Mechanism Affecting the Performance and Stability of a Centrifugal Impeller by Changing Bleeding Positions of Self-Recirculating Casing Treatment

Abstract

This study aimed to investigate the influence of the bleeding position of a self-circulating casing on the aerodynamic performance of a transonic centrifugal compressor. Three types of self-circulating structures with the bleeding positions of 11% Ca (the axial chord length of the blade tip), 14% Ca and 20% Ca from the leading edge of the blade were studied by using the numerical simulation method, with the Krain impeller taken as the research object. It was found that all three types of self-recirculating casing treatments can expand the stable operating range of the impeller, and that at medium and small flow rates, the total pressure ratio and efficiency of the impeller increase gradually with the backward movement of the bleeding position. The self-circulating casing treatment can restrain the development of tip leakage vortex, reduce the blockage area, and improve the stability of the impeller by sucking low-energy fluid. The farther back the bleeding position is, the greater the bleeding mass flow rate of the self-circulating casing for the low-energy fluid in the blade-tip passage becomes. Additionally, a greater inhibition effect on the tip leakage vortex, and a better effect of improving the performance and stability of the impeller, can be obtained. The best air bleeding position is 20% Ca, but it is not directly above the blade-tip blockage center of the solid wall casing passage. Instead, it is downstream of the blockage area.

1. Introduction

The flow inside a centrifugal compressor is rather complex. Typical internal flow phenomena of the centrifugal compressor include: slip phenomenon, secondary flow, tip leakage flow, interaction of shock and boundary layer, “jet-wake” phenomenon, etc. The combined effect of these flow phenomena profoundly affects the aerodynamic performance and stability of the centrifugal compressor. Given that self-recirculating casing treatment can improve the stable operating range of the compressor without negatively affecting the compressor performance, self-recirculating casing treatment has been widely studied. The self-recirculating casing treatment of the centrifugal compressor was first studied by Fisher in 1988 [1], and the experiment revealed the mechanism of action of the self-recirculating casing treatment: the pressure difference is used as the driving force to pump the gas from downstream to upstream and inject it. Meanwhile, the self-recirculating casing treatment exercises almost no effect on the adiabatic efficiency of the compressor while improving its stability.

In 2001, Hunziker [2] et al. found that self-recirculating casing treatment broadens the stability range of a rotor, since the bleed port of the self-recirculating casing treatment can successfully extract the interstitial vortex and reduce the inlet angle of the incoming airflow, as well as the Mach number of the airflow at the tip of the blade. Masahiro Ishida [3,4,5] designed an annular self-recirculating casing structure using an experimental and numerical method for a centrifugal impeller, and found that the self-recirculating structure effectively sucked the impeller tip leakage vortex into the annular groove by forming an inlet return flow, and the stable operating range of the impeller was significantly widened without affecting the impeller characteristics.

In 2016, Sewoong Jung [6] studied the self-recirculating casing treatment of the centrifugal compressor, and found that the bleed port position and width are main factors affecting the performance of the self-recirculating casing treatment. In general, when the bleed port width is increasingly widened and the bleed position is moved further downstream, the stability will be enhanced, while the efficiency will be correspondingly reduced. In addition, placing vanes in the bridge of the self-circulating casing reduces the vortex in the self-circulating casing to eliminate the interference with the main flow in the main passage, reduce losses, and increase the circulation flow mass through the self-circulating casing, thus ultimately improving stability. Guillou [7] measured the reflux and circumferential momentum injection effects of self-circulating casing treatment in a centrifugal compressor at near-surge conditions using particle image velocimetry (PIV). However, Semlitsch [8] studied self-circulating casing treatment in a centrifugal compressor using Large Eddy Simulation (LES), and found that a portion of the airflow returned from the blade passage to the main stream upstream of the compressor through the self-circulating structure under near-stall conditions, thereby expanding the stabilized operating range of the centrifugal compressor.

Zheng Xinqian [9] studied the centrifugal impeller self-circulating casing treatment using numerical calculation and experimental validation, and found that the suction ring groove sucked up the gap leakage vortex, thus blocking the running trajectory of the gap leakage vortex in the blade passage. At the same time, the return flow changed the angle of attack of the inlet, which in turn inhibited the flow separation in the guide wheel part of the impeller and delayed the stall. In the literature [10], the effects of axially symmetric self-circulating casing treatment and non-axisymmetric self-circulating casing treatment at the compressor surge point were compared based on an investigation of the non-axisymmetric self-circulating casing treatment, and asymmetric self-circulating casing treatment was found to be more effective in enhancing compressor stability. Li et al. [11] found that the self-circulating casing slows down the increase of the circumferential propagation speed during the stall process, thereby promoting the improvement of the stall margin. He [12] found that the self-circulating casing could eliminate the vortex structure at the tip of the impeller inlet, thus eliminating the regional rotational instability and stall. Guo [13] studied the counter-rotating axial-flow compressor using an experimental method and found that self-circulating casing reduces the unsteady interference between the adjacent rotors.

