Calculation and simulation of turbocharger flow field and optimization analysis of impeller structure

Abstract

Aiming at the problem of low efficiency of the JP80D turbocharger rotor system, an optimization analysis of the turbocharger impeller was carried out. Since the second-order critical speed of the rotor system will produce resonance hazards within the system’s operating speed range, the second-order speed needs to be optimized away from the working speed. Therefore, this paper adopts the methods of finite element analysis and Campbell diagram analysis. The three parameters of impeller’s long and short blade combination, blade thickness and blade forward inclination angle are optimized by single-variable progressive optimization method, and then the compressor is simulated by finite element. Finally, by comparing the distribution of the internal flow field characteristics of the compressor, the optimal structural parameter scheme is obtained. By optimizing the impeller to make the second-order speed far away from the working speed, the internal flow field is in an excellent working state. It greatly improves the unbalanced performance of the rotor system, and avoids the problem of low efficiency due to basic excitation and unbalance.

Keywords

Turbocharger flow field simulation structure optimization

1. Introduction

With the intensification of environmental pollution, the depletion of renewable resources on the planet, and implementing environmental protection, energy saving and emission reduction policies, the development and application of engines have presented a huge challenge. Turbocharging technology is one of the most effective and economical methods to improve engine performance and reduce engine pollution emissions [1]. The supercharging is a technology that uses a supercharger to compress the air or combustible mixture before feeding it into the cylinder to improve air density and increase intake air volume. After supercharging, although the working volume of the cylinder remains unchanged, the fresh air or mixed gas charge density that enters the cylinder per cycle increases, which increases the actual mixed gas charge. Therefore, not only can the fuel burn more fully but also the amount of fuel added per cycle can be increased, to achieve the purpose of improving engine power and economy and improving emission performance [2]. Turbochargers generally use centrifugal compressors. Centrifugal compressors are not only complex in geometry, but also in internal gas flow conditions. They are three-dimensional, viscous, and unsteady flows, and there are different forms of secondary flow [3, 4]. Therefore, studying the internal flow field flow characteristics of the turbocharger is of great significance for improving the design, optimization and performance of the turbocharger.

For the internal flow field characteristics of turbochargers, many researchers have conducted a lot of research. Lu Longhui et al. studied the turbine flow field of axially adjustable variable nozzle supercharger for automotive diesel engines, conducted tests on different operating conditions of the supercharger, analyzed the changes of the turbine internal flow field, and investigated the effects of high and low speed blades on the turbine characteristics [5]. Rujing Lei studied the flow field analysis, the flow field distribution of internal pressure and velocity, and the overall performance of turbocharge compressors with different structures and parameter was simulated by using computational fluid dynamics software [6]. By simulating the actual flow characteristics of the turbocharger’s pressurizer during engine operation under different operating conditions, Liu Sirong et al. analyzed the variation of the internal flow field of the pressurizer with the rotational speed and the blade top clearance [7]. Fu Dingyuan studied the computational simulation software and related mathematical models, and considered the interaction between the volute and the impeller and the influence of the non-uniform airflow on the flow field and performance of the supercharger respectively [8]. Yuan Wei et al. conducted 3D numerical simulations of the compressor gap flow and comparative analysis revealed the flow characteristics of the gap region, which is helpful for understanding the understanding of the internal flow field of the compressor [9]. Min Zhou et al. conducted a simulation study on the flow field characteristics of the turbine stage of an automotive turbocharger based on the computational fluid dynamics two-phase flow technique, to analyze the exhaust gas particle mass concentration, exhaust gas flow rate, pressure and temperature variation patterns of the turbine stage at different turbine speeds [10]. Hong-Yi Wu developed a numerical model associated with preliminary design of a turbine for utilization of geothermal energy. It provides an input for three-dimensional (3D) simulation of the flow field, in terms of the commercial software ANASYS-CFX [11]. The thermal design of the mixture ORC radial inflow turbine is carried out by Jiaxi Xia, and the CFD simulation is performed to investigate the 3D flow characteristic of the designed turbine. Meanwhile, the helical groove seal of the turbine shaft is designed and analyzed through CFD method [12]. Angie L. Espinosa Sarmiento [13] used 1D and 3D CFD model. The performance characteristics and the 3D flow field at design and off-design operating conditions showed that the optimization resulted in better blade loading and higher efficiencies over the entire operating range studied.

