Experimental investigation of flow instability evolution in a low-speed two-stage axial compressor

A low-speed two-stage axial flow compressor with inlet guided vane was tested. Based on its performance, the near-stall condition was determined. The transient pressure signals on the casing wall were obtained along the circumferential and axial directions. Data statistics method was applied to analyze the features of the pressure signals on the working conditions. The variance of pressure increased along streamwise direction under the large flow rate condition. Meanwhile, it was influenced by the interaction between the stator and the rotor at the inlet of the second stage as well. On the near-stall condition, a modal wave like signal was found in time domain, whose frequency was about 47% of the impeller rotation frequency, accompanied with a broad-band feature in the low-frequency region. The first-stage rotor was found to stall with the analysis on the variance of the pressure. While there was no obvious unstable character observed in the second stage, the parameter at the inlet of the second stage revealed that the disturbance generated in the first stage was suppressed by the second stage. These signals’ features could be used to predict the appearance of instability in the two-stage axial flow compressor.


Introduction
Multi-stage axial flow compressors are applied widely in industry.The internal flow would be influenced by the interaction between the stator and the rotor.When stall happens in a stage, stall cells would propagate around the annulus of the rotor.At the same time, the flow could be influenced by the downstream cascades.
It is widely accepted that there are two types of stall precursors in compressor.According to the length scale of the disturbance, they can be divided into spike and modal wave.Spike is a stall precursor associated with short length scale disturbances.Emmons et al. [1] first explained the generation and propagation mechanism of spike based on the experimental results.The increase of the attack angle under high loads was thought to be the reason behind the formation and propagation of stall cells.Modal wave is a disturbance sequence related to long length scale disturbances proposed by Moore and Greitzer [2].It could be considered as a small sinusoidal velocity fluctuation revolving around the annulus at 20% to 50% of rotor rotation speed.Although this stall precursor was first obtained through physical modeling, it was subsequently discovered and confirmed by McDougall et al. [3] and numerous researchers in experiments.
These two types of stall precursors were independent and physically different events [4].Huang et al. [5] clarified the flow instability mechanism of a 1.5-stage high-loaded axial compressor through the experiments.It was found that the compressor rotor developed from a spike-wave stall precursor to a rotating stall at a lower speed, while a classic surge occurred at higher speed from a spike-wave precursor surge.When the speed was even higher, at 90% of its corrected speed, the compressor underwent the process of modal wave precursor, spike-wave precursor, and surge.The type of stall precursors could be determined based on the compressor characteristic curve and the critical angle of attack [6].
With the development of technology and the improvement of computility, the study of stall precursors has transitioned from experimental research to a combination of experimental and computational research.Fulukawa et al. [7] conducted experiments and unsteady numerical simulation analysis on an axial compressor rotor isolated from the stator.It was found that the tip leakage vortex at the leading edge of the blade would break under near-stall conditions, causing self-excited oscillations, and leading to the occurrence of spike.And the spike stall cell was thought to be formed due to the blockage zone on the radial vorticity side with velocity vectors directed upstream in a transonic compressor [8].Some endeavors focused on capturing the typical unstable flow features by numerical and experimental techniques.Hutchings et al. [9] found that a broadband hump at around 50% of the blade passing frequency was present in the pressure spectra prior to stall.And the spacing of these peaks was found to be exactly equal to the measured stall cell speed once rotating stall was established.
In order to effectively prevent the unstable flow phenomena, it is necessary to understand their generation conditions and development characteristics.Ando et al. [10] obtained the unsteady compressor characteristics by using a precision pressure transducer and a one-dimensional single hotwire anemometer.It was shown that stall inception of the compressor was induced earlier in the large cycle compared with the case of the top cycle.Young et al. [11] introduced the skewness and irregularity of the period-averaged static pressure signal to evaluate the pressure wave deformation and instability of the system.Irregularity changed regularly as approaching to stall condition.But it was sensitive to the size of tip leakage and eccentricity.Zhang et al. [12] analyzed the stall evolution in a centrifugal compressor with these parameters.The unsteady static pressure signals were measured at the inlet of impeller and diffuser.But the measurement was limited to flow field in static components.The information about the flow field in the blade passages or tip could not be obtained.The pre-stall stage and the stall stage were predicted accurately when there was an increase in irregularity and a dramatic decrease in skewness.Even though some parameters were proposed to predict the generation of instability, the physical meaning of these parameters are still not clear.And the interaction between the cascades is not considered.
In this study, the performance of a two-stage axial flow compressor with inlet guided vane was studied by transient pressure measurements.The generation and development of flow instability during the evolution process were analyzed and compared with the previous numerical results.

