Experimental investigation of characteristics of instability evolution in a centrifugal compressor

Hnzhi ZHANG, Ce YANG,*, Ben ZHAO, Wei ZHAO, Chenxing HU,Wenli WANG, Jining GAO, Shijun SUN

aSchool of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China

bInstitute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China

cSchool of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

KEYWORDSCentrifugal compressor;Impellers;Pressure measurement;Rotating instability;Stability;Stall

AbstractThe stable range of operation for the centrifugal compressor significantly influences the dynamic,economic,and environment-friendly characteristics of power systems.A deep understanding of the characteristics of instability evolution is necessary to improve the compressor stability.A centrifugal compressor equipped with a vaneless diffuser is experimentally investigated using highresponse static-pressure measurements.The results obtained indicate that three typical rotationalspeed ranges exist based on the different instability evolution characteristics,which reveals the various impeller–diffuser matching behaviors over the entire speed range.At low-speed ranges((40%–75%)Nmax,Nmaxis the maximum rotational speed),the compressor exhibits stable,Rotating Instability(RI),impeller stall(diffuser stall),and surge modes.The impeller stall mode is induced by RI and propagates downstream, resulting in the diffuser stall and compressor surge modes.In the medium-speed range((75%–85%)Nmax),the compressor exhibits stable,diffuser stall,RI,and surge modes.In the high-speed range ((85%–100%)Nmax), the compressor exhibits stable, diffuser stall,and surge modes.The dominant instability position is shifted from the impeller to the diffuser as the rotational speed increases.Both the impeller and diffuser stall present an irregular sawtooth static-pressure wave and exhibit broadband frequency spectrum patterns.

1.Introduction

To simultaneously satisfy power, stability and environmental requirements, the pressure ratio and stable operating range of a compression system is required to be improved constantly.Stall and surge not only limit the operating range of the compressor, but also deteriorate the compressor performance and induce mechanical excitation.Therefore, the determination of the onset and development of instabilities and increasing the compressors stability has long been a vigorous research field1–4.

The instability characteristics of axial compressors have been widely studied.The instability disturbance can be classified into Rotating Instability (RI), spike stall, modal stall,and surge, according to the various characteristics such as wavelength and frequency.RI typically occurs at the peakpressure-ratio point even before it, and presents a broadband distribution with a 30%–50% Blade Passing Frequency(BPF).5–7The spike stall is a short-scale circumferential disturbance,which normally locates at the blade tip region and comprises an abrupt formation.8,9However, modal stall is characterized by low-amplitude and long-scale circumferential disturbances and progressive growth.10,11Based on these instability disturbances,the related active/passive control strategies were applied, and the compressor stall-margin improvement was achieved12,13.

For a centrifugal compressor, the instability evolution presents relatively complicated characteristics because components such as diffuser vanes and volute have an evident influence on the instability characteristics.For the centrifugal compressor equipped vaned diffuser, the instability typically appears in the vaneless space or diffuser inlet position.In the work of Oakes et al.,14the stall comprised a nine-lobed stall pattern in the vaned diffuser of the high-speed centrifugal compressor.And the author highlighted that this stall is similar to the rotating stall in a multistage axial compressor.Spakovszky and Roduner15investigated the spike and modal stall mechanism in a centrifugal compressor and demonstrated that,either short or long wavelength stall precursors occur depending on the amount of endwall blockage in the vaneless space.Zheng et al.16,17experimentally investigated the surge and stall in a turbocharger centrifugal compressor equipped a vaned diffuser.Their results show that, at a low rotational speed, the centrifugal compressor experiences a stable, stall, and deep surge conditions with the flow rate decreasing.At a high rotational speed,the compressor operation shifts from a stable status to a mild and then a deep surge.Moreover, many other experimental and numerical investigations have been performed on vane diffuser centrifugal compressors with respect to stall propagation behaviors, stall cell formation.18–21Some control strategies have been applied in vane diffuser centrifugal compressors based on similar results, and their effectiveness has been proven22–24.