In this paper, the impeller of JP80D turbocharger is optimized for the problem of low efficiency of the rotor turbocharger system. The three parameters of impeller’s long and short blade combination, blade thickness and blade rake angle are optimized by single variable progressive optimization, and then finite element simulation of the compressor is carried out. Comparing the distribution of flow field characteristics inside the compressor, we get the optimal structural parameter scheme. It provided a way to avoid unbalance faults because of underlying excitation and imbalance.

2. Turbocharger 3D modeling

The commonly used turbocharger is structurally divided into the compressor, turbine, intermediate, bearing and housing, etc. The basic construction is to mount the turbine and the compressor on the same shaft [14]. Figure 1 shows the three-dimensional model of the turbocharger. Figure 2 shows the internal structural diagram of the turbocharger.

Figure 1.

Three-dimensional model of the turbocharger.

Figure 2.

Internal structure diagram of the turbocharger.

The compressor is one of the main components of the turbocharger. The internal structure is generally divided into impeller, volute, air inlet and diffuser. Its main working process is: after the engine is started, the turbo compressor starts to work. At the same time, the external air enters the volute under the pressure difference, and the impeller coaxial with the turbine rotates at high speed. Under the centrifugal force generated by the rotation, the air gradually moves towards both ends of the volute. When the air flows into the diffuser, its velocity and pressure will increase at the same time, thereby increasing the intake air volume.

3. Establishment of simulation model and simulation process

3.1 Flow field modelling

For the flow field analysis, the geometric solid model of the real flow field is first required. Considering the irregularity of the shape of the flow channel in the compressor housing, it is not easy to carry out the steady-state fluid simulation directly, so it is necessary to simplify the processing of the compressor housing and retain the flow channel part of the compressor housing to get the three-dimensional flow field research model. Figure 3 shows 3D solid model and the simplified computational model. By simplifying the original model of the turbocharger, the computational domain model of the compressor casing is obtained. Compared with the original compressor flow channel model, its geometric parameters are more accurate, and the shape of the compressor casing flow channel can be restored more realistically and comprehensively.

3.2 Grid division

In this paper, the unstructured mesh is used to explore the internal flow field of the compressor housing considering the complexity of its internal flow path. The grid division is shown in Fig. 4.

Figure 3.

Model of compressor.

Figure 4.

Mesh model of flow field inside compressor.

3.3 Related settings of boundary conditions

In the analysis process of this paper, according to the engine at the rated speed of 6 $\times$ 10 ${}^{4}$ r/min, the boundary conditions of the internal flow passage of the compressor casing are set [15].

Fluid inlet: the mass into the flow as the boundary conditions of the compressor shell airflow inlet, given the temperature, pressure, velocity and other corresponding conditions at the inlet, so that it is more consistent with the actual flow situation. The velocity at the inlet is 130 m/s, the temperature is 25 ${}^{\circ}$ C, and the pressure is 100 kPa.

Fluid outlet: the inlet back pressure is used as the boundary condition of the airflow outlet of the compressor shell. For the convenience and accuracy of data acquisition, the outlet pressure value is 300 kPa and the outlet temperature is 157 ${}^{\circ}$ C, which is 430 K.

The inlet direction is axial in the compressor shell, the outlet direction is radial, the airflow is steady state, and the gas is compressible flow. Because the flow velocity of air is high under the influence of pressure difference, the effect of gravity on the results of the flow field calculation is not significant and can be neglected.

3.4 Compressor shell flow field simulation results

The kinetic energy dissipation rate $\varepsilon$ and the pulsation kinetic energy $k$ are used to build the $k$ - $\varepsilon$ dual equation to solve. The solution format adopts the implicit format, and coupled solution is used to obtain the steady-state solution. The computational process was iterated approximately 500 times and its results converged. The computed distributed flow fields of pressure, temperature, velocity, and turbulent kinetic energy in the compressor shell are shown in Figs 5–8.

