## Abstract

The identification of stall inception mechanisms and stability-limiting components in a centrifugal compressor is required for the development of effective surge suppression approaches. Part I of this two-part paper investigates the surge signature of a centrifugal compressor at subsonic, transonic, and supersonic inlet tip conditions, and Part II considers the relationship of the surge signature with the compressor static pressure characteristics, as well as the impeller leading edge relative tip Mach number. Experiments were performed in the single stage centrifugal compressor (SSCC) facility at Purdue University with both steady performance and dynamic pressure data recorded. Results show the presence of both mild and deep surges on the compressor map. Deep surge occurs at subsonic and supersonic impeller tip relative Mach numbers while the mild surge is observed as the tip relative Mach number nears unity. Long length-scale modal oscillations can be detected only at the transonic operating condition while spike disturbances are identified as the precursor to instability at subsonic and supersonic tips relative Mach numbers. Finally, the impeller is determined to be the origin of instability throughout most of the compressor map. The observation of impeller-induced instability refreshes the conventional understanding that the diffuser is typically the stability-limiting component for centrifugal compressors with vaned diffusers and suggests various surge suppression approaches may be necessary to achieve range extension throughout a compressor map.

## 1 Introduction

To achieve maximum efficiency at high Mach numbers, it is almost mandatory for modern turbochargers and turboshaft engines to use vaned diffusers. While vaned diffusers allow for higher efficiency than vaneless diffusers, vaned diffusers have the disadvantage of reducing stall margin. In centrifugal compressors with vaneless diffusers, a surge may be induced by a rotating stall in either the impeller or vaneless diffuser [14]. However, it is generally agreed that the stationary vaned diffuser tends to be the stability-limiting component in centrifugal compressors with vaned diffusers due to the relatively high blockage and large non-uniformity associated with the diffuser entrance flow. Experiments by Toyama et al. [5] showed that the diffuser inlet region (the vaneless and semi-vaneless space) is critical to the stability of the compressor stage, which was also supported by the analysis of static pressure rise coefficients as reported by Hunziker and Gyarmathy [6]. Furthermore, recent studies [713] on centrifugal compressor stall inception indicate that the onset of instability for highly loaded stages with vaned diffusers typically occurs in the diffuser inlet region, which is the case for both modal- and spike-type stalls.

Different surge suppression techniques are used depending on whether the impeller or diffuser is destabilizing the compression system. For centrifugal compressors with a vaneless diffuser, where inducer stall often contributes to instability, the most common and effective map width enhancement technique is an impeller recirculation device or so-called “ported shroud”. The application of this passive stability control device was first reported by Fisher [14] and recently documented by Sivagnanasundaram et al. [15] and Guillou et al. [16] for turbocharger compressors. The ported shroud consists of a bleed slot and cavity that pneumatically connect the inducer region to the compressor inlet. The slot and cavity recirculate the reversed flow from the inducer tip region back to the impeller inlet to improve both blade loading and incidence at the impeller leading edge (LE) near the shroud which results in an increase in surge margin.

The stabilization techniques for centrifugal compressors with vaned diffusers mostly target the flow at the diffuser inlet region, including both active flow injection and passive casing treatments. The potential for air injection to improve centrifugal compressor stability was investigated by Skoch [9,10] using the NASA CC3 compressor facility. Two experiments were conducted with flow either injected from the shroud side or the hub side. Results from the shroud-side injection experiments showed both a significant improvement in surge margin and the ability to recover from the deep surge. In contrast, hub-side injection provided only a minor improvement in the stable operating range. Approaches for casing treatments in vaned diffusers include circumferential slots in the vaneless space [17] and porous-throat diffusers [18,19], both of which reduce the propensity for reversed flow at near-stall conditions through redistribution of near-shroud low momentum fluid. The circumferential slot is similar in functionality and geometry to that of the ported shroud at the inducer but is targeted to modify flow features at the impeller trailing edge (TE) rather than the impeller leading edge. As first reported by Raw [18], porous-throat diffusers feature openings at the throat of each diffuser passage that connect the individual passages with a communicating manifold. Galloway et al. [19] recently performed a comprehensive investigation of the stability enhancement of a turbocharger centrifugal compressor using a porous-throat diffuser and confirmed that the stability enhancement associated with the porous diffuser is achieved by balancing the circumferential pressure non-uniformity at the diffuser throat.

