Investigating a New Method-Based Internal Joint Operation Law for Optimizing the Performance of a Turbocharger Compressor

Abstract

A well-matched relationship between the compressor and turbine plays an important role in improving turbocharger and engine performance. However, in the matching of turbocharger and engine, the internal operation relationship between compressor and turbine is not considered comprehensively. In order to fill this gap, this paper proposed the internal joint operation law (IJOL) method based on the internal operating characteristics of the compressor and turbine using a combination of experimental and simulation methods. On this basis, the optimization method of the compressor was proposed. Firstly, according to the basic conditions of turbocharger, the compressor power consumption and the turbine effective power at a fixed speed were solved. Secondly, the power consumption curve of the compressor and the effective power curve of the turbine were coupled to obtain the power balance point of the turbocharger. Then, the internal joint operating point was solved and coupled to obtain the IJOL method. Finally, the IJOL method was used to optimize the blade number and the blade tip profile of the compressor. The simulation results showed that for the blade number, the 8-blade compressor had the best overall performance. For the blade tip profile, compared with the original compressor, the surge performance of the impeller inlet diameter reduced by 3.12% was better than that of the original compressor. In addition, in order to compare this to engine performance with different compressor structures, a 1D engine model was constructed using GT-Power. The simulation results showed that the maximum torque of the engine corresponding to the impeller designed by the IJOL method was 4.2% higher than that of the original engine, and the minimum brake specific fuel consumption was 3.1% lower. Therefore, compared with the traditional method, the IJOL method was reasonable and practical.

1. Introduction

Turbocharging technology is widely used to increase the power output per swept displacement of an internal combustion engine (ICE). As a result, the engine size can be greatly decreased, and fuel consumption and gas emissions may be reduced [1,2,3,4,5]. The centrifugal compressor is a key component of the turbocharger, and its aerodynamic performance has a significant impact on the operation of turbocharged ICEs. An accurate understanding of the matching characteristics of the compressor and turbine is beneficial to improve the performance of the turbochargers and the ICEs [6,7,8,9,10]. In addition, it is necessary to carry out design and optimization investigations based on matching operating characteristics between the compressor and turbine in the design and optimization of the turbocharger compressors. Hatami et al. [11] and Hosseinimaab et al. [12] concluded that the matching operating characteristics in the compressor and turbine had an important role in turbocharger performance. However, most of the existing studies have focused on the design and optimization of the turbocharger based only on the improvement of the performance of the compressor itself, but not on the comprehensive performance of the turbocharger itself.

At present, scholars have carried out research on the optimization of the aerodynamic performance and design of the structures of the compressors. Ekradi et al. [13] presented an integrating three-dimensional (3D) blade parameterization method to optimize the centrifugal compressor impeller with splitter blades. The results showed that at the design point, the isentropic efficiency increased by 0.97%, and the mass flow rate and total pressure ratio increased by 0.65% and 0.74%, respectively. Ma et al. [14] compared four optimization algorithms to improve the operating stability of a centrifugal compressor and found that, compared to the reference design, the stall margin of the centrifugal compressor was improved by 1.87% with the optimization using the particle swarm optimization algorithm. Shaaban et al. [15] proposed a new radial vaneless diffuser design method to improve the centrifugal compressors’ performance. The results indicated that under swirl flow and jet-wake conditions, the diffuser pressure coefficient increased 6.6% and the diffuser loss coefficient decreased 4.7%. Tüchler et al. [16] used a coupled approach of computational fluid dynamics and genetic algorithm to optimize an automotive compressor. The results showed that the shorter splitter and varied pitch fraction both increase near surge and peak efficiency. Zamiri et al. [17] investigated the influences of blade squealer tips on the aerodynamic performance of a centrifugal compressor. The results showed that at the design point, the use of squealer tips increased the compressor efficiency by 0.32%. Aparna et al. [18] and Moussavi et al. [19] concluded the same results. However, the compressor is affected by the fluctuation of the ICEs’ admission, which make the flow rate and pressure of the compressor periodically change with the ICEs’ operating process. This could further affect the engine performance. For example, the compressed air supercharging system could improve the driving force during the phase of the engine’s increasing crankshaft rotational speed [20]. Therefore, it is noteworthy to pay attention to the operating characteristics between the compressor and the engine, which are important for improving the overall performance of the supercharger and the ICEs [21,22].