Zuo Pan [14] carried out a multi-objective optimization study on the casing treatment of a centrifugal compressor using numerical simulation, and found that five structural parameters, namely the position and width of the bleeding section, the angle of the jet section, and the upper and lower inclination of the annular cavity, exercised the most significant effects on the aerodynamic performance of the compressor. Kang Jianxiong [15] studied self-circulating casing treatment, and found that the self-circulating casing treatment changes the angle of the inlet airflow to improve the flow capacity of the tip passage of the impeller, and suppresses the blade-tip stall by absorbing the low-energy flow and leakage flow at the tip of the blade and spraying them into the impeller inlet. However, the differences are that under the stall point condition, the casing treatment affects the distribution of the size of the blade stall zone along the spreading direction, that the blade tip stall zone decreases, and that the blade root stall zone increases. Considering the circular design of the Coanda nozzle, numerous studies on air injection at the top of the compressor blades have undoubtedly proposed the Coanda nozzle as the most preferred choice, which ensures the jet flow is close to the wall of the casing.

However, throughout most of the published literature, the arrangement of self-circulating casing treatment jets on centrifugal presses is perpendicular to the casing line [15,16,17,18,19], which is not conducive to the wall-hugging flow of the jet stream. In addition, it should also be noted that there exists little research on the bleeding position of self-circulating casing of the centrifugal compressor, let alone the unclear research on the bleeding position. Additionally, the flow mechanism of the centrifugal compressor performance and stability affected by the bleeding position has not been fully understood.

Herein, to explore the influence of the axial position of the bleeding port on the enhanced stability ability of the self-circulating casing treatment and the performance of the compressor, the “Coanda profile” was adopted for the injection port, and the three-dimensional unsteady numerical investigation was carried out by changing the axial position of the bleeding port of the self-circulating casing, as was described in relevant research by Wang Wei [20].

2. Numerical Methods

SRV2-O [21], a transonic high-pressure ratio centrifugal impeller with splitter blades, was chosen as the study object. Krain [21,22] successively conducted an experimental and numerical study of this impeller and compared it.

Table 1. Design parameters of the SRV2-O impeller.

Parameters	-	Unit	Value
Number of main/split blades	$Z_m/Z_s$	-	13/13
Design flow rate	m	kg/s	2.55
Design speed	n	rpm	50,000
Total pressure ratio	${\pi }_{12}^{*}$	-	6.1
Efficiency	${\eta }_{12}$	-	0.84

shows the performance parameters and geometric parameters of this impeller.

The numerical simulation used Numeca software for single-channel unsteady calculation, and the IGG/Autogrid5 module was adopted by the grid generation. Additionally, the O4H-type grid topology was chosen by the main passage; the butterfly grid by the blade tip gap; and the H-type grid topology by the inlet and outlet extension sections. The grid topology diagram is shown in Figure 1. Three different grid numbers of 0.93 million, 1.3 million and 2.2 million were set for grid independence verification, and the near-wall grids were encrypted for all three grid numbers to ensure y+ < 10.

Numerical calculations were performed using the Fine Turbo module in the Numeca software; the Spalart–Allmaras turbulence model was selected to solve the full 3D Reynolds time-averaged Navier–Stokes equations in the relative coordinate system; the TVD windward format with second-order accuracy was selected for spatial discretization; and the number of physical time steps for the rotor to turn through a blade pitch was set to 30, while that of virtual time steps under each physical time step was set as 20.

The boundary conditions were set as follows: the inlet was given the total temperature and total pressure; the outlet was given the average static pressure; and the wall was adiabatic with no slipping boundary conditions. The performance curve was obtained by increasing the back pressure, and the resolution of the static pressure was 200 pa near the stall point, until a stable convergence solution could not be obtained. The convergence criterion was that the unsteady calculation could be considered to converge when the inlet and outlet flow rates and total performance parameters (e.g., total pressure ratio, efficiency, etc.) were monitored to vary periodically with time.

The literature [23] revealed that at the design speed, the blockage mass flow obtained by the numerical calculation of Krain impeller was 5–10% higher than the experimental value. The calculated blockage mass flow was 3.03 kg/s, and the blockage mass flow of the experimental value was about 2.864 kg/s. The error of the comparative experimental value was 5.7% in this paper, which is in line with the error range.

For the Krain impeller with splitter blades, the performance of the generated meshes with numbers of 0.93 million, 1.3 million and 2.2 million was compared; the central difference format and the second-order upwind format were used, respectively; the K-E model and S-A model were selected for turbulence model verification; and the calculated results were jointly compared with the experimental data. Herein, “Central” indicates the central difference format; “Upwind”, the second-order upwind format; “93 m”, “130 m”, etc., the corresponding grid numbers; “K-E”, the k-epsilon turbulence model; “S-A “, the Spalart–Allmaras turbulence model; and “Exp”, the experimental results. Additionally, the dimensionless relative flow rate (calculated mass flow rate/blockage mass flow rate) was chosen as the horizontal coordinate of the performance curve for comparison.

