## Abstract

In the first part of the paper, surge signatures and the underlying mechanisms thereof for a high-speed centrifugal compressor were investigated using signals from fast-response transducers installed along the flow path. The compressor surge signature is observed to vary as the impeller inlet tip flow transitions from subsonic to supersonic conditions. Spike-type deep surge is observed at subsonic and supersonic impeller inlet tip conditions while modal-type mild surge occurs at 90% speed with transonic inlet tip conditions. In Part II of the paper, a detailed analysis of the static pressure rise characteristics at the stage, component, and subcomponent levels is conducted. Additionally, the influence of the impeller inlet conditions on the instability is also considered. A connection between the surge mechanism and component static pressure rise characteristics is shown which exhibits the potential for prediction of the stall inception mechanism including identification of the destabilizing component. Furthermore, the transition from subsonic to transonic impeller inlet conditions is shown to be the cause of the unique mild surge instability at 90% speed. Lastly, both experimental and computational results are utilized to investigate the development of a shock wave at the impeller leading edge. The shock is considered to be critical to stage stability at speeds where the compressor experiences transonic inlet conditions.

## 1 Introduction

As reported in Part I of the paper, the compressor surge signature varies as impeller inlet tip flow changes from subsonic to supersonic conditions. At subsonic and supersonic impeller inlet tip conditions, instability manifests as spike-type deep surge while modal-type mild surge occurs at 90% speed with transonic inlet tip conditions. Though the surge signature can be characterized using signals from fast-response pressure transducers, the necessary instrumentation and data acquisition systems are not typically available in field application. In the rare instances where the instrumentation may be available, detection of a disturbance prior to full stage instability is difficult due to either the low amplitude of the disturbance in the case of modal waves or extremely rapid growth in the case of a spike-type disturbance. Therefore, an alternative approach for surge signature identification based on more readily available measurements is of great value to the research community. For axial compressors, Camp and Day [1] found that the shape of the total-to-static pressure rise characteristics can be used to predict the stall inception mechanism of the compressor: spike-type stall occurs if the compressor stalls before the slope of stage total-to-static pressure rise characteristic changes from negative to positive; and modal waves exist prior to stall if the compressor stalls with a positive slope for the total-to-static pressure rise characteristic. However, the applicability and effectiveness of Camp and Day’s approach on high-speed centrifugal compressors is still uncertain as the surge mechanisms may differ significantly between axial and centrifugal compressors. In axial compressors, the interaction between the tip leakage vortex and the passage shock can result in the breakdown of the vortex thereby inducing rotating stall in the compressor [2,3], while historically the vaned diffuser is considered to dominate surge events in centrifugal compressors.

However, as shown in Part I, the observation of surge induced by a spike-type disturbance originating in the impeller inducer 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 underlying surge mechanisms may impact the reliability of the Camp and Day criterion. Moreover, the efficacy of surge suppression approaches heavily depends on whether the impeller or diffuser limits the compressor operating range, and recent studies have shown that the component from which instability originates may vary with rotational speed [46]. In the case of centrifugal compressors with vaneless diffusers, where inducer stall is an important driver for instability, the most common and effective map-width enhancement technique is the impeller recirculation device or so called “ported shroud” [710], which consists of a slot and cavity connecting the inducer region to the compressor inlet. It recirculates the reversed flow from the impeller inducer tip region back to the impeller inlet and, thus, improves the blade loading and incidence at the impeller leading edge near the shroud. Ultimately, an increase in surge margin is attained. On the other hand, 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 such as hub/shroud injection [11,12], vaneless space bleed [13], porous throat diffuser [4,14], etc.

Therefore, to effectively implement map-width enhancement techniques for modern high-speed centrifugal compressors with vaned diffusers, two questions must be answered: (1) Is it possible to utilize stage or component static characteristics to identify the stall mechanism and the component from which instability originates? And (2) Is there a connection between the surge signature and impeller inlet tip condition? Part II of this paper aims to address the above questions through examination of the static pressure characteristics and analysis of the dynamic pressure signal during compressor surge. Results of the component and subcomponent characteristics are investigated to identify the stability-limiting component at each individual speed, and the criterion from Camp and Day [1] is examined alongside the surge signatures identified in Part I. The influence of the impeller inlet conditions on the compressor surge signature is also analyzed. Correspondingly, the content of the paper is structured as follows: First, a brief summary of Part I of the paper, including an overview of the facility and surge signatures at different speeds, is provided in the Facility and Instrumentation and Operability and Surge Signatures sections. Second, the connections between surge signatures and static characteristics are examined in detail. Lastly, the influence of impeller inlet tip conditions on the compressor surge signature is investigated to expound on the relationship between rotational speed and instability pathology documented in recent studies [46].