Currently, scholars have conducted research on the matching of the compressor with the ICEs. Mousavi et al. [23] suggested a new algorithm for turbocharger matching. Chen et al. [24] proposed a novel pseudo-Mean Average Precision (MAP) optimization method to achieve full-operation-range performance optimization of a compressor. The results indicated that by using the optimization method, the choke flow rate increased by 20% and the maximum efficiency increased to 80%. In order to improve the accuracy of matching, Huang et al. [25] established a lumped model to calculate compressor adiabatic efficiency and the heat transfer properties of a turbocharger. Wu et al. [26] also proposed a method to match a two-stage turbocharging system, and they found that with adopting the method, the engine torque increased more than 10% and the engine low fuel consumption area was broadened. In order to improve engine performance, Hosseinimaab et al. [12] employed a hybrid optimization approach (including modern and numerical optimizers) to modify the compressor geometry. However, they did not consider the effect of the turbine on the supercharger and engine performance. Li et al. [27] presented a new method to predict the performance MAPs of automotive turbocharger compressors. The results indicated that the method could be used for the preliminary design of turbocharger compressors with both vaneless and vaned diffusers. However, most of the existing studies only match the compressor with the ICEs. Actually, the performance at both ends of the turbocharger is limited by the structural properties of another end, and a complete performance map is usually unavailable [28]. Therefore, the research on the internal matching characteristics of the compressor and turbine play an important role in improving the performance of turbochargers and ICEs.

Turbochargers can effectively improve the power and fuel economy of ICEs, reduce emissions, and miniaturize ICEs. For a turbocharger, the internal matching characteristics between the compressor and turbine determine its operating performance, which in turn determines the matching performance of the turbocharger to the engine. There is no in-depth and systematic research on the internal matching between the compressor and turbine, and the important role of the internal matching of their joint points, in the design of turbochargers, is not fully reflected. To fill this gap, this study proposed an optimization method for the compressor based on the internal joint operating characteristics between the compressor and turbine. The rest of this study is organized as follows: Section 2 is devoted to the design and validation of the compressor and turbine models, introducing the test turbocharger performance test bench. Section 3 proposes an optimization method for the compressor based on the IJOL method of the turbocharger, including the calculation of turbine and compressor powers, and the coupling to obtain the internal joint operation curve of the turbocharger. Section 4 presents the optimized design of the blade number and the blade tip profile of the compressor using the IJOL method and compares the optimization results with the traditional method. Section 5 summarizes the main results of this study.

2. Materials and Methods

To clearly demonstrate the research idea of this study, an investigation procedure of the study is shown in Figure 1. Firstly, based on the basic conditions of turbocharger operation, since there was energy loss between the output power at the turbine end to the power consumption at the compressor end, the power transfer coefficient was proposed to characterize the bearing friction loss of the intermediate body. Then, based on the simulation and self-cycling experiments, the powers of turbine and compressor were calculated, and the coupling obtained the internal joint operation curve. Secondly, a compressor optimization method based on the internal joint operation law (IJOL) was proposed, and the blade number and blade tip profile were optimized. The optimization simulation results were compared with the traditional method. Finally, experiments were conducted to verify the results. Compared with the traditional method, the IJOL method was more reasonable and practical.

2.1. Research Objects

A 4-cylinder automotive engine turbocharger was used as the research object. Figure 2 shows the three-dimensional (3D) structure of the physical prototype of the turbocharger.

Table 1. Turbocharger parameters.

Item	Value	Item	Value
Outlet diameter D1t of compressor impeller (mm)	44	Inlet diameter of turbine impeller (mm)	37.6
Inlet diameter of compressor impeller (mm)	32.1	Outlet diameter of turbine impeller (mm)	33.1
Blade number of compressor	8	Blade number of turbine	11
Diffuser height (mm)	2.5	Turbine impeller inlet blade angle (°)	0
Design pressure ratio	2.2	Turbine impeller inlet blade height (mm)	5.1
Rated speed (r/min)	220,000	Turbine impeller axial length (mm)	18.9
Flow range (kg/s)	0.02–0.13	Turbine impeller exit mean blade angle (°)	56.4
Displacement of gasoline engine (L)	1.5	Type of cooling	oil cooling + water cooling

lists the parameters of turbocharger.