Experimental Setup
The two-stage axial compressor was tested in the test rig with low rotating speed.The axial compressor is comprised with the inlet guided vane (IGV), the first stage rotor (R1), the first stage stator (S1), the second stage rotor (R2), and the second stage stator (S2).The rotor blades twist from hub to tip, while stator blades are almost straight.The direction of outlet flow at the second stage stator is axial.The tip diameter of the blade is 0.6 m.More information about the parameters of the compressor and blade installation arrangement can be found in reference [13].A photograph of the axial compressor test experiment is shown in figure 1.The compressor is driven by a motor with a power of 75 kW.The test rig includes the inlet pipe, the low-speed two-stage axial flow compressor, and the motor.The probes were set on the casing side along the circumferential and axial directions.In axial positions, the inlet section of R1 (R1LE), the outlet section of R1 (R1TE), the inlet section of R2 (R2LE) and the outlet section of R2 (R2TE) were selected.
Eight measuring points were designed on each section, denoted as point 1-8.For the section R1LE, measuring points 1 to 5 were evenly arranged within a circumferential range of 72° corresponding to the four blade passages of R1.The angular difference among points 5, 6, 7 and 8 was 90°, corresponding to 5 complete blade passages.The circumferential propagation characteristics of stall cells on the nearstall condition could be observed by comparing the phase difference of dynamic pressure signal fluctuations at these points.The measuring points on section R1TE were pivoted for 20° in the direction of compressor rotation according to the angular difference caused by the movement passing through R1.For section R2LE, measuring points 1 to 5 are evenly arranged within a circumferential range of 57.6° corresponding to the four blade passages of R2.The angular difference among points 5, 6, 7 and 8 was 72°, corresponding to 5 complete blade passages.The measuring points on section R2TE were pivoted for 14° accordingly.