## 2 Facility and Instrumentation

The experiments in the present study were conducted in the single stage centrifugal compressor (SSCC) facility at Purdue University. The SSCC facility houses an experimental honeywell centrifugal compressor. Details of the compressor performance and documentation of the facility are provided in Ref. [15]. The primary flow path of the compressor is shown in Fig. 1. The entire stage includes the inlet housing, transonic impeller, vaned diffuser, bend, and deswirl vanes. The inlet housing delivers the flow to the impeller 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 (impeller tip Mach number) of approximately 1.7, and the entire stage produces a total pressure ratio near 6.5 at design point. No surge suppression techniques, active or passive, were incorporated into the stage for this study.

Fig. 1
Fig. 1
Close modal

Steady performance of the compressor stage and its subcomponents is characterized using the total pressure and total temperature measurements at 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 characterize the stage and component static pressure characteristics. Two temperature measurements (180 deg apart) are recorded just upstream of the impeller leading edge to gauge the level of flow recirculation around the inducer. Though not detailed here, extensive fast-response pressure transducers are also installed throughout the flow path for stall inception and surge signature characterization (see Fig. 2 in Part I for details on the layout of the fast-response pressure transducers). Further details of the data acquisition system are provided in the Facility and Instrumentation section in Part I of the paper.

Fig. 2
Fig. 2
Close modal

## 3 Numerical Setup

In order to gain a more detailed understanding of the flow behavior, a computational model of the compressor stage was utilized. All computations were performed using ansys cfx 19.2. ANSYS TurboGrid was used to generate structured grids for the impeller, diffuser, and deswirl domains, the sizes for which are given in Table 1. A grid convergence study was performed using the method described by Celik et al. [16], with the grid convergence indices for stage total pressure ratio (TPR) and stage efficiency shown in Table 2. Grid 2 was selected as the computational costs associated with the finer grid were not commensurate with the improvement in results. A uniform total pressure and total temperature were assigned for the inlet boundary condition, representing standard day operating conditions. Mass flowrate exit boundary conditions were used for all simulations, as none were near the choked condition for their respective speed. Due to the high computational cost of a full annulus model, and since only steady operating conditions were simulated, the compressor was modeled with a single passage of each component on the assumption of rotational periodicity. Stage mixing planes were utilized between domains as shown in Fig. 2 to account for changes in reference frame as well as changes in pitch between components. Heat transfer effects were accounted for in the impeller domain by applying an experimentally measured temperature profile to the impeller shroud boundary. The other surfaces in the model were treated as adiabatic. The kω-based baseline (BSL) model was used for turbulence closure as it provided more stable convergence and better agreement with experimental results than the other turbulence models tested. All solid surfaces in the model were assigned a roughness corresponding to that specified in the respective manufacturing drawing. Conversion from centerline average roughness to sand grain roughness was accomplished using a factor of 7.58, which was taken as an average of the values reported by Koch and Smith [17], Shabbir and Turner [18], and Hummel et al. [19]. Comparisons with experimental measurements were made at design speed and part speed conditions with the simulated results showing good agreement with the experiment [20,21]. All results presented were simulated at stable operating points just above the choked condition for their respective speed.

Table 1

Grid summary

DomainGrid 1Grid 2Grid 3
Inlet/impeller3,733,0008,703,00019,921,000
Diffuser2,662,0006,165,00013,929,000
Deswirl/outlet1,240,0002,790,0006,320,000
Total7,635,00017,658,00040,170,000
DomainGrid 1Grid 2Grid 3
Inlet/impeller3,733,0008,703,00019,921,000
Diffuser2,662,0006,165,00013,929,000
Deswirl/outlet1,240,0002,790,0006,320,000
Total7,635,00017,658,00040,170,000
Table 2

Grid convergence study results

EfficiencyTPR
GCI120.139%1.229%
GCI230.050%1.677%
EfficiencyTPR
GCI120.139%1.229%
GCI230.050%1.677%

## 4 Operability and Surge Signatures

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 effects of humidity on corrected conditions [22]. 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 Part I of the present work. The surge signature at each speed is classified as either deep or mild surge as indicated by a red square or blue triangle in figure, respectively. The term deep surge used in the present work follows the definition by Greitzer: significant reversed flow occurs during the surge cycle [23]. As shown in the compressor map, 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 in Refs. [1,6], occurs. In this case, the instability is less violent than that of the deep surge, and global flow reversal is not observed.