2.2. Setting Model Parameters

In the compressor numerical model, the impeller of the compressor was the equal-length blade and the impeller outlet with angle bending. The diffuser adopted a bladeless diffuser. The principle geometric structure and original turbocharger compressor fluid domain model are shown in Figure 3 and Figure 4.

The compressor model consisted of five parts, which were the inlet domain, impeller rotation domain, diffuser domain, volute domain and outlet domain. The turbulence model used the Shear Stress Transport (SST) two-equation model, and the mathematical model used the Reynolds-averaged Navier–Stokes system of equations [30]. The model walls were all set as smooth, non-slip adiabatic walls [31], and wall temperature in the simulation was set as the compressor or turbine wall temperature under fixed boundary conditions (speed and flow rate) of the experiments. The fluid was defined as an ideal gas, and the fluid viscosity was set as a function of temperature. The total inlet pressure of the compressor was set to 101.325 kPa, the total inlet temperature was 293.15 K, and outlet boundary set to the mass flow rate (kg/s) corresponding to the turbocharger speed. For turbine model, the specific parameter settings can be seen in our previous paper [32].

In order to validate the accuracy of numerical model, a mesh independence analysis was conducted. The total pressure, efficiency and power consumption of the compressor with different grid numbers are shown in Figure 5. It can be seen from the figure that the performance curve of the compressor was smoothly distributed and almost constant when the grid number reached above 3,358,000, so it could be considered that the grid number met the simulation requirements. Therefore, the grid number of 3,358,000 was chosen to use in the calculation.

2.3. Test Preparation and Model Validation

The compressor and turbine performance experiments were conducted on a Kratzer turbocharger test bench. Figure 6 shows the physical illustration and schematic diagram of the bench arrangement. The test bench was capable of measuring performance parameters of both the compressor and turbine, with automated data acquisition and processing functions. The bench could realize accurate control of turbocharger speed, compressor and turbine inlet and outlet parameters. The compressor inlet was equipped with a pressure and temperature regulator, which could be automatically adjusted in real time to ensure a smooth inlet temperature and pressure. Sensors were arranged in the turbine inlet and outlet pipes to improve the accuracy of temperature and pressure acquisition. The fuel for the experiment was liquefied petroleum gas, which could automatically correct the air-fuel ratio of the gas according to the turbine inlet temperature.

During the experiment of compressor performance, at the set turbocharger speed, the surge point and choke point of the compressor were to be found firstly. Then, experimental points evenly between the surge point and choke point were set. Finally, data were collected in turn to form the pressure ratio-flow performance curve at the same speed.

The validation experiments of the compressor and turbine were carried out on the Kratzer turbocharger test bench, and the following three speed conditions of 110,000 r/min, 150,000 r/min and 190,000 r/min were selected to represent the low, medium and high speeds of the turbocharger operation, respectively. In this study, the validation method was used in previous papers [31,33].

Figure 7 shows the turbocharger performances between the experiments and simulation. For pressure ratio of compressor, it can be seen that the maximum error was 4.71% at the high pressure ratio condition at 190,000 r/min, which was within the acceptable range. For expansion ratio of turbine, the experiment and simulation of the swallowing capacity were in good agreement with each other and had a maximum error value of 2.62% at the speed of 150,000 r/min, which was within the acceptable range. This discrepancy was attributed to the simplification of the secondary feature in the geometry, the optimal application scope of the SST model and manufacturing error [34,35]. Therefore, the turbocharger model could meet the simulation requirements and can be used for further study.

3. Internal Joint Operation Law Analysis

3.1. Coupling of Internal Joint Operation Curves

The compressor and turbine are the two working parts of the turbocharger; both are rigidly connected by the rotor shaft, and the compressor and turbine have the same speed, and the working condition of the compressor and turbine is related to the engine working process. In this study, the numerical simulations were conducted based on the assumption of static state operation. There were three basic conditions for the operation of the turbocharger, including speed balance, flow rate balance and power balance.

Speed balance: The compressor, turbine and rotor shaft have the same speed.

$$n_C=n_T=n_R$$

(1)

where, $n_C$ is the compressor speed (r/min), $n_T$ is the turbine speed (r/min), and $n_R$ is the rotor shaft speed (r/min).

Flow rate balance: The leakage mass flow rate is negligible because it is very small [36]. The compressor operating mass flow rate plus the engine fuel mass flow rate equals the turbine operating mass flow rate.

$$m_T=m_C+m_F$$

(2)

where $m_T$ is the turbine operating flow rate (kg/s), $m_C$ is the compressor operating flow rate (kg/s), and $m_F$ is the fuel flow rate (kg/s).