The vaneless diffuser is most commonly applied in small turbocharge centrifugal compressors owing to its simple and small geometry.The instability behaviors of vaneless diffuser centrifugal compressors have also received attention since the 1980 s.K?mmer and Rautenberg25found that the stall behaviors differed at different rotational speeds in the vaneless diffuser equipped centrifugal compressor.At low rotational speed conditions, the inducer stall determines the stall line of the stage,which is caused by a stationary and aperiodic reverse flow zone in the impeller eye with a strong self-induced swirl component.With the rotational speed increasing, the rotating stall occurs and the circumferential propagation speed increases.Lawless and Fleeter26investigated the stall behaviors of a low-speed centrifugal compressor with a vaneless diffuser (without volute) using acoustic measurements.The stall transition was observed to be a gradual process, finally a large-scale stall occurred with the pressure waves growing.The stall cell behaviors are characterized by one or more weak,peripherally distorted pressure waves, and finally developed into the finite stall pattern.Kang JS and Kang SH27experimentally investigated a vaneless diffuser centrifugal compressor (without volute) and found that, at all three test speeds,the magnitude of the first spatial harmonic increased linearly at the impeller shaft frequency for several impeller revolutions.The results strongly suggest that the impeller shaft frequency participates in the stall process and can be used as a stall warning method.Iwakiri et al.28investigated the rotating stall in a vaneless centrifugal compressor and found that, at the developed stage of rotating stall, the number of disturbances is 1,and the frequency is 0.7–0.8 times the shaft frequency based on the unsteady static-pressure signal.And the numerical results show that the tornado-type separation vortex dominated the flow field, which is caused by the full-blade leading-edge separation.He et al.29,30experimentally investigated the instability behaviors in a centrifugal compressor with and without diffuser vanes and found that the stall and surge behaviors differed with the rotational speed.The diffuser vanes can eliminate the rotating stall in the diffuser at all rotational speeds, but have a finite effect on the rotating instabilities in the impeller.Many numerical investigations have also been conducted to capture the instability structure and reveal the stall mechanism31–34.

From the above literature,a major challenge in determining the detailed stall and surge mechanism is that the compressor configuration and rotational speed extend over a significantly large range.The present study is focused on a centrifugal compressor with a vaneless diffuser and volute, and the instability evolution characteristics of the impeller and diffuser are investigated via high-response static-pressure measurements.The instability evolution behaviors in the impeller and diffuser were analyzed based on the time and frequency domain characteristics of the unsteady static-pressure signals over the entire speed lines.The instability onset position,evolution behaviors,and streamwise propagation behaviors are discussed in detail.

2.Experimental methodology

2.1.Study model and experimental setup

The study model is a centrifugal compressor comprising a vaneless diffuser and volute,which is applied for a commercial turbocharger product.Table 1 lists the main geometric parameters of the centrifugal compressor.The compressor impeller had seven main blades and seven splitter blades.The compres-sor maximum rotational speed Nmaxis 1.1×105r/min,and the maximum pressure ratio exceeds 3.

Table 1 Main geometry parameters of centrifugal compressor.

To obtain the compressor performance characteristics and unsteady static-pressure signal at the impeller and diffuser inlet simultaneously,Fig.1 presents a schematic and photograph of the test rig.At one rotational speed, the operating point from choke to surge was controlled by the exit throttle valve.At each operating point,the flow rate,inlet,and outlet stagnation parameters were measured to determine the compressor pressure ratio and efficiency performance.The testing environment conditions are 102.3 kPa and 291.53 K,and the corrected compressor rotating speed N and mass flow rate m at the corrected status (101.3 kPa, 298 K) can be obtained from the following formulas:

where Nrand mrare the real measured rotating speed and mass flow rate, Tt,inand pt,inare the total temperature and pressure at the compressor inlet.In the compressor performance description, the pressure ratio π and efficiency η were defined as following:

Fig.1 Schematic and photograph of test rig.

where Tt;outand pt;outare the total temperature and pressure at the compressor outlet, and k is the specific heat ratio.More experimental setup information for compressor performance measurement can be found in Ref.35Meanwhile, the unsteady static-pressure signals at the impeller and diffuser inlet were measured using high-response transducers.The locations of the high-response static-pressure transducers are presented in Fig.2.At the impeller inlet (5 mm away from the main blade leading edge),six transducers were evenly distributed in the circumferential direction of 0°,60°,...,360°,and the Volute Tongue (VT) location is approximately 50°.At the diffuser inlet,two transducers were located at 180° and 240° circumferential positions.The high-response pressure transducers are piezoresistive and obtained from Kulite Semiconductor Products Inc.,all of which have an uncertainty of ± 0.1% of the full range.Static-pressure signals from the transducers were transmitted to the high-speed synchronous acquisition equipment from Dewetron Company.The sampling frequency of each pressure transducer was set as 200 kHz, which is over six times the Blade Passing Frequency (BPF) of the full blades at the maximum rotational speed.In Section 3,BPF of the main blade for each rotational speed is defined as follows:

where z = 7 is the main blade number, fsis the impeller shaft frequency.

Fig.2 High-response transducer location.