Fig. 3
Fig. 3
Close modal

Furthermore, the compressor map was also divided into three regimes based on 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 are in reference to the impeller leading edge tip relative Mach number unless explicitly stated otherwise. The surge signature at the impeller leading edge at subsonic (85%), transonic (90%), and supersonic (100%) conditions are also shown in the figure. Detailed discussion of the surge signature, including characteristics of the inception phase as well as the overall cycle, is provided in Part I.

## 5 Interpreting Surge Signatures With Static Pressure Coefficients

According to observations by Camp and Day [1], the shape of the total-to-static pressure rise characteristics can be used to predict the stall inception mechanism of the compressor in axial compressors: spike-type disturbances occur if the compressor stalls before the slope of the stage total-to-static pressure rise characteristic change from negative to positive, and modal waves exist prior to stall if the compressor stalls with a positive slope in the total-to-static pressure rise characteristic. In this section, the criterion given by Camp and Day was examined with data acquired in the present study. Additionally, as discussed extensively by Hunziker and Gyarmathy [24], the slope of the static pressure rise characteristic will be utilized to discuss the degree to which various stage components and subcomponents contribute to the overall stability of the machine.

### 5.1 Relationship With Stage and Component Characteristics.

Static-to-static pressure rise characteristics were used for all the results presented in the present work due to the limited availability of total pressure measurements. The static-to-static pressure rise coefficient is defined as
$ΨS−S=ΔP1/2ρt0U22$
(1)
where ΔP is the static pressure rise in either the compressor stage or the individual subcomponent of interest. In all cases, the static pressure coefficient was computed using area-averaged values of static pressure from multiple locations around the circumference. The static pressure rise characteristics are given as a function of the dimensionless inlet flow coefficient, which is obtained using
$Φ=m˙ρt0D22U2$
(2)
where $m˙$ is the compressor inlet mass flowrate, ρt0 is the stagnation density at station 0, and U2 is the wheel speed at the impeller exit. The damping of the natural flow oscillations of the compression system is proportional to the slope of the static pressure characteristic (∂Ψ/∂Φ) with a negative value representing a dynamically stable system and a positive value indicating a dynamically unstable system.

The static pressure rise coefficients of the full stage (from inlet housing through the deswirl vanes, stations 0–6), impeller (stations 1–2), and the vaneless space through the diffuser (stations 2–5) are presented in Figs. 4(a)4(c), respectively. The slope of the characteristics between the last stable operating points prior to instability is highlighted in red for a positive slope (destabilizing) or blue for a negative slope (stabilizing). Prior to surge, the slopes of the stage characteristics in Fig. 4(a) remain negative (blue) at all tested speeds from 40% to 100% excluding 90% corrected speed. At 90% speed, the slope of the static pressure characteristic switches to positive (red) prior to the onset of mild surge. According to the criterion from Camp and Day [1], the compressor will experience modal disturbances at 90% corrected speed and spike-type disturbances at the remaining tested speeds. This prediction agrees well with the findings based on signals from the fast-response pressure transducers discussed at length in Part I: modal waves were only observed at 90% corrected speed and spike-type surge dominates the rest of speeds.

Fig. 4
Fig. 4
Close modal

Transition from the subsonic regime (40–85% corrected speed) to the transonic/supersonic regime (90–100% corrected speed) is accompanied by a change in the shape of the impeller static pressure rise characteristic (Fig. 4(b)). The characteristics are fairly similar in shape up to 80% speed. However, as the impeller relative tip Mach number approaches the transonic condition in choke at 85% speed, the slope of the characteristic is distinctly more positive at low loading conditions along the 85% characteristic than the other subsonic speeds. At low values of flow coefficient on the transonic and supersonic speedlines (90–100% corrected speed), the slope of the static pressure characteristic is also markedly more positive than at the lower corrected speeds. The positivity of the slope indicates that the impeller is destabilizing at these conditions, but the stage as a whole can maintain stability despite the destabilizing nature of the impeller. The diffuser is stabilizing throughout the compressor operating range, Fig. 4(c), and notably strongly stabilizing at near stall conditions on the supersonic speedlines. In total, the stage, impeller, and diffuser static pressure characteristics show that the overall stage is less tolerant to the destabilizing nature of the impeller at subsonic operating conditions than at supersonic conditions: the impeller static pressure characteristic is only slightly positive, or in some cases still negative, when instability occurs at or below 85% speed. In contrast, at 90% speed and above the stage maintains stable operation despite the distinctly more positively sloped impeller characteristics (indicating strongly destabilizing operating conditions for the impeller) for low values of flow coefficient.

