Numerical investigations on the effect of asymmetric inlet conditions on the performance variations of centrifugal compressor

The high adoption frequency of inlet bent pipes result in variations between the operating performance and design value. In this paper, the performance of centrifugal compressor while adopting two inlet bent pipes, i.e., Pz and Pu, are simulated through the verified simulation method, respectively, and the flow field characteristics of inlet pipes are analyzed and quantitatively characterized. The analysis shows that centrifugal compressor’s performance with Pz and Pu both decrease to a certain degree. The flow field of symmetric swirling distribution both occurred on the outlet plane of Pz and Pu, and the circumferential distortion degree of plane (PCD) with Pz and Pu shows an increasing trend as the flow rate increases. The PCD of Pz with different rotational speed are always higher than that of Pu. The degradation degree of centrifugal compressor’s performance of Pz and Pu both increase with the increasing of PCD, and it is higher by adopting Pz, the pressure ratio degradation degree reaches 6.82% while it reaches 7.38% in efficiency degradation degree. It is found that there is a power law relation between the degradation degree of pressure ratio and PCD, and an exponential relationship between the efficiency degradation degree and PCD.


Introduction
In the automotive industry, centrifugal compressors are extensively adopted, such as in air compression systems and turbochargers [1], because it has the advantages of high pressure ratio of single-stage, low production cost and compact structure [2].The design premise of centrifugal compressors is uniform axial inlet direction, however, because of the space limitation in actual installation environment, the installation frequency of inlet bent pipes becomes higher in the upstream position of centrifugal compressors.The installation of inlet bent pipes creates an asymmetric inlet environment at the inlet location of centrifugal compressors [3], which leads to the differences between actual and design performance.
Most of the early researches on the effects of asymmetric inlet environment on the performance changes of compressors were mostly focused on axial compressors [4,5].With the extensive application of centrifugal compressors, the performance variations of centrifugal compressors with asymmetric inlet conditions have attracted the attention of many researchers and the investigations are carried out mainly through numerical simulation methods and experimental measurements.Zhou et al. [6] used a distortion generator to produce asymmetric flow conditions at the inlet location of centrifugal compressor, and the performance with and without the existence of inlet distortion was compared; the results of experiment showed that with the existence of radial combined distortions at the inlet location of centrifugal compressor, the tip distortion had no significant effect on the performance while the hub distortion could cause surge of centrifugal compressor.Ariga et al. [7] carried out the performance test of a low speed compressor by using an inlet honeycomb to generate distortion flow condition, it was found that unfavorable influences on efficiency was caused by inlet distortion, and non-uniformities of axial velocity increased as the flow rate rise.Due to the long research period and high expenditure of experimental methods, the computational fluid dynamics (CFD) method with low implementation cost and powerful function is adopted by more researchers [8], and related works has been carried out.Zhang et al. [9] numerically simulated the influences of inlet pipes with different lengths and diameters on the changes in performance of centrifugal compressors, it was found that the parameters of inlet pipes had an effect on the load at the inlet location of the compressor, which affects centrifugal compressor's performance; when the inlet pipe was longer or the diameter was smaller, the loss in total pressure of the inlet pipe was larger, so these parameters should be considered when selecting the inlet pipe.Li et al. [10] used numerical method to simulate inlet flow distortion of centrifugal compressor caused by a 90-degree bent pipe, and compared the changes in the performance of centrifugal compressor when the bent pipe was located at different positions in the axial direction; the results indicated that the position of the bent pipe had an effect on the deterioration extent in the performance of centrifugal compressor, and there was a greater impact while the bent pipe located further away from the impeller inlet.Zhao et al. [11] set up different circumferential installation position of 90-degree inlet elbows and simulated the influences on the compressor's performance, and the results showed that when changing the circumferential installation position of inlet bends from one to another would have a significant effect on the efficiency of the centrifugal compressor; it was recommended that the unfavorable installation direction relative to the volute in the inlet system should be avoided.Li et al. [12] numerically simulated the efficiency changes of centrifugal compressors under three different schemes of curved inlet pipe conditions, the research showed that different schemes of curved inlet pipes have different effects on the centrifugal compressor's performance; among them, the centrifugal compressor's efficiency with the adoption of W1.25 and W0.75 curved inlet pipe models was lower than that with the case of 90degree inlet elbow.
Many researches have shown that the adoption of inlet bent pipes affect the performance of centrifugal compressors, it is helpful to clarify the influence of asymmetric flow conditions generated by different inlet bent pipes on the centrifugal compressor's performance, which can provide references for designing and optimizing the inlet pipes.In the previous studies related to the asymmetric flow conditions of centrifugal compressor, there are many investigations on the changes in centrifugal compressor's performance caused by single 90-degree inlet elbow.However, few researches have been conducted on the adoption of double elbow inlet pipe, which may cause direction change of air flow, resulting in performance changing of centrifugal compressors.Therefore, two kind of inlet pipes are established in this paper, i.e., double inlet bent pipes with unchanged air flow direction (Pz) and changed air flow direction (Pu), then the numerical simulation research on the change laws of the centrifugal compressor's performance is researched, and the quantitative relationship between the distorted flow field formed on the outlet plane of Pz and Pu as well as the degradation degree of performance is established, which can be used as theoretical references for the improvement of asymmetric flow at the inlet location of centrifugal compressors.