The stall and surge investigations of former decades developed the belief that the diffuser dominates the surge events in centrifugal compressors with vaned diffusers, but this belief is becoming less monolithic with the advancement of both centrifugal compressor designs and instrumentation technologies. Numerous studies have demonstrated that the success of stability control devices in surge suppression is either limited near the design speed or covered only a small portion of the compressor map [811]. That the efficacy of surge suppression is a function of operating speed suggests the surge mechanism itself may also be a function of rotational speed [20,21], and the variation of the surge mechanism with design speed may manifest as an abrupt decrease of the surge margin at high speeds [2024]. The phenomena responsible for reduced surge margin at high rotational speeds, sometimes referred to as a “kink” in the surge line, remain unclear.

Some studies, such as that by Galloway et al. [19] have begun to expound on the relationship of the surge mechanism with rotational speed. They showed that a porous-throat diffuser improved compressor operating range at all speeds except 90%, for which the surge margin was unchanged. The authors hypothesized that the impeller, rather than the diffuser, was the stability-limiting component at that operating speed. The development of instability in a turbocharger centrifugal compressor stage was explicitly considered in relation to the rotational speed of the impeller in recent works by Sun et al. [23], He and Zheng [24], Dielenschneider et al. [21], and Paul et al. [20]. While deep surge occurred at all speeds in Refs. [23,24], the precursors to global instability were different at low, middle, and high speeds. Specifically, the researchers observed stall and mild surge prior to deep surge at the low speeds, mild surge was evident at most operating conditions not in choke in the middle-speed range, and at high speeds deep surge could be abruptly encountered with no precursor instability. Sun et al. also observed that the origin of the compressor instability varied with speed. Additionally, He and Zheng developed a mathematical model based on a mass-spring-damper system to explain the unusual behavior of the compressor stage at the middle-speed range.

While these recent studies [1921,23,24] have identified that the origins and mechanisms of instability in centrifugal compressors appear to be related to rotational speed, a clear picture of the physical processes leading to instability has not yet been attained. Delving into the origins of instability to improve the community’s understanding of centrifugal compressor surge and its relationship with rotational speed and inlet conditions serves as motivation for the present work. Moreover, this paper seeks to establish the flow phenomena responsible for the sudden reduction in surge margin often observed in high-speed machines and relate those phenomena to the stability and damping of the stage and components.

The machine Mach number and impeller tip relative Mach number of the compressor used in the present study are comparable to that of modern high-speed stages such as those investigated by Galloway et al., Sun et al., He and Zheng, Dielenschneider et al., and Paul et al. In Part I of the paper, the surge signatures and the underlying mechanisms of instability in a high-speed centrifugal compressor with a vaned diffuser are investigated within an operating envelope from 40% to 100% corrected speed covering subsonic, transonic, and supersonic impeller tip relative Mach numbers. The compressor surge signature at each tested speed is identified on the compressor map.

## 2 Facility and Instrumentation

The experiments in the present study were conducted in the single stage centrifugal compressor (SSCC) facility at Purdue University, West Lafayette, IN. The SSCC facility houses an experimental Honeywell centrifugal compressor. The details of the compressor performance and documentation of the facility are provided by Lou et al. [25]. In the present work, the axisymmetric inlet configuration was utilized, and the radial gap between the impeller and the diffuser has been reduced relative to the baseline compressor configuration in Ref. [20]. The compressor is driven by a 1400-horsepower electric motor via a 30.46:1 ratio gearbox. Compressor data were acquired from 40% to 100% corrected speed from choke to surge while measuring both steady performance and dynamic pressure signals.