### 5.2 Relationship With Subcomponent Characteristics.

The static pressure rise characteristics are further considered at the subcomponent level in Fig. 5. In addition, to the positive and negative slopes highlighted in red and blue, some of the component slopes were near zero and, as such, are shown in gray. In some cases there was significant overlap between speedlines which made interpretation of the static pressure charactersistics difficult, so an artificial offset is imposed on the ordinate between each speadline to improve readability.

Fig. 5
Fig. 5
Close modal

Figure 5(a) shows the static pressure characteristic of the inlet housing. The inlet housing acts as a stabilizing component at all speeds and serves to suppress the destabilizing effect of the inducer, shown in Fig. 5(b). The inducer is destabilizing through the majority of the compressor operating range, except for low loading to approximately peak efficiency at 100% corrected speed. The destabilizing effect is generally weaker at the subsonic speedlines and stronger at high loading conditions with transonic and supersonic impeller relative tip Mach numbers. The aft portion of the impeller, from the knee to the exducer, typically acts as a stabilizing component from 40% to 85% corrected speed (Fig. 5(c)). Like the inducer, the aft portion of the impeller is also stabilizing from choke to peak efficiency at 100% speed but is strongly destabilizing at the high loading conditions past peak efficiency. The inducer and knee-to-trailing-edge portions of the impeller are both strongly destabilizing for the extent of the transonic (90%) speedline.

The diffuser inlet region is critical to the stability of the centrifugal compressor stage: both the vaneless space and semi-vaneless space provide a stabilizing effect over the entire speed range (Figs. 5(d) and 5(e)). Notably, the semi-vaneless space is strongly stabilizing, especially at high speeds, as can be observed the steepness of the negative slope and largest scale for the static pressure coefficient in Fig. 5. In contrast to the diffuser inlet, the diffuser passage is strongly destabilizing over the entire operating range from choke to pre-surge (Fig. 5(f)). This agrees with the findings reported by Hunziker and Gyarmathy [24]. Finally, there is a neutral-to-weak destabilizing effect from the diffuser covered exit (downstream of the diffuser passage to the diffuser trailing edge radius), as shown in Fig. 5(g).

From the analysis of the static pressure coefficients in Figs. 4 and 5, the stability of the impeller is critical to the stability of the entire stage. At subsonic speeds, instability is encountered soon after, if not before, the impeller characteristic switches from negative (stabilizing) to positive (destabilizing). Although the impeller has been identified as the destabilizing component, as well as the origin of instability from 90% to 100% speed (see Part I for details), the stability of the stage as a unit is dominated by the stabilizing effect of the diffuser. The steep negative slope of the diffuser near instability outweighs the shallower positive slope of the impeller, resulting in negatively sloped stage characteristics at all but 90% speed. Thus, the diffuser governs the type of instability experienced by the stage at all speeds except 90%, and in accordance with the theory of Camp and Day [1], a spike-type disturbance is observed when the slope of the stage characteristic is negative. At 90% speed, the only speedline with a positively sloped stage characteristic and modal waves is observed as a precursor to instability through frequency analysis, also in accordance with Camp and Day.

It is hypothesized that continued throttling of the compressor at 90% speed would result in an “S-shaped” characteristic with regions of mild surge followed by stable operation and finally deep surge similar to that observed by Emmons et al. [25] and He and Zheng [5]. The S-shaped characteristic inherently presents with alternating positive and negative slopes which resulting in manifestations of instability as spikes or modal waves at different mass flowrates on the same speedline. However, the mild surge encountered in the present work was considered the boundary of stable operation to preserve the integrity of the instrumentation and test article, so this hypothesis could not be verified.

The static pressure characteristics provide insight into the stage stability throughout the compressor map. The stage instability manifests as a modal disturbance at 90% corrected speed while spike-type surge occurs at all other tested speeds confirming the theory of Camp and Day for centrifugal compressors. Additionally, the impeller exhibits a tendency toward steep, positively sloped static pressure characteristics at high loading conditions above 90% corrected speed. Therefore, the type of instability (spike or modal) is governed by the stage characteristic, but the destabilizing impeller is the origin of instability (as established in Part I) regardless of instability type. Yet, the difference between the manifestation of spike disturbances at subsonic and supersonic speed tip conditions discussed in Part I remains unresolved. Additionally, the static pressure rise characteristics prompt an additional question: why is the stage able to maintain stability at destabilizing impeller operating points at high speed but not low speed? To shed light on the above questions, the flow features for subsonic, transonic, and supersonic impeller inlet tip flow were examined using multidisciplinary measurements in the following section.