2.2.Data processing

To better understand the behavior of the unsteady staticpressure fluctuation and capture the instability evolution pattern,the raw pressure signals should be processed before analysis.The periodic static-pressure irregularity and skewness were used to evaluate the unsteadiness and pressure-wave deformation of the unsteady pressure signals.The obtained results indicated that the irregularity and skewness could effectively predict the RI and stall behaviors in an axial compressor.36–38The data analysis process is illustrated in Fig.3.First, the period-averaged pressure waves were calculated for n rotor revolutions; 20 rotor revolutions were considered in this study.The period-averaged pressure trace and individual pressure traces are indicated by red and black lines, respectively, in Fig.3(a).The period-averaged pressure comprises a wave over one rotor revolution and differs from the timeaveraged pressure, which is a single value, as indicated by the black dashed line in Fig.3(a).The static-pressure trace can be divided into two parts:

Fig.3 Data analysis of pressure fluctuations.

The irregularity is the Root-Mean-Square (RMS) value of the deviation part, which can reflect the dispersion of a data set.The smaller the irregularity,the smaller the deviation from the average value, and vice versa.For the unsteady pressure signal, the irregularity can indicate the strength of the pressure-wave deformation during different rotor revolutions and the pressure fluctuation unsteadiness.

where s denotes the standard deviation.Skewness is defined as the third-order normalized moment of data, which is a measure of the degree of asymmetry relative to the average value.By measuring the skewness coefficient, the asymmetry degree and direction of data distribution can be determined.For the unsteady pressure signal, the skewness describes how an individual pressure trace diverges from the period-averaged pressure trace.Negative skewness indicates that, over a period of time, there are a greater number of low-pressure samples than high-pressure samples,suggesting that the low-pressure region dominates the local measurement region,as marked by the red dash circle in Fig.3(c).Based on the studies in axial compressor,36,37the low-pressure region generally indicates the RI phenomenon,which is caused by the spatial vortex attached on the casing wall.The spatial vortex will be induced by the interaction between the reverse leakage and the main flow at rotor inlet region.Due to the forming,rotating and shedding behaviors of the spatial vortex at rotor inlet region,the low-pressure region has the high unsteadiness and the corresponding RI has the characteristics of broadband, multi peak and intermittent occurrence, etc.

3.Results and analysis

3.1.Compressor performance

Fig.4 Compressor performance characteristics.

Fig.4 presents the compressor performance characteristics of the experiment.The abscissa in Fig.4 represents the mass flow rate m.For the pressure ratio curves(Fig.4(a)),the red dashed line indicates the surge limit by connecting the minimum-flowrate point for different rotational speeds.The rotational speeds and the corresponding machine Mach number Ma are marked for each speed line.The machine Mach number is the ratio of the impeller outlet tip velocity to the acoustic velocity at inlet conditions.The compressor surge is identified by the remarkably large fluctuations (with very low frequency and large amplitude) in the unsteady static pressure signal, and accompanying with the loud noise in the experiment.Before the surge occurs, the minimum flow rate points were obtained as the near-surge points, and were connected as the surge line in Fig.4(a).From the speed lines of (45%–82%)Nmax, the surge margins were relatively large, and the compressor had a wide stable operating range.However, from the speed lines of(82%–100%)Nmax,the surge margin was significantly reduced,which resulted in a knee in the surge line.39This implies that the compressor instability evolution behaviors are significantly different when the rotational speed varies.According to the conventional criterion for compressor instability,unstable flow occurs when the slope of the compressor pressure ratio curves becomes positive.40In Fig.4,the positive-slope portions are in blue,indicating the flow range with unstable flow.In the unstable flow range, the compressor efficiencies exhibited an obvious descent with the flow rate reducing, as shown in Fig.4(b).Obviously,the widths of the unstable flow ranges at different speed lines varied, which requires a more detailed investigation of the instability evolution, as presented in the next sections.

3.2.Instability evolution at impeller inlet

To describe the instability evolution at the impeller inlet,Fig.5 presents the static-pressure irregularity curves during the throttling process at various rotational speeds.In the figure,the colored lines indicate the static-pressure irregularity at various circumferential angle θ,and the black line indicates the circumferential averaged value.The abscissa of the figure represents the mass flow rate, and the scale of the abscissas in every sub-figure is the same.From Fig.5, it can be observed that,as the rotational speed increased, three typical instability evolution behaviors occurred at the impeller inlet.