Table 2. Comparison of near-stall-point performance under different turbulence models.

Turbulence Model	Mass Flow Rate	Total Pressure Ratio	Isentropic Efficiency
S-A	0.8344	6.9051	0.8056
K-E	0.8558	6.9243	0.8174
Exp	0.8315	6.1823	0.8340

reveals that there was little difference in the pressure ratio of the S-A model and K-E model in the comparison of turbulence models, while the efficiency of the K-E model was closer to the experimental value. However, the stall point flow rate of the K-E model was quite different from the experimental value.

As can be seen from

Table 3. Comparison of near-stall-point performance in different differential formats.

Difference Scheme	Mass Flow Rate	Total Pressure Ratio	Isentropic Efficiency
Central	0.8392	6.8729	0.7974
Upwind	0.8344	6.9051	0.8056
Exp	0.8315	6.1823	0.8340

, in the comparison between the central difference scheme and the second-order upwind scheme, there was little difference between the pressure ratio of the central difference format and the second-order upwind format, and the efficiency and stall mass flow rate calculated by the second-order upwind format are more consistent with the experimental values, when the S-A model was applied.

As shown in Figure 2, the pressure ratio efficiency curve for the 0.93 million grid quantity compared to both the 1.3 million and 2.2 million grid quantities was not significantly different, and the 0.93 million grid quantity satisfied the grid irrelevance requirement. As shown in Figure 3, the efficiency curve of the calculated results for the 1.3 million grid quantity fit the experimental value more closely than the 0.93 million and 2.2 million grid quantities. In addition, compared with the results of numerical calculations made by Krain [22] for this centrifugal impeller (“Krain cal” in Figure 3), the pressure ratio curve calculated by the numerical model was found to better fit the experimental data than those calculated by Krain at almost all mass flow rate points, indicating that the pressure ratio in this paper had fewer errors with the experimental values.

In summary, the overall trends of pressure ratio and efficiency with mass flow rate for the 1.3 million grid with the S-A turbulence model and second-order upwind format were more consistent with the results of the experiment. However, the pressure ratio and efficiency performance curves obtained by numerical simulation under the number of 1.3 million grids were quite different from the experimental values. The overall pressure ratio was higher than the experimental value, while the overall efficiency was lower. Kang S [20] believed that the error between numerical simulations and experimental values is caused by the different processing methods of the experimental data and the numerical calculation data. The numerical simulation of the total outlet pressure was directly calculated from the changed outlet static pressure, while the experimentally measured total outlet pressure is calculated from the measured total outlet temperature, mass flow rate and wall static pressure, and the defined blockage factor assuming a certain blockage factor, which makes the measurement performance highly dependent on the assumed blockage factor and the measurement accuracy of the average static pressure.

To further illustrate the accuracy and feasibility of the proposed numerical method, a comparative analysis of the internal flow field of the compressor is depicted in Figure 3 [21], which presents the locations of the experimental laser measurement planes of the rotor passage in the flow direction at the design mass flow rate.

Figure 4 describes the comparison of the relative Mach number distribution between numerical simulations and experimental measurements for different planes, and the experimental data were extracted from the reference [21].

It can be observed from Figure 4 that the trends of the relative Mach number distribution of each plane of the numerical simulation and the experimental results were essentially similar, and that the relative Mach number distributions of planes 4 and 10 were not only consistent with the trends of the experimental results, but the values are also in good agreement. In general, the adopted numerical method can more accurately predict the total performance trend and internal flow field details of the Krain impeller, and was used in all the following explorations here.

3. Self-circulating Casing Design

Figure 5 and Figure 6 show the relative Mach number distribution in the blade passage. The following flow field diagrams are all time-averaged calculation results unless otherwise specified. Herein, “PE” stands for peak efficiency condition, and “NS” denotes near-stall condition. The relative Mach number distribution under the PE condition indicates the existence of a small amount of low energy air flow in the flow passage (red line area in Figure 5). However, considering the small distribution range, it exerted no effect on the flow in the whole passage. Under the NS condition, a larger range of lower velocity air flow can be obviously observed near the pressure surface at the leading edge of the main blade. Additionally, the low-Mach-number area occupies most areas of the tip of the splitter blade, and blocks most areas of the passage.

Figure 6 depicts the relative velocity vectors of the two working conditions at 98% blade height. The low-speed airflow in the passage is represented by the red dashed area in the figure, while the red arrows indicate the approximate flow direction of the airflow in the red dashed area. In terms of the solid-walled casing under the NS working condition, a large area of low-speed airflow flowing from the blade suction surface to the pressure surface can be observed in the main blade passage (see the red dashed area in Figure 6b), which caused blockage and greatly reduced the circulation area in the passage. Under the PE condition, the area of this low-speed airflow was obviously reduced, and the low-speed airflow flowed along the suction surface of the main blade.