The primary flow path of the compressor and key design parameters are given in Fig. 1 and Table 1, respectively. The entire stage includes the inlet housing, transonic impeller, vaned diffuser, bend, and deswirl vanes. The inlet housing delivers the flow to the impeller’s eye. The impeller is backswept and has 17 main blades and 17 splitter blades, and the diffuser consists of 25 aerodynamically profiled vanes. The compressor design speed is about 45,000 rpm with a machine Mach number of approximately 1.7, and the entire stage produces a total pressure ratio near 6.5 at the design point. In the present work, the exducer tip clearance was adjusted through the axial translation of the impeller, and the exit tip gap was set at 7.4% of the impeller exit blade height at all operating conditions. Bleed flow slots are located at the hub and shroud of the vaneless space, and they are maintained at design values of 1% and 0%, respectively, of the inlet mass flowrate at all operating conditions. No surge suppression techniques, active or passive, were incorporated into the stage for this study. The definitions for inlet flow coefficient and loading coefficient as given in Table 1 are
$Φ=m˙ρt0D22U2$
(1)
and
$ψ=cp(Tt6−Tt0)U22$
(2)
respectively.
Fig. 1
Fig. 1
Close modal
Table 1

Aerodynamic design point and geometric parameters for the SSCC compressor

ParameterValue
Pressure ratio∼7.0
Rotational speed44,750
Specific speed0.27
Machine Mach number∼1.7
Diffuser vane count25
Backsweep angle45 deg
Inlet flow coefficient (Φ)0.040
ParameterValue
Pressure ratio∼7.0
Rotational speed44,750
Specific speed0.27
Machine Mach number∼1.7
Diffuser vane count25
Backsweep angle45 deg
Inlet flow coefficient (Φ)0.040

Steady performance of the compressor stage and its subcomponents is characterized using the total pressure and total temperature measurements at the compressor inlet (station 0), diffuser exit (station 5), and deswirl exit (station 6), as indicated in Fig. 1. Static pressure taps are located throughout the flow path to calculate the stage and component static pressure characteristics. Two temperature measurements (180 deg apart) are recorded just upstream (US) of the impeller leading edge to gauge level of flow recirculation around the inducer.

Numerous fast-response pressure transducers are also installed throughout the flow path, as shown in Fig. 2. There are ten fast-response transducers installed along the impeller chord from the impeller leading edge to 40% of the meridional impeller chord (locations 1 through 10). Three circumferentially spaced fast-response transducers are installed just upstream of the impeller leading edge (location 0 in Fig. 2). An additional 24 (two sets of 12) transducers are distributed across two different portions of the vaneless space and corresponding diffuser passages. The two diffuser passages instrumented with fast-response transducers are separated by approximately one-third of the annulus. In each instrumented portion of the diffuser, there are four transducers along the diffuser vane and an array of 4 × 2 sensors in the vaneless space. The two rows of transducers in the vaneless space are at 2% and 4% radius ratios. The four sensors in each row are equally spaced from 0% diffuser pitch to 75% diffuser pitch. Out of the four transducers along the diffuser vane, three are installed on the suction side (SS) and one on the pressure side (PS). They are located at the diffuser leading edge, throat, and downstream (DS) of the throat, as shown in Fig. 2. The Kulite locations called out with colored circles correspond to positions in the flow path referenced throughout the proceeding discussion of the compressor surge signature.

Fig. 2
Fig. 2
Close modal

All steady pressures are measured using high-accuracy pressure scanners. Pressures at the compressor inlet (station 0) and along the shroud of the inlet housing (between stations 0 and 1) are measured using sensors with the range of 2.5–5.0 psid and uncertainties less than 0.12%. The remaining pressures are measured using 100 psid sensors with an uncertainty of less than 0.05% full-scale. The total temperatures at the compressor inlet and exit, as well as the temperatures near the impeller leading edge, are measured using K-type thermocouples which have an uncertainty of less than 2.2 °C. A calibrated ASME standard Venturi flowmeter is used to measure the mass flowrate with an uncertainty of less than 1.2%. Signals from fast-response transducers were acquired using an in-house high-speed data acquisition system. The analog millivolt signals from the fast-response pressure transducers are amplified and digitized at a frequency of 100 kHz during surge data acquisition. At stable operating conditions, data were acquired at a sample rate of 1000 kHz with a 190 kHz low-pass analog filter. Where digitally filtered data are presented, a digital low-pass filter was applied during post-processing to remove high-frequency components related to the blade passing events. The cutoff frequency of the low-pass filter was specified as four times the shaft frequency which resulted in cutoff frequencies between 1 kHz and 3 kHz for the operating ranges considered within the scope of this paper.

