty diesel engine to optimize its performance during a load increase (20% to 100% in 1 s) at a constant speed (1200 RPM) transient process. The results showed that the transient control scheme using the low-pressure EGR system resulted in a 42.1% reduction in the peak value of soot emission, a 24.8% decrease in the peak value of NOx emission, a 9.14% decrease in ISFC and a 30.6% increase in maximum IMEP achieved in 1 s, compared to the steady-state optimization control scheme without EGR. Transient control scheme using the high-pressure EGR system resulted in a 24.4% reduction in the peak value of soot emission, a 31.8% reduction in the peak value of NOx emission, a 9.52% reduction in ISFC, and a 31.7% increase in maximum IMEP achieved in 1 s. The comparison of high and low-pressure EGR systems revealed that the low-pressure EGR system produced lower compromising emissions, while alterations in control parameters for the diesel engine with a high-pressure EGR system had a more significant impact on the transient process performance.

1. Introduction

Despite the challenges imposed by stringent emission regulations and the increasing presence of electric vehicles, diesel engines remain the predominant power source for over 95% of new heavy-duty commercial vehicles worldwide [1]. This highlights the ongoing requirement to enhance their performance. During real-world engine operation, a substantial portion of the engine’s runtime is dedicated to transient processes [2], which have a greater impact on total emissions compared to steady-state engine operation [3]. Thus, the optimization of engine performance during transient processes holds practical significance.

Through the study of the transient process, it was found that the most crucial reason for the deterioration of transient process performance was the air–fuel mismatch caused by turbocharger lag [4]. So, a steeper load increase results in a significant deterioration of emissions [5,6]. Many scholars have researched transient process fuel and turbine control to solve the air–fuel mismatch problem. Zhang H et al. studied the torque response of load increase transient process at different speeds on a two-stage turbocharged diesel engine with bypass. The results show that the torque response time of the transient process can be effectively reduced by rapidly increasing the fuel quantity and closing the bypass valve, and the increase in engine speed helps to reduce torque response time [7]. By studying 5 s transient process of torque increasing at a constant speed, Liu Z et al. found that compared with constant loading rate during the entire transient process, the sectional-stage loading strategies, which have a greater first-stage loading rate, can effectively improve torque response performance [8].

The newly implemented Euro VII emission regulations set even more stringent limits for PM and NOx emissions compared to Euro VI, highlighting the need for vehicles to implement effective strategies for reducing emissions. One commonly employed approach is using Exhaust Gas Recirculation (EGR) systems, which help lower NOx emissions from diesel engines by decreasing the oxygen concentration in the combustion chamber and increasing specific heat capacity [9,10,11]. Currently, the widely used EGR systems can be classified into two forms: high-pressure circuit and low-pressure circuit. The high-pressure EGR system directly transfers exhaust gases from the turbine inlet to the intake manifold, while the low-pressure EGR system routes the gases from the turbine outlet to the compressor inlet. New diesel engines often adopt one of these EGR systems, although some engines utilize both systems simultaneously [12]. The high-pressure EGR system offers a quicker response time due to its shorter gas path, which is beneficial during cold start conditions [13,14,15,16]. On the other hand, the low-pressure EGR system exerts less impact on the turbine and allows for more extensive adjustments of the EGR rate [17,18].

However, during transient processes, the combined effect of the gas path response delay and EGR can lead to a further reduction in oxygen charge within the cylinder, causing a significant deterioration in soot emissions. Despite having high filtration efficiency for soot emissions, frequent regeneration of the Diesel Particulate Filter (DPF) can lead to a reduction in fuel economy [19]. Galindo J et al. have shown that the torque response time with EGR is 2 s slower than without EGR, and the response time of the transient process is successfully reduced by using a pressurized air tank (PAT) and installing an electric supercharger at the compressor outlet in series [20]. Research by Luján J. M. et. al. found that during the transient process of a full load increase, the exhaust pressure and negative pressure at the compressor inlet increase due to the rapid increase in air mass. And keeping the back pressure valve open can help avoid the EGR overshoot when a low-pressure EGR circuit is used [21]. Pennington et al. conducted a study on the effects of reducing Variable Geometry Turbocharger (VGT) opening and EGR valve opening during a 2 s–10 s constant speed load increase transient process. They found that this approach effectively reduced turbocharger lag, resulting in decreased fuel consumption and carbon emissions. However, it also led to a substantial increase in NOx emissions due to the boost degree being closer to the steady state value [22]. Zhang et al. studied the transient process of 5 s constant speed torque increase on a two-stage turbocharged diesel engine. The results show that the best compromise emission can be obtained by closing the EGR valve at 1.5 s and opening it at 4 s through open-loop control. When the exhaust oxygen concentration is controlled as a closed-loop target, although the EGR opening curve similar to the open-loop control obtained, the emission will deteriorate due to the delay of closed-loop control [23].