It is also noted that the relative position of the low-speed airflow in the passage changes from being basically flush with the leading edge of the main blade under the PE condition to being upstream of the blade under the NS condition. This indicates that with the gradual throttling of the impeller, from PE to NS conditions, the low-speed airflow in the blade-tip passage gradually increases, and the direction of airflow gradually changes from flowing along the passage to flowing from the blade suction surface to the adjacent blade pressure surface. Additionally, the low-speed airflow gradually moves upstream to the impeller passage, thus reducing the circulation area of the blade-tip passage, which is also the cause of the blockage of the blade-tip passage under NS conditions.

The above pictures show that the low-energy air region of the compressor was located in the main blade passage inlet under near-stall conditions, and the position of the bleeding port of the self-circulating casing directly affected the bleeding ability of the self-circulating casing for the low-energy fluid in the passage. To this end, three kinds of self-circulating casings with different bleeding air positions were designed on the basis of the solid-walled casing, with the other structural parameters of the self-circulating casing remaining unchanged. The structure of the self-circulating casing is shown in Figure 7, where m is the axial length of the injector; k, the axial distance between the trailing edge of the injector and the leading edge of the main blade; l, the axial distance between the leading edge of the bleeding port and the leading edge of the main blade; x, the axial length of the bleeding port; and α and β, the jet angle and bleeding angle, respectively.

Herein, the position of the injector and jet parameters of the self-circulating casing are kept unchanged, and the self-circulating structure remains consistent with the number of main blade passages, with 13 passages uniformly arranged in the circumferential direction. The design values of the self-circulating casing structure parameters are given in

Table 4. Basic design parameters of self-circulating casing.

Parameter	Value	Parameter	Value
α (°)	30	k (mm)	18.57
β (°)	70	l (mm)	Variable quantity
m (mm)	8.56	x (mm)	8
n (mm)	6.23	y (mm)	25

.

The three different bleeding positions were 11% Ca, 14% Ca, and 20% Ca in this paper (Ca represents the axial chord length of the blade tip of the main blade, and corresponds to “0.11”, “0.14” and “0.2” in the present casing). The structure of the self-circulating casing at different bleeding positions on the meridian plane is shown in Figure 8. “SRC” represents the self-circulating casing; “C” the circumferential coverage; and “B” the location of the bleeding port. The circumferential coverage of a single SRC was 20°, indicating a circumferential coverage of about 72%. Additionally, the distances L1, L2 and L3 from the center of the bleeding ports to the leading edge of the main blade increased correspondingly with the backward movement of the bleeding port.

Figure 9 presents the structure of the numerical model after adding the self-circulating casing. In the numerical calculation, the self-circulating casing treatment was set as a stationary block. In order to ensure the data transfer between the rotor passage and the self-circulating structure, there were two layers of sliding blocks between the rotor blade tip and the self-circulating structure, and the sliding blocks were fully non-matching coupled with the rotor passage and the self-circulating casing, respectively. Additionally, H-type mesh topology was selected for both the sliding blocks and the self-circulating structure, and the other mesh settings were established as described previously.

The meridian surface mesh topology is shown in Figure 10. The large deflection in the direction of the bleeding section and the jet section made it difficult to avoid the generation of the vortex system, thus causing the flow loss in the self-circulating casing. To this end, the Coanda profile was used in the jet section of all self-circulating casings to minimize the flow loss in the self-circulating structure. In order to ensure the orthogonality of the self-circulating casing structure while generating the grid, the suction angle was set to 70° and the jet angle to 30°.

4. Results and Discussion

4.1. Total Performance Analysis

Figure 11 shows the unsteady total performance curves of the centrifugal impeller when treated with solid-wall casing and self-circulating casing with different bleeding positions, where “SW” stands for solid-wall casing. The three self-circulating casing treatment structures were found to reduce the near-stall mass flow rate of the centrifugal impeller, and the near-stall mass flow rate of the centrifugal impeller increasingly lowered as the bleeding position gradually moved back. This indicates the efficiency of the self-circulating casings with different bleeding positions in broadening the stable working range of the compressor to a certain extent. Additionally, the improvement degree of the impeller stability by the self-circulating casings is proportional to the backward degree of the bleeding position.

However, no obvious difference was observed in the stability expansion effect of the self-circulating casings with the bleeding positions at the front and the middle, and the self-circulating casing with the bleeding position at the back had the most significant improvement in the stable working range. In the medium- and small-mass flow rate ranges, the pressure ratio of the self-circulating casings were larger than those of the solid-wall casing, and the pressure ratio increased with the rearward movement of the bleeding position. This indicates that the improvement of the impeller pressure ratio is proportional to the rearward degree of the bleeding position of the self-circulating casing.