## 3 Operability and Surge Classification

Figure 3 shows the compressor map in terms of the normalized total-to-total pressure ratio calculated from area-averaged flow properties at the stage inlet and exit (stations 0 and 6, respectively). The corrected speed and mass flowrate were determined according to procedures that account for the effects of humidity on corrected conditions [26]. At each corrected speed, the compressor was gradually throttled until surge occurred. The onset of surge was identified using signals from the fast-response pressure transducers instrumented along the flow path shown in Fig. 2. The surge signature at each speed is classified as either deep or mild surge as indicated by a red square or blue triangle in Fig. 3, respectively. The terms mild surge and deep surge used in the present work follow the definitions given by Greitzer: mild surge events are mass flow fluctuations smaller than the stable mass flowrate passing through the machine whereas deep surge is distinguished by significant or global reversed mass flowrates through the compressor stage [27,28]. The compressor map shows that deep surge occurred at all tested speeds except for 90% corrected speed. At 90% speed shortly after the compressor is loaded above the choked condition, a mild surge, similar to that reported by Refs. [1,19,23,24], occurs. In this case, the instability is less violent than that of the deep surge, and global flow reversal is not observed. Notably, the compressors investigated by Galloway et al. [19], He and Zheng [24], and Dielenschneider et al. [21] exhibit a similar “kink” in the surge line on the compressor map. Additionally, the compressor stages investigated by Emmons et al. and He and Zheng both encountered mild surge only slightly out of choke in this same region.

Fig. 3
Fig. 3
Close modal

The compressor map was divided into three regimes based on the impeller leading edge tip relative Mach number, as indicated in Fig. 3. In the context of the present work, the state of the inlet conditions as subsonic, transonic, and supersonic is in reference to the impeller leading edge tip relative Mach number unless explicitly stated otherwise. Besides exhibiting a different manifestation of surge, the 90% speed characteristic is also a demarcation of the three different operating regimes of the compressor in terms of the impeller leading edge relative tip Mach number. Below 90% corrected speed, the tip relative Mach number is subsonic, and the compressor has a wide stable operating range at these speeds. The relative tip Mach number is near unity at 90% speed and coincides with the narrowest stable range available to the stage. At corrected speeds greater than 90%, the relative tip Mach number transitions from transonic to supersonic, and the operating range of the compressor increases with increasing rotational speed.

The compressor surge signatures at subsonic, transonic, and supersonic inlet tip conditions will be the focus of Part I of the paper, and the relationship of the surge signature with the compressor steady characteristics as well as the impeller leading edge tip relative Mach number will be discussed in Part II.

## 4 Surge Signatures

The surge signatures of the centrifugal compressor stage at 100% (supersonic tip) and 85% (subsonic tip) speeds are shown in Figs. 4(a) and 4(b), respectively, and the mild surge event at the transonic impeller tip conditions (90% speed) is presented in Fig. 4(c). The surge signatures are characterized in terms of raw, unsteady pressure measurements acquired with high-frequency pressure transducers at various locations in the flow path, as shown in Fig. 2. In each figure, the abscissa is time in rotor revolutions, the ordinate is static pressure, and surge initiates at the zeroth revolution. To facilitate the comparison of surge signatures at different speeds, measurements from the same number of rotor revolutions are shown, covering one or multiple surge cycles.

Fig. 4
Fig. 4
Close modal

The surge cycles at 100% speed (Fig. 4(a)) and 85% speed (Fig. 4(b)) are qualitatively similar when examined on the timescale of hundreds of revolutions. At both speeds, the compressor experiences a global flow breakdown with large-magnitude, low-frequency pressure oscillations throughout the entire flow path. Therefore, the surge at 100% and 85% speeds is termed as deep surge. Additionally, the intensity of the pressure oscillation increases from compressor inlet toward diffuser exit with the increase of static pressure along the flow path. In contrast to the deep surge at 85% and 100% speeds, a mild flow instability was observed at 90% speed. Each instance of flow instability, highlighted by the orange regions in Fig. 4(c), is characterized by a group of small, high-frequency oscillations. These oscillations were observed throughout the compressor flow path, and therefore, the instability is termed surge rather than rotating stall. However, surge at 90% speed is less severe, and the overall amplitude of the disturbances is less than half of the amplitude of the deep surge pressure signals at both 85% and 100% speeds. Consequently, the surge at 90% speed is termed as mild surge. The mild surge witnessed in the present work is reminiscent of the stall bursts documented in a study on instability during speed transients in the same facility [29]. During the mild surge events, there is no evidence of global reversed flow, though there is a relatively small drop in static pressure in the vaneless space. In addition, the duration of each mild surge is shorter: mild surge occupies 20 rotor revolutions compared to a surge cycle of approximately 70 rotor revolutions at design speed.