The study will focus on heavy-duty diesel engines with a low-pressure EGR system or a high-pressure EGR system, respectively, investigating the impact of coordinated changes in fuel quantity, VGT opening degree, and EGR system parameters on transient process performance. By proposing a comprehensive performance evaluation index for individual transient processes, the study aims to explore control parameter variation schemes for optimizing the torque response, fuel consumption, and emissions during transient processes.

2. Experimental Work

2.1. Experimental Setup

The WP12 heavy-duty diesel engine used in this study is shown in

Table 1. Engine Specifications.

Item	Value
Engine type	4-stroke L6 diesel
Bore × stroke (mm)	126 × 155
Variable valve actuation system	RIVCA [24]
Intake boosting	Two-stage turbocharge with VGT
Compression Ratio	17:1
Combustion chamber	BUMP [25]
Injection system	Common rail
Maximum injection pressure (MPa)	180 MPa
Maximum power (kW/rpm)	353/2100
Maximum torque (Nm/rpm)	1970/1300–1500

for its main parameters. The experimental engine test bench system is shown in Figure 1a. The intake boosting system adopts a two-stage turbocharging system, with a VGT as the high-pressure stage and a fixed geometry turbocharger as the low-pressure stage. The fuel system uses the BOSCH second-generation high-pressure common rail fuel system with the maximum injection pressure of 180 MPa. The high- and low-pressure exhaust gas recirculation systems are shown in Figure 1b,c, respectively. An Engine Control Unit (ECU) developed by the research group is used for more flexible engine control parameters.

In order to study the transient characteristics of heavy-duty diesel engines, a large number of high-responsivity sensors and test equipment were used on the test bench, including KISTLER’s 4007b intake pressure sensor and 4049A water-cooled exhaust pressure sensor. In order to analyze the combustion state in the cylinder, KISTLER’s high-precision cylinder pressure sensors were installed in six cylinders of the engine. The test equipment is shown in

Table 2. Equipment of the transient measurement.

Equipment	Type
Air flow meter	AVL FMT700-P
Fuel mass flow meter	AVL733s + AVL753c
In-cylinder pressure sensor	Kistler 6125C
Intake pressure sensor	Kistler 4007B
Exhaust pressure sensor	Kistler 4049A
Exhaust-gas analyzer	Horiba MEX-7100DEG Cambustion CLD500
Soot measurement	AVL483

.

To improve the accuracy of fuel consumption measurements during a single transient process, this study utilizes the cycle fuel injection quantity recorded by the ECU as a basis for calculation. To guarantee the validity of the data, the fuel consumption readings from the ECU were calibrated during a steady-state operation. The calibration results are shown in Figure 2. The fuel consumption is calculated by the ECU through the rail pressure and the injector injection pulse width. This method can also ensure reliability in a single transient process [26,27,28].

The average indicated fuel consumption rate of a transient process is calculated using Equation (1)

$$\mathrm{I}\mathrm{S}\mathrm{F}\mathrm{C}=\frac{\int m_{ecu}∆t}{\int P∆t}$$

(1)

where $\mathrm{I}\mathrm{S}\mathrm{F}\mathrm{C}$ is indicated fuel consumption rate (g/kWh), $m_{ecu}$ is fuel consumption measured by ECU (g/s), $P$ is engine power (kW) and is calculated using Equation (2).

$$P=\frac{S\times T}{9550}$$

(2)

where $S$ is engine speed (r/min), $T$ is indicated torque (N∙m). Due to the poor correspondence between the torque measured by the dynamometer and the engine cycle, $T$ is calculated using Equation (3), and IMEP is calculated using Equation (4).

$$T=\frac{318.3\times IMEP\times V_s\times i}{\tau }$$

(3)

$$\mathrm{I}\mathrm{M}\mathrm{E}\mathrm{P}=\frac{\int pdv}{V_s}$$

(4)

where $\mathrm{I}\mathrm{M}\mathrm{E}\mathrm{P}$ is indicated mean effective pressure (MPa), $V_s$ is engine cylinder displacement (m³), $i$ is number of cylinders, $\tau$ is number of engine strokes, $p$ is pressure in cylinders (MPa), $v$ is cylinder volume (m³).

The comprehensive evaluation of the transient process performance necessitates consideration of its IMEP response, ISFC, and emissions. A lower ISFC and reduced emissions indicate improved performance. To this end, the IMEP response of the transient process is quantified by Equation (5).

$${\tau }_{IMEP}=\frac{P_T-P_1}{P_T}\times 100\%$$

(5)

where $P_T$ is the target of IMEP, in this paper, the value is defined as 2 MPa, $P_1$ is the IMEP at the end of 1 s transient process. This parameter quantifies the discrepancy between the IMEP and the target value at the end of the 1 s transient process. A smaller value signifies proximity to the target value, demonstrating a better IMEP response. The ${\tau }_{IMEP}$ can therefore be utilized as performance index of the transient process, with a smaller value indicating superior performance.