Figure 5.

Internal pressure field.

Figure 6.

Internal velocity field.

Figure 7.

Internal temperature field.

Figure 8.

Kinetic energy field.

From Figs 5–7, we can be found that at the near-wall surface of the compressor casing, generating a surface layer has an impact on the pressure and velocity, making the phenomenon of high pressure and low velocity at the near-wall surface because the gas itself is viscous. Due to the small space of the flow channel fluid velocity, part of the pressure energy into macro kinetic energy in the process of fluid flow. It results in a rapid increase in regional velocity at the nozzle and a reduction in pressure. As can be seen from Fig. 8, the overall flow of gas in the compressor casing is relatively smooth, and turbulence is produced only at the vortex tongue, which is due to the collision between the outlet gas flow and the inlet gas flow in this part.

4. Impeller optimization design and calculation

4.1 Analysis of critical speed

In practice, high-speed rotors can operate at tens to hundreds of thousands of revolutions per minute. At such high speeds, superchargers are subjected to loads such as centripetal forces, aerodynamic forces and thermal stresses. These loads generate excitation forces, which produce periodic changes near the impeller, and when the excitation force is equal or equal to an integer multiple of the impeller’s intrinsic frequency, the impeller will resonate. Resonance will lead to an instant increase in the amplitude of the rotor, the stress of blade and impeller also increase, and working for a long time in the resonance state will cause the impeller and blades to be damaged in advance, thus damaging the supercharger and affecting the normal work. The critical speed is a key parameter to determine whether there is resonance of the rotor at operating speed due to unstable rotational speed. When the instability caused by the critical speed occurs, the structural parameters of the rotor need to be changed to ensure that the critical speed is changed while the working speed remains unchanged, to avoid the rotor from resonating at the working speed.

The first ten order natural frequencies of the rotor system are shown in Table 1. In the Campbell diagram, the horizontal axis represents velocity, the vertical line represents frequency, and the horizontal line represents the natural frequency of each order. The part of forced vibration, that is, the frequency component related to velocity, appears in the rays drawn from the origin. From this, we can find the variation characteristics of all frequency components of rotor vibration in the entire speed range, and obtain the critical speed of the rotor system. The Campbell diagram of the rotor system can be drawn through analysis and solution as shown in Fig. 9.

Table 1
The first ten natural frequencies of the rotor system

Order	Frequency (HZ)	Order	Frequency (HZ)
1	75.85	6	2070.8
2	755.62	7	5072.6
3	755.82	8	5083.5
4	1303.6	9	5865.2
5	2061.5	10	5867.9

Figure 9.

Campbell diagram for rotor system model.

The critical speed corresponding to the high order is far beyond the normal operating speed range of the rotor and does not need to be studied. The working speed of the turbocharger is between 6 $\times$ 10 ${}^{4}$ r/min and 12 $\times$ 10 ${}^{4}$ r/min, and the second-order critical speed is within the operating speed range, which will cause resonance damage to the rotor system. Therefore, the structure of the rotor system needs to be optimized so that the second-order critical speed is far away from the normal operating speed. Table 2 shows the critical speed of the first three orders of the rotor system.

Table 2

Critical speed of rotor system

Order	1	2	3
Rotational speed (r/min)	17189	72576	128919

4.2 Structural optimization of the impeller

There are many impellers structural parameters that affect the performance of the compressor, such as bearing stiffness, material density, manufacturing, operation, and assembly. In this paper, the performance of the optimized compressor and the effect on the critical speed will be analyzed by changing the impeller blade combination, blade thickness and the twists degree of the blade rake.

The material of the compressor impeller is aluminum alloy, the density is 2700 kg/m ${}^{3}$ , the Poisson’s ratio is 0.3, and the elastic modulus is 70 GPa. The material of the turbine is high temperature alloy steel, the density is 7850 kg/m ${}^{3}$ , the Poisson’s ratio is 0.3, and the elastic modulus is 200 GPa.