Power balance: Figure 8 shows the energy transfer process in the turbocharger. Power transfer from the turbine end to the compressor end of the process would lose part of the energy, which is the bearing friction loss. The turbine output power minus the losses of intermediate body is equal to the compressor power consumption. Based on the law of conservation of energy, the calculation formula is as follows:

$$P_T=P_C+P_{Loss}$$

(3)

where $P_T$ is the turbine output power (W), $P_C$ is the compressor power consumption (W), and $P_{Loss}$ is the power loss of intermediate body (W).

The heat losses at a turbocharger were heat dissipating into the environment, heat flows within the turbocharger as well as active cooling through cooling water and oil, all due to high temperature gradients. In the simulation, the heat loss dissipating into the environment was not considered, which was neglected. Due to the wall temperature in the simulation that was set as the compressor or turbine wall temperature under fixed boundary conditions (speed and flow rate) of the experiments, the heat loss from heat flow in the turbocharger was considered, and the heat loss was included in the turbine output power and compressor consumption power. This was because the turbocharger bench test was a hot blow experiment, and it can be seen from Figure 9 that the simulated values of the compressor and turbine efficiencies basically match the experimental values, indicating that the heat flows in the turbocharger had been considered in the simulation calculation.

Turbine output power refers to the power generated by the exhaust gas impinging on the rotation of all blades. Compressor power consumption refers to the work consumed to drive all the blades to rotate for compressing the fluid. The power calculation formula is as follows:

$$P=T_{all blades}\times \omega$$

(4)

where, $P$ is the turbine output power or the compressor power consumption (W), $T_{all blades}$ is the total torque of all blades (N·m), $\omega$ is the angular velocity (rad/s).

The compressor power consumption is equal to the turbine effective power, and there is power transfer loss (bearing friction loss) between the turbine output power and turbine effective power in intermediate body. Therefore, the power transfer coefficient ${\eta }_P$ is used to define the ratio of the compressor power consumption to the turbine output power.

$${\eta }_P=P_C/P_T$$

(5)

The power transfer coefficient ${\eta }_P$ could relate the compressor power consumption to the turbine output power and thus to couple the joint operation curve inside the turbocharger.

At the fixed speed, the turbine output power and the compressor power consumption were calculated by the simulation and turbocharger self-cycling experiments. Figure 10 shows the self-cycling experiment values of the compressor outlet pressure and turbine inlet pressure compared with the simulated values. As it can be seen that the self-cycling experiment values and simulation values were in good agreement, the error was in the allowable range.

Based on the turbine output power and compressor power consumption calculated under the self-cycling experiment conditions, the power transfer coefficient is calculated by Equation (5), as shown in Figure 11.

It should be noted that the power transfer coefficients obtained by the self-cycling experiments could not cover all the flow rate points on the speed line, and there was a certain error. However, the focus of this study was the performance difference caused by the change of structures, and the power transfer coefficients could meet the needs of performance evaluation and comparison between different compressor structures.

The turbine effective power is the maximum power that can be obtained at the compressor end. The turbine effective power is obtained by transforming the turbine output power through Equation (5), as shown in Figure 12.

In the fixed-speed line, the compressor power consumption curve and turbine effective power curve were superimposed and coupled. The horizontal coordinate of intersection point of both the compressor and turbine at the time of coupling were the compressor working flow rate, and the intersection point of the power balance was obtained, as shown in Figure 13. The significance of the proposed joint operation point was to obtain a joint curve reflecting the turbocharger operation on the basis of considering the internal matching of the compressor and turbine.

By analogy, the compressor power consumption curves and turbine effective power curves for all speeds were superimposed and coupled to obtain the joint operation points of the turbocharger at each speed, as shown in Figure 14.

3.2. Propose the Total Efficiency Calculation Method of the Compressor

According to the internal joint operation curve, the total efficiency at the joint point is calculated by the following equation:

$${\eta }_{tot}={\eta }_T\times {\eta }_C\times {\eta }_P$$

(6)

where ${\eta }_{tot}$ is the total efficiency of the turbocharger.