In this paper, the fuel-oxygen equivalence ratio (${\mathsf{\Phi }}_o$), which reflects the correlation between in-cylinder oxygen and fuel, is chosen as an index due to using the EGR system. The calculation method is presented in Equation (6).

$${\mathsf{\Phi }}_o=\frac{\frac{m_{fuel}}{m_o}}{{\left(\frac{F}{O_2}\right)}_{stioc}}$$

(6)

where $m_{fuel}$ is in-cylinder fuel quality (g),${ m}_o$ is in-cylinder oxygen quality (g), ${\left(\frac{F}{O_2}\right)}_{stoic}$ is theoretical fuel oxygen ratio, the value is defined as 0.304.

2.2. Transient Process Control Parameters

Diesel engine users aim to achieve a quicker torque response and improved fuel efficiency while adhering to emission regulations. This study sets the duration of the transient process at 1 s and simulates a load change of 20% to 100%. The general control parameters for the load increase at a constant speed transient process are presented in

Table 3. General control parameters.

Engine Speed (r/Min)	Fuel Quantity (mg/Cycle)	VGT Opening Degree (‰)	Intake Temperature (°C)	Injection Timing (°ATDC)	EGR Valve Opening (%)
1200	40–210	500–665	40	1~−2	15

.

The initial transient process adopts the control strategy without EGR, and the control parameters are obtained by steady-state optimization. The fuel quantity and VGT opening degree are shown in Figure 3a, and the performance parameters are shown in Figure 3b and

Table 4. Transient process performance parameters.

Control Scheme	IMEP Response	ISFC (g/kWh)	Peak Value of Soot (mg/m3)	Peak Value of NOx (ppm)
Case0	30.0%	232.8	175.9	1297.8

.

Our research group has developed an independent diesel engine electronic control system based on MPC5554 [29], which enables the design of the diesel engine control parameters by time changes. The fuel quantity control and VGT opening degree control curves are displayed in Figure 4a. In this study, FCC refers to the fuel quantity control curve, while VCC represents the VGT opening degree control curve.

The EGR valve control parameters are obtained by setting the valve opening time in the transient process, and the EGR valve opening in Figure 4b is calculated according to Equation (7). The EGR valve adopts a control strategy that closes at the beginning of the transient process and opens at a specified time.

$${\varnothing }_{EGR}=\left\{\begin{array}{c}\begin{array}{c}0\times f_{EGR} 0\le t\le T_{EGR}\\ f_{EGR} T_{EGR}<t\end{array}\end{array}\right.$$

(7)

where ${\mathrm{\varnothing }}_{EGR}$ is EGR valve opening degree during transient process, $f_{EGR}$ is EGR valve opening degree obtained by steady-state optimization, $f_{EGR}$ is 15% in this study, $T_{EGR}$ is valve opening time during transient process, $t$ is running time of transient process.

3. Results and Discussion

3.1. The Effect of Coordinated Control of Low-Pressure EGR, Fuel Quantity, and VGT Opening on Transient Process Performance

The results from the low-pressure EGR system test have shown that the entry of exhaust gas into the cylinder experiences a significant delay, resulting in an impact on the cylinder that surpasses the 1 s duration of the transient process when the low-pressure EGR is opened after 0.7 s. Therefore, the maximum allowable time for the low-pressure EGR opening is defined as 0.7 s. The opening time of the low-pressure EGR valve is divided into four intervals ranging from 0.1 to 0.7 s, with a step size of 0.2 s. When three fuel control curves, four VGT control curves, and four EGR valve opening times are used, a total of 48 distinct control schemes are generated. The nomenclature of the control schemes in this study follows the pattern of ‘fuel control curve + VGT control curve + EGR valve opening time’. For example, FCC1 + VCC1 + L0.1 represents the transient process utilizing fuel quantity control curve 1, VGT opening degree control curve 1, and a low-pressure EGR valve opening time of 0.1 s.

3.1.1. Effect on IMEP Response and ISFC

As depicted in Figure 5, a strong correlation between the IMEP curve and the FCC can be observed. During the transient process, a rapid increase in fuel quantity results in a higher IMEP growth rate in the early stage. Before 0.2 s, the IMEP increase is primarily controlled by the change in fuel quantity due to the buffering effect of the low ${\mathsf{\Phi }}_o$ in diesel engine at low load and the turbocharger lag.

Figure 5 demonstrates that the IMEP growth rate of the transient process employing VCC2 is the lowest as time advances. The slower reduction speed of VGT in VCC2 results in a swifter increase in the ${\mathsf{\Phi }}_o$ and a more pronounced deviation from steady-state conditions, thereby suppressing the growth rate of IMEP. A comparison of various fuel quantity control curves reveals that the largest disparity in IMEP exists among transient processes utilizing FCC1. This can be attributed to the higher growth rate of fuel quantity in FCC1, resulting in an increased supply of exhaust energy to the turbine.