Lastly, an essential difference in the surge dynamics at different speeds is whether the compression system can reestablish stable operation after a surge event. At 85% speed, a single surge cycle occurs; following surge, the pressures at each meridional location return to the pre-surge levels, and stable operation is reestablished for the duration of the revolutions shown in Fig. 4(b). In fact, no further surge events occurred prior to opening the throttle valve to shift the operating point to a more stable operating condition. This behavior was common at the subsonic speed lines investigated in the present study: one to a few surge cycles might occur successively followed by a relatively long period (more than 100 revolutions) of stable operation before additional surge events occurred. At the transonic characteristic (90% speed), stable operation is regained after the initiation of each mild surge event, and the number of revolutions of stable operation between mild surge events is greater than that occupied by the adjacent instabilities. As shown in Fig. 4(c), the pressure levels in the machine briefly reach their pre-surge levels after exiting the mild surge and achieve near-constant pressure prior to onset of the next mild surge. The mild surge events continued until the throttle valve was opened. Unlike the subsonic and transonic operating conditions, stable operation is not achieved at any point in the surge cycle at 100% speed, and surge cycles occurred successively until the throttle valve was opened. The pressures at some locations in the flow path in Fig. 4(a), such as downstream of the diffuser throat, are still rapidly changing as the proceeding surge cycle begins. The time-varying pressure levels in the surge cycle indicate that the volume of the flow path is still being filled when subsequent surge cycles occur.

Figure 5 shows zoomed-in views of the surge signatures at 100% and 85% speeds with filtered pressure signals to illustrate the development of a single surge cycle. Like the surge cycles in Figs. 4(a) and 4(b), the development of surge at 100% (Fig. 5(a)) and 85% (Fig. 5(b)) corrected speeds is also similar. Each surge cycle includes three phases: inception, backflow, and recovery. The duration of the three phases is represented by light-blue, purple, and light-brown areas in the figures. At both speeds, surge begins with rapid pressure increases upstream of the diffuser throat signifying stagnation of the flow as the impeller is unable to overcome the system losses. Then, the pressure in the diffuser falls off sharply as the high-pressure fluid flows from the diffuser out through the impeller inlet, indicating backflow throughout the stage . The diffuser backflow results in increased pressure in the impeller as the flow upstream of the diffuser throat stagnates and reverses direction. Recovery starts in the vaneless space at both speeds, indicated by the purple dashed line in Fig. 5(b), as the impeller again begins pumping fluid through the stage.

Fig. 5
Fig. 5
Close modal

Despite the qualitatively similar surge cycles, there are differences in details of the surge signatures at 100% and 85% speeds. First, the duration of the surge cycle varies with speed. At 100% speed, each surge cycle lasts approximately 70 rotor revolutions (Fig. 4(a)) which is significantly longer than the 40 revolutions per cycle at 85% speed (Fig. 4(b)). There are also greater pressure spikes downstream of the diffuser throat as surge initiates at 100% speed (Fig. 5(a)) compared to 85% speed (Fig. 5(b)). Lastly, there are differences during the surge inception phase at 100% and 85% speeds, indicated by the light-blue areas in Figs. 5(a) and 5(b). Surge inception at 100% speed can be characterized by the rapid growth of a few discrete disturbances that bring the compressor into deep surge within five rotor revolutions. In contrast, the surge inception at 85% speed appears to be a continuous process: the flow upstream of the diffuser throat experiences a rapid yet smooth increase in pressure that results in deep surge. Details of the surge inception are discussed in the following section, and the mechanisms which give rise to differences in the surge cycles will be discussed throughout both parts of the paper.