From (45%–73%)Nmax(Figs.5(a)–5(c)), as the flow rate decreased, the static-pressure irregularity first increased and then decreased.The static-pressure irregularity represents the strength of unsteadiness.In general,the irregularity had a minimum value at the near-design operating conditions and increased continuously as the compressor throttled into unstable conditions.In the case of this centrifugal compressor, the static-pressure irregularity had a maximum value at the nearpeak pressure point, and as the flow rate reduced to the surge limit, the static-pressure irregularity reduced again.These experimental results differ from the static-pressure irregularity behaviors observed in axial compressors36.

For the 82%Nmaxspeed line (Fig.5(d)), the static-pressure irregularity behavior changed significantly.That is, from the near-design point to the surge limit, the static-pressure irregularity increased continuously and did not reduce again, suggesting that the instability phenomenon occurred at the impeller inlet,while the entire compressor instability evolution changed.For the (90%–100%)Nmaxspeeds (Fig.5(e)–5(f)), as the flow rate decreased from near choke to the surge limit,the static-pressure irregularity did not increase significantly,implying that the compressor surged with no occurrence of instability phenomena at the impeller inlet.Moreover, for the rotational speed ranging of(90%–100%)Nmax,the stall occurs in the compressor diffuser region, and triggers surge immediately, which is discussed in detail in Section 3.3.These differences in the stall onset position and mechanism resulted in a large reduction in the compressor surge margin, as shown in Fig.4(a).

In the comparison of the different rotational speeds, it was observed that the static-pressure irregularity values increased as the speed increased.For example, the maximum value at the 82% speed line was greater than those at the 73%, 63%,and 45% speed lines.For the near-choke point, the staticpressure irregularity values also increased as the rotational speed increased, indicating that the unsteadiness effect increased as the speed increased.

To further analyze the static-pressure evolution characteristics during the throttling process, Fig.6 presents the staticpressure skewness curves during the throttling process at various rotational speed lines.In the (45%–73%)Nmaxspeed range, the skewness had the minimum values corresponding to the flow-rate range of the maximum irregularity values(Fig.5).However, at the other flow rates, the skewness remained near the 0 value.The large negative skewness indicates that the RI phenomenon occurred at the impeller inlet in the corresponding flow-rate range, as shown in Fig.3(c).Meanwhile, the RI phenomenon first increased and then decreased again, indicating that, at the impeller inlet region,the compressor instability evolution passes the stages of RI and stall and finally surges.

Fig.5 Static-pressure irregularity curves at impeller inlet during throttling process at various rotational speed lines.

In the case of the 82%Nmaxspeed line, the compressor surged after the static-pressure skewness decreased to a certain negative value,suggesting that the instability evolution behaviors are different from those of the low-rotational-speed lines,even though an apparent RI occurs at the impeller inlet region.Furthermore, for the speed lines of (90%–100%)Nmax, there was no obvious reduction in the static-pressure skewness during the throttling process,indicating that no RI or other instability phenomena occurred at the impeller inlet; thus, the compressor stall is expected to occur in the diffuser region.

To describe the instability evolution at the impeller inlet in greater detail, the raw and period-averaged static-pressure curves at 180° circumferential positions for the typical speed lines are presented in Fig.7.The three typical speed lines are 63%Nmax, 82%Nmax, and 100%Nmax, and the corresponding operating points A, B, and C are also indicated in Fig.6.The abscissa and ordinate represent the time (rev) and static pressure,respectively.The time range is 5 impeller revolutions,and the pressure scales are 30, 40, and 60 kPa for the 63%Nmax, 82%Nmax, and 100%Nmaxspeed lines, respectively.In the case of the 63%Nmaxspeed line, it is apparent that the instability evolution at the impeller inlet shifts from stable to RI, stall, and then surge.At near-design point A, the individual pressure trace basically coincides with the period-averaged trace, indicating a small irregularity and near-zero skewness.At point B, the irregularity increases, and a low-pressure region is formed, which indicates that large negative skewness and RI occur.Finally, at the near-surge point C, the blade loading decreases significantly, and impeller stall occurs.The stall destroyed the regular blade passing effect and resulted in a much non-regular pressure trace.However, owing to the reduction in the pressure fluctuation magnitude (blade loading),the irregularity was reduced as compared to that at point B, which is different from the axial compressor.Normally, in the axial compressor, when the compressor enters the stalling condition,the experiment should be stopped and the flow rate is far from the surge limit.Therefore,the irregularity evolution is constantly increasing until the stall limit,and at this moment the rotor still has the certain work capability.However,for the centrifugal compressor experiment in the present work, the experiment stopped just before the compressor entering the surge condition.During the developed stall conditions (nearsurge),the impeller lost the work capability and the static pressure shape was significantly destroyed, as shown in point C in Fig.7(a).

