Effects of the radial blade loading distribution and B parameter on the type of flow instability in a low-speed axial compressor

Qiushi LI,Simin LI,Tianyu PAN,c,*

aNational Key Laboratory of Science and Technology on Aero-Engine Aerothermodynamics,Collaborative Innovation Center for Advanced Aero-Engine,Beijing 100083,China

bSchool of Energy and Power Engineering,Beihang University,Beijing 100083,China

cDepartment of Mechanical Engineering and Materials Science,Duke University,Durham NC 27708,USA

KEYWORDS Axisymmetric disturbance;B parameter;Flow instability;Low-speed axial compressor;Radial blade loading distribution

Abstract Previous studies showed that an axisymmetric hub-initiated disturbance defined as partial surge may initiate the stall of a transonic compressor;to reveal the instability evolution under full-span incompressible flow for different levels of hub loading and B parameter,an experimental investigation is conducted on a single-stage low-speed compressor.Experimental results show that under a uniform in flow condition without inlet flow distortion,a modal-type stall inception dominates in this low-speed compressor.When an inlet screen introducing hub distortion is used to increase the hub loading,a compressor stall is initiated by a modal wave,but large disturbances are present in the hub region before the compressor stall,which become stronger as the hub loading increases.Under high hub loading and large B parameter(implemented by adding hub distortion through an inlet screen and enlarging the outlet plenum volume,respectively),a compressor stall is triggered by an axisymmetric hub-initiated disturbance,which is much different from the modal-like disturbances.The beginning of this axisymmetric disturbance may be captured over 800 rotor revolutions prior to the onset of stall,and the amplitude grows with time.The disturbance is hub-initiated because the disturbance signal at the hub is detected much earlier than that at the tip;meanwhile,the frequency of this axisymmetric disturbance changes with the length of the inlet duct.The characteristics of instability evolution in the low-speed compressor are also compared with those in a transonic compressor.

1.Introduction

When an axial compressor is throttled to the stall limit,the steady axisymmetric flow pattern becomes unstable.Two types of dynamic instability,surge and rotating stall,have been well studied for turbomachinery compressors.Surge is a largeamplitude oscillation in the entire system,while rotating stall is an asymmetric phenomenon with one or several stall cells rotating at a fraction of the rotor speed.1Either type can be catastrophic for the performance of compressors(a substantial drop of performance in a stall situation),so predicting the condition for an occurrence of compressor instability is an essential part in the pursuit of both researchers and engineers.

The physical description of surge and rotating stall was firstly theoretically presented in the form ofa ductcompressor-plenum model,2,3based on which aBparameter was established to identify which type of instability might be triggered in a given pump system.TheBparameter can be physically interpreted as the ratio of the pressure difference across a compressor over the inertial force.

In the past several decades,a few distinctive inceptions leading to rotating stall in an axial compressor have also been reported,such as the known modal wave and ‘spike”-type inceptions,as well as a new type of stall inception,partial surge.Moore and Greitzer4theoretically predicted the modal wave,which was later observed by McDougall et al.5in experiments.It is defined as a primarily two-dimensional longwavelength disturbance that appears about tens of rotor revolutions prior to stall cells.The modal wave propagates circumferentially at about 20%–50%of the rotor speed,and the scale of its wavelength is approximately the machine circumference.Different from the modal wave,the ‘spike”-type inception has not been analyzed theoretically.It was firstly identified by Day6in experiments and defined as a three-dimensional disturbance with a short wavelength on the scale of one or several blade pitches.Spike rotates at 70%–80%of the rotor speed,and it takes less than five rotor revolutions from the first detection of a spike to the formation of a large stall cell(much shorter than the formation of the modal-type inception).6–9More recently,partial surge10,11was found and identified in a transonic axial compressor.During the evolution of partial surge-triggered instability,disturbances initially appeared in the hub region and developed quite slowly.It could take thousands of rotor revolutions from the initial appearance of hub disturbances to the final compressor stall.The frequency of partial surge is related to the Helmholtz oscillation of the compression system,and high hub loading is the key factor for the occurrence of partial surge.While a largeBparameter of the compression system is another significant feature of the transonic compressor test rig.