The traditional method of calculating the total efficiency of a turbocharger is to multiply the maximum efficiency of the turbine, the maximum efficiency of the compressor and the mechanical efficiency, which is not objective enough. This was because, on the one hand, the highest efficiency point of the turbine and the highest efficiency point of the compressor are often not in the same operating point. On the other hand, the work of the supercharger is a dynamic process; the actual efficiency of both the turbine and the compressor are changing, making different operating conditions have different total efficiency of the supercharger [37]. Therefore, the concept of joint point was proposed in this study to calculate the turbocharger total efficiency, compressor and turbine performances.

Figure 15 shows the distribution of compressor efficiency for the joint operating conditions on the compressor efficiency MAP. It can be seen from the figure that the efficiency of the joint point operating condition did not go through the maximum efficiency point of the compressor. Therefore, the efficiency of the compressor calculated based on the joint operating point was related to the speed and compressor working flow rate, synchronized with the turbine operating condition, and closed to the actual situation of the turbocharger, which was practical.

3.3. Internal Joint Point Operation Law (IJOL) Method

In the process of compressor design and optimization, pressure ratio, surge margin, choke flow rate and efficiency are important performance parameters [38]. In this study, the compressor performance index included pressure ratio, surge margin, choke flow rate, joint point efficiency and maximum efficiency. The formula for calculating the surge margin is shown below [39]:

$$SM=\left(\frac{\frac{{\pi }_s}{m_{scor}}}{\frac{{\pi }_w}{m_{wcor}}}-1\right)\times 100\%$$

(7)

where ${\pi }_s$ is the pressure ratio at surge, $m_{scor}$ is corrected flow rate at surge, ${\pi }_w$ is the pressure ratio of working point, $m_{wcor}$ is corrected flow rate at the working point. The larger the surge margin, the better the surge performance of the compressor.

The formula for calculating the compressor performance index is shown below:

$${\varphi }_c=A_1\times \frac{S_{R_{surge}}}{S_{O_{surge}}}+A_2\times \frac{{\eta }_{R_{joint point}}}{{\eta }_{O_{joint point}}}+A_3\times \frac{{\pi }_R}{{\pi }_O}+A_4\times \frac{m_R}{m_O}+A_5\times \frac{{\eta }_{R_{max}}}{{\eta }_{O_{max}}}$$

(8)

where ${\Phi }_C$ is the calculated compressor performance index. $S_{R_{surge}}$ and $S_{O_{surge}}$ were the surge margin of remodel and original compressors.${\eta }_{R_{joint point}}$ and ${\eta }_{O_{joint point}}$ were the efficiency of joint point.${\pi }_R$ and ${\pi }_O$ were the pressure ratio.$m_R$ and $m_O$ were the mass flow rate.${\eta }_{R_{max}}$ and ${\eta }_{O_{max}}$ were the maximum efficiency. The parameters of $A_1$, $A_2$, $A_3$, $A_4$ and $A_5$ were the weighting factors of surge margin, joint point efficiency, pressure ratio, choke flow rate and maximum efficiency. For the weight distribution of each parameter, turbocharger compressor work was increasingly close to the surge line, operating stability was critical for the compressor [40] and needed to broaden the compressor stable working regions, so the joint point of the surge performance weight distribution was the largest. The efficiency and pressure ratio of the joint point of the compressor directly reflected the compressor performance, which in turn determined the engine intake performance, so the efficiency and pressure ratio of the joint point of the compressor weight distribution were second only to that of surge performance. The choke flow of the compressor only needed to be greater than the maximum working flow of the engine, so the choke flow and maximum efficiency weights were the smallest. The weighting coefficients are shown in

Table 2. Weight assignment for each performance parameter.

	Surge Margin	Joint Point Efficiency	Pressure Rate	Choke Flow Rate	Maximum Efficiency
Weight distribution	30	25	25	10	10

.

4. Results and Discussion

4.1. Analysis of Compressor Blade Number Based on IJOL Method

The compressor impeller is the most important component that affects the compressor performance, so the compressor impeller was selected for optimization.

4.1.1. Optimization of the Blade Number

Four groups of compressors with blade numbers of 7, 8, 9 and 10 were designed, and the 3D modeling of each group was kept consistent with that of the original compressor. The same topology and meshing method were used for the impeller models, and the optimization study was carried out at three speeds of 110,000 r/min, 150,000 r/min and 190,000 r/min, respectively.