As shown in Figure 6, due to the high ${\mathsf{\Phi }}_o$ causing combustion deterioration around 0.5 s, the IMEP growth rate of the transient process employing FCC1 + VCC1 + L0.1 and FCC1 + VCC2 + L0.1 experienced a substantial decrease. Subsequently, around 0.8 s, the IMEP attained in the transient process utilizing FCC2 + VCC3 + L0.1 and FCC2 + VCC4 + L0.1 exceeds that of these two control schemes despite the lower fuel quantity, primarily due to the lower equivalence ratio. The results indicate that the transient process employing FCC2 demonstrates a fuel increase rate that is better aligned with the turbine’s acceleration. In the initial stage, the excessive elevation of ${\mathsf{\Phi }}_o$ is prevented. Subsequently, the fuel increase rate decelerates significantly in parallel with the heightened increase rate of intake pressure induced by the highly accelerating turbine, effectively suppressing the subsequent increase rate of ${\mathsf{\Phi }}_o$. Consequently, a higher rate of IMEP increase is attained in the latter stage.

Affected by the fuel quantity increasing speed, the IMEP response of the transient process using FCC3 is the slowest and is gradually suppressed in the later stage of the transient process. The reason for this phenomenon is that while a uniform increase in fuel quantity can maintain a low ${\mathsf{\Phi }}_o$ during the early and middle stages, the acceleration of the turbine is the lowest. As the fuel quantity gradually increases to a high level in the later stage, the rapid increase in the ${\mathsf{\Phi }}_o$ leads to a significant deterioration in combustion.

Figure 5 reveals that the process utilizing FCC1 demonstrates a rapid IMEP response but a higher ISFC. However, despite the increased energy supply to the turbine during the early stage, the turbine’s rotational inertia and efficiency hinder its ability to keep pace with the rapid increase in fuel quantity. As a result of this discrepancy, there will be an excessive growth of ${\mathsf{\Phi }}_o$ and a deterioration in combustion, ultimately leading to an increased ISFC.

When FCC1 or FCC2 is chosen as the fuel quantity control curve, the transient process employing VCC2 exhibits the highest ISFC. This is due to the rapid increase in fuel quantity growth rate in the early stage combined with the lowest turbine acceleration brought by VCC2, leading to a significant deterioration in the ${\mathsf{\Phi }}_o$, ultimately resulting in a higher ISFC and a decrease in IMEP growth rate. When FCC3 is used, the transient process with VCC1 has the highest ISFC. FCC3 has a small change in fuel quantity in the early stage, and the turbine acceleration is low. In the middle and late stages of the transient process, when the fuel quantity substantially exceeds the initial state, the VGT opening of VCC1 has already begun to increase rapidly, which makes it difficult to promote the acceleration of the turbine. This mismatch between VCC1 and FCC3 results in the highest ISFC.

It can be seen that when the fuel quantity increases at constant speed, the VGT control curve with a smaller VGT opening in the middle and late period can obtain better IMEP response and fuel consumption rate. If the fuel quantity increases at a high rate in the early stage and then at a low rate in the late stage, the VGT opening control curve with a fast-decreasing VGT opening degree can obtain optimal IMEP response and ISFC.

As shown in Figure 7, delaying the opening of the EGR valve results in a longer acceleration time for the turbocharger. This leads to a higher rate of increase in the intake airflow, which effectively compensates for the increase in fuel quantity and the gradual decrease in oxygen concentration in the intake. It weakens the dilution effect of EGR and reduces the deterioration of the ${\mathsf{\Phi }}_o$. Therefore, compared to the strategy of FCC1 + VCC1 + L0.1, the strategy of FCC1 + VCC1 + L0.3 achieved a 3.28% reduction in ISFC and a 6.18% increase in maximum IMEP achieved in 1 s. These results demonstrate a significant improvement.

When the EGR valve is opened at 0.5 s, the intake oxygen concentration starts to decrease in the latter part of the transient process. At this time, the turbocharger has a longer acceleration time, and the airflow increases rapidly while the increase in fuel quantity slows down significantly. Therefore, the increase in airflow can fully offset the effects of the increase in fuel quantity and the gradual decrease in intake oxygen concentration, causing the ${\mathsf{\Phi }}_o$ to decrease gradually. The ISFC of FCC1 + VCC1 + L0.7 compared to FCC1 + VCC1 + L0.5 only decreased by 1.05%, and the maximum IMEP achieved in 1 s increased by 1.95%. The data shows that the impact of low-pressure EGR on IMEP and fuel consumption is already relatively small when it is opened at 0.5 s.