Although not presented here, the surge signature at all the speeds shown on the compressor map in Fig. 3 was also investigated. In general, the observations given for surge at 100% speed are consistent with the characteristics of the instability at 95%, and the observations of surge at 85% speed are representative of the instabilities at all other measured speeds between 40% and 80% speeds.

## 5 Surge Inception

To understand the origin of surge at each speed, the pressure traces leading up to and immediately after the initiation of surge at subsonic, transonic, and supersonic inlet tip conditions were investigated in further detail.

### 5.1 Surge Inception at Supersonic Inlet Tip Conditions.

Figure 6 presents the same instance of surge at 100% speed that is shown in Figs. 4(a) and 5(a), but only ten revolutions of the raw signal surrounding the initiation of surge are shown. The first disturbance prior to surge was observed at the impeller leading edge, indicated by the green circle in Fig. 6. Prior to the initiation of surge, the signal at the impeller leading edge is well organized and dominated by the blade passing events. The disturbance disrupts the impeller flow, develops rapidly, and results in degradation of pressure rise throughout the impeller, bringing the entire compression system into surge in less than five rotor revolutions.

Fig. 6
Fig. 6
Close modal

To understand the propagation of the disturbance in the impeller circled in Fig. 6, the dynamic pressure traces at the impeller leading edge are investigated in detail. Figure 7 shows the filtered static pressure signals at the onset of surge from three pressure transducers just upstream of the impeller leading edge. The abscissa is time in rotor revolutions, and the ordinate represents the circumferential orientation of the transducers around the annulus. The blue background in Fig. 7 coincides with the revolutions in the blue inception region indicated in Fig. 6, and the blue line tracks the propagation of the disturbance around the impeller. The initiation of surge is again indicated by the green dash-dot line.

Fig. 7
Fig. 7
Close modal

With the signature of the blade passing frequency removed by a digital low-pass filter, the disturbance at the impeller leading edge can be distinguished as a peak in pressure increasing in magnitude with time. In the absolute reference frame, the disturbance travels in the same direction as the impeller at approximately 85% of the wheel speed. Observing from Figs. 6 and 7 that full-stage instability develops from the disturbance in less than five rotor revolutions, the disturbance at 100% speed can be classified as a spike according to the definition provided by Camp and Day [30]. Moreover, long wavelength modal waves could not be distinguished in steady operation prior to stage instability which eliminates modal stall as the origin of the surge event.

Although not detailed here, the surge signature at 95% corrected speed was also investigated. Both 95% and 100% speeds, the two operating conditions with supersonic impeller leading edge relative tip Mach numbers, exhibited similar instability characteristics. At 95% speed, a spike also occurs in the impeller which quickly (less than ten rotor revolutions) destabilizes the entire compressor system resulting in deep surge.

The phenomenon of surge induced by a spike-type disturbance originating in the impeller inducer contradicts the conventional understanding that the diffuser is typically the stability-limiting component for centrifugal compressors with vaned diffusers. In many studies, the region from the vaneless space to the diffuser throat has been identified as the origin of a disturbance that limits the lowest mass flowrate at which stable operation can be maintained for a given speed [68,12,19,31]. However, it is noteworthy that most earlier experiments examining surge events do not have fast-response transducers placed at the impeller leading edge or along the impeller shroud, and the typical surge identification transducers placed at the inlet plenum may not be able to capture the transient pre-surge impeller rotating stall phenomena. To the best knowledge of the authors, this is the first time the transient pre-surge inducer spike phenomenon has been characterized in a high-speed centrifugal compressor with a vaned diffuser.

Though this is the first time the inducer spike has been documented in the open literature, recent experiments with high-speed impellers have begun to hypothesize that the impeller may be the stability-limiting component in some cases [19,22]. In the studies, two different surge suppression approaches targeting the vaned diffuser of an advanced turbocharger centrifugal compressor, including a vaned diffuser recirculation technique and a porous-throat diffuser, were implemented to extend the compressor’s stable operation range. While improvement of the surge margin was achieved at some speeds, both techniques failed to extend the surge margin at 90% corrected speed. In Refs. [19,26], the 90% speed line corresponds to a machine Mach number of approximately 1.45 and is similar to the values of machine Mach number where the impeller-induced surge is observed in the present study. Though additional work is necessary to confirm the universality of these observations, the identification of impeller-induced surge indicates that the impeller may be more important to the stability of high-speed centrifugal compressor stages than once thought. Furthermore, the efficacy of surge suppression approaches is heavily reliant on the correct identification of the stability-limiting component, and high-speed centrifugal compressors may not be able to rely on range extension throughout the compressor map for surge suppression techniques applied to only one component.