Figure 16 shows the effect of the blade number on the pressure ratio at different speeds. It can be seen that the pressure ratio increased with an increase in the blade number. When the blade number was greater than 8, the increased amplitude of the pressure ratio was limited. At 190,000 r/min, the difference between the outlet pressures of a 7-blade compressor and an 8-blade compressor were more than 4.5 kPa. Further observation found that the overall surge line of the four groups of blades was relatively close, but the choke line moved to the left with an increase in the blade number. With an increase in the blade number, the working flow range of the compressor became narrower. Specifically, at low and medium speeds, with the blade number increased, the surge flow slightly increased and the joint point surge margin gradually decreased. At high speed, there was no significant difference in the surge flow and surge margin for different blade numbers (as shown in

Table 3. Comparison of surge performance of compressors with different blade numbers.

	7		8		9		10
Speed (r/min)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)
110,000	0.0193	10	0.0198	9.5	0.0201	9.2	0.0204	8.9
150,000	0.0373	8	0.0377	7.6	0.0380	7.3	0.0381	7.2
190,000	0.0508	12.4	0.0508	12.4	0.0509	12.3	0.0506	12.6

).

Figure 17 shows the effect of the blade number on the efficiency. It can be seen that near the joint point, the more the blade number, the higher was the efficiency. However, the difference was not obvious; the design point efficiency of the 10-blade compressor was about 1% higher than the design point efficiency of the 8-blade compressor. The 7-blade compressor’s joint point efficiency decreased significantly compared with other blade numbers, especially in high speed. As can be seen in

Table 4. Comparison of performance indexes of compressors with different blade numbers.

	7	8	9	10
Mean surge margin (%)	10.13	9.83	9.60	9.57
Mean joint point efficiency (%)	64.5	65.1	65.8	65.9
Mean joint point pressure ratio	1.871	1.953	1.967	1.978
Maximum efficiency (%)	72.296	73.029	73.675	74.07
Choke flow rate (kg/s)	0.1385	0.137	0.136	0.134
Performance index	99.6	100.0	99.8	99.8

, for the compressor performance index, an 8-blade compressor was the highest, while the 7-blade compressor performance index decreased more, indicating that the 8-blade compressor had the best performance and high comprehensive performance at the joint point.

4.1.2. Blade Tip Profile Optimization

The compressor’s impeller inlet diameter, outlet diameter and diffuser height have an important impact on the performance of the compressor. The change of blade tip profile could change the compressor inlet diameter, diffuser height and compressor transition arc profile, and therefore affected the performance of the compressor.

There were three schemes for the optimization of the blade tip profile. Scheme A: Compared with the original compressor, the impeller inlet diameter was reduced by 3.12%, and the diffuser height remained unchanged. Scheme B: Compared with the original compressor, the impeller inlet diameter remained unchanged, and the diffuser height was reduced by 20%. Scheme C: Compared with the original compressor, the impeller inlet diameter and diffuser height were reduced by 3.12% and 20%, respectively. The percentage of impeller inlet diameter and diffuser height for three structures as compared with original compressor is shown in Figure 18.

Figure 19 shows the comparison of the pressure ratio of the four compressors at various speeds. It can be seen from the figure that there was no significant difference in the pressure ratio at the joint point of low and middle speeds. At the joint point of high speed, the pressure ratio of Scheme A was slightly smaller than that of the original compressor, but the difference was within 1.2%. Near the joint point of low and medium speeds, the pressure ratio of Scheme A and the original compressor had a wide overlap part. Overall, the pressure ratio of Scheme A was closest to those of the original compressor.

For surge performance, it can be seen from the

Table 5. Comparison surge performance of compressors with different blade tip profile.

	Original		Scheme A		Scheme B		Scheme C
Speed (r/min)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)
110,000	0.0198	9.5	0.0180	11.3	0.0180	11.3	0.0158	13.5
150,000	0.0377	7.6	0.0345	10.8	0.0370	8.3	0.0335	11.8
190,000	0.0508	12.4	0.0465	16.7	0.0500	13.2	0.0454	17.8

that all three schemes improved the surge flow rate as compared with the original compressor. The surge margin of Schemes A and C was above 10%, which met the requirements of the surge margin, while the surge margin of the original compressor was below 10% at low and medium speeds.