3.1.2. Effects on Soot and NOx

Soot formation is predominantly influenced by high temperatures and an inadequate oxygen supply. As the ${\mathsf{\Phi }}_o$ increases, the concentration of oxygen within the cylinder decreases, leading to an increased likelihood of local low oxygen concentration and, subsequently, a significant rise in soot production. Additionally, a high ${\mathsf{\Phi }}_o$ results in reduced residual oxygen during later stages of combustion, making it challenging to oxidize soot. Therefore, Reducing the ${\mathsf{\Phi }}_o$ is an effective approach to lowering soot emissions [30]. As illustrated in Figure 8, the soot emission changes little before 0.4 s, owing to the low ${\mathsf{\Phi }}_o$ during the initial stages of the transient process, which serves as a buffer for increases in fuel quantity.

Due to the rapid increase in the ${\mathsf{\Phi }}_o$ in the early stage, the soot of the transient process using FCC1 began to increase rapidly at the earliest time. For the transient process using FCC3, the slow growth of intake flow rate in the later stage resulted in the fastest growth of the ${\mathsf{\Phi }}_o$, leading to the highest peak value and fastest growth rate of soot emissions. Additionally, the slow response of intake flow resulted in a slow decrease in the high ${\mathsf{\Phi }}_o$ after the peak, causing high soot emissions to persist for a longer period.

The overall trend of NOx emissions is closely aligned with the change in the fuel quantity control curve. As the fuel quantity and ${\mathsf{\Phi }}_o$ increase, mixing fuel and gas in the cylinder becomes more challenging, causing an increase in the proportion and amount of diffusion combustion. The prolonged high temperature in the cylinder results in a corresponding increase in NOx emissions. As a result, the NOx emission of FCC1 + VCC4 + L0.1, which has the largest fuel quantity and low ${\mathsf{\Phi }}_o$, is the highest, reaching 783.8 ppm.

By comparing Figure 8 and Figure 9, it can be found that when the EGR valve opens at 0.1 s, the EGR enters the cylinder earlier and there is no obvious spike in NOx emission throughout the transient process. As the EGR valve opening is delayed, NOx emission rises significantly. Delaying the opening of the low-pressure EGR valve, the peak value of soot emission decreases with the decrease in the ${\mathsf{\Phi }}_o$.

There is a significant slowdown in the rate of reduction in soot emissions after reaching the peak for the FCC3 + VCC1 + L0.7 in Figure 9c. The air path delay causes the exhaust gases to enter the cylinder only after the peak of soot emissions of FCC3 + VCC1 + L0.7 is produced. The slowest turbo response of FCC3 + VCC1 + L0.7 leads to a slow airflow mass increase, and the lower intake oxygen concentration further weakens the effect of increasing airflow mass, leading to a slowdown in the rate of soot emission reduction.

The values of soot and NOx emissions during the transient process for various control schemes are analyzed statistically. The maximum peak value of soot emission is 312 mg/m³, and the maximum peak value of NOx emission is 1040 ppm. Given the significant difference between the two values, the data are non-dimensionalized according to Equation (8).

$$N_{ave}=\frac{N}{\overline{N}}$$

(8)

where $N_{ave}$ is dimensionless processing result, $N$ is the original data, and $\overline{N}$ is the average of original data. This method not only eliminates the influence of dimension and magnitude but also reflects a discrete degree of the original data. The results are depicted in Figure 10, and the comprehensive emission value $D_p$ is calculated. The definition of $D_p$ is shown in Equation (9).

$$D_p=\sqrt{{(N_{soot-ave}\times W_{soot})}^2+{{(N}_{NOx-ave}{\times W}_{NOx})}^2}$$

(9)

where $D_p$ is comprehensive emission value, $N_{soot-ave}$ is the dimensionless result of soot emission peak value, $N_{NOx-ave}$ is the dimensionless result of NOx emission peak value,$W_{soot}$ is the soot emission weight, $W_{NOx}$ is the NOx emission weight, and the weights of soot and NOx are both taken as 1 in this paper. The smaller the value of $D_p$ is, the closer the emission peak value of the transient process is to 0, and the lower the comprehensive emission is.

From Figure 10, with the delay of the EGR valve opening, the emission distribution gradually moves towards the direction of higher NOx and lower soot emission. By comparing the value of $D_p$, the optimal transient processes are using the three control schemes in the red circle, which are FCC2 + VCC3 + L0.1, FCC2 + VCC4 + L0.1, and FCC2 + VCC4 + L0.3. It can be observed that since the low-pressure EGR has a minimal impact on the turbine, the opening of the low-pressure EGR valve mainly influences the intake oxygen concentration, resulting in a more negligible optimization of soot emission. The introduction of EGR effectively reduces NOx emissions. Thus, for a comprehensive reduction in NOx and soot emissions, the opening time of the low-pressure EGR valve should be set at 0.1 s or 0.3 s.