4.2.1 Effect of blade combination on compressor performance and critical speed

In this section, the effect of the combination of the number of long and short blades on the internal flow field of the compressor and the performance of the turbocharger is studied, as shown in Figs 10 and 11. Figures 10 and 11a are for two long and four short blades; Fig. 10 and 11b are for three long and six short blades; Figs 10 and 11c are for four long and eight short blades.

Figure 10.

Cloud image of pressure field distribution of different blade combinations.

Figure 11.

Velocity field distribution cloud image of different blade combinations.

From Figs 10 and 11, the pressure and velocity change laws of the three combinations are basically the same. The pressure at the inlet end is higher, and as the gas flow enters the flow channel through the impeller rotation, part of its pressure energy is converted into kinetic energy, resulting in a gradual drop in pressure. In the flow area of the compressor casing, the pressure and flow velocity at the inlet end are definitely the highest compared with other areas, and the compressed gas impacts the impeller at high speed from the front, at which the kinetic energy is converted into pressure energy to push the impeller to rotate at high speed, and the cloud chart shows that the pressure at the impeller is the highest.

Figure 12.

Pressure distribution of center section of blade.

Figure 13.

Velocity distribution of center section of blade.

Figures 12 and 13 shows the pressure and velocity curves at different distances from the central section of the blade. It can be seen that under the condition that the blade combination is three long blades and six short blades, the pressure in the internal flow channel is the smallest and the speed is the fastest. Small pressure means that the viscous force of the gas acting on the compressor shell wall is small, which helps the compressed gas to have a larger expansion ratio. Fast speed means that the frictional resistance between the gas and the wall of the compressor casing is small, so that the compressed gas can enter the cylinder through the inner runner more quickly, thus increasing the air intake. It can be seen that the efficiency and performance of the turbocharger can be improved under the condition that the blade combination is three long blades and six short blades.

The critical speed Campbell diagram for the blade combination of three long blades and six short blades after the optimization comparison analysis is shown in Fig. 14. The diagram shows that when the blade combination is changed, the first-order critical speed of this rotor increases, the second and third-order critical speeds remain basically unchanged and the fourth-order critical speed increases compared with that before optimization. Table 3 shows the first three-order critical speeds of the rotor system before and after optimization obtained from the Samcf software solver.

Although its second-order speed is still within the working speed range, it has decreased compared with that before optimization, and the third-order critical speed has increased compared with that before optimization, which broadens the safe working range.

Table 3

Optimize the critical speed of the front and rear rotor systems

Order	1	2	3
Before optimization (r/min)	17189	72576	128919
After optimization (r/min)	20054	71615	132884

Figure 14.

Campbell diagram of critical speed of three long blades and six short blades.

4.2.2 Effect of blade thickness on compressor performance and critical speed

The optimization of the blade combination in the previous section improves the critical speed, but does not fully meet the requirements. Therefore, on this basis, the optimization of the blade thickness and its influence on the internal flow field of the compressor will continue to be studied. In this section, the internal flow field at the end of the compressor is studied for blade thicknesses of 0.4 mm, 0.6 mm, 0.8 mm, 1.0 mm, and 1.2 mm, respectively. Figures 15 and 16 show the simulation cloud diagrams of the internal flow field of the compressor with different blade thicknesses.

Figure 15.

Pressure field distribution nephogram of impeller with five blade thickness sizes.

Figure 16.

Velocity field distribution nephogram of impeller with five blade thickness sizes.

Figure 17.

Pressure distribution of center section of blade.

From Figs 15 and 16, under the conditions of various blade thicknesses, the variation laws of pressure and velocity in a single compressor casing are basically the same as the results in the previous section. Combining the pressure and velocity curves at different distances from the central section of the blade from Figs 17 and 18, it can be seen that its pressure in the internal flow channel is the smallest and the velocity is the fastest where the blade thickness is 0.8 mm. The efficiency and performance of the turbocharger can be improved.