Some previous experimental results showed that in a given axial compressor,the instability evolution and the type of stall inception could change with some factors.Day found that the type of stall inception changed with the variation of the tip clearance.7Camp and Day postulated that both the inlet guide vane’s and stator angles could affect the stall inception.9Spakovszky et al.12studied the instability process of a compressor by blowing bleed air through the compressor blade tip region.The result turned to be a spike inception in the tip region where there was no blowing,but a modal-wave inception in the presence of blowing.Nie13and Zhang et al.14studied the effect of the radial loading distribution on a single-stage compressor and observed a switch between spike and modal wave by setting various radial distortion screens.Simpson and Longley15also obtained similar results by varying gauze inclination and stator stagger angles.Based on the theory model from Sun et al.16,Li et al.17suppressed the nonlinear amplification of stall precursor disturbances with Stall Precursor-Suppressed(SPS)casing treatment,which can also be treated as changing the radial loading distribution.Our previous work18presented that a stall inception initiated by partial surge would occur as long as the diffusion factor at the hub was high enough.When the blade tip loading was increased by mounting inlet screens which introduced flow distortion before the tip region of a compressor,the stall inception changed from partial surge to spike,so it was believed that the radial distribution of blade loading could alter the type of stall inception.Meanwhile,the variations of tip clearance,inlet guide vane or stator installation angle,and inlet flow distortion could also be attributed to some extent to the redistribution of radial loading.

In this paper,an experimental investigation is conducted in a single-stage low-speed compressor to reveal the evolution of instability under full-span incompressible flow.In our previous studies on partial surge,compressor instability was initiated by partial surge in a transonic compressor,so the flow in the tip region was transonic.However,the low-speed compressor in this study operates under full-span incompressible flow.It is unknown how the differences between flow patterns will affect the evolution of compressor instability.It is either unknown if a hub-initiated axisymmetric disturbance such as partial surge could also be detected in the low-speed compressor by varying the distribution of radial loading or theBparameter of the system.

This paper is organized as follows.Firstly,the test facility and data acquisition instruments are brie fly introduced in Section 2.Then,a series of experiments is conducted for a variety of distributions of radial blade loading arranged in different experimental settings,and results are presented in Section 3.In the results,a type of instability inception that appears like partial surge is found under the conditions of high hub loading and largeBparameter,and with the help of data analysis,the detailed characteristics of the instability evolution are presented.Finally,the instability evolution of the tested lowspeed compressor is compared and discussed with that of a transonic compressor in Ref.18in Section 4 before conclusions are drawn in Section 5.

2.Experimental facilities and instrumentation

On a single-stage low-speed axial compressor test rig at Beihang University(BUAA),experiments are conducted to study the evolution process of stall instability in a low-speed axial compressor with incompressible flow throughout the blade span.Both the rotor and stator blades of the compressor have a C4 profile.Detailed design parameters of the test compressor are specified in Table 1.The design rotational speed of the compressor rotor is 3000 r/min and the rotor is driven by an Alternating Current(AC)motor embedded in the hub.

In this paper,the flow through the compressor is controlled by the axial position of the throttling cone after the test benchexhaust pipe.During the whole test,the rotational speed of thecompressor is controlled by an inverter to ensure that the compressor works at the design speed.