Fig.6 Static-pressure skewness curves at impeller inlet during throttling process at various rotational speed lines.

Fig.7 Raw and period-averaged static-pressure curves at 180° circumferential positions for typical rotational speeds.

In the case of the 82%Nmaxspeed line, the instability evolution at the impeller inlet only exhibited a shift from stable to RI and finally surged, indicating that the stall occurs at the other component of the compressor.In general, RI is a pre-stall phenomenon that cannot trigger the compressor surge.In the case of the 100%Nmaxspeed line, it can be observed at the impeller inlet that the flow field is always stable.When the throttling of the flow rate is continued from point B, the compressor surges abruptly, indicating that the compressor instability was determined by the diffuser rather than the impeller.

3.3.Frequency analysis at impeller inlet

From the above analysis of the instability evolution at the impeller inlet, the instability behaviors can be divided into three paths for the three typical speed ranges: low speed((40%–75%)Nmax), medium speed ((75%–85%)Nmax), and high speed((85%–100%)Nmax).In the next section,these three typical rotational speed lines are discussed in detail based on the frequency characteristics.

3.3.1.Low rotational speed

Fig.8 presents the frequency characteristics at the six circumferential positions at three typical operating points of the 63%Nmaxspeed line.The ordinate represents the pressure magnitude obtained through a fast Fourier transform analysis of the static-pressure signals; the left and right axes represent the frequency and circumferential positions, respectively.The unit coordinates of the frequency axis indicate the impeller shaft frequency fs; thus, the main BPF was 7fs.At the nearchoke point m = 0.32 kg/s, the frequencies of the BPF dominated the flow field at the impeller inlet region.Similar frequency characteristics can be observed from m = 0.32 kg/s to m = 0.19 kg/s, indicating that there is no unstable disturbance at the impeller inlet.At m = 0.16 kg/s, corresponding to the largest irregularity and smallest skewness, a broadband with a dominant frequency of 55%BPF is observed,which is a typical RI phenomenon.5–7Furthermore, at the RI operating point,the magnitude of the BPF frequency is still greater than that of the RI frequency, which can maintain the relative regular pressure fluctuation and high blade loading, as shown in Fig.7(a).

When the flow rate is reduced to the near-surge point of 0.08 kg/s, the broadband frequency of the RI disappears,instead by the stall frequency also with broadband from(20%–50%)fs.At this operating point, impeller stall occurs,and the skewness increases to zero again.The RI is caused by the impeller inlet vortex structure and its deformation,shedding, etc., which are induced by the tip leakage vortex,reversal flow, and main flow.Therefore, the vortex evolution results in a high unsteadiness in the vortex number, propagating number, etc., which further results in the broadband phenomena in the frequency domain.In this case, the impeller stall evolved from the RI, which is one reason the broadband phenomenon also exists in the stall condition.As the RI further developed into an impeller stall, the interface between the tip leakage flow and main flow further moved out of the impeller and finally resulted in a recirculation vortex at a large scale, which also had a high unsteadiness.Meanwhile, the asymmetric volute structure caused a circumferential nonuniform tip leakage flow, and thus, the strengths and sizes of the recirculation vortex varied at different circumferential positions.Therefore, the stall disturbance also had a certain frequency range, and the dominant disturbance signal could not be clearly distinguished.As shown in Fig.8(b), the BPF at θ = 180° and θ = 240° reduced significantly compared to those of the other circumferential positions.Similarly, the BPF at the θ = 180°position reduced significantly at the stall condition(Fig.8(c)),indicating that the instability disturbance is stronger at the corresponding position and representing the asymmetric volute influence.Further investigations to obtain a more accurate and comprehensive description of the RIinduced impeller stall should be conducted using numerical methods.Moreover, the BPF magnitude was reduced to a magnitude lower than that of the stall disturbance under stall conditions, which is different from the RI phenomenon and consistent with the observation in Fig.7(a).

Fig.8 Frequency characteristics at six circumferential positions at three typical operating points of 63%Nmaxspeed line.

To further observe the characteristics of RI, Fig.9 shows the more detailed frequency spectrum evolutions from stable to near surge conditions at 63%Nmaxspeed line.Clearly, the RI has the broadband and multi peak characteristics, and its dominant frequency part moves to left with flow rate decreasing.Compared to RI onset point (m = 0.18 kg/s), the lower frequency part (smaller than the impeller shaft frequency) is obviously increased at RI point (m = 0.16 kg/s).Then from m=0.14 kg/s,the RI is gradually vanishing and the stall dominates the impeller inlet flow field.In other words, the RI and stall coexist in a certain flow range (m = 0.14 – 0.16 kg/s),which is a significant link between the stall and RI.