The thickness distribution of the blade is also an important factor affecting the critical rotor speed, and its rotor critical speed effect is analyzed by changing the blade thickness size. Figure 19 is the Campbell diagram of the critical rotational speed with a blade thickness of 0.8 mm after optimization and comparison analysis. It can be seen that when the blade thickness is changed, the first, second and third order critical speeds are decreased compared to before optimization, and the fourth order critical speed is increased. Table 4 shows the first three orders of critical speed of the rotor system before and after optimization obtained from the Samcf software solver. The values show that the second-order critical speed has approached the normal operating speed of the rotor, and the third-order critical speed has been increasing. The optimized solution still produces a slight resonance hazard to the rotor system, and further optimization is needed to ensure that the second-order critical speed of the rotor system is far from the operating speed range.

Table 4

Optimize the critical speed of the front and rear rotor system

Order	1	2	3
Before optimization (r/min)	17189	72576	128919
After optimization (r/min)	16235	61110	135610

Figure 18.

Velocity distribution of center section of blade.

Figure 19.

Campbell diagram of critical speed with blade thickness of 0.8 mm.

4.2.3 Influence of blade forward bending angle on compressor performance and critical speed

In this section, the internal flow field of the turbocharger compressor is studied under the condition that the blade forward bending angle is 15 ${}^{\circ}$ , 30 ${}^{\circ}$ , 45 ${}^{\circ}$ , 60 ${}^{\circ}$ and 75 ${}^{\circ}$ . Figures 20 and 21 show the simulation clouds diagram for the internal flow field of the compressor with different blade forward bending angle.

Figure 20.

Pressure field distribution cloud map of the impeller with five angles.

Figure 21.

Velocity field distribution cloud map of the impeller with five angles.

Figure 22.

Pressure distribution of impeller center section at five angles.

From Figs 20 and 21, the change law of the pressure and velocity are basically the same. The pressure at the inlet end is larger as the airflow rotates through the impeller into the flow channel, and part of its pressure energy will be converted into kinetic energy leading to a lower pressure relative to the inlet. Through Figs 22 and 23 contrast analysis of the pressure distribution with different blade forward bending angle, it can be seen that its pressure in the internal flow channel is the smallest under the condition that the blade forward bending angle 45 ${}^{\circ}$ . The small pressure indicates that the viscous force between the gas and the wall surface of the compressor shell is small, which helps the gas being compressed in to have a larger expansion ratio. The analysis of the velocity shows that the velocity does not vary much between 45 ${}^{\circ}$ , 60 ${}^{\circ}$ and 75 ${}^{\circ}$ . It can be seen that when the blade forward bending angle is 45 ${}^{\circ}$ , the efficiency and performance of the turbocharger can be improved.

Figure 23.

Velocity distribution of impeller center section with five angles.

Figure 24.

Campbell diagram of critical speed when blade tilt Angle is 45 ${}^{\circ}$ .

As an important parameter to change the shape of the impeller, the change of the blade forward bending angle is also an important factor to influence the critical speed of the rotor system. Figure 24 is the critical speed Campbell diagram under the condition that the blade forward bending angle is 45 ${}^{\circ}$ after the optimization comparison analysis. From the all Figures, it can be seen that the first, second and critical speed are decreased, and the second-order decrease is obvious. The third and fourth order critical speed has increased. Table 5 shows the first three orders of critical speed of the rotor system before and after the optimization obtained from the Samcf software solver. The table shows that the second and third order critical speed of the rotor system after optimization is 53665 r/min $\sim$ 138468 r/min, which is not within the normal operating speed of turbocharger 6 $\times$ 10 ${}^{4}$ r/min $\sim$ 12 $\times$ 10 ${}^{4}$ r/min. The fatigue damage caused by rotor vibration has been greatly avoided, the safe working range of the rotor has been expanded and the rotor dynamics performance has been improved.