In order to quantitatively measure the effect of the self-circulating casing treatment on the stability margin and efficiency of the centrifugal impeller, two parameters, i.e., the stall margin improvement (SMI) and the peak efficiency improvement (PEI), were introduced and defined as follows:

$$SMI=\left[\left(\frac{{\pi }_{ct,stall}^{*}}{{\pi }_{sw,stall}^{*}}\right)\times \left(\frac{M_{sw,stall}}{M_{ct,stall}}\right)-1\right]\times 100\%$$

(1)

$$PEI=\left[\left({\eta }_{ct,peak}^{*}-{\eta }_{sw,peak}^{*}\right)/{\eta }_{sw,peak}^{*}\right]\times 100\%$$

(2)

where π* represents the total pressure ratio; M, the flow mass; η*, the isentropic efficiency; the subscripts sw and ct, the solid-wall casing and the casing treatment, respectively; and stall and peak, the near-stall condition and peak efficiency condition, respectively.

Table 5. Stall margin improvement and peak efficiency improvement of self-circulating casings with different bleeding positions.

	M Stall (kg/s)	${\mathit{\pi }}_{\mathit{s}\mathit{t}\mathit{a}\mathit{l}\mathit{l}}^{*}$	SMI/%	PEI/%
SW	2.5437	6.9274	/	/
SRCC0.72B0.11	2.2736	7.1883	16.09	−0.29
SRCC0.72B0.14	2.2531	7.2434	18.05	−0.17
SRCC0.72B0.2	2.1881	7.3316	23.03	−0.22

presents the stall margin improvement and peak efficiency improvement of the compressor with different axial bleeding positions of the self-circulating casing, which reveals that the self-circulating casing treatment with the bleeding air positions at 11% Ca, 14% Ca, and 20% Ca produced a stall margin improvement of 16.09%, 18.05%, and 23.03%, respectively. Meanwhile, the peak efficiency improvements are −0.29%, −0.17%, and −0.22%, respectively. The above quantitative analysis has also found that the stall margin of the compressor increased gradually as the position of the bleeding position moved backward, which means that the ability of the self-circulating casing to expand the stability gradually increased, but the difference in the amount of stall margin improvement between 11% Ca and 14% Ca was not significant. With the gradual backward movement of the bleeding position, the peak efficiency increases instead of decreasing, but the effect of peak efficiency improvement decreases gradually.

4.2. Comparison Analysis of Flow Field

Figure 12 shows the relative Mach number distribution of the rotor channel slice section with different self-circulating casing structures under the time-averaged flow field, with each slice uniformly distributed at the same interval and perpendicular to the Z-axis. Figure 13 depicts the relative Mach number distribution for different casing structures at 95% of the blade height. Herein, flow field comparisons were performed under the near-stall mass flow rate conditions of the solid-walled casing. The following flow field diagrams, unless otherwise specified, are the results of time-averaged calculations.

The relative Mach number distribution cloud diagrams in Figure 12 and Figure 13 show that under the near-stall mass flow rate of the solid-wall casing, low-Mach-number regions could be found in the impeller main blade passage and the tip passages of the splitter blades, which are represented by the red dotted area in the Figures. However, the low-Mach-number regions in the impeller main blade passage were significantly reduced, and the low velocity airflow was suppressed, after adopting the self-circulating casing with different bleeding positions. However, no significant change was observed in the low-Mach-number regions in the splitter blade passage, indicating that the self-circulating casing treatment can effectively pump the low-speed region in the main passage and have the onset of the stall delayed, but it has less inhibitory effect on the low-speed airflow in the spitter blade passage.

Figure 12 and Figure 13 clearly reveal that the low-Mach-number area in the main blade passage basically disappeared after the 0.2 Ca self-circulating casing was adopted, while there was still a small amount of low-Mach-number area in the main blade passage of 0.11 Ca and 0.14 Ca. This perfectly indicates the weak “pumping” effect of the self-circulating casing of 0.11 Ca and 0.14 Ca on low-speed airflow at this flow rate. Additionally, it can also be seen that the low-Mach-number range in the main blade passage of 0.14 Ca was smaller than that of 0.11 Ca, and the low-Mach-number region was more backward. In terms of the distribution of the relative Mach number, the further back the bleeding position of the self-circulating casing is, the better the inhibition effect on the low-speed area becomes, and the stronger the stability expansion ability of the self-circulating casing will be. According to Figure 12 and Figure 13, the 0.11 Ca bleeding port was located directly above the center of the low-velocity area, but was endowed with the worst efficiency in suppressing the low-velocity airflow in the main flow passage.

Figure 14 shows the relative velocity vector diagrams for different casing treatments at the 98% blade height. Under the near-stall flow rate of the solid-wall casing, a large area of low-speed airflow flowing from the suction surface of the blade to the pressure surface can be observed in the main blade passage (see the red dotted area in Figure 14a). This very airflow causes blockages in the passage, thus greatly reducing the flow area in the passage. After adopting the self-circulating casing, the low-speed airflow was significantly suppressed from the suction side to the pressure side in the main blade passage (the red dotted area in Figure 14). The red arrow in Figure 14 represents the flow direction of the airflow.