Fig.10 presents the frequency characteristics at six circumferential positions at the RI and stall operating points of the 45%Nmaxand 73%Nmaxspeed lines.The instability behaviors of the 45%Nmaxand 73%Nmaxspeed lines are the same as that of the 63%Nmaxspeed line.Therefore, it can be concluded that,in the low-speed range in the present centrifugal compressor,the instability evolution occurs from stable to RI,impeller stall,and then surge.Furthermore,the stall disturbance signal has a broadband frequency distribution similar to that of the RI, which is caused by the high unsteadiness of the impeller inlet vortex structure and the circumferential discrepancy induced by the volute.

3.3.2.Medium rotational speed

Fig.11 presents the frequency characteristics at the six circumferential positions at three typical operating points of the 82%Nmaxspeed line.From near choke to the point of the emergence of RI, the mild broadband with the 58%BPF phenomenon occurs at the 120°and 180°circumferential positions first.The phenomenon of the RI occurring at a certain circumferential position first was induced by the non-uniform pressure circumferential distribution due to the volute.When the flow rate decreases to m = 0.20 kg/s, RI occurs at all the circumferential positions.In contrast to the cases of the low speed, the RI phenomenon was not weakened again during the throttling process.In addition, there was no impeller stall before the compressor surge.Therefore, it can be conjected that the stall occurred in the vaneless diffuser region at the 82%Nmaxspeed line and finally triggered the compressor surge.

3.3.3.High rotational speed

Fig.12 presents the frequency characteristics at the six circumferential positions at three typical operating points of the 100%Nmaxspeed line.From the near-choke to the near-surge point, the BPF was always the dominant frequency, and there was no obvious instability disturbance.Therefore, the compressor instability evolution behaviors cannot be determined by observing the frequency spectrum at the impeller inlet region, which is consistent with the time domain results presented in Figs.5–7.As in the case of the 82%Nmaxspeed line,it can be speculated that compressor stall occurs in the diffuser region at a high speed.To verify this speculation, the staticpressure frequency spectrum characteristics at the diffuser inlet are discussed in the next section.

3.4.Frequency analysis at diffuser inlet

From the analysis of the unsteady static-pressure signal at the impeller inlet in Sections 3.2 and 3.3, in the low-speed range,the compressor instability path is from stable to RI, stall,and then surge, and stall inception can be captured efficiently by detecting the RI phenomenon.In the medium- and highspeed ranges,the compressor surged with either the occurrence of impeller RI or the impeller was stable, indicating that stall occurred in the diffuser region.As the rotational speed increased, the stall onset position transitioned from the impeller to the diffuser.Therefore, further analysis is required for instability evolution in the diffuser.

Fig.9 Pressure frequency spectra at θ = 180° with flow rate decreasing at 63%Nmaxspeed line.

Fig.10 Frequency characteristics at six circumferential positions at RI and stall operating points of 45%Nmaxand 73%Nmaxspeed lines.

Fig.11 Frequency characteristics at six circumferential positions at three typical operating points of 82%Nmaxspeed line.

Fig.13 presents the static-pressure frequency spectrum at the 180° circumferential position at the impeller inlet and diffuser inlet for the near-surge points of the three typical rotational speeds.The detailed positions of the static-pressure transducers are shown in Fig.2.At the 63%Nmaxspeed line,stall disturbances exist at both the impeller and diffuser inlet,and the dominant stall frequency is 0.6fs.In the diffuser, the stall frequency spectrum is also a broadband distribution,which is similar to the RI phenomenon.

In the case of the 82%Nmaxspeed line(Fig.11(c)),a typical RI occurs at the impeller inlet with a dominant frequency of 40%BPF under near-surge conditions.However, at the diffuser inlet, a low-frequency disturbance exists with 0.2fs–0.8fs,indicating that the stall occurs in the diffuser.Therefore,in the medium-speed range, the compressor instability path is from stable to impeller RI, diffuser stall, and then to surge.

For the 100%Nmaxspeed line (Fig.12(c)), there were no obvious low-frequency disturbances at the impeller inlet.Moreover, the magnitude scale is incomplete, and the expanded view is the complete scale view.It can be observed that the BPF has an absolute dominant effect on the flow field at the impeller inlet.At the diffuser inlet, a low-frequency disturbance of 0.2fs–0.8fsoccurs, indicating that a diffuser stall exists.Therefore, in the high-speed range, the compressor instability path is from stable, diffuser stall, to surge.Under stable impeller operating conditions,the diffuser stall triggered the compressor surge rapidly, resulting in a significant reduction in the stable compressor surge margin in the high-speed range, as shown in Fig.4(a).This phenomenon also indicates the bad matching characteristics between the impeller and diffuser in the high-speed range for this centrifugal compressor.