Table 5

Optimize the critical speed of the front and rear rotor system

Order	1	2	3
Before optimization (r/min)	17189	72576	128919
After optimization (r/min)	15270	53665	138468

Table 6

Stress and strain of impeller before and after optimization at different speeds

Rotate speed (r/min)	70000	90000	110000
Optimized front impeller stress (MPa)	13.518	22.204	33.167
Optimized rear impeller stress (MPa)	13.153	21.735	32.5
Optimized front impeller strain	0.019058	0.031304	0.046761
Optimized rear impeller strain	0.018544	0.030643	0.032594

Figure 25.

Relationship between stress and rotational speed.

4.3 Analysis of impeller stress and strain performance before and after optimization

The following analysis will compare the maximum stress and strain of the impeller before and after optimization under different working conditions.

Figure 26.

Relationship between strain and rotational speed.

It can be seen from Fig. 25 that the maximum stresses of the optimized impeller are smaller than those before optimization at different working speeds. From Table 6, it can be seen that the maximum stress gradually increases with the increase of the rotational speed. For the same rotational speed, the maximum stress after optimization is smaller than the maximum stress before optimization. It indicates that the optimized impeller undergoes less elastic deformation than the pre-optimized one, and the strength of the optimized impeller is higher than the pre-optimized one, which is in line with the ideal criteria, and the optimized solution is feasible.

It can be found from Fig. 26 that the maximum strain distribution trends of the impeller before and after optimization are also roughly the same under different working conditions. The maximum strain of the optimized impeller between 7 $\times$ 10 ${}^{4}$ $\sim$ 9 $\times$ 10 ${}^{4}$ r/min is slightly higher than that before optimization, and the maximum strain of the optimized impeller at 9 $\times$ 10 ${}^{4}$ $\sim$ 11 $\times$ 10 ${}^{4}$ r/min is smaller than that before optimization. When designing the impeller, the distance between the front end of its blade and the inner wall of the compressor is between 0.5 mm and 0.8 mm. It can be seen that the strain does not have much effect on the strength of the impeller before optimization, but the optimized value is smaller than that before optimization.

5. Conclusion

In this paper, the problem of Calculation and Simulation of Turbocharger Flow Field and Optimization Analysis of Impeller Structure, and the JP80D turbocharger is used as the research object.

The critical speed analysis of the rotor system with base excitation and unbalanced forces was solved, and the Campbell diagram was derived and the first-order, second-order and third-order critical speeds were solved. The second-order critical speed of the rotor was found to be 72,576 r/min in the operating speed range of 6 $\times$ 10 ${}^{4}$ r/min $\sim$ 12 $\times$ 10 ${}^{4}$ r/min, which will cause resonance hazard to the turbocharger.

The pressure and velocity distribution characteristics are optimal under the condition that the combination of long and short blades is three long blades and six short blades. The second-order critical speed is 71615 r/min in the operating speed range, but it is decreased from before optimization.

The pressure and velocity distribution characteristics are optimal when the blade thickness is 0.8 mm. The second-order critical speed of 61,110 r/min is close to the normal operating speed of the rotor, but still produces a slight resonance hazard to the system.

The impeller at a forward tilt angle of 45 ${}^{\circ}$ . Its pressure and velocity distribution characteristics are optimal, and the second-order critical speed is 53665 r/min, far away from the operating speed of 6 $\times$ 10 ${}^{4}$ r/min. This greatly improves the turbocharger acceleration performance to improve the imbalance failure problem arising from the base excitation and unbalance effect.

The stress comparison analysis before and after optimization shows that the maximum stress after optimization is smaller than the maximum stress before optimization. This shows that the elastic deformation of the impeller after optimization is smaller than that before optimization, and the strength of impeller after optimization is higher than that before optimization. The strain before and after optimization is compared and analyzed, and the displacement deformation after optimization is obtained to be smaller than that before optimization.

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Calculation and simulation of turbocharger flow field and optimization analysis of impeller structure

Abstract

Keywords

1. Introduction

2. Turbocharger 3D modeling

3.1 Flow field modelling

3.2 Grid division

3.4 Compressor shell flow field simulation results

4.1 Analysis of critical speed

Table 1 The first ten natural frequencies of the rotor system

4.2.1 Effect of blade combination on compressor performance and critical speed

References

Table 1
The first ten natural frequencies of the rotor system