Fig.1 shows the schematic layout of the test rig and detailed measurement arrangements for the experiments.The development of a compressor instability precursor is mainly examined based on the signals detected at the measuring points shown in the figure,when the rotor rotates clockwise as observed from the inlet.Measuring pointAis located at the compressor inlet where the air velocity is zero,and a standard atmospheric pressure gauge and a thermometer are arranged to obtain the characterization of the compressor performance.In SectionB,the compressor flow is monitored through four wall static pressure measurement holes evenly spaced along the circumference.The total pressures at the compressor inlet and outlet are determined by the steady total pressures recorded by two combs with five holes in the radial direction and mounted in SectionsCandF,respectively.In addition,the steady pressures are also captured in SectionsCandFby the static pressure measurement holes.The steady flow data along with the ambient conditions(rotational speed,pressure,and temperature)is used to compute the compressor performance.The dynamic data is acquired by Kulite high frequency response pressure transducers which collect data at a relatively higher sampling rate of 70 kHz.Five such transducers(D1–D5)are circumferentially mounted through the rotor outer casing(at 0°,72°,144°,126°,and 288°)upstream from the rotor leading edge at about 10%of the tip cord.Another dynamic total pressure probe(E1)is placed at the location of about 5%axial chord length downstream from the stator root(at 0°),to detect small disturbances that occur in the hub region.The probe is characterized by a 6.9-mm-in-diameter stem and aflushmounted 5-psi(1 psi=6894.757 Pa)absolutetransducer which has a sampling rate of 50 kHz.The radial location of the transducer can be adjusted by changing the clamping position of the probe stem.

3.Experimental procedure and results

In the experiments,starting from the compressor choke point,the throttling procedure of the compressor is implemented via a slow adjustment to the throttling cone.When the compressor reaches a near-stall point,the position of the throttling cone will be fixed until the compressor falls into an unstable working condition.Meanwhile,the dynamic data is acquired to monitor and track the occurrence and development of disturbances.After the compressor has gone through a complete instability process,the cone returns back to the initial position,and the whole data acquisition procedure is accomplished.

3.1.Increasing blade hub loading

Different from the previous work19which has demonstrated that spike-type inception emerges in this low-speed compressor with an increase of blade tip loading,the experiments in this paper focus on the effect of increased blade hub loading on the instability evolution.Fig.2(a)shows that the blade hub loading is varied by a hub distortion screen installed before the inlet.The screen is composed of two parts,a support screen and a circular screen.The support screen has much lower screen solidity,so a loss of the total pressure is mainly produced by the circular screen,and the effect of the support screen can be neglected.The mounting position of the hub distortion screen is upstream from the rotor at a distance of the compressor’s Outer Diameter(OD),and the diameter of the circular screen is about 0.7OD.The screen solidity can be calculated by

Fig.2 Hub distortion screen.

Fig.1 Schematic diagram of low-speed compressor test rig measurement arrangements.

wheredis the thickness of screen elements andlis the spacing between screen elements.20These two geometric parameters are illustrated on a single mesh shown in Fig.2(b).Screen solidity can be used to describe the screen stagnation;the higher the screen solidity used in the experiment is,the larger total pressure loss it will induce.Behind the hub distortion screen,the inlet flow before the rotor is still circumferentially uniform,but the axial velocity in the hub region decreases owing to the total pressure loss.As a result,the blade loading and the inlet attack angle in the hub region increase.

In this section,three groups of data acquired in different experimental setups are analyzed.The case with uniform inlet flow is defined as the Baseline;Case 1 and Case 2 stand for situations with increased hub loading,and the only difference between them is that a circular screen with higher solidity(stronger distortion)is used in Case 2.Fig.3 represents the total pressure loss at the last steady point in test SectionC,which is caused by the inlet circular screen.The total pressure loss is defined as the ratio between the drop of total pressure after the distortion screen over ρU2mid,where ρ is the density of the air andUmidstands for the rotor mid-span velocity at the design speed.The 10%blade span position is taken as the hub region,and the 90%blade span position represents the tip region.As a result,the total pressure loss in the hub region is much higher than that at the tip,indicating that the blade hub loading is indeed increased.

The compressor performance is shown in Fig.4.The pressure rise coefficient ψtsis calculated as

wherepoutletstands for the static pressure at the compressor outlet,pt，inletstands for the total pressure at the compressor inlet.The flow coefficient φ is defined as

wherevis the local axial velocity.