Fig.13 Static-pressure frequency spectrum at 180° circumferential position at impeller inlet and diffuser inlet for near-surge points of three typical rotational speeds.

Fig.14 Raw and low-pass filtered static-pressure signals at 180°circumferential position for near-surge points of three typical rotational speeds.

On comparing the diffuser frequency spectrums at different speeds, it can be observed that, as the rotational speed increased,the BPF effect increased significantly,while the stall disturbance magnitudes showed no obvious change, resulting in a reduction in the diffuser stall effect on the flow field as compared to BPF.In particular, for the 63%Nmaxspeed line,the diffuser stall disturbance completely dominated the flow field.That is, the low-speed line could permit a more obvious stall phenomenon.

To observe the stall disturbance in detail, Fig.14 presents the raw and low-pass filtered static-pressure signals at the 180°circumferential position for the near-surge points of three typical rotational speeds.The gray, black, and red lines indicate the raw,(6/7)BPF,and(1/7)BPF low-pass filtered signals,respectively.For the 63%Nmaxspeed line (Fig.14(a)), the(6/7)BPF low-pass filtered signals covered the raw signals,indicating that at the near-surge point,the static-pressure fluctuation was determined by the frequency component lower than BPF.The (1/7)BPF low-pass filtered signals, which were lower than the impeller shaft frequency fs,can present the main fluctuation behaviors of the raw signals.Therefore, the stall disturbances ((1/7)BPF low-pass filtered signals) had a dominant effect on the flow field and exhibited similar behaviors in the case of both the impeller and diffuser.

In the case of the 82%Nmaxspeed line (Fig.14(b)), at the impeller inlet,the(6/7)BPF low-pass filtered signals still exhibited large fluctuations, as indicated by the black line.The(6/7)BPF low-pass filtered signals had very small fluctuations,indicating that there was no stall disturbance (lower than fs).Therefore, the instability disturbances were mainly located between (1/7)BPF and (6/7)BPF, indicating the strength of the RI phenomenon.At the diffuser inlet,the disturbance magnitude of the (6/7)BPF low-pass filtered signals was much smaller than that of the raw signals, indicating that a larger BPF influence exists.Furthermore, the (1/7)BPF low-pass filtered signals still exhibited a relatively large fluctuation as compared to the impeller inlet, indicating that a stall disturbance emerged in the diffuser.As in the low-speed range, the stall disturbance also presents an irregular sawtooth wave pattern, corresponding to the broadband frequency distribution.The obvious static-pressure fluctuation difference between the impeller inlet and diffuser inlet indicated that the stall onset position was transferred from the impeller to the diffuser.

Fig.15 Static-pressure frequency spectra and irregularity comparison at 180°circumferential position for stall onset point at three lowspeed lines.

In the case of the 100%Nmaxspeed line (Fig.14(c)), the(1/7)BPF and (6/7)BPF low-pass filtered signals exhibited the same fluctuation pattern and magnitude, and their magnitude can be ignored as compared to the raw signals, which demonstrates that BPF dominated the flow field,and the impeller was stable.At the diffuser inlet,all the raw,and(6/7)BPF and(1/7)BPF low-pass filtered signals had similar fluctuation patterns,indicating that the stall disturbance occurred with the same behaviors as those of the medium-speed range.In contrast,the compressor instability behaviors were completely determined by the diffuser region in the high-speed range.

3.5.Discussion

From the above analysis, the compressor instability evolution characteristics at various rotational speeds were confirmed.For the medium-and high-speed ranges,the compressor instability was determined by the diffuser, although the RI phenomenon occurred in the impeller in the medium-speed range.For the low-speed range, one question still exists.At the near-surge point, the stall occurs at both the impeller and diffuser,and the stall disturbance magnitudes are basically the same.Therefore, it is difficult to determine which components the stall first occurs at or which component plays a more significant role during the stall stage.

To further detect the streamwise position of the stall emerging in the low-speed range, Fig.15 presents the static-pressure frequency spectrum(Figs.15(a)-15(c))and irregularity comparison(Fig.15(d))at the 180°circumferential position for the stall onset point at three low-speed lines.The stall onset point is the flow rate at which the RI was reduced significantly, and the stall disturbance occurred.The integral of the lowfrequency(lower than fs)can be used to represent the strength of the stall disturbance,which can be applied to determine the original position of the stall disturbance.41The low-frequency area is indicated in red in Figs.15(a) - 15(c).