## 6 The Effect of Inlet Flow Regime on Compressor Stability

The impeller leading edge tip relative Mach number has served as a demarcation between the differences in the development of stage instability throughout the present discussion. Therefore, it is important to understand the differences in the flow field among the different operating regimes.

### 6.1 Impeller Inlet Tip Flow Features.

The frequency content of one of the high-frequency pressure transducers near the impeller leading edge (location 1 in Fig. 1) for three stable loading conditions at four corrected speeds is shown in Fig. 6. At stable operating conditions, five seconds of continuous data were recorded at a sample rate of 1 MHz for each of the high-frequency pressure transducers shown in Part I of the paper, and the frequency content in Fig. 6 is computed by applying an averaged fast Fourier transform algorithm to the dynamic data. Each column of subfigures in Fig. 6 is a constant speed, and each row represents a similar loading condition with near stall in the top row, peak efficiency in the middle row, and choke in the bottom row. The frequency is normalized by the shaft frequency to give the amplitude of the time-resolved pressure variation as a function of engine order. The largest peak corresponds to the main blade frequency of 17-per-revolution. The secondary peak at the 34th engine order corresponds to combined main-blade-splitter-blade passage frequency. It must be noted that the range of the ordinate is not constant to accommodate the different amplitudes of the frequency content at each speed.

Fig. 6
Fig. 6
Close modal

At 60% corrected speed (Figs. 6(a)6(c)), there is broadband energy at the sub-blade-pass frequencies, and the energy floor increases and consolidates to lower frequencies from choke to stall. The “broadband hump” in the frequency spectrums highlighted in Figs. 6(a)6(c) is the classical representation of rotating instabilities as discussed by Day [26], and the growth in the amplitude of the sub-blade-pass frequencies with decreasing mass flowrate is similar to observations by He and Zheng at low rotational speeds.

The 60% corrected speed operating conditions are shown because the impeller leading edge relative tip Mach is subsonic at all loading conditions. In contrast, the transition from subsonic to transonic operating conditions can be observed at 85% speed in Figs. 6(d)6(f). Near stall, which are both the lowest mass flowrate and lowest tip relative Mach number recorded at 85% speed, the frequency content is similar to the frequency content at 60% speed. However, as the mass flowrate increases from near stall to peak efficiency to choke, the amplitude of the blade pass frequency increases dramatically, and the energy floor simultaneously drops and coalesces at discrete frequencies. The rapid increase in the strength of the blade pass frequency from near stall to choke corresponds to the development of a shock near the impeller leading edge as the tip relative Mach number approaches one.

At 90% speed (Figs. 6(g)6(i)), the frequency content is localized at blade passing frequencies and is similar at all loading conditions on the speedline. The discrete frequency components at frequencies unassociated with the blade pass are much smaller than that at the 85% speed choked condition, highlighted in Fig. 5(f). At 100% speed (Figs. 6(j)6(l)), the distribution of the frequency content is again dominated by the blade pass frequency with a low energy floor relative to the subsonic operating conditions. The low energy floor corresponds to the highly organized signal observed at the impeller leading edge presented in Part I. The rotating instabilities observed at low speeds and significant strengthening of the blade pass pressure signature are consistent with the observations made by He and Zheng [5].

Numerical simulations were used to support the inferences on shock development at the impeller leading edge presented in Fig. 6, and computational simulations of the SSCC stage at part speed conditions confirm the formation of a shock at the impeller leading edge. As shown in Fig. 7, at 90% speed, the shock extends across the main blade passage at the impeller shroud, indicating a supersonic flow in the region. At lower speeds, the leading edge shock is not present in the simulations. From the frequency analysis compiled in Fig. 6 and leading edge shock shown in Fig. 7, it is inferred that the formation of a shock at the impeller leading edge as the impeller tip relative Mach number approaches unity serves to suppress low-frequency rotating instabilities and results in a well-organized flow at the impeller leading edge.

Fig. 7
Fig. 7
Close modal

The suppression of rotating instabilities can be observed explicitly in Fig. 8. Here, the ratio of the power content at sub-blade-pass frequencies to the power of the blade pass frequency is plotted on a logarithmic scale as a function of the isentropic impeller relative Mach number for each of the stable operating points in the compressor map shown in Fig. 3. The power of the signal contained in the sub-blade-pass frequencies is obtained by computing the integral of the square of the amplitude spectrum between 0 and just less than the blade pass frequency. The same is done to calculate the power of the blade pass frequency itself, but the bounds of the integral are placed just above and just below the blade pass frequency. The isentropic impeller relative Mach number is an estimate of the actual relative tip Mach number and is computed from the impeller leading edge tip speed and isentropic Mach number relationship using the leading edge static pressure and inlet housing total pressure.