Performance of the compressor
Total pressure coefficient and flow rate coefficient are used to represent the performance of the compressor.The definition of total pressure coefficient is as follows: where t P  is the total pressure rise,  is the density of the gas and m u is the velocity at the mean radius.And the definition of flow rate coefficient is as follows: where m Q is the mass flow rate and D is the diameter of the pipe.
The performance curve of the compressor is shown in figure 3.With the decrease of flow rate, the pressure rise first increases to the maximum value.As the flow rate further decreases, the pressure rise reduces.And obvious aerodynamic noise is generated in the compressor.On this condition, the compressor operates unstably and stalls.The last stable operating point is determined as the near-stall condition.6 for point 1 at section R1LE, section R1TE, section R2LE and section R2TE along axial direction, corresponding to the points' arrangement in figure 2. The pressure rise at each stage can be observed.Leaving with high speed, the gas flow diffuses in S1, and then flows into R2.The interaction between S1 and R2 makes the fluctuation amplitude increase.The fluctuation amplitude at section R2LE is much larger than that of other axial positions.The time-averaged pressure distribution along axial direction at the blade tip is shown in figure 7 for different flow rate.The pressure load is represented with pressure rise ratio defined as follows: where P ̅ is the time-averaged pressure of the relevant section, P ̅ R1LE is that at section R1LE and P ̅ R2TE is that at section R2TE.The difference of this ratio at the inlet and outlet of rotor can indicate its pressure rise capability.The pressure rise ratio is increased at section R1TE due to the compression process with different flow rates.Then there is a decrease of pressure rise ratio at S1.It might be caused by the flow direction change and energy loss in this process.The gas is further compressed in R2.But the pressure rise in the first stage is larger than that in the second stage, indicating that the first stage plays a major role in the compression process.
The pressure rise in the first stage decreases when the flow rate is decreased from 16795 m 3 /h to 13415 m 3 /h, indicating the decrease of pressurization capability of the first stage.So R1 experiences flow instability on the near-stall condition firstly.Under this circumstance, the pressure rise in R2 takes up a larger part.The increase of pressure rise in R2 helps to compensate the insufficient pressure rise in the first stage.This compensation allows the two-stage compressor to maintain its pressure rise capability.
The fluctuation amplitude of pressure signal is represented by the variance.The axial distribution of variance of pressure signal is shown in figure 8 for different flow rates.The fluctuation increases along the axial positions from section R1LE to section R2LE, and then it decreases at section R2TE.It is consistent with the pressure signal mentioned above.It exhibits the interaction between S1 and R2.Apart from that, the difference of blade number and blade passing frequency could also be the cause of the large fluctuation amplitude at section R2LE.It is consistent with previous numerical simulation results in reference [14] that the leading edge of R1 is overloaded as the flow rate decreases to the near-stall condition, resulting the great increase of fluctuation amplitude.R2 helps to compensate for the load of the first stage and stabilize the system on the near-stall condition.
The compensation of pressure rise and load for the first stage as well as the decrease of fluctuation of pressure in the second stage exhibits suggest that the second stage restrains the development and expansion trend of the unstable disturbance generated in the first stage under near-stall condition.

Characteristics on near-stall condition at 2700 rpm
The pressure signals of the near-stall condition are shown in figure 9, compared with those in figure 6.It can be seen that the flow in R1, especially at its leading edge, is severely unstable due to the overload of the blade.The disturbances shown with red circles are very obvious.The first stage gets into the stall condition firstly and experiences unstable flow status.There is still a margin for pressure increase in the second stage.The propagation of disturbance at section R1LE is analyzed with the pressure signal at different circumferential positions, as shown in figure 10, compared with those in figure 4.An obvious modal wave like signal is observed in time domain with a period of about twice the rotating period, indicating the appearance of one stall cell moving around the anulus.When the flow rate reaches the near stall condition, the obvious broad-band features are observed in the low-frequency region of the pressure fluctuation spectra.Compared with those on the high flow rate condition, this low-frequency region is closely related to the unstable flow phenomenon in the compressor.Some complex vortex structures appear in the blade passages.A heavy-loaded region was found at section R1LE in previous numerical simulation [14].And a back-flow region was found at the blade tip near the leading edge, resulting in the broad-band low frequency features.It indicates that the instability characteristics generate in the axial flow compressor on this condition.The amplitude of broad-band features in the low-frequency region significantly decreases at the trailing edge compared to that at section R1LE, which suggests the decrease of the degree of instability at this position.
At the same time, the blade passing frequency of R2 (BPF2) is observed in the pressure fluctuation spectrum of the leading and trailing edge of R1.It is shown that R2 played a significant role in the flow of the first stage on near stall conditions.There is no clear peak of BPF1 in the spectra of the second stage.The disturbance propagates from the first stage is not so strong.For section R1TE, the amplitude of BPF2 is larger than that of BPF1, so the pressure fluctuation is more significantly affected by the second-stage rotor.This corresponds to the results of time-domain analysis.Even though the second stage plays a compensation role, its own flow field is also affected, and unstable disturbances are enhanced.
It should be noted that in the pressure fluctuation spectra of sections R1LE, R1TE, R2LE, and R2TE, a low-frequency feature with prominent amplitude is observed before the broad-band region in figure 11-14.This frequency keeps its value in the spectra of the four axial positions, which is about 47% of the IRF on this condition.It must be a frequency from the same disturbance source.Compared with the previous time-domain analysis, this characteristic frequency of 0.47 f IRF is resulted from the circumferential propagation of the stall cell.