After adopting the self-circulating casing, the angle between the airflow direction and the suction surface of the blade became smaller, and the self-circulating casing enhanced the flow capacity of the blade passage. By comparing the three self-circulating casings, the airflow direction in the blade flow path with the 0.2 Ca and 0.14 Ca casing treatment was found to basically follow the suction surface of the blade. However, after the 0.11 Ca casing treatment, the airflow direction in the blade passage still demonstrated a certain angle with the suction surface. Judging from the low-speed area of the blade tip (the red dashed area in Figure 14), the area of the low-speed region gradually decreases with the rearward movement of the bleeding position, which confirms the strongest effect of the 0.2 Ca on enhancing the flow capacity of the impeller flow path.

As can be seen from the distribution of leakage flow at the tip gap shown in Figure 15, the range and scale of leakage flow generated from the impeller gap were reduced at the inlet of the self-circulating casing treatment after the self-circulating casing treatment, indicating the efficiency of the self-circulating casing treatment in effectively pumping the leakage flow and inhibiting the development of the leakage flow. Figure 15 also reveals that the leakage flow below the bleeding port almost completely disappeared after the 0.2 Ca self-circulating casing treatment, and that the coverage of the leakage flow in the passage after the bleeding port was smaller than other structures. Additionally, the leakage flow range in the main blade passage was significantly suppressed, and the 0.2 Ca casing treatment performed particularly well in suppressing the leakage flow compared with the other two structures. This is due to the 0.2 Ca casing bleeding port almost fully covering the leading edge of the blade leakage flow, and, because the bleeding port and the injector pressure difference was the largest, it had the strongest suction effect.

The bleeding position of the 0.11 Ca casing treatment at the front led to the incompleteness of the suction of the gap leakage flow at the leading edge of the blade, and the weakest inhibition effect on the gap leakage flow. In this case, the entire impeller passage was still full of leakage streamlines. Given that the bleeding port of the 0.14 Ca casing treatment was centered, it failed to completely suck the leakage flow in the gap behind the leading edge of the blade, so the suppression effect on the leakage flow was weaker than that of the 0.2 Ca casing treatment. Consequently, as the axial position of the bleeding port was rearward, the suction effect of the self-circulating casing on the leakage flow gradually became significant.

Figure 16 depicts the absolute vorticity cloud map and static pressure contour distribution at the 98% blade height, which approximates the relative position of the main flow/leakage flow interface and the vortex core trajectory. The absolute vorticity is defined as:

$${\xi }_{\mathrm{n}}=\frac{|\nabla \times \overrightarrow{V}|}{2\omega }$$

(3)

where $\overrightarrow{V}$ denotes the absolute velocity vector, and $\omega$ represents the rotational angular velocity of the compressor rotor.

The black dotted line represents the relative position of the vortex core trajectory, while the red dashed line represents the main flow/leakage flow interface. It can be observed that under the near-stall flow rate of the solid-wall casing, the interface between the main flow and the leakage flow almost blocks the front of the entire main blade passage, and that the vortex core trajectory also develops from the blade suction to the adjacent blade pressure surface. After the self-circulating casing treatment, the main flow/leakage flow interface in the impeller passage and the vortex core trajectory of the leading edge of the blade tip were deflected towards the suction surface of the blade, effectively improving the flow condition of the blade-tip passage.

However, the vortex core trajectory of 0.11 Ca and the main flow/leakage flow interface were both more biased towards the blade pressure surface. Compared with 0.2 Ca, the angle between the vortex core trajectory of 0.14 Ca and the suction surface is larger, and no obvious difference can be observed between 0.14 Ca and 0.2 Ca in improving the passage flow area.

Figure 17 presents the distribution of the relative airflow angle at the impeller inlet along the blade height, and the relative airflow angle is defined as follows:

$${\theta }_r={\tan }^{-1}\left(\frac{W_t}{W_z}\right)·\frac{{180}^{°}}{\pi }$$

(4)

As shown in the Figure, the relative airflow angle of the impeller inlet was reduced in the 80–100% blade height range after the casing treatment. The decrease of the relative airflow angle of the inlet indicates the decrease of the incidence of the incoming flow at the inlet, which correspondingly leads to the decrease of the tangential component of the relative velocity of the inlet airflow, suggesting the increasingly stronger flow capacity of the tip passage and the reduced blockage of the tip passage.