The data at several stable points before the compressor is throttled to stall in each case is labeled by symbols with the same shape in Fig.4.The stall point is marked by a hollow symbol with the same shape for each case,right before the compressor falls into rotating stall and becomes unstable.The profile of Baseline is the characterization of the compressor’s performance under uniform in flow,and the positions of stall points in the other cases are not diverged so much from that in Baseline despite increased hub loading.In all the analyses hereinafter,Revolution 0 is defined to be the time when the position of the throttling cone is fixed after the last steady point.

Fig.3 Distributions of total pressure losses for Baseline,Case 1 and Case 2.

Fig.4 Performance map for different distributions of radial loading.

To distinctly observe disturbances propagating in the circumferential direction under uniform in flow,the dynamic static pressure data recorded by sensorsD1–D5is plotted in the order ofD1-D2-D3-D4-D5-D1in Fig.5.The data is processed by a low-passfilter with a cutoff frequency of 2 Hz and a high-passfilter with a cutoff frequency of 30 Hz(0.6N,Nstands for the rotor rotating frequency).21A disturbance appears after the 360th revolution and propagates at approximately 28.3%N(dash line).In about 20 revolutions later,it develops into large-amplitude fluctuations propagating at 32.8%N(arrow line).The pressure rise of the compressor drops rapidly after the emergence of large-amplitude fluctuations,which finally turn into a stall cell.According to the known characteristics of stall inceptions,this disturbance is identified as a modal-type inception.

With the same method,the data obtained in Cases 1 and 2 is processed and plotted in Figs.6 and 7,respectively.For Case 1,a modal-like disturbance appears near the 440th revolution,and after about 30 revolutions,it develops into a rotating stall cell.Under much higher hub loading as in Case 2,a modal-like disturbance appears after the 720th revolution and develops into a final rotating stall cell within about 40 revolutions.Figs.5–7 show that the time intervals between the starting of a modal wave and final stall cells are about 20,30,and 40 revolutions,respectively,suggesting that it takes longer time for a modal wave to develop into a stall cell with an increase of hub loading.

Fig.5 Detailed instability evolution under uniform in flow situation without inlet flow distortion(360th–410th revolution).

Fig.6 Detailed instability evolution in Case 1(435th–485th revolution).

Fig.7 Detailed instability evolution in Case 2(719th–769th revolution).

Fig.8 shows the dynamic total pressure recorded byE1in the hub region.The amplitude of the modal-like disturbance becomes increasingly larger from the Baseline setting with uniform in flow to the cases with increased inlet hub distortion,suggesting larger pressure fluctuations with an increase of hub loading.Although the stall inceptions remain to be modal waves in Baseline,Case 1,and Case 2,the entire instability evolution has changed with the hub distortion.The largeamplitude disturbance formed at the blade root makes the flow unstable in the hub region and intensifies the mixing of flow in the radial direction.

Fig.8 Comparison of dynamic total pressure data in hub region from E1.

Fig.9 shows the measured pressure rises at different span locations during the instability evolution in the test SectionsCandF.For the Baseline setting,the total pressure rise keeps almost constant in the whole span before the compressor falls into stall.This trend is changed in Case 1:the total pressure rise in the hub region drops in advance before the stall onset and increases a little at the middle span and at the tip.When the hub loading is further increased in Case 2,the total pressure rises in both the middle span and the hub region drop before the compressor stall,indicating that the blade hub region has already been unstable with separated flow and lost the capacity to compress thefluid in the pre-stall phase.Accordingly,the decrease of mass flow in the hub region makes the streamline deflect and remits the flow in the tip region,so the total pressure rise increases in the tip region.The stall cells are caused by a drop of the total pressure rise in the tip region,while the modal-type disturbance is more likely to emerge in the hub region with an increase of hub loading.The physical mechanism of the prolonged time interval is that the re-distribution of radial loading intensifies the transfer and mixing of flow in the radial direction,delays the modaltype disturbance spreading in the circumferential direction,and finally changes the process of the development of the modal-type disturbance into stall cells.