Conclusions
Stall may result in degradation in performance.In order to effectively prevent the unstable flow, it is necessary to understand the generation conditions and development characteristics of them.The generation and development of flow instability during the evolution process were analyzed.
On the large flow rate conditions, the transient pressure signals exhibited the corresponding periodicity as the impeller rotated.The fluctuation amplitude of the transient pressure gradually increased in streamwise direction but significantly increased at section R2LE due to the interaction between the cascades.
As the flow rate decreased, a cluster of characteristics of the pressure fluctuation in time domain were first affected.Broad-band features in the low-frequency region began to appear in frequency domain.
When the flow rate further decreased to the near-stall condition, a modal wave like signal was observed with a frequency of about 47% of the impeller rotation frequency at section R1LE.R1 first got into the stall condition and experienced flow instability, while no obvious unstable character was observed in the second stage.The variance of the pressure at section R1TE did not increase with that of section R1LE.Instead, it showed a significant decrease in trend.This suggested that the second stage of the compressor significantly suppressed the development and expansion tendency of the unstable disturbance generated in the first stage.
The results showed that the generation and development of instability in the axial compressor could be forecasted based on the broad-band features and the peak with high amplitude in the low-frequency region.

Figure 1 .Figure 2 .
Figure 1.Axial compressor test equipment.To analyze the stall cell propagation in the flow field, the pressure fluctuations near the tip of rotor blades were measured with multi-point synchronous dynamic measurement using high-response static pressure sensors.Dynamic static pressure was measured by KULITE XTL-140M dynamic pressure sensors.The natural frequency is 300 kHz and the measurement range is 0-3.5 bar.The positions of the pressure probes are shown in figure 2.

Figure 3 .
Figure 3. Performance curve of the compressor.

3. 2 .
Pressure signals on stable working conditions at 2700 rpmThe pressure fluctuation signals at section R1LE are shown in figure4, where points 1 to 5 are aligned vertically to exhibit the rotating direction.The corresponding periodic characteristic can be obtained as the blade passing these points.And the phase difference is observed for different circumferential positions as shown with the arrow.The time-averaged value and variance of pressure at different points are consistent with each other at the maximum flow rate.

Figure 4 .
Figure 4. Pressure fluctuation with maximum flow rate.The spectra of pressure signals of point 1 at the section R1LE and section R1TE are shown in figure 5.The blade passing frequency of R1 (BPF1), the impeller rotating frequency (IRF) and its doubling frequencies are captured.No significant peaks can be found for frequencies below IRF.

Figure 5 .
Figure 5. Pressure spectra with maximum flow rate.The pressure fluctuation signals are shown in figure6for point 1 at section R1LE, section R1TE, section R2LE and section R2TE along axial direction, corresponding to the points' arrangement in figure2.The pressure rise at each stage can be observed.Leaving with high speed, the gas flow diffuses in S1, and then flows into R2.The interaction between S1 and R2 makes the fluctuation amplitude increase.The fluctuation amplitude at section R2LE is much larger than that of other axial positions.

Figure 6 .
Figure 6.Pressure signal at different axial positions with maximum flow rate.The time-averaged pressure distribution along axial direction at the blade tip is shown in figure7for different flow rate.The pressure load is represented with pressure rise ratio defined as follows:

Figure 7 .
Figure 7. Axial distribution of pressure with different flow rate.The pressure rise ratio is increased at section R1TE due to the compression process with different flow rates.Then there is a decrease of pressure rise ratio at S1.It might be caused by the flow direction change and energy loss in this process.The gas is further compressed in R2.But the pressure rise in the first stage is larger than that in the second stage, indicating that the first stage plays a major role in the compression process.The pressure rise in the first stage decreases when the flow rate is decreased from 16795 m 3 /h to 13415 m 3 /h, indicating the decrease of pressurization capability of the first stage.So R1 experiences flow instability on the near-stall condition firstly.Under this circumstance, the pressure rise in R2 takes up a larger part.The increase of pressure rise in R2 helps to compensate the insufficient pressure rise in the first stage.This compensation allows the two-stage compressor to maintain its pressure rise capability.The fluctuation amplitude of pressure signal is represented by the variance.The axial distribution of variance of pressure signal is shown in figure8for different flow rates.The fluctuation increases along