In order to quantify the variation of the blockage degree in the whole impeller passage after the treatment of different self-circulating casings, Figure 18 shows the distribution of the dimensionless blockage area of the blade tip passage along the axial direction under the time-averaged results of the unsteady calculation. The dimensionless blocked area is defined as the ratio of the blocked area to the maximum blocked area of the solid wall casing. The dimensionless axial distance 0 in the Figure is the leading edge of the main blade, and 1 is the leading edge of the splitter blade. The blockage of the blade tip passage was found to be significantly reduced in most of the range after the self-circulating casing treatment, which is the main reason why the self-circulating casing can improve the stability margin of the compressor.

In the passage in front of the splitter blade along the axial direction, the dimensionless blockage area of the blade tip shows an overall trend of first increasing and then decreasing. The ability of self-circulating casings with the bleeding port in different axial positions to reduce the degree of blockage in the blade tip passage varied. As the axial position of the bleeding port gradually moved back, the blockage degree of the impeller tip passage decreased gradually. In the leading edge of the splitter blade passage, the dimensionless blockage area gradually decreased with the backward movement of the bleeding port, indicating that the three different casing treatments can not only reduce the blockage in the main blade passage, but also reduce the blockage in the splitter blade passage to a certain extent. Additionally, the reduction degree of the blockage increased with the backward movement of the bleeding port.

Figure 19 depicts the variation of the blockage ratio within its blade-tip passage for different casing structures at 50% τ over a full cycle (a physical time step of 30 set in the unsteady calculation within one scale pitch of a single passage), where the horizontal coordinates represents different physical moments. The blockage ratio is defined as:

$$B_R=\frac{A_b}{A}\times 100\%$$

(5)

where A denotes the selected cross-sectional area, and A_b represents the area within the cross-sectional area where the relative axial velocity W_Z is less than zero. The blockage ratio, as with the above blockage area, can reflect the magnitude of the blockage in the flow passage. As can be seen from Figure 19, under the near-stall flow rate of the solid wall, the blockage area ratio of different self-circulating casing structures changed with time at 50%τ, and all reached the peak within 20–30 physical time steps. However, the blockage area of the blade tip is smaller than the solid wall in most of the time after the casing treatment, suggesting the significant effect of the self-circulating casing treatment on increasing the flow area in the solid wall impeller passage. Among the three types of self-circulating casings, the 0.2 Ca casing performed best in improving the flow area of the blade tip passage. Additionally, with the backward movement of the bleeding port, the reduction degree of the self-circulating casing on the blockage area of the blade tip increased correspondingly.

Figure 20 describes the variation curves of the normalized bleeding flow mass rate with physical time for the three self-circulating structures. The normalized bleeding mass flow rate is defined as the ratio of the actual bleeding flow mass rate to the impeller design flow mass rate. Considering the phase difference between the relative positions of the bleeding port and the blade at different times, obvious fluctuations can be observed in the bleeding flow mass rate. The bleeding mass flow rate and the position of the bleeding port were found to be closely related. In addition, the bleeding flow mass rate gradually increased as the bleeding position moved to the rear, and the bleeding mass flow rate of the self-circulating casing at the back was greater than that of the front casing at each moment. Among them, the 0.11 Ca casing provided the worst bleeding capacity, and even the bleeding mass flow rate was almost zero at some moments. Additionally, with the backward movement of the bleeding position, the change of bleeding mass flow rate at different times was found to be gradually stabilized. The further back the bleeding position is, the more stable the bleeding mass flow will be.

It was found that, by combining with the change of the tip blockage ratio in Figure 19, the peak time of the bleeding mass flow rate does not directly correspond to the time when the tip blockage ratio drops the most, and a certain phase difference is observed. Additionally, the persistent suction effect can minimize the blockage of the tip passage at a certain moment.

Figure 21 shows the blockage distribution of different casing structures at the 99% blade height of the blade tip in the main blade passage under the near-stall mass flow rate. The red area represents the area where W_z is less than zero, i.e., the blocked area. The blade tip passage is almost completely blocked under the near-stall flow rate of the solid-wall casing, but the blockage in the blade tip passage is improved after adding the self-circulating structure. The blockage area of the blade tip passage gradually decreased as the bleeding position gradually moved back, which is highly consistent with Figure 18 and Figure 19. The favorable improvement effect of the self-circulating casing on the blockage of the blade tip passage near stall is thus confirmed. The 0.2 Ca casing, among the three casings, presented the best stabilizing effect.

Figure 22 shows the absolute Mach number and streamline distribution inside the self-circulating structure at different bleeding positions. Different self-circulating structural blocks take the circumferential section of the same radial height. “IN” refers to the injector, and “BL” represents the bleeding port. It is obvious from the comparison that the Mach number distribution is quite different in the three different structures of the self-circulating casing. The value of the absolute Mach number area also increases gradually with the back of the bleeding position. Among them, a large range of low-Mach-number area can be observed in the 0.11 Ca self-circulating casing, indicating the smallest flow speed of the air flow from the bleeding port to the injector during this process. The streamline can reflect the flow direction of the airflow entering the self-circulating casing structure. An obvious vortex structure was generated after the airflow entered the self-circulating casing of the three different structures, which suggests the existence of flow loss. The further back the bleeding port is, the smaller the size of the vortex becomes.