Fig. 8
Fig. 8
Close modal

From Fig. 8, at 90%, 95%, and 100% corrected speed the ratio of the power in the sub-blade-pass frequencies to the power of the blade pass frequency is 1–2 orders of magnitude smaller than at the subsonic operating conditions. The low-frequency energy level drops off sharply around an isentropic relative Mach number of 0.9 and coincides with the formation of shock structures at the impeller tip. The transition from subsonic to transonic inlet conditions can be observed at 85% as the power ratio rapidly drops from near stall to choke, in agreement with the observations of the frequency content in Figs. 6(d)6(f) as well as the part speed numerical results.

### 6.2 Interpreting the Impeller Leading Edge Temperature Measurements.

Lastly, quantification of the impeller inlet flow field is considered through examination of the air temperature in the impeller leading edge tip region. The air temperature in this region can be used as a proxy for leading edge flow recirculation. At optimum or low values of incidence, flow proceeds through the impeller with little inducer recirculation. However, as the leading edge incidence approaches large values, a portion of the flow that has been worked by the inducer flows backward along the shroud. Due to the work input from the inducer, the temperature of the recirculating air near the shroud is greater than the total temperature at the inlet rating plane, and the ratio of the shroud temperature to the inlet total temperature increases with increasing levels of recirculation.

To evaluate the relative level of impeller tip recirculation, the compressor total pressure ratio map is again shown in Fig. 9. In this presentation of the compressor map, each of the operating points has been colored by the impeller leading edge shroud temperature (Ts1) normalized by the inlet total temperature at station 0 (Tt0; see Fig. 1 for instrumentation locations). In the subsonic operating range, from 40% to 85% corrected speed, the normalized leading edge temperature increases as loading increases, which implies both the amount of inlet recirculation and the impeller leading edge incidence are also increasing with increased loading. The recirculation is understood to be the source of the broadband, low-frequency energy observed in Figs. 6(a)6(d) near stall at 60% and 85% corrected speed. In contrast, the shroud temperature ratio is low throughout the extent of the transonic and supersonic speedlines from which the level of inlet recirculation is inferred to remain low, as well.

Fig. 9
Fig. 9
Close modal

Computational results were used to confirm the presence of recirculation in the inducer that was inferred from the leading edge temperature measurements. A contour of meridional velocity for the subsonic case at 80% corrected speed is shown in Fig. 10(a), where a large low momentum region is present at the inducer shroud. A similar contour at 100% corrected speed (Fig. 10(b)) confirms that the recirculation region is not present for the supersonic case.

Fig. 10
Fig. 10
Close modal

In a detailed investigation of impeller inlet recirculation in a turbocharger compressor, Schreiber [10] also observed the presence of inlet recirculation along much of the low mass flowrate side of lower speed characteristics. The presence of inlet recirculation contributed to impeller stability, allowing large operating ranges at low speeds. The disappearance of recirculating flow at high speeds coincided with the development of a shock at the impeller leading edge consistent with the behavior documented in the present work. However, the work did not comment on the relationship of the impeller leading edge shock and inlet recirculation in the context of stage stability. Similar observations were made by Dielenschneider et al. [27] and Paul et al. [28].

The remainder of the present work seeks to provide insight into this interaction: how the presence or absence of inlet recirculation or an impeller leading edge shock affects stage stability and surge pathology. The differences in the inlet flow field between the subsonic and supersonic conditions are the origin of the previously discussed differences in surge inception as well as the tolerance/intolerance of the stage to unstable impeller operating points. In concurrence with observations made by Schreiber [10] and He and Zheng [5], the presence of impeller tip recirculation indicates that the impeller can maintain stable operation with large incidence and possibly inducer stall at subsonic tip Mach numbers. At the same time, the recirculating flow leads to a high level of energy in the spectral content of the pressure signals typical of the rotating instabilities as discussed by Day [26] (Figs. 6(a), 6(d), and 8).