In summary,with an increase of hub loading,although the compressor still has a modal-type stall inception,the amplitude of disturbance increases.After detailed examination of the data,it is found that the amplitude of pressure fluctuations in the hub region is much larger than that in the tip region before the stall onset,thus enhancing the transfer and mixing of flow in the radial direction,which in turn prolongs the development of the modal inception into rotating stall.Although the stall inception is not converted to any type similar to partial surge,the characteristics of the evolution of compressor instability change with an increase of hub loading.

3.2.High hub loading and large B parameter situation

Based on the results with increased blade hub loading,another experimental setup defined as Case 3 is arranged with both the inlet hub distortion screen and an additional outlet plenum,so the experiment of Case 3 is operated under high hub loading and largeBparameter.The exhaust duct in Fig.1 is replaced by an outlet plenum with a larger diameter,so the plenum volume between the AC motor and the throttling cone is enlarged.

Thenon-dimensionalparameter ‘B” can reflectthe dynamic response of a compression system to unstable flow,and it is defined in terms of the resonant frequency of the system as

Fig.9 Variations of total pressure rises at different span locations before and after the compressor stall.

where ω is the Helmholtz resonator frequency andLCstands for the effective length of the inlet duct;or,equivalently,in terms of the physical parameters of the system as

whereais the speed of sound,Vpdenotes the exit plenum volume,andACdenotes the flow-through area of the inlet duct.

As a result,theBparameter of the entire compression system is increased in Case 3 and closer toBcrit(criticalBparameter),which is used to distinguish surge and rotating stall.Bcritof the tested low-speed axial compressor is calculated with the theoretical compression system model proposed by Greitzer,2,3which turns to be about 1.1.

The system parameters in different experimental cases are listed in Table 2.TheBparameter of the original compression system under uniform in flow is about 8%of the calculatedBcrit,and about 41%ofBcritin Case 3.Thus,for Case 3,it could be predicted that rotating stall will still occur,but the entire system is more sensitive to the axisymmetric disturbance.Meanwhile,the compressor in Case 3 is operated under higher hub loading(represented by the total pressure loss at the hub listed in Table 2;the definition of total pressure loss is the same as that in Fig.3).

Fig.10 shows the detailed process of instability evolution in Case 3 from the 1135th to 1185th revolution illustrated with the same data processing method introduced above.A salient difference in Case 3 is that the pre-stall disturbance turns axisymmetric,as depicted by the vertical dash lines at around the 1140th revolution,instead of the circumferentially rotating pre-stall disturbance in the Baseline setting with uniform in flow.The period of these axisymmetric disturbances is about 1.89 revolutions,corresponding to a frequency of 26.5 Hz,which is about 53%N.After about 30 revolutions,the compressor falls into a stall phase,and the initial stall cells indi-cated by arrow lines rotate in the circumferential direction at about 35.1%N.

Table 2 Parameters of different experimental cases

Fig.10 Detailed instability evolution in Case 3(1135th–1185th revolution).

In order tofind more information about the axisymmetric disturbance,Fig.11 shows the static pressure signals collected at the tip(byD1)and the total pressure signals at the hub(byE1)during the complete instability evolution.The ordinate is the dynamic static and total pressure nondimensionalized by the maximum static and total pressure after the compressor stall respectively.At the beginning of instability evolution,the hub signal shows large-amplitude pressure fluctuations,while the tip signal clearly shows patterns of temporal variation in the amplitude of pressure fluctuations.From 0 to 350th revolution,the amplitude of pressure fluctuations is very small,and a careful observation of the five circumferential signalsfinds no axisymmetric disturbance.Then at around the 380th revolution,the disturbance shows up with small peaks and grows up in amplitude as time goes on.After a continuous disturbance with a large amplitude is developed,the compressor falls into stall after the 1170th revolution.It takes about 800 revolutions from the first detection of large-amplitude disturbances in the tip region to the final stall of the compressor.

Fig.11 Instability evolution in Case 3.

For the convenience of comparison,the signals at the rotor tip and hub of Fig.11 are expanded from the 360th to 390th revolution in Fig.12.A disturbance with a period of 1.89 revolutions firstly occurs near the 367th revolution in the hub region,and then after the 380th revolution,a disturbance with the same period is observed in the tip region.The axisymmetric disturbance as mentioned in Fig.10 can be detected in both the tip and hub regions,and the emergence of an axisymmetric disturbance with the same frequency at the hub is prior to its emergence at the tip.