In the case of the 45%Nmaxspeed line, the stall strength at the diffuser inlet was significantly smaller than that at the impeller inlet,indicating that the impeller inlet was the original stall onset position and the diffuser stall was induced by the impeller stall.Similarly,for the 63%Nmaxand 73%Nmaxspeed lines,the stall strengths at the diffuser inlet were also less than those at the impeller inlet.However, the difference in stall strength between the diffuser and impeller decreased as the rotational speed increased, which can be also observed from comparing the irregularity at inlets of impeller and diffuser,as shown in Fig.15(d).The blue triangles and red circles represent the impeller and diffuser inlets respectively, and the rotating speed increases from left to right.It can be found that the irregularities at impeller inlet are larger than those at diffuser inlet,and the irregularity differences between the impeller and diffuser inlets decrease with rotating speed increasing,which are consistent with the observation from frequency spectrum characteristics.It can be conjected that when the speed passes a certain value, the diffuser stall strength should be greater than that of the impeller stall.Thus, the diffuser stallplays a major role in the compressor instability evolution, as shown in the medium- and high-speed ranges.Furthermore,at the impeller inlet (upper figures), a high magnitude disturbance with (1/7–4/7)BPF frequencies also exists, which indicates the notable phenomenon of the co-existence of stall and RI, implying that the impeller stall was induced by RI.Therefore,in the low-speed range,the stall occurs at the impeller inlet first owing to the RI effect and then induces the diffuser stall and compressor surge.Based on the above discussion,the compressor instability evolution can be summarized as shown in Table 2.

Table 2 Compressor instability evolution characteristics at various rotational speeds.

4.Conclusions

The characteristics of instability evolution in a turbocharger centrifugal compressor were investigated via high-response static-pressure measurements in this study.The time and frequency domain behaviors of unsteady pressure signals were analyzed for various rotational speeds, and the characteristics of the typical instability phenomena were discussed.The main results are summarized as follows.

(1)Based on the unsteady static-pressure fluctuations at the impeller inlet,including the pressure irregularity and skewness curves during the throttling process,three typical speed ranges were distinguished: low ((40%–75%)Nmax), medium((75%–85%)Nmax),and high((85%–100%)Nmax)speed ranges.The instability paths exhibited an obvious difference at each speed range.As the rotational speed increased, the dominant instability position shifted from the impeller to the diffuser.

(2) In the low-speed range, the compressor instability shifted from stable to RI, impeller stall (diffuser stall), and then surge.The RI is indicated by the low-pressure region(large negative skewness and high irregularity) and exhibited the evolution behaviors of arising and fading again.Due to the forming, rotating and shedding behaviors of the spatial vortex at impeller inlet region, the low-pressure region has the high unsteadiness and corresponding RI has the characteristics of broadband, multi peak and intermittent occurrence.

(3)The impeller stall was induced by RI,propagated to the downstream diffuser, and finally led to diffuser stall and compressor surge in the low-speed range.The RI and stall coexist in a certain flow rate range for the low-speeds, which is a significant link between the stall and RI.The impeller and diffuser stall presented an irregular sawtooth pressure wave and exhibited a broadband frequency spectrum similar to that of RI.Both the high unsteadiness of recirculation vortex and asymmetric volute structure are responsible for the broadband behaviors of stall.Compared to RI, the impeller stall disturbance magnitude reduced significantly and caused a large blade loading deterioration at the tip region.

(4) In the medium-speed range, the compressor instability path shifted from stable to diffuser stall, RI, and then surge.The diffuser stall occurred before the RI fading and impeller stall emergence, indicating that a transition speed range exists for the instability behavior change.In the high-speed range,the compressor shifted from stable to diffuser stall and then surge.The diffuser stall occurred when the impeller remained stable and caused a rapid compressor surge,resulting in a large reduction in the compressor surge margin.These instability behavior variations at different rotational speeds also indicate that a good match between the impeller and diffuser can optimize the surge margin over the entire speed range.

(5) On comparing the unsteady static-pressure signal characteristics at the impeller and diffuser inlet for all the speed lines,the RI phenomenon only occurred in the impeller rather than in the diffuser, indicating that the blade rotating effect was the necessary condition for the RI generation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (Nos.51906006, 51736001 and 52006217) and the Beijing Institute of Technology Research Fund Program for Young Scholars, China.