The effect of blade tip profile on the efficiency of the compressors is shown in Figure 20. It can be seen that the efficiencies of the three schemes were improved as compared with the original compressor near the joint point of each speed, and the joint point of Scheme A was 0.7–1.5% higher than that of the original compressor. In addition, the highest efficiency of Scheme A was 0.8% higher than that of the original compressor.

For compressor performance index, as can be seen in

Table 6. Comparison of performance indices of different blade tip profiles.

	Original	Scheme A	Scheme B	Scheme C
Mean surge margin (%)	9.83	12.93	10.93	14.37
Mean joint point efficiency (%)	65.1	66.5	66.1	66.5
Mean joint point pressure ratio	1.953	1.943	1.954	1.936
Maximum efficiency (%)	73.029	73.845	71.225	71.965
Choke flow rate (kg/s)	0.137	0.130	0.131	0.127
Performance index	100.0	109.5	103.0	113.3

, because the choke flow rate of Scheme C did not meet the maximum working flow rate of the engine, it could not be used as an optimized structure. Scheme A had the highest compressor performance index and the best overall performance among the available options. Compared with the original compressor, Scheme A had obvious comprehensive advantages.

In summary, Scheme A was the best blade tip profile in the operating conditions range. Therefore, when the impeller inlet diameter was reduced by 3.12% and diffuser height remained unchanged, the overall performance of the compressor was higher than that of the original compressor, especially in terms of surge performance and joint point efficiency.

4.2. Comparison and Validation Analysis of the IJOL and Traditional Methods

For the traditional method, the optimization goal is to pursue the maximum efficiency of the compressor [41,42]. Therefore, the index for evaluating the optimization results of traditional methods is the maximum efficiency. In order to compare the IJOL method with the traditional method, the original impeller structure, the splitter-blade impeller designed by the traditional method and the structure determined by the IJOL method with the impeller inlet diameter reduced by 3.12% were selected for comparison. The inlet and outlet diameters of the compressor impeller optimized based on the traditional method were the same as those of the original compressor. The numbers of main blades and splitter blades were each 5. In addition, the main blade was 3.5 mm higher than the splitter blade at the inlet guide vane, and the radial parts of the main and splitter blades had the same 3D shape. The main blade shape remained the same as the original compressor blade.

A comparison of the pressure ratio of the three structures is shown in Figure 21. It can be seen that the surge line of the traditional method moved to the left compared with the original compressor, but the leftward shift of its surge line was not as large as that of the IJOL method. The specific values are shown in

Table 7. Comparison of surge performance of different compressor structures.

	Original		Traditional Method		IJOL Method
Speed (r/min)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)	Surge Flow Rate (kg/s)	Surge Margin (%)
110,000	0.0198	9.5	0.0180	11.3	0.0196	9.7
150,000	0.0377	7.6	0.0345	10.8	0.0371	8.4
190,000	0.0508	12.4	0.0465	16.7	0.0502	13.0

. The lower the speed, the smaller was the surge margin of the traditional method, while the surge line of the IJOL method basically moved to the left as a whole, among which the improvement of the surge margin at low speed was obvious. At the joint points of low and middle speeds, the pressure ratio of the traditional method was not significantly different from that of the original compressor. While at 190,000 r/min, its pressure ratio was lower than that of the original compressor, which was especially obvious at high speed and high flow rate.

The efficiency comparison of the three structures is shown in Figure 22. Near the joint point of 150,000 r/min, the efficiency of the traditional method was the same as the original compressor, while at other speed joint points the efficiency of the traditional method was lower than that of the original compressor. The efficiency of the IJOL method was higher than that of the original compressor at all joint points. As can be seen in

Table 8. Comparison of performance indexes of different compressor structures.

	Original	Traditional Method	IJOL Method
Mean surge margin (%)	9.83	12.93	10.37
Mean joint point efficiency (%)	65.1	66.5	64.3
Mean joint point pressure ratio	1.953	1.943	1.861
Maximum efficiency (%)	73.029	73.845	73.901
Choke flow rate (kg/s)	0.137	0.13	0.132
Performance index	100.0	99.9	109.5

, the performance index of the traditional method was lower than that of the original compressor, while the performance index of the IJOL method had obvious advantages and was the best performance structure in the operating conditions.