### 5.2 Surge Inception at Subsonic Inlet Tip Conditions.

Figure 8 shows the raw signal of the meridionally distributed pressure transducers just before and after the initiation of surge for 85% corrected speed. In contrast to the supersonic tip conditions shown in Fig. 6, the pressure signal at the impeller leading edge is much less structured, and the blade pass signal cannot be clearly distinguished. Though not shown here, the low-pass filtered dynamic pressure signal prior to surge at the impeller leading edge reveals much greater levels of broadband low-frequency content at subsonic relative tip Mach numbers than at supersonic operating conditions. The frequency content of the pressure signals, discussed at length in Part II of the paper, reveals a “broadband hump” in the spectrum of the subsonic operating conditions classically representative of rotating instabilities as defined by Day [32].

Fig. 8
Fig. 8
Close modal

The initiation of surge at 85% speed does not begin with a distinct disturbance. The mean pressures at 40% of the impeller chord and in the vaneless space do not appear to be constant in the five revolutions prior to the initiation line, but the pressures do not deviate enough from the time average value between revolutions −5 and 0 to grow nonlinearly and bring about full stage instability. From revolutions 0 to 5, however, rotating instabilities throughout the flow path (circled and highlighted in Fig. 8) occur contemporaneously with the pressure increase at the impeller 40% meridional location. Together the compound disturbances in the impeller and diffuser initiate the global backflow associated with the deep surge. The surge inception process at the remaining subsonic conditions was also investigated, and though there are small differences, the inception process presented in Fig. 8 is representative of surge signatures from 40% speed to 80% speed.

It should be noted that the low-frequency pressure oscillations in the revolutions preceding surge in Fig. 8 may appear like the modal waves that have been identified by other researchers. This possibility was investigated, and a coherent low-frequency structure could not be identified. Thus, the instability at 85% speed is considered a spike due to its rapid growth with no distinguishable preceding modal waves, but in further contrast to 100% speed, no distinct disturbance was detected rotating around the impeller or diffuser during the inception phase. Additionally, at supersonic tip Mach numbers, a discrete disturbance leading to global instability was identified. At 85% speed, as with the other subsonic conditions investigated, no single event in either the impeller or diffuser could be attributed to the origin of compressor surge. Therefore, the component responsible for the origin of the instability could not be identified with time-resolved pressure measurements from 40% speed to 85% speed.

### 5.3 Surge Inception at Transonic Inlet Tip Conditions.

As might be expected from the previously noted differences in surge cycles, the inception of mild surge at the transonic operating condition is dissimilar to the subsonic and supersonic regimes. Figure 9 shows the filtered static pressure traces leading to the mild surge event at 90% speed with the darkening background indicating the increasing amplitude of the disturbance. The disturbance grows to a relatively mild oscillation in pressure encompassing the entire stage in ten revolutions. Like the subsonic surge signatures, the origin of the disturbance is not clear from the meridional pressure traces. Once the oscillations grow to affect the entire stage, there is evidence of circumferential propagation, as shown in Fig. 10. The disturbances rotate around the impeller leading edge at approximately 70% of the wheel speed and persist for around 20 revolutions. Once reaching the peak amplitude, the oscillations behave as an underdamped system, and stable operation is gradually restored.

Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

Having established the propagation rate of the disturbance around the circumference, the origin of the instability at the transonic operating condition can be identified. Figures 11(a) and 11(b) show the frequency content of the dynamic pressure measurements acquired at the impeller leading edge and in the diffuser, respectively, for 1000 revolutions prior to the first instance of the mild surge. The ordinate is amplitude in units of pressure. The abscissa is normalized by the shaft frequency, and only the frequency content between zero and the shaft frequency is shown. Although the peak is small relative to the energy floor, the indicated frequency at the impeller leading edge in Fig. 11(a) (engine order 0.7) coincides with the circumferential propagation rate of the full-scale disturbance identified in Fig. 10 (70% of the rotation speed). In contrast, there is no distinct peak within the highlighted frequency band in the diffuser, shown in Fig. 11(b). Therefore, the impeller is considered to be the origin of the disturbance leading to mild surge. Additionally, the presence of low amplitude oscillations at the impeller leading edge results in the classification of the instability as a modal oscillation according to the criterion given by Camp and Day [30].