## 7 Surge Signature, Static Pressure Characteristics, and Inlet Flow Regime

At subsonic inlet conditions, the rotating instabilities observed in the frequency spectrums shown in Figs. 6(a)6(c) are a result of the impeller inlet recirculation documented in Figs. 9 and 10(a). This connection is supported by the growth of the broadband hump associated with rotating instabilities from choke to near stall and corresponding increasing levels of recirculation in Fig. 9. The inlet recirculation fosters high levels of broadband flow energy around the impeller leading edge at near stall conditions and is likely the origin of global instability: the rotating instabilities associated with the impeller inlet recirculation provide constant background disturbances which increase with decreasing mass flowrate. As the impeller approaches the unstable portions of the static pressure rise characteristics in the subsonic operating range (Fig. 4(b)), the diminishing stability of the impeller allows for nonlinear growth of the rotating instabilities from local disturbances into global flow breakdown.

While the impeller inlet recirculation provides the background disturbance from which the global instability originates, it simultaneously serves as a stabilizing damper in the mass-spring-damper system often used to mathematically model the stability of a compression system [5,23,29]. Inlet recirculation arises as shown in Fig. 9 or the contour in Fig. 10(b) and is usually axisymmetric [10,30]. The presence of recirculation inherently creates aerodynamic blockage at the inducer tip. The amount of recirculation, and correspondingly blockage, increases with decreasing mass flowrate as shown at the subsonic operating conditions in Fig. 9 and documented by Harley et al. [30] and Schreiber [10]. The presence of the inlet recirculation induces a positive swirl component at the inducer tip and, by the nature of aerodynamic blockage, reduces the flow area at the impeller leading edge. Due to the reduced flow area, the bulk flow entering the impeller outside the recirculating tip region does so at a reduced incidence relative to a case where no blockage is present. Thus, the recirculation stabilizes the impeller by creating more favorable incidence conditions at low mass flowrates [10]. Moreover, the recirculation not only adjusts to provide stability and favorable incidences at different operating points but also serves to dampen local flow disturbances. When operating near instability, the recirculation region acts as a “cushion” which dynamically grows and shrinks to compensate for transient restrictions in the local mass flowrate due to rotating instabilities.

The damping property of the recirculation gives insight into the isolated surge events at subsonic conditions. When the compressor operating point is near the unstable portion of the characteristic yet maintaining stable operation, such as the last stable operating point at 85% speed where the slope of stage static pressure rise characteristic is slightly negative (Fig. 4(a)), the low-frequency disturbances may periodically surpass the threshold at which the damping properties of the system are unable to compensate for the instability of the overall stage. The inlet recirculation reaches a level where the increased disturbances outweigh the damping, and the stability of the diffuser is also decreasing as evidenced by the flattening of the static pressure rise coefficient. In this case, the instability grows nonlinearly into a global disturbance. When isolated surge events occurred, the compressor was at an operating condition at which the disturbance threshold only occasionally exceeded the damping properties of the inlet recirculation. Further throttling would result in increased amplitudes of the broadband rotating instabilities (also associated with the inlet recirculation) which are too large to be damped by the recirculating inlet flow, and consequently, rapid, repeating surge events. The impeller inlet recirculation is therefore critical to the stage stability at subsonic impeller tip relative Mach numbers: it provides a damping mechanism that extends the overall range of each speedline by inducing favorable incidence conditions yet is also the source of the rotating instabilities which induce surge.

At transonic inlet conditions, the positively sloped stage static pressure rise coefficient (Fig. 4(a)) and the frequency content during the revolutions prior to surge (reported in Part I) together confirm that modal waves lead to the inception of a mild surge event. The frequency of the modal waves in the present work is a greater fraction of the shaft frequency (∼0.7 engine order) than what is typically reported (less than 0.4 engine order) [1,31]. The development of mild surge just out of choke in the transonic operating range is similar to the behavior documented by He and Zheng [5] and Sun et al. [6]. Additionally, in agreement with Schreiber’s study [10], the extension of the impeller leading edge shock across the impeller passage (Fig. 7) severely restricts, if not eliminates, the presence of impeller inlet recirculation (Fig. 10). Synthesizing the observations in the present work with that of other researchers, it is likely that the mild surge disturbance at 90% speed disrupts the impeller leading edge shock. As the shock dissipates due to growth of the disturbance (Fig. 10 in Part I), impeller inlet recirculation is no longer prevented by a discontinuity in the flow field. Impeller inlet recirculation resumes in conjunction with interruption of the leading edge shock structure and results in a brief period of increased blockage and positive swirl at the impeller tip associated with the inlet recirculation [10]. Corresponding to the increased blockage, incidence is reduced along the remainder of the blade span where bulk flow is not blocked by the recirculation region. The favorable incidence condition allows the impeller to regain stability, and as the mild surge disturbance dissipates the leading edge shock reappears. The mild surge cycle then repeats. During this process in the impeller, the fluctuations in bulk flowrate extend into the diffuser. However, the diffuser is operating at a highly stable condition as evidenced by the steep negative slope of the static pressure rise characteristic (Figs. 4(c) and 5(e)) at 90% speed, and the diffuser provides an anchor of stability for the stage, preventing the impeller from driving the system into deep surge. The interaction of the impeller inlet recirculation and inducer leading edge shock is likely the cause of the “kink” in the surge line often observed in high-speed centrifugal compressors as well as the mild surge events that occur just beyond choke at transonic operating conditions [4,5,8].