3.1.3. Comprehensive Performance of Transient Process

Given the large difference in the values of emission, IMEP response, and ISFC, the IMEP response and ISFC are non-dimensionalized using Equation (8). The results are depicted in Figure 11 and the comprehensive performance index $D_C$ of the transient process is calculated using the method outlined in Equation (10).

$$D_C=\sqrt{{{(\tau }_{IMEP-AVER}\times W_{IMEP})}^2+{\left({ISFC}_{AVER}\times W_{ISFC}\right)}^2+{\left(D_p\times W_p\right)}^2}$$

(10)

where ${\tau }_{IMEP-AVER}$ is the dimensionless result of IMEP response, $W_{IMEP}$ is the IMEP response weight, ${ISFC}_{AVER}$ is the dimensionless result of ISFC, $W_{ISFC}$ is the ISFC weight, $W_p$ is the emission weight. The three weights in this paper are taken as 1.

The performance parameters of the three control schemes closest to zero in Figure 11 are shown in

Table 5. Transient process performance parameters.

Control Scheme	IMEP Response	ISFC (g/kWh)	Peak Value of Soot (mg/m3)	Peak Value of NOx (ppm)
FCC1 + VCC4 + L0.5	7.4	219.0	105.5	977.6
FCC2 + VCC4 + L0.5	8.2	211.5	101.8	975.4
FCC2 + VCC4 + L0.7	7.4	209.4	99.1	1009.5

. The transient process emissions are improved when the low-pressure EGR valve is opened at 0.3 s, but the torque response is slow. On the other hand, when the low-pressure EGR valve is opened at 0.7 s, NOx emissions are higher. Compared to Case0 without EGR, the peak value of soot emission in FCC2 + VCC4 + L0.7 is reduced by 42.1%, the peak value of NOx emission reduced by 24.8%, the fuel consumption rate is decreased by 9.14%, and the IMEP in 1 s increased by 30.6%. The optimization of the transient performance is substantial.

3.2. The Effect of Coordinated Control of High-Pressure EGR, Fuel Quantity, and VGT Opening on Transient Process Performance

During the transient process, the rise in exhaust energy due to increased fuel quantity is a prerequisite for the turbo to accelerate. However, opening the high-pressure EGR valve decreases the energy available to the turbine and slows its response. Therefore, the coordinated control of high-pressure EGR with fuel quantity and VGT will significantly impact the transient performance. In this section, the opening time of high-pressure EGR valve is divided into five opening times from 0.1 s to 0.9 s with a step of 0.2 s. When three fuel quantity control curves, four VGT opening degree control curves, and five EGR valve opening times are used, a total of 60 different control parameter combinations are generated. The control scheme in this section is named according to the way of “fuel quantity control curve + VGT opening degree control curve + EGR valve opening time”, such as FCC1 + VCC1 + H0.1, which represents that the transient process uses fuel quantity control curve 1, VGT opening degree control curve 1, and the high-pressure EGR valve opens at 0.1 s.

3.2.1. Effect on IMEP Response and ISFC

When the high-pressure EGR valve is opened at 0.1 s, it can be seen in Figure 12 that the IMEP growth rate of all transient processes has been severely suppressed. Rapidly increasing the fuel quantity and reducing the VGT opening can boost exhaust pressure and improve turbine response. However, high-pressure EGR is driven by the pressure difference between the exhaust and intake, and the increase in exhaust pressure will cause more exhaust to be diverted from the turbine inlet. Therefore, the promotional effect of rapidly increasing fuel quantity and reducing VGT opening on turbine response is greatly weakened. Additionally, the higher the ${\mathsf{\Phi }}_o$, the lower the oxygen concentration in the exhaust gas. The same amount of exhaust gas entering the cylinder causes a more significant reduction in oxygen concentration, resulting in a vicious cycle of the ${\mathsf{\Phi }}_o$.

The high-pressure EGR causes the transient processes using FCC1 and FCC2 to operate in a state of high ${\mathsf{\Phi }}_o$, resulting in poor combustion and a maximum ISFC of 334 g/kWh. For the transient process using FCC3, the slow increase rate of fuel quantity can ensure that the early stage of the transient process works at a relatively low ${\mathsf{\Phi }}_o$, leading to a lower degree of combustion deterioration and a relatively low ISFC.

As the EGR valve opening time is delayed to 0.5 s, it is obvious from Figure 13 that the lower ${\mathsf{\Phi }}_o$ improves the IMEP growth rate when the EGR valve is not opened. When the high-pressure EGR valve is opened at 0.5 s, the VGT opening of VCC2, VCC3, and VCC4 are all at their minimum, causing a large amount of exhaust to enter the cylinder and deteriorating the ${\mathsf{\Phi }}_o$. The transient process using FCC1 has the highest exhaust pressure difference and the most serious EGR rate overshoot, resulting in a decrease in IMEP.