Fig.12 Detailed instability evolution(360th–390th revolution).

The signals recorded byD1andE1in Case 3 are also processed with the Windows Fourier Transform(WFT)method,and the time–frequency variations of both signals are demonstrated in Fig.13(a).The ordinate is the magnitudes of the Power Spectral Densities(PSDs).Two salient peaks are marked:one at a lower frequency(around 19 Hz)belonging to the disturbance leading to rotating stall cells(38%N),and the other at a higher frequency(around 26.5 Hz)belonging to the axisymmetric pre-stall disturbance(53%N),as shown in Figs.10 and 12.Both signals recorded at the tip and hub show that the amplitude of the axisymmetric disturbance grows with time(or revolutions)in the pre-stall phase.After the amplitude of the axisymmetric disturbance boosts to a certain level,the compressor falls into rotating stall with the amplitude of the lower-frequency disturbance rising abruptly.Compared with the WFT result of Case 2 in Fig.13(b),the growth of the amplitude of the axisymmetric disturbance is the main reason leading to the final stall of the compressor in Case 3.

Fig.13 WFT analysis of data recorded by D1and E1.

Fig.14 Comparison of axisymmetric disturbances at the tip and hub.

Fig.15 Flow coefficient change during instability evolution.

The magnitudes of PSDs of the axisymmetric disturbances at the tip and hub are also compared in Fig.14.The pressure fluctuations in the hub region have larger amplitudes,and the peak amplitude also appears earlier.Meanwhile,the growth of amplitude in the hub region is faster than that in the tip region before the compressor stall,as shown by the arrow lines in Fig.14.Hence,the results in both Figs.12 and 14 suggest that the axisymmetric disturbance leading to the compressor stall more likely initiates in the compressor hub region.

The temporal variation between the flow coefficients before and after the compressor stall is shown in Fig.15.With an increase of hub loading,the fluctuations of the flow coefficient also increase.Meanwhile,a comparison between the results of Baseline,Case 1,and Case 2 also shows a slow decline phase located at about 50 revolutions before the compressor totally falls into stall.Compared with the above three cases,Case 3 shows much larger fluctuations(with the same pattern of variation as the pressure signal recorded byD1in Fig.11).At around the 350th revolution(when the axisymmetric disturbance emerges),the flow coefficient starts to decrease slowly andfluctuate more acutely(when the amplitude of axisymmetric disturbance grows).Finally,the flow coefficient decreases abruptly right before the compressor becomes totally unstable.

In summary,the evolution of instability in Case 3 shows the following behaviors:

(1)When the inlet screen introducing hub distortion is mounted before the rotor,the distribution of radial loading is changed,and the hub loading is much higher than the tip loading.During the throttling process of the compressor,the flow is relatively easier to separate in the hub region than in the tip region.As a result,the amplitude of disturbances in the hub region is larger than that in the tip region before the compressor stall.

(2)When a large outlet plenum is installed between the compressor and the throttling cone,theBparameter of the compression system is increased from 8%Bcritto about 41%Bcrit,so the system is much more sensitive to an axial disturbance.An axisymmetric disturbance is firstly found in the hub region,and then large-scale flow separation is gradually diffused to the tip region along the radial direction,leading to a weakened flow capacity of the entire blade passages.After that,the flow coef ficient of the system fluctuates fiercely.Ultimately,with the appearance of large-amplitude stall cells,a compressor stall occurs.

Finally,an extra experiment is also conducted with a shorter inlet duct installed before the screen,and the rest of the experimental setup remains to be the same as in Case 3(with the same inlet screen and large-volume outlet plenum).Experimental results display the same phenomena when the original inlet duct is installed.A compressor stall is also triggered by an axisymmetric disturbance initiated at the hub.The only difference is that the disturbance propagates at a speed of 57%N,which is a little faster than that in the system with the original inlet duct.It is also reflected from another aspect that the axisymmetric disturbance is closely related to the system oscillation.The variations of the geometric parameters of the compression system can affect the propagation of the axisymmetric disturbance.