4.3. Comparative Analysis of Engine Performance with Optimized Structures of Two Methods

The optimal compressor structures based on the traditional method and the IJOL method were the splitter-blade impeller and the impeller inlet diameter reduced by 3.12% structures. A 1D engine model in Figure 23 was constructed using GT-Power for engine performance simulation and analysis. The basic assumptions [43] in this simulation are as follows:

• The working fluid was a uniform state, and the air entering the cylinder and the residual exhaust gas were completely mixed instantaneously;
• Air and mixed gas were considered ideal gases, and their thermodynamic parameters were affected by the temperature and composition of the gas;
• A steady flow process was regarded for the process of working fluid;
• The import and export kinetic energy of the working fluid was negligible, and there was no leakage during the combustion process;
• The combustion heat release process was regarded as a thermodynamic process in which the external heats the working fluid inside the system in accordance with the established heat release law.

In the simulation, except for the change of the turbocharger structure, the rest of the engine structural components and settings were kept unchanged.

As can be seen in Figure 24, the IJOL method had the highest overall torque and the lowest brake-specific fuel consumption (BSFC) at low and medium engine speeds, while the traditional method was the opposite. Compared with the original engine, the maximum torque of the IJOL method was 4.2% higher and the minimum BSFC was 3.1% lower, while the maximum torque of the traditional method was 2.4% lower and the minimum BSFC was 1.2% higher than that of the original engine. The reason was that the performance index of the IJOL method was highest in the three compressor structures, while the performance index of the traditional method was smallest. The better overall performance of the compressor could further increase engine torque and reduce BSFC [44]. Therefore, the impeller inlet diameter that was reduced by 3.12% designed by the IJOL method instead of the original impeller could improve the power and fuel economy of the engine at low and medium speeds.

4.4. Experimental Verification and Comparison of Compressor Optimization

Experimental analysis was performed on three structures of the compressor optimized based on the IJOL method and the traditional method. Figure 25 shows the pressure ratio for the three structures. It can be seen from the figure that the pressure ratios of the IJOL method were all equal to or slightly higher than that of the original compressor, and the pressure ratio was 1.49% higher than that of the original compressor near the joint point at high speed. The pressure ratio of the traditional method was basically the same as the original compressor at the joint point of low and medium speeds, and was lower than the original compressor at high speed. It was further observed that both the IJOL and the traditional methods had smaller surge flow and higher surge margin than that of the original compressor. Compared with original compressor, the IJOL method had a maximum reduction of 13.91% in the surge flow rate and a maximum increase of 6.07% in the surge margin, which was a significant improvement.

Figure 26 shows the efficiency for the three structures. The maximum efficiency of the original compressor was set to the reference value of 100%. Near each joint point, the efficiency of the IJOL method was higher than that of the original compressor, with higher values of 0.8% and above.

From the analysis, the experimental results of compressor performance and simulation conclusions were consistent. Therefore, both optimized compressor structures could reduce the surge flow of the compressor, and the impeller optimized by the IJOL method with the impeller inlet diameter reduced by 3.12% had pressure ratio and efficiency advantages near the joint points, which could improve the power and fuel economy of the engine in the low and medium speeds.

5. Conclusions

In this study, according to the basic conditions of turbocharger internal operating characteristics, the turbocharger joint points were determined, and the internal joint operation law (IJOL) was obtained. A compressor optimization method was proposed based on the IJOL, and the blade number and blade tip profile were selected for optimal application design. The following conclusions were obtained within the scope of this study:

• Based on the joint operating characteristics of the two ends of the turbocharger compressor and turbine, the IJOL method of the turbocharger was coupled using the performance distribution of the compressor and turbine, and the calculation method for the total efficiency of the turbocharger was improved. The efficiency of the compressor obtained using the IJOL method was synchronized with the working of the two ends, which was closer to the actual situation, and more practical.
• Based on the IJOL method, the effects of the blade number and the blade tip profile on the performance were analyzed. For the blade number, the 8-blade compressor had the best overall performance. For the blade tip profile, the compressor with the impeller inlet diameter reduced by 3.12% as compared with the original compressor had better surge performance.
• Compared with the traditional method, the maximum efficiency of the IJOL method was slightly lower, but its joint point performance was higher than that of the traditional method.
• Compared with the performance of the original engine, the power and fuel economy of the engine designed based on the traditional method were worse than those of the original engine. The maximum torque of the engine based on the IJOL method was 4.2% higher than that of the original engine, and the minimum BSFC was 3.1% lower. Compared with the traditional method, the IJOL had obvious advantages.