By delaying the opening of the high-pressure EGR valve, the turbocharger can have a longer acceleration time under high acceleration and obtain a higher air intake flow. At this point, even though part of the exhaust gas is diverted, the turbocharger still can maintain a high response speed, and the lower ${\mathsf{\Phi }}_o$ also increases the oxygen content in the exhaust. Their combined effect leads to a lower ${\mathsf{\Phi }}_o$ and substantial improvement in the ISFC. Compared to the transient process with the EGR valve opened at 0.1 s, the maximum ISFC decreases by 27.6% (FCC1 + VCC1 + H0.1 versus FCC1 + VCC1 + H0.5), and the maximum IMEP achieved in 1 s increases by 29.2% (FCC1 + VCC4 + H0.1 versus FCC1 + VCC3 + H0.5).

By comparing the ${\mathsf{\Phi }}_o$ of FCC1 + VCC3 + H0.5 and FCC1 + VCC4 + H0.5, it becomes evident that the opening of the high-pressure EGR valve causes more exhaust to be diverted due to the higher exhaust intake pressure of VCC4. Simultaneously, the higher EGR rate decreases the intake oxygen concentration, leading to a higher growth rate of ${\mathsf{\Phi }}_o$ for VCC4 compared to VCC3 during the later stage. Consequently, this weakens the promotional effect of VCC4s small VGT opening degree on turbine acceleration during the later stage.

Postponing the opening of the high-pressure EGR valve to 0.9 s further reduces its impact on the IMEP, as shown in Figure 14. The VGT opening has already begun to increase, causing the pressure difference between the exhaust and intake to decrease rapidly. As a result, the opening of the EGR valve does not introduce excessive exhaust into the cylinder. Additionally, the turbocharger has already reached a high speed and acceleration, and the intake air pressure is rapidly increasing, quickly mitigating the impact of the EGR valve opening.

3.2.2. Effects on Soot and NOx

As shown in Figure 15, when the EGR valve opens at 0.1 s, the rate of NOx emissions increases at a reduced rate and there is no notable spike. When the EGR valve opening is delayed to 0.5 s, the lack of EGR restrictions in the early stages leads to a significant increase in NOx emissions. Once the EGR valve opens, the overshoot of the EGR rate caused by the high difference in intake pressure leads to a substantial decrease in NOx emissions. When the EGR valve opening is delayed to 0.9 s, NOx emissions have a significant spike due to the late opening of the EGR valve, and the maximum NOx peak value increases by 25.7% (FCC1 + VCC3 + H0.5 versus FCC1 + VCC4 + H0.9). The high-pressure EGR’s influence on the ${\mathsf{\Phi }}_o$ leads to a significant reduction in soot emissions as the opening of the high-pressure EGR valve is delayed. The peak value of soot emission decreases from 1385.5 mg/m³ to 112.9 mg/m³, with a decrease of 91.8% (FCC3 +VCC1 + H0.1 versus FCC2 + VCC4 + H0.9).

Figure 16 shows the dimensionless result of the transient process’s peak soot and peak NOx emissions using Formula (7). As the EGR valve opening is delayed, the emission points gradually move toward the lower right corner. The three working conditions with the best comprehensive emission are shown in the red circle, and the opening time of EGR valve is 0.7 s. When the EGR valve is opened at 0.7 s, the VGT opening of all control schemes is in an increasing state, effectively reducing the overshoot of the EGR rate. At the same time, a longer EGR valve closing time combined with a rapidly increasing fuel quantity allows the turbocharger to have higher acceleration capability. Under these conditions, soot emission is reduced to a level similar to the transient process with the EGR valve opened at 0.9 s. Opening the EGR valve at 0.7 s can effectively suppress the high NOx emissions caused by the large fuel quantity in the later stage of the transient process, resulting in the best comprehensive emissions.

3.2.3. Comprehensive Performance of Transient Process

The IMEP response and ISFC in dimensionless form, calculated using Equation (8), are plotted together with $D_p$ in Figure 17. By computing the $D_C$, three transient processes with optimal overall performance can be determined, and their specific parameters are shown in

Table 6. Transient process performance parameters.

Control Scheme	IMEP Response	ISFC (g/kWh)	Peak Value of Soot (mg/m3)	Peak Value of NOx (ppm)
FCC1 + VCC4 + H0.7	6.9	217.8	182.9	896.7
FCC2 + VCC3 + H0.7	8.2	211.2	140.4	879.4
FCC2 + VCC4 + H0.7	7.4	210.6	132.9	885.7

.