Geometry of centrifugal compressor
The structure of centrifugal compressor investigated in this paper mainly consists of the static component, such as (a) inlet pipe, (c) diffuser, and (d) volute, as well as the rotating component (b) impeller, as shown in figure 1.There are ten main blades and ten split blades of the impeller, while the diffuser has vaneless parallel wall structure.The main geometric structure parameters of the components are shown in table 1.  Outlet diameter of the impeller (mm) 75 Tip clearance (mm) 0.5

Numerical simulation method
In this paper, the Reynolds Average Navier-Stokes equations were solved and SST κ-ω turbulence model was employed to simulate the three dimensional flow characteristics of centrifugal compressor based on Fluent software.The second order upwind was used to discretely solve the convection term, while the first order upwind was employed for diffusion term.The governing equations are as follows: Continuity equation: where ρ denote the air density; u, v and w represent the value of velocities in different directions of x, y and z, respectively; t is time.The momentum equations in direction of x is shown below: where μ is the dynamic viscosity of air; p represents the pressure acting on the fluid element; Su denotes generalized source items, respectively.The form of energy equation is as follows: where T is the temperature of air; λ represent the coefficient of heat transmission; cp means the specific heat capacity of the fluid while ST denote the generalized source item.
SST κ- turbulence model possesses the advantages of both standard κ-ε and standard κ- models as well as modifies the turbulence term in the equation.The standard κ- model is used to process the flow at the area near the wall while the κ-ε model is employed to treat the flow in other regions [13].
The equation of turbulent kinetic energy κ is shown below: Turbulent dissipation  is calculated as follows: where Gk represent the turbulent kenetic energy generated by the average velocity gradient; Yk and Yω denote the dissipation of k and ω caused by turbulence, while Гk and Гω are the effective diffusion coefficients of them, respectively; Dω means the convection-diffusion term; Sk and Sω denote the source terms.
Inlet pressure was set as inlet boundary condition with the direction of air perpendicular to the inlet surface during the solution process.Outlet pressure was given as outlet boundary condition within the large mass flow rate operating range, while the mass flow rate condition was chosen when operating mass flow rate was lower.The working medium was ideal gas, and the adiabatic no-slip boundary condition was given to the walls.The rotational speed as well as direction were set to the correspond rotating walls, and the others were stationary walls.

Mesh partitioning and independence testing of computational domain
The software of ANSYS TurboGrid was used to optimize the topology of single passage of impeller [14], and the structured mesh with high quality was achieved, then the whole passage mesh of impeller was replicated.10-layer mesh was set up for the boundary layer of impeller with the height of the first layer grid was 0.007mm, and the value of y+ was controlled to be less than 10.ICEM software was employed to generate unstructured mesh of the other components, which had a high adaptability to complex geometry, and the quality of mesh was higher than 0.3, which can be used for numerical simulation.The mesh of each component of the centrifugal compressor can be seen in figure 2. In order to investigate the changes in total numbers of mesh on the results of numerical simulation and save computing resources, the independence test on the total mesh number of computational domain was necessary to be performed.Ten sets of mesh schemes were generated with same height of first layer and same topology of mesh.The pressure ratio and efficiency of the centrifugal compressor were compared to observe the performance changes of centrifugal compressor with different total numbers of mesh, which were simulated under the condition of 6×10 4 rpm and mass flow rate of 0.043 kg/s.The change trend of simulated pressure ratio and efficiency with total mesh number can be seen in figure 3. The variations in figure 3 showed that as the total mesh number exceeds scheme 7, i.e., 8,983,652, the pressure ratio and efficiency remain basically constant, so the total mesh numbers of computational domain is chosen as mesh scheme 7.

Verification of numerical simulation method
In order to validate the credibility of the employed numerical simulation method, the experimental performance of centrifugal compressor at different speeds was obtained based on the performance test rig of centrifugal compressor, which was shown in figure 4. The PLC program on the host computer was used to regulate the rotational speed of centrifugal compressor during the experiment process, and the regulating valve installed on the outlet pipe was used to adjust the outlet pressure.Pressure sensors and temperature sensors were installed on both inlet and outlet pipes, respectively.The pressure and temperature of inlet and outlet locations were recorded after the centrifugal compressor working stably for five minutes, as well as the value of double folium flowmeter.By changing the rotational speed and pressure of outlet location, the measured pressure and temperature of the inlet and outlet locations under different operating conditions were substituted into the equations to obtain the performance of centrifugal compressor.The performance of centrifugal compressor with rotational speed of 6×10 4 rpm, 8×10 4 rpm and 10×10 4 rpm were finally obtained.The equations of pressure ratio and efficiency are shown as follows: ( 1) 1 where P1 and P2 are the total pressure of inlet and outlet locations of centrifugal compressor, respectively, while Ta and T4 denote the temperature of inlet and outlet locations, and k is isentropic coefficient.
(   5. The results in figure 5 indicated that the change trend of simulated performance in pressure ratio and efficiency was consistent with the performance measured experimentally, and the difference of them was less than 10%.The reason of the variation between them may be the differs in computational model and experimental prototype.There may be some machining accuracy deviation and surface roughness during the machining process, which was different with the smooth wall as well as adiabatic wall conditions given in the simulation process, resulting in deviation between the simulation and experiment results [15].With the increase of rotational speed, the velocity of air in centrifugal compressor was higher, more mechanical energy was used to overcome the vibration and temperature rise generated during the operating process, and the kinetic energy converted into fluid decreased relative to the low rotational speed conditions.Therefore, the difference between experimental measurement and numerical simulation results increased gradually under high rotational speed condition.However, the simulation results could predict the operating conditions and the range of high efficiency condition of the centrifugal compressor accurately, the agreement between them was well during the whole operating conditions, which indicated that the chosen numerical simulation method in this research was credible.

Performance analysis of centrifugal compressor
Three types of inlet pipes were modeled in this paper, i.e., straight pipe (Ps), double inlet bent pipes with unchanged air flow direction (Pz) and changed air flow direction (Pu).The length of each inlet pipe was 360mm, which was about 10 times the impeller inlet diameter, the models was shown in figure 6.The simulated performance of centrifugal compressor adopting different types of inlet pipes under three rotational speeds of 6×10 4 rpm, 8×10 4 rpm and 10×10 4 rpm was shown in figure 7. It showed that the performance of centrifugal compressor adopting Pz and Pu was lower than the performance with Ps under each rotational speed condition.The centrifugal compressor's performance with Pz was lower than those of Pu, which indicated that the changes in geometric structure of intake pipes caused differences in its influences on the performance of centrifugal compressor.When the air flow direction was not changed in Pz, the distorted flow distribution presented on the outlet plane of it produced performance degradation effect on the centrifugal compressor.

Analysis of flow field characteristics
The performance changes of centrifugal compressor with different structures of inlet pipes lead to variations in the performance degradation extent of centrifugal compressor, which was caused by different distorted flow field formed at the outlet location of inlet bent pipes.In order to investigate the effect of different distorted flow field on the centrifugal compressor's performance, plane m1 at 100mm from the impeller inlet of each inlet pipes were chosen, as shown in figure 6, as well as the flow field characteristics of plane m1 were analyzed.The dimensionless total pressure and streamline distribution were illustrated in figure 8 and figure 9, the mass flow rate of centrifugal compressor with Ps, Pz and Pu was set to Q=0.08514 kg/s, 0.08516 kg/s and 0.08515 kg/s, respectively.The dimensionless total pressure was obtained by dividing the local total pressure by the atmosphere pressure, which was 101,325 pa.Total pressure distribution on plane m1.As can be seen in figure 8 and figure 9 that the distribution of streamlines and total pressure on plane m1 of Ps were uniform, while the symmetric swirling flow filed distribution were formed on plane m1 of Pz and Pu, and the dimensionless total pressure distributions also presented near symmetric distribution state.From the inlet direction, single symmetric swirling structure was formed on plane m1 of Pz, which is located in upper area, and the total pressure in this area was also higher.The flow field distribution on plane m1 of Pu presented double symmetric swirling structure, and the main symmetric swirling in upper area occupied a larger area of plane m1, while the symmetric swirling at lower area occupied a smaller area, and the total pressure of this area was also relatively low.
From the distribution state of total pressure on plane m1 of inlet pipes, it can be found that the total pressure distribution of both Pz and Pu was distorted and was no longer uniformly distributed.When the flow with distorted distribution state of total pressure entered the channel of impeller, it leaded to deterioration on centrifugal compressor's performance.The non-uniformity flow characteristics caused by inlet bent pipes was mainly manifested in the form of circumferential distortion [6], which can be quantitatively expressed by the degree of circumferential distortion (CD) [16], which was calculated by the following equation: where (PAV)i represents the average total pressure of different circles on plane m1; (PAVLOW)i denotes the average value of those which were lower than the average total pressure of the circle.The chosen nine circles on plane m1 was shown in figure 10, which were 0.1R to 0.9R, respectively, where R represent the radius of inlet pipe.The variation of CD on plane m1 while adopting two types of inlet bent pipes under rotational speed of 10×10 4 rpm and high efficiency condition was presented in figure 11. Figure 11 showed that the CD at each circle on plane m1 of Pz and Pu showed an overall trend of increasing with the increment of R.However, the increasing CD rate of Pu was smaller than that of Pz, and the CD of Pu was lower than that of Pz at higher radius area.The change of CD reflected the reduction degree in total pressure on the circumference of different radius on plane m1, so the decrease degree in circumferential total pressure of Pz was higher at higher radius area than that of Pu.Due to the impeller structure of hub, the flow at the area with lower radius of inlet pipe was converged to the channel of impeller, while the flow at higher radius area entered the passage of impeller directly.Therefore, when the flow at higher radius area had a high degree of circumferential distortion, it had a greater impact on the flow distribution of impeller, resulting in a significant impact on the centrifugal compressor's performance.

Effect of distorted flow field on the centrifugal compressor' performance
In order to establish the quantitative relationship between the distorted flow field formed on plane m1 of inlet bent pipes and the degradation degree of centrifugal compressor' performance, the degree of circumferential distortion on plane m1 (PCD) was introduced, which was obtained by the following equation: where N is set to 9, Ri denotes the radius of different circles on plane m1, while CDi denotes the degree of circumferential distortion of different circles.Then the values of pressure ratio and efficiency under several same flow rate conditions of centrifugal compressor with three inlet pipes at three rotational speeds were extracted, the degradation degree of centrifugal compressor' performance was defined, i.e., the pressure ratio degradation degree δπ and efficiency degradation degree δη, which were calculated as follows: where πi and ηi are the centrifugal compressor's pressure ratio and efficiency while adopting Pz or Pu, and πs and ηs represent that of Ps, respectively.Figure 12 showed the change trend of PCD with mass flow rate on plane m1 when adopting Pz and Pu.It can be obtained from figure 12 that the PCD of Pz and Pu under each rotational speed both raised with the increasing of mass flow rate, and the PCD of Pz showed a higher growth rate.The PCD of Pz and Pu at different rotational speed maintained a consistent growth trend.The PCD of Pz reached the maximum value of 0.048 under high rotational speed and large flow rate condition, while it was 0.023 for Pu.
Figure 12.PCD on plane m1. Figure 13 showed the variation trends in degradation degree of centrifugal compressor' pressure ratio and efficiency with PCD on plane m1 of two inlet bent pipes.It can be concluded that there was a power function relation between the pressure ratio degradation degree δπ and PCD, while it showed an exponential function relation between the efficiency degradation degree δη and PCD.The fitting functions were showed as below: where a, b, y0, A and R0 represent the fitting function' coefficients, respectively, the value of them are listed in table 2  It can be seen from figure 13 that both δπ and δη of centrifugal compressor while adopting Pz and Pu maintained the increasing trend with the increment of PCD on plane m1 of inlet pipes, which indicated that the increment of PCD lead to higher deterioration degree of centrifugal compressor's performance.The degradation degree of centrifugal compressor's performance when adopting Pz was always higher than that of Pu under each rotational speed, because the flow field with higher PCD was formed with the adoption of Pz, so it exerted greater influence on the centrifugal compressor's performance.Under high rotational speed, the maximum δπ of centrifugal compressor with Pz and Pu reached 6.82% and 5.70%, and the maximum δη reached 7.38% and 5.25%, respectively.The quantitative relations between the centrifugal compressor's performance degradation degree and PCD with different inlet bent pipes can be used as reference to predict the centrifugal compressor's performance operating in similar environments.

Conclusions
In this paper, the centrifugal compressor's performance with straight inlet pipe under three rotational speeds was simulated through numerical method based on the Fluent software, and the reliability of numerical simulation method was validated by the experimental results obtained from the performance test rig of centrifugal compressor.Then the inlet bent pipes was established, i.e., double inlet bent pipes with unchanged air flow direction (Pz) and changed air flow direction (Pu), and the centrifugal compressor's performance while adopting Pz and Pu was numerically simulated.Finally, the flow field characteristics on the outlet plane of inlet bent pipes as well as its effect on the centrifugal compressor's performance was analyzed, the main conclusions were drawn as follows: (1) The centrifugal compressor's performance while adopting Pz and Pu was reduced compared to the adoption of straight inlet pipe, where the centrifugal compressor's pressure ratio and efficiency with Pz were always lower than those when adopting Pu under different rotational speed conditions.
(2) The flow field distribution with single symmetric swirling structure was formed at the outlet of Pz, while double symmetric swirling structure was presented on the outlet plane of Pu.The distribution state of total pressure on plane m1 of both Pz and Pu was distorted, the reduction degree of circumferential total pressure on plane m1 of Pz at higher radius area was higher than that of Pu.
(3) The PCD of Pz and Pu on plane m1 at each rotational speed both raised with the increasing of flow rate, and the PCD of Pz showed a higher growth rate.The changing trend of PCD for Pz and Pu at different rotational speed maintained consistent.The maximum PCD of Pz reached 0.048, while it was 0.023 for Pu.

Figure 1 .
Figure 1.Components of centrifugal compressor.Table 1. Main geometric structure parameters of the components.

Figure 2 .
Figure 2. Mesh of the main components.

Figure 3 .
Figure 3. Performance changes with different mesh schemes.

Figure 4 .
Figure 4. Performance test rig of centrifugal compressor.

Figure 5 .
Figure 5. Performance comparison between simulated and experimental results.The performance comparison between numerical simulation and experimental results of centrifugal compressor with different rotational speed was shown in figure5.The results in figure5indicated that the change trend of simulated performance in pressure ratio and efficiency was consistent with the performance measured experimentally, and the difference of them was less than 10%.The reason of the variation between them may be the differs in computational model and experimental prototype.There may be some machining accuracy deviation and surface roughness during the machining process, which was different with the smooth wall as well as adiabatic wall conditions given in the simulation process, resulting in deviation between the simulation and experiment results[15].With the increase of rotational speed, the velocity of air in centrifugal compressor was higher, more mechanical energy was used to overcome the vibration and temperature rise generated during the operating process, and the kinetic energy converted into fluid decreased relative to the low rotational speed conditions.Therefore, the difference between experimental measurement and numerical simulation results increased gradually under high rotational speed condition.However, the simulation results could predict the operating conditions and the range of high efficiency condition of the centrifugal compressor accurately, the agreement between them was well during the whole operating conditions, which indicated that the chosen numerical simulation method in this research was credible.

Figure 6 .
Figure 6.Different computational models of centrifugal compressor.

Figure 10 .
Figure 10.Selected nine circles on plane m1.Figure 11.Variations of CD at different circles.

Figure 11 .
Figure 10.Selected nine circles on plane m1.Figure 11.Variations of CD at different circles.

Figure 13 .
Figure 13.Performance degradation degree changes with PCD.

Table 1 .
Main geometric structure parameters of the components.

Table 2 .
and table 3. Coefficients of power function.

Table 3 .
Coefficients of exponential function.