Fig. 11
Fig. 11
Close modal

## 6 Conclusions

Surge signatures from a transonic centrifugal compressor are investigated within an operating envelope from 40% to 100% corrected speed. Experiments were performed in the SSCC facility at Purdue University, West Lafayette, IN with both steady performance and dynamic pressure data recorded. The test speeds cover a wide range of impeller tip relative Mach numbers, which are representative values for centrifugal compressors in turbochargers and small aeroengines.

Results show the presence of both modal- and spike-surges on the compressor map, where modal-type surge occurs at 90% corrected speed and spike-type surge dominates all other speeds. At 90% corrected speed, the impeller stalled at loadings just above the choked conditions and acted as the destabilizing component. Modal waves leading to mild surge events were observed in the impeller with a rotational speed equal to 70% of the shaft speed.

The details of the spike-type surge signature vary with changes in operating speed. At subsonic inlet conditions near the impeller leading edge (from 40% speed to 85% speed), the inducer can tolerate larger levels of incidence due to reduced loss at lower Mach numbers, and the origination of the disturbance prior to the onset of surge is not clear. A compound effect is exhibited in which both the impeller and the diffuser passage appear to contribute to the development of surge. While the vaneless space remains in stable operation, both the impeller and the diffuser passage experience a local flow breakdown and quickly bring the entire compression system into surge. At high speeds such as 95% and 100% speeds, with the impeller leading edge tip relative Mach number exceeding unity, the inducer stalls at a much smaller incidence due to the increased losses associated with higher Mach numbers. A spike-type disturbance occurs near the impeller leading edge and rapidly brings the entire compression system into deep surge. This is the first time a spike-type disturbance originating in the impeller has been documented in a centrifugal compressor with a vaned diffuser.

The observation of impeller-induced, spike-type surge has refreshed the conventional understanding that the diffuser is typically the stability-limiting component for centrifugal compressors with vaned diffusers. This is of great importance since the efficacy of surge suppression approaches heavily depends on whether the impeller or diffuser limits the compressor operating range. Additionally, these observations support the findings of recent studies conducted on an advanced turbocharger compressor with similar machine Mach number [19,22] in which the impeller was hypothesized to be the stability-limiting component at 90% speed.

Lastly, a question arises from the change in surge signature with corrected speed: what causes the differences in surge signature between the subsonic, transonic, and supersonic operating regimes? To answer this question, a detailed analysis of the static pressure rise characteristics at the stage, component, and subcomponent level was conducted in conjunction with the examination of the influence of the impeller inlet conditions. These findings are discussed in Part II of the paper.

## Acknowledgment

The authors would like to thank Honeywell, Inc., for sponsoring this study. The authors are grateful to Mr. Darrell James of Honeywell for his helpful insights into data interpretation. The authors would also like to thank Mr. William Brown and Mr. Matthew Fuehne at the Purdue Compressor Research Laboratory for their help in preparing and conducting the experiments.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

## Nomenclature

• b =

•
• r =

•
• D =

diameter

•
• T =

temperature

•
• U =

wheel speed

•
• $m˙$ =

mass flowrate

•
• cp =

specific heat at constant pressure

•
• Nc =

corrected speed

•
• DS =

downstream

•
• LE =

•
• PS =

pressure side

•
• SS =

suction side

•
• TE =

trailing edge

•
• US =

upstream

•
• ρ =

density

•
• Φ =

inlet flow coefficient

•
• ψ =

### Subscripts

• t =

stagnation properties

•
• 0 =

housing inlet

•
• 1 =

impeller inlet

•
• 2 =

impeller exit

•
• 3 =

diffuser inlet

•
• 4 =

diffuser throat

•
• 5 =

diffuser exit

•
• 6 =

deswirl exit

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