At supersonic impeller tip relative Mach numbers, inlet recirculation is all but eliminated by the discontinuity of the leading edge shock (Figs. 9 and 10). The removal of inlet recirculation and strengthening of the inducer shock correspond to suppression of rotating instabilities at the impeller leading edge; the perturbations in the flow field are both fewer and smaller without the presence of recirculation. The result is a clean, structured flow field that is beneficial to stability of the compressor stage.

While the loss of inlet recirculation reduces the disturbances associated with rotating instabilities, it also means removal of a major damping component in the mass-spring-damper representation of the compression system. The loss of the damping properties of the inlet recirculation is quantified by the component static pressure rise coefficients in Figs. 4(b), 5(b), and 5(c). As the level of inlet recirculation decreases at the high mass flowrate side of the 85% speedline and is nearly eliminated at 90% speed and above (Figs. 8 and 9), the slopes of the static pressure rise characteristics become increasingly positive indicating instability in the components—i.e., loss of damping. Due to the removal of the damping properties of inlet recirculation, a relatively minor disturbance in the flow field can rapidly destabilize the entire compression system at supersonic tip relative Mach numbers (such as the spike in Fig. 6, Part I) despite the strongly stabilizing traits of the vaned diffuser (Fig. 4(c)). Furthermore, the development of the spike at the impeller leading edge, in conjunction with positively sloped impeller static pressure characteristics in Fig. 4(b), establishes that the impeller is the origin of instability at the supersonic speedlines.

The rapid succession of surge events, in contrast to the isolated surge events at low speeds, is also explained both by the organization of the flow field and reduced damping. The backflow process associated with surge destroys the structure of the inlet flow field, and the structure is not restored during the recovery period of the surge cycle. Without the damping properties of the inlet recirculation to absorb transient disturbances, the stage cannot support operation on the unstable side of the characteristic without reestablishment of the pre-surge inlet flow field. Therefore, the compressor surges repeatedly without attaining stable operation at any point in the surge cycle until the throttle valve is opened.

The presence of the leading edge shock also is a major contributor to the narrowing operating ranges at supersonic tip relative Mach numbers. Since the shock is present across the entirety of the speedlines at supersonic tip relative Mach numbers, the level of recirculation remains nearly constant from choke to stall (Fig. 9). As such, the blockage associated with inlet recirculation is also constant, and the effective aerodynamic flow area does not decrease from choke to stall. Therefore, unfavorable, high incidence conditions are encountered much more rapidly than at subsonic operation where inlet recirculation enables dynamic adjustment of the effective flow area. Ultimately, the lack of inlet recirculation at supersonic tip relative Mach numbers results in narrower operating ranges.

The net result of the impeller leading edge shock and near elimination of inlet recirculation cannot be described as either strictly beneficial or detrimental in terms of impact on stage stability. However, understanding the interacting physical phenomena is critical to the success of high-speed centrifugal compressor designs. The impeller is inherently less stable at supersonic operating conditions without the presence of inlet recirculation to damp flow disturbances. Simultaneously, the suppression of rotating instabilities by the leading edge shock reduces broadband flow energy, and the impeller can maintain stable operation with reduced damping because there are fewer, smaller perturbations from which global instability may initiate. Finally, suppression of inlet recirculation by the leading edge shock prevents dynamic adjustment of the effective inlet area and incidence resulting in diminished operating range at high speeds.

## 8 Conclusions

In this two-part paper, surge signatures from a transonic centrifugal compressor, together with its component and subcomponent static pressure characteristics, are investigated within an operating envelope from 40% to 100% corrected speed. Experiments were performed in the SSCC facility at Purdue University 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 of values for centrifugal compressors in turbochargers and small aeroengines.

Results show the presence of both modal- and spike-type surge on the compressor map, where modal-type surge occurs at 90% corrected speed and spike-type surge dominates all other speeds. The spike-type surge signature varies with the regime of the impeller tip relative Mach number. At subsonic impeller inlet tip conditions, compressor surge is induced by a compound effect from impeller and the diffuser passage. While the vaneless space is in stable operation, both the impeller and the diffuