Numerical study on the effect of radial inlet chamber on the performance of oblique flow compressor

The oblique flow compressor is one of the key components in compressed air energy storage (CAES) system, which has the advantages of high single-stage pressure ratio, wide operating range, high efficiency and large mass flow. In this paper, a numerical method is used to study the first-stage oblique flow compressor in a compressor group with radial inlet chamber (RIC), and the oblique flow compressor performance with axial inlet is compared. The results show that the RIC makes the overall performance curve of compressor shift downward, the stable working range is reduced by 15.75%, and the isentropic efficiency and pressure ratio are reduced by 1.54% and 1.57% respectively under the design conditions. The RIC makes the impeller inlet aerodynamic parameters circumferential distribution non-uniformity, which declines the compressor performance. And the rotation of the impeller also destroys the original symmetrical flow distribution of the RIC.


Introduction
Compressed air energy storage (CAES) system is a kind of power energy storage system that can store electric energy for a long time and large capacity.Compared with other energy storage methods, CAES system equips characteristic of high efficiency and fast response time.It plays a significant part in realizing large-scale grid connection between renewable energy and grid peak shaving.It is considered to be one of the large-scale physical energy storage technologies equipped the most development potential [1][2][3].As a key component of CAES system, the compressor performance directly determines the CAES system efficiency and economy.RIC is an important component of high-power compressor unit, air flow from radial into RIC, after folding into axial intake, this process will not only bring flow loss, but also cause uneven distribution of compressor inlet airflow, resulting in deterioration of downstream component performance.Compared with the axial uniform air intake method, the RIC reduces the variable efficiency of the compressor by 1%-3% [4].
The RIC research has attracted the attention of scholars.Wang [5,6] studied the RIC internal flow in detail through numerical simulation.Wang found that a series of vortices generated by the air flow in the RIC annular channel.They were the main reasons for pressure loss and outlet flow distortion, and outlet flow was greatly affected by the impeller.Dong [7] found through numerical simulation that the RIC changes the impeller performance.Under the designed mass flow, the compressor efficiency and total pressure ratio are reduced by 3.12% and 0.19% respectively.The impeller leading edge average attack angle decreases by about 1.4° in the entire operating working conditions.Mund [8] studied the intake system of a gas turbine and found a 0.1% loss of inlet pressure resulted in a 0.2% loss of power for a duty gas turbine.Chen [9] found that the RIC main structural parameters are the key factors affecting the total pressure loss and outlet air flow angle, and these structural parameters mainly affect the development of vortex and flow turbulent kinetic energy in the RIC.Grimaldi [10] experimentally tested the overall performance of compressor units with different RIC models and found that there needed to be a balance between the complexity of the RIC structure and the impact on first-stage performance.Xin [11] numerically calculated compressor with uneven guide vanes and the results show that the guide vanes wake and the pressure load threaten the impeller safe operation.Pazzi [12] tested the performance of a typical RIC through numerical simulation and experiment, and found that the number and structure of shunt blades in the RIC have a great influence on the flow field, mainly because it can change the distribution of aerodynamic parameters in the tangential direction.Koch [13] and Flathers [14,15] added shunt vanes to the RIC and found that the flow loss increased but the outlet uniformity improved.Han [16][17][18] measured the flow field in the RIC in detail and found that the large number of vortexes generated by airflow and flow separation were the core reasons for flow loss and outlet distortion.
In summary, it can be seen that previous research are mainly the RIC internal flow and its influence on compressor performance.And less involves the interaction between the RIC and the compressor.And the influence of RIC flow loss and distortion on compressor independently is still insufficient.In this paper, the effects of flow loss and distortion on oblique flow compressor performance under different mainstream flow rates are studied through numerical simulation.The coupling characteristics of RIC and compressor and the distribution of internal flow field and aerodynamic parameters of RIC are studied.

Research object
The research object is oblique flow compressor in a CAES system.The compressor and RIC structure are illustrated in figure 1.The spiral channel profile line in RIC is calculated from literature [19].In order to consider the influence of RIC flow loss and distortion on compressor performance, 3 calculation models are selected, as shown in Figure 2. Model 1 is a single-channel model of an oblique flow compressor, assuming that there is no flow loss of RIC and uniform outlet.The Model 1 inlet boundary condition sets as designed total temperature and pressure.Model 2 assumes that the RIC outlet is uniform but has flow loss.So the single-channel model of oblique flow compressor is adopted, and the inlet boundary condition of each working point is the compressor inlet average total temperature and pressure corresponding to the working point in Model 3. Model 3 is a full-channel model of RIC and oblique flow compressor.The Model 3 inlet boundary condition sets as designed total temperature and pressure.

Performance indicators
The RIC performance is defined by total pressure loss coefficient  and total pressure distortion coefficient .

Numerical simulation methodology
The calculation domain in this paper mainly includes RIC and compressor components.The RIC is generated by unstructured mesh and the other domains are divided by structured mesh.In order to capture the flow field detail in calculation domain, some walls are refined.The first boundary layer is set as 1×10 -5 m.And the y+ value is less than 1.After grid independence verification, the RIC grids number is 2.2 million and compressor single-channel is adopted as 1.57 million.The computational domain and mesh structure are shown as figure 3. The numerical calculation in this paper adopts SST turbulence model.And the total temperature and pressure are used for the inlet boundary conditions.Since compressor chock condition is sensitive to pressure and the surge condition is sensitive to mass flow, the outlet boundary condition adopts static pressure in large flow range and mass flow in small flow range.The dynamic and static interface transmits information by frozen rotor method.The pressure ratio and efficiency are monitored during calculation process.When the monitored parameters tend to be stable, and the inlet and outlet mass flow difference is less than 0.005, the residual is less than 10 -5 , the calculation is considered to be the convergence.

Numerical simulation validation
The numerical methods are adopted to calculate HPCC impeller performance and compare with experimental results [20,21].The results are shown in figure 4. It can be seen that numerical calculation and experimental results are in small differences.The maximum error of total pressure ratio and isentropic efficiency is 0.8% and 1.2% respectively.So the numerical methodology selected in this paper has high accuracy.

Oblique flow compressor characteristics
In order to investigate the RIC influence on oblique flow compressor performance, the pressure ratiomass flow and isentropic efficiency-mass flow characteristic curves of 3 models are calculated separately.The results are illustrated in figure 5.It can be seen that Model 1 total pressure ratio decreases with the increase of mass flow.At design point, the isentropic efficiency is maximum.When mass flow is deviated from design point, the isentropic efficiency gradually decreases.After adding the RIC, the tendency of total pressure ratio and isentropic efficiency of Model  Figure 6 shows the variation curves of RIC outlet  in Model 3, the pressure ratio difference between Model 2 and Model 3 and the difference in isentropic efficiency with the mass flow. increases with the increase of mass flow.In the range from near surge point to design point, the difference in both gradually decreases.In the range from design point to near chock point, the difference increases first and then remain stable.After near chock point, the difference in isentropic efficiency and pressure ratio decreases gradually.The pressure ratio difference and the total pressure distortion coefficient change curve Figure 6.The relationship between isentropic efficiency difference, pressure ratio difference and total pressure distortion coefficient with mass flow.
Figure 7 shows the shaft power characteristic curves for the 3 models.With the increase of mass flow, Model 1 shaft power gradually increases.When the mass flow increases further, the shaft power begins to decrease.The reason is the flow deviating too far from the designed mass flow, the impeller flow capacity is limited, internal flow becomes complex, flow separation and various vortices cause impeller to be unable to do work normally on the gas, and the shaft power begins to decrease.The shaft power of Model 2 and Model 3 has the same trend as that of Model 1.The shaft power of Model 3 deviates from Model 1 within 3% over the entire working range, and the shaft power of Model 3 decreases by 1.09% at the designed mass flow.Near the chock point, the shaft power of Model 3 is more reduced than that of Model 1, and is smaller than that of Model 2. Model 2 shaft power is greater than that of Model 3 under other working conditions.In order to analyze RIC influence mechanism on compressor performance, the impeller leading edge circumferential average attack angle is studied.As can be seen from figure 8, the leading edge of 3 models has a positive attack angle in small mass flow area.As the mass flow increases, the attack angle gradually decreases and becomes a negative attack angle.The unevenness brought by RIC reduces the circumferential average attack angle of impeller leading edge about 1°, and the flow loss of RIC has little effect on the attack angle.Figure 9 shows the inlet velocity triangular schematic diagram of impeller leading edge, in which u is tangential speed, w is relative speed, and c is absolute speed.The impeller inlet air flow produces pre-rotation affected by RIC, the attack angle decreases, so that the impeller does a decrease in working capacity, thereby reducing the compressor performance.

RIC characteristics
The turning of the gas in RIC is the main cause of the impeller inlet unevenness.The impeller rotation will also affect RIC internal flow.For this reason, a separate RIC is also calculated, and the outlet was extended to avoid backflow.The performance indicators of the two under designed conditions are illustrated in Table 1.It can be seen that impeller reduces  of RIC by 10.72%, and the polytropic efficiency increases by 0.87%.The impeller rotation reduces the velocity gradient of RIC outlet, and  of RIC decreases, so RIC internal flow mixing loss is reduced.

Flow field analysis 3.2.1. RIC
Since the structure of RIC is symmetrical, the gas flow inside it is also symmetrical, but impeller rotation affects the RIC inside flow.Figure 11 (a) shows the static pressure distribution at RIC section 1.It can be seen that the flow symmetry in the RIC alone is better, and there is a low-pressure zone above shaft due to large bending loss in annular convergence channel.Comparing figure 11 (a), the low-pressure area in section 1 is offset in impeller rotation direction, but the offset is small.From figure 11 (b), the static pressure distribution of RIC meridian channel is basically the same in the two cases, indicating that the RIC influence on RIC in axial direction is less than that in circumferential direction.Figure 11 (c) shows RIC outlet distribution of static pressure.The impeller increases the static pressure of entire RIC outlet.and RIC outlet low-pressure area is offset more in impeller rotation direction than the offset degree of section 1.This is because the section 1 is far from the impeller, and the impeller influence on RIC has been weaken.

Impeller inlet section
The impeller inlet aerodynamic parameters distribution directly affects impeller inside flow, which in turn affects compressor stage performance.Figure 12 shows aerodynamic parameters distribution of 3 model inlet sections (section 3).As shown in figure 12

Impeller channel
The impeller inlet distortion brings more uncertainty to the already complex flow.span, gas flow rate in the left impeller outlet and the left channel is greater than that on the right, and a large low-pressure area appears on tailing edge of the right part of the blade.At 90% span, the distortion of gas flow in impeller is further amplified, and a high-speed zone appears on left tailing edge.In summary, with the increase of blade height, the flow distortion inside impeller gradually increases, and the high Mach number region will be further developed inside the impeller.Figure 14 shows the entropy increase of impeller in Model 3. It can be seen from the figure that at 10% span, due to the influence of upstream RIC, a large entropy increase area appears in the red circle position.The high entropy increase area is mainly distributed in the middle of blade channel.At 50% span, areas of high entropy increase gradually develop to impeller trailing edge.At 90% span, the flow velocity is large, violent flow separation occurs on impeller surface, the flow loss increases, and high entropy increase area is mainly concentrated in impeller downstream channels.

Conclusion
In this paper, the numerical calculation in an oblique flow compressor with RIC and the comparison of compressor performance with axial intake conditions is executed.The conclusions are as follows: a.The RIC shifts oblique flow compressor performance curve downward, reducing the stable operating range by 15.75% and the surge margin by 15.71%.Under the designed point, the total pressure ratio and isentropic efficiency of whole stage are reduced by 1.57% and 1.54% respectively.
b. Due to RIC influence, static pressure and relative Mach uniformity in impeller leading edge are destroyed.The Mach distribution on left half side is significantly higher than that on right.The difference between the maximum and minimum static pressure in RIC outlet accounts for 10.93%.The influence between RIC and impeller is mutual, and the impeller destroys the originally symmetrical flow field in RIC, so that the low-pressure area of RIC outlet is offset in impeller rotation direction.
c.The distortion caused by RIC is the main reason for compressor performance decline, and RIC reduces leading edge circumferential average attack angle, which reduces impeller working capacity.