Figure 8 .
Figure 8. Pressure variance distribution with different flow rates.The variance distribution reflects the compensation of the second stage on the near-stall condition more clearly.The fluctuation amplitude first decreases as the flow rate is decreased from the condition when the valve is fully open.The flow field is stabilized as approaching the designed condition.As flow rate further decreases, the fluctuation amplitude increases at all sections.When the flow rate is decreased to 13415 m 3 /h, the distribution pattern changes.The fluctuation amplitude of pressure signal at section R1LE increases significantly while that of other positions increases a little, resulting in a decrease of variance in the first-stage rotor.This indicates that the second stage of the compressor significantly suppressed the development and expansion trend of the unstable disturbance generated in the first stage.It is consistent with previous numerical simulation results in reference[14] that the leading edge of R1 is overloaded as the flow rate decreases to the near-stall condition, resulting the great increase of fluctuation amplitude.R2 helps to compensate for the load of the first stage and stabilize the system on the near-stall condition.The compensation of pressure rise and load for the first stage as well as the decrease of fluctuation of pressure in the second stage exhibits suggest that the second stage restrains the development and expansion trend of the unstable disturbance generated in the first stage under near-stall condition.

Figure 9 .
Figure 9. Pressure fluctuation of measuring points on near-stall condition.

Figure 10 .
Figure 10.Pressure signal at R1LE on near-stall condition.Flow instability is further analyzed in frequency domain on the near-stall condition, as shown in figure 11, 12, 13 and 14.When the flow rate reaches the near stall condition, the obvious broad-band features are observed in the low-frequency region of the pressure fluctuation spectra.Compared with those on the high flow rate condition, this low-frequency region is closely related to the unstable flow phenomenon in the compressor.Some complex vortex structures appear in the blade passages.A heavy-loaded region was found at section R1LE in previous numerical simulation[14].And a back-flow region was found at the blade tip near the leading edge, resulting in the broad-band low frequency features.It indicates that the instability characteristics generate in the axial flow compressor on this condition.The amplitude of broad-band features in the low-frequency region significantly decreases at the trailing edge compared to that at section R1LE, which suggests the decrease of the degree of instability at this position.At the same time, the blade passing frequency of R2 (BPF2) is observed in the pressure fluctuation spectrum of the leading and trailing edge of R1.It is shown that R2 played a significant role in the flow of the first stage on near stall conditions.There is no clear peak of BPF1 in the spectra of the second stage.The disturbance propagates from the first stage is not so strong.For section R1TE, the amplitude of BPF2 is larger than that of BPF1, so the pressure fluctuation is more significantly affected by the second-stage rotor.This corresponds to the results of time-domain analysis.Even though the second stage plays a compensation role, its own flow field is also affected, and unstable disturbances are enhanced.It should be noted that in the pressure fluctuation spectra of sections R1LE, R1TE, R2LE, and R2TE, a low-frequency feature with prominent amplitude is observed before the broad-band region in figure11-14.This frequency keeps its value in the spectra of the four axial positions, which is about 47% of the IRF on this condition.It must be a frequency from the same disturbance source.Compared with the previous time-domain analysis, this characteristic frequency of 0.47 f IRF is resulted from the circumferential propagation of the stall cell.

Figure 11 .
Figure 11.Pressure spectrum on near-stall condition at the section R1LE.

Figure 12 .
Figure 12.Pressure spectrum on near-stall condition at the section R1TE.

Figure 13 .
Figure 13.Pressure spectrum on near-stall condition at the section R2LE.

Figure 14 .
Figure 14.Pressure spectrum on near-stall condition at the section R2TE.