The data in the table demonstrates that the optimal time to open the high-pressure EGR valve is at 0.7 s. An early opening of the EGR valve will significantly impact the turbocharger’s response speed. The sharp deterioration of the oxygen equivalence causes severe emission degradation and a reduction in IMEP. On the other hand, if the high-pressure EGR valve is opened too late, it will result in an excessive peak value of NOx emissions. Compared to the case0 without EGR, the optimal control scheme FCC2 + VCC4 + H0.7 reduces the peak value of soot by 24.4%, NOx by 31.8%, increases the maximum IMEP achieved in 1 s by 31.7%, and lowers the ISFC by 9.52%. The comprehensive transient performance optimization is significant.

3.3. Comparison of Transient Performance between High- and Low-Pressure EGR Systems

Figure 18 displays the dimensionless peak values of soot and NOx emissions for both high- and low-pressure EGR systems. The values shown represent the average calculated from all the data of the two EGR systems. The figure demonstrates that high-pressure EGR influences the response of the turbocharger by extracting exhaust from turbine inlet, resulting in a notable impact on soot emissions while reducing NOx emissions. In contrast, low-pressure EGR can effectively reduce NOx emissions without significantly impacting soot emissions, thereby achieving a lower compromise emission level. Among the transient processes evaluated, the combination of FCC2 + VCC3 + L0.1 yields the lowest comprehensive emission, with a peak value of 164.7 mg/m³ for soot and 753.2 ppm for NOx.

The IMEP response and ISFC results in dimensionless form, calculated using Equation (8), are plotted together with $D_p$ in Figure 19. By computing the $D_C$, three transient processes with optimal overall performance can be determined, and their specific parameters are shown in

Table 7. Transient process performance parameters.

Control Scheme	IMEP Response	ISFC (g/kWh)	Peak Value of Soot (mg/m3)	Peak Value of NOx (ppm)
FCC2 + VCC3 + H0.7	8.2	211.1	140.4	879.4
FCC2 + VCC4 + H0.7	7.4	210.6	132.9	885.7
FCC1 + VCC4 + L0.1	10.8	225.9	158.8	783.8

.

From the distribution of performance points in Figure 19, it can be observed that the performance points of the low-pressure EGR system are relatively centralized, while the high-pressure EGR system has a wider distribution range and a significant gap between its upper and lower limits of transient performance. This phenomenon indicates that the impact of control parameter changes on the transient performance is more prominent when using high-pressure EGR. The optimal transient process parameters show that using high-pressure EGR can result in better IMEP response rate and ISFC, while using low-pressure EGR can result in lower compromising emissions.

4. Conclusions

This study conducted a transient bench test on a two-stage turbocharged heavy-duty diesel engine to optimize its performance during a load increase (20% to 100% in 1 s) at a constant speed (1200 RPM) transient process. The cooperative control of fuel quantity, VGT opening degree, and EGR valve was used to achieve the best transient process performance. The main outcomes of the study are summarized in the following points:

• The fuel quantity control curve (like FCC1 and FCC2) that increases fuel quantity faster during the early stage can accelerate the turbine more. And in the later stage, combining the higher growth rate of intake pressure with the lower fuel quantity growth rate can reduce the ${\mathsf{\Phi }}_o$ growth rate. The fuel quantity change mode should be paired with a rapidly decreasing VGT opening change mode (like VCC3 and VCC4) to achieve better transient performance.
• Due to its minimal impact on the turbocharger, the low-pressure EGR has a smaller influence on the equivalence ratio. When the opening of the low-pressure EGR valve is delayed until 0.5 s, the impact on the equivalence ratio becomes relatively small. Further delaying the opening of the EGR valve would result in a significant deterioration in NOx emissions.
• The use of the optimal scheme resulted in a 42.1% reduction in the peak value of soot emission, a 24.8% decrease in the peak value of NOx emission, a 9.14% decrease in ISFC, and a 30.6% increase in maximum IMEP achieved in 1 s, compared to the steady-state optimization control scheme without EGR.
• Prematurely opening the high-pressure EGR valve significantly impairs turbocharger response speed and excessively dilutes the intake oxygen concentration, leading to a substantial deterioration in IMEP and indicating specific fuel consumption. The optimal timing for opening the high-pressure EGR valve is in the later stage of the transient process when the VGT opening starts to increase, reducing the overshoot in the EGR rate resulting from excessive pressure differential across the intake. The optimal timing for opening the high-pressure EGR valve is 0.7 s. At this point, the impact of the EGR valve opening on the equivalence ratio is relatively small, and it effectively mitigates the excessive NOx emissions generated during the later stage of the transient process.
• The use of the optimal control scheme resulted in a 24.4% reduction in the peak value of soot emission, a 31.8% decrease in the peak value of NOx emission, a 9.52% decrease in ISFC, and a 31.7% increase in maximum IMEP achieved in 1 s, compared to the steady-state optimization control scheme without EGR.
• When using high-pressure EGR, the transient performance is more sensitive to the change of control parameters, and the mismatch of control parameters will significantly deteriorate transient performance. The use of low-pressure EGR is easier to obtain better compromise emissions.