( a ) 1 .
Structure of RIC (b) Structure of main flow parts Figure Structure of compressor and RIC.

Figure 2 .
Figure 2. Computational passage configuration for the 3 models.

P
are respectively satisfied the area-weighted average total pressure ** max PP  and ** min PP  .

Figure 3 .
Figure 3. Computational domain and mesh structure of mainstream channels.
The difference in isentropic efficiency and total pressure distortion coefficient change curve (b)

Figure 8 .
Figure 8. Variation trend of the average attack angle around the leading edge.

Figure 9 .
Figure 9. Speed triangle at the impeller inlet.

Figure 10
Figure 10 shows the trend of impeller outlet relative airflow angle.The relative airflow angle of 3 models increases with the increase of mass flow.Except for individual working points, the relative airflow angle of the impeller outlet of Model 3 is basically the same compared with the oblique flow compressor in the whole working range, indicating that the unevenness caused by RIC has little effect on the relative airflow angle at the impeller outlet.

Figure 10 .
Figure 10.Variation trend of relative airflow angle at impeller outlet.

Figure 11 .
Figure 11.Distribution of static pressure in each section of RIC.
(a) and figure12 (b), when calculating oblique flow compressor separately, the impeller inlet static pressure and absolute Mach number are evenly distributed along the circumferential, and the tangential air flow angle of the inlet section is about 0° and the distribution is relatively uniform.By comparing figure12 (c) and figure12(a), due to the influence of uneven distribution at RIC outlet, the impeller inlet flow symmetry is destroyed.The static pressure changes greatly along the circumferential distribution.There is a continuous highpressure area near hub in lower right, and there is an intermittent low-pressure area near shroud in upper left.The difference between maximum and minimum static pressure in this section accounts for 10.93%.The absolute Mach number of the impeller inlet section varies greatly along the circumferential direction, and Mach number distribution on left half side is significantly higher than that on right half.Since air flow turns from radial to axial after flowing through RIC, the air flow produces spiral and rotation, which is divided into axial flow and tangential flow before entering impeller.Tangential flow is key reason for impeller inlet uneven aerodynamic parameters.Tangential airflow angle distribution uniformity of leading edge is destroyed, and there is a large tangential airflow angle area near lower left of hub and near upper right of shroud.The tangential flow of lower and upper half of airflow are roughly opposite, which is the main reason for the flow loss.
Figure 13 illustrates the relative Mach distribution at different blade heights of impeller rotation surface.It can be seen from figure 13 (a) and figure 13 (b) that gas flow velocity inside the impeller gradually increases from leading edge to tailing edge, and gradually increases from hub to shroud.The impeller internal flow symmetry is better.After considering uneven distribution of air flow brought by RIC, the circumferential symmetry is destroyed.Every channel has unique flow characteristics, and the internal flow separation is intensified.As shown in figure 13 (c), at 10% span, the flow velocity on impeller outlet left side is slightly higher than on right.The flow separation occurs in blade right part.At 50%

Figure 13 .
Figure 13.Relative Mach counters of the rotating surface of the impeller.

Figure 14 .
Figure 14.Entropy increase counters of impeller in Model 3.
3 with mass flow are consistent with those of Model 1.But the stable working range of Model 3 is reduced by 15.75% compared with Model 1, and the surge margin is reduced by 15.71%.The characteristic curve of Model 3 is shifted downward as a whole.The total pressure ratio range (maximum pressure ratio minus minimum pressure ratio) and isentropic efficiency range (maximum efficiency minus minimum efficiency) are reduced by 35.08% and 43.75% respectively.At the designed point, the pressure ratio and efficiency of Model 3 are reduced by 1.57% and 1.54% respectively compared to Model 1. Comparing model 1 and Model 2, under large mass flow conditions, the compression ratio and isentropic efficiency of Model 2 decrease significantly, and other working conditions are basically consistent with Model 1. Comparing the performance curves of the 3 models again, it can be found that the flow loss of the RIC has little effect on pressure ratio and isentropic efficiency of oblique flow compressor.The RIC outlet distortion is key reason for decline in the oblique flow compressor performance.

Table 1 .
Performance comparison of two radial inlet chambers under designed condition.