Figure 23 shows the variation of the suction/injection mass flow rate in the self-circulating casing with different axial positions of the bleeding port. The horizontal coordinates in Figure 23 are the ratio of the distance from the center of the self-circulating structure injector to the leading edge of the impeller to the distance from the center of the bleeding port to the leading edge of the impeller. In terms of the design mass flow rate of this compressor for the suction/injection mass flow rate, the vertical coordinate is dimensionless. Figure 23 reveals that with the back movement of the axial position of the bleeding port, both the bleeding mass flow rate and the jet mass flow rate of the self-circulating structure also increased gradually.

Figure 24 shows the comparison of absolute total temperature and absolute total pressure along the blade height at the impeller outlet of different casing structures. The total temperature and total pressure of the impeller were obviously improved after the self-circulating casing treatment. With the bleeding position gradually moving back, the total pressure and total temperature at the impeller outlet increase correspondingly. The most obvious increase in total temperature and total pressure was observed in the case of the 0.2 Ca casing. However, the total temperature and total pressure still failed to directly reflect the change of the efficiency, since the calculation formula of the adiabatic isentropic efficiency is:

$${\eta }_R^{*}=\frac{{\pi }_k^{*}{}^{\frac{k-1}{k}}-1}{\frac{T_k^{*}}{T_1^{*}}-1}$$

(6)

where, “${\eta }_R^{*}”$represents the adiabatic efficiency; “${\pi }_k^{*}$” the pressure ratio; “$T_k^{*}$” the total temperature of the rotor outlet; “$T_1^{*}$” the total temperature of the rotor inlet; and “R” the rotor.

Figure 25 shows the efficiency comparison of the primitives of different casing structures, of which, the right figure is the efficiency comparison of the partial enlargement of the blade tip. The efficiency of the impeller is found to exhibit an increasing trend compared with the solid-wall casing at most blade heights after the self-circulating casing treatment, which is consistent with the performance shown in Figure 11. Additionally, at the blade tip area, the primitive efficiency of the self-circulating structure is higher than that of the solid-wall casing, indicating the ability of the self-circulating casing in to effectively improve the efficiency of the impeller near the stall point. In the case of different self-circulating casing structures, the further back the bleeding position is, the greater the efficiency improvement will be. Among them, 0.2 Ca presents the best improvement efficiency, but the overall improving degree is rather limited, which is completely consistent with the flow-efficiency performance curve above.

5. Conclusions

Herein, three kinds of self-circulating casing treatment structures with different bleeding positions were designed and studied. The flow mechanism of self-circulating casing treatment to expand compressor stability and affect compressor performance was revealed via detailed flow field comparative analysis. The main conclusions are as follows:

(1) After the treatment of the self-circulating casings with different bleeding positions, the stall margin improvement of the compressor considerably increased. The self-circulating casing treatment with bleeding positions at 11% Ca, 14% Ca, and 20% Ca produced an improvement of 16.09%, 18.05% and 23.03% in stall margin, respectively. Meanwhile, peak efficiency improvements of −0.29%, −0.17% and −0.22% were obtained. In addition, the further back the bleeding position, the greater the improvement of the total pressure ratio and efficiency of the impeller under medium- and small-mass flow rates, and the absolute value of the efficiency improvement increases to about 1%.

(2) With the change of the bleeding position of the self-circulating casing, the three kinds of self-circulating casings exhibited different enhancement effects. The further back the bleeding position, the greater the bleeding mass flow rate of the self-circulating casing for the low-energy fluid in the impeller tip passage. Additionally, the corresponding effect of reducing the blade-tip blockage will be more obvious, and the ability to improve the performance and stability of the impeller becomes stronger. However, the bleeding port of the self-circulating casing with the largest bleeding mass flow rate and the best expansion effect was not directly above the blocking center of the blade tip passage in the solid-wall casing, but instead above the downstream of the blocking area.

(3) The axial position of the bleed port was changed, so that the pressure difference between the self-circulating casing injector and the bleeding port changed, and the suction capacity of the self-circulating casing changed. The change of the bleeding position makes the range of the blade leading edge leakage flow covered by the bleeding port different, and covers more leading edge leakage flow while the suction capacity is enhanced, which had a better improvement effect on the blockage of the blade tip passage.

(4) At different moments, the blockage degree in the blade-tip passage and the bleeding mass flow rate of the self-circulating casing presented different changes, and the peak moment of the bleeding mass flow rate did not directly correspond to the moment when the tip passage blocking ratio decreased the most. A fixed-phase difference was observed.

In this paper, the bleeding position was studied numerically. In the future, it is hoped that the calculation results in this paper will be verified by experiments, and the effects of the circumferential coverage ratio of the self-circulating casing on the compressor will be studied.