4.Discussion

In this section,disturbances leading to stall instability in both a low-speed(this study)and a transonic compressor(at 65%of the design rotor speed18)are compared in Table 3,and possible causes are discussed below.

Table 3 Disturbances leading to stall instability in a lowspeed and a transonic compressor.

With an increase of hub loading,the initial position of the disturbance is transferred to the hub region in both compressors,because of a redistribution of radial loading.Although the low-speed compressor still shows modal waves before the compressor stall,the type of disturbance is changed from spike to partial surge in the transonic compressor.The relative magnitude of blade hub loading might be the key factor determining these two different phenomena in the low-speed and transonic compressors.

Under high hub loading and largeBparameter,the instability inceptions of the two compressors reveal some similarities and some differences:

Similarities.Partial surge is firstly found in the transonic compressor with high blade loading in the hub region.The pre-stall disturbance of partial surge is hub-initiated and axisymmetric,and the earliest perturbation can be detected over hundreds of revolutions prior to full compressor instability.All these features are shared by the disturbances in the lowspeed compressor under high hub loading and largeBparameter situations.

Differences.The frequency of partial surge is determined by the Helmholtz frequency of the entire compression system,which can be varied by the system parameters such as the inlet duct length.The inlet duct length can also affect the frequency of the axisymmetric disturbance in Case 3,but this frequency is not consistent with the Helmholtz frequency of the entire system.

For a duct-compressor-plenum system,one hypothesis is proposed in Ref.22that if the length of the inlet duct is so long that the increased flow resistance and inlet duct volume are comparable to the pumping capacity of the compressor,an‘inlet duct oscillation’will occur,and the frequency of this oscillation is also determined by the Helmholtz frequency of the system,but the plenum in such a system is the volume of the inlet duct.In this study,the flow resistance caused by the hub distortion screen is comparable to the pumping capacity of the tested low-speed compressor,and the volume between the screen and the compressor may also form a plenum which can host the Helmholtz oscillation.The physical connection needs a further study between the axisymmetric disturbance initiated at the hub in this paper and the system oscillation.

5.Conclusions

In this study,the evolution of partial surge-type instability inception is studied in a low-speed axial compressor.Measured data is presented in both the time and frequency domains to reveal the dynamic features of flow phenomena related to the initiation of instability.The key findings are as follows:

(1)With an increase of blade hub loading,the experimental results of the low-speed compressor show that a modaltype stall inception occurs in all cases,under uniform and distortion in flows.However,the initial position of the modal-like disturbance changes to the hub region with an increase of hub loading.In contrast,the experimental results in a transonic compressor operating at 65%of the design rotor speed demonstrate that when the hub loading is increased,not only the initial position but also the type of stall-inception disturbance change,i.e.,spike is replaced by partial surge.

(2)Under high hub loading and largeBparameter,an axisymmetric disturbance is detected about 800 revolutions prior to the compressor instability in the lowspeed axial compressor.In the course of instability evolution,no typical spike or modal wave is observed.Furtherdata analysesindicatethatan axisymmetric disturbance is more likely to initiate in the blade hub region,and the occurrence of this axisymmetric disturbance is related to the compression system oscillation.This axisymmetric disturbance has both similarities with and differences from partial surge.

(3)The experimental results show that the instability of the low-speed compressor can be affected by both the distribution of radial loading and theBparameter of the compression system,which is consistent with the results obtained in the transonic compressor.In the low-speed compressor,the distribution of radial loading can affect the initial position of the pre-stall disturbance,while theBparameter determines the response of the compression system to axial disturbances.

Acknowledgements

The authors acknowledge the supports of the National NaturalScienceFoundation ofChina(Nos.51636001and 51706008),Aeronautics Power Foundation of China(No.6141B090315)and China Postdoctoral Science Foundation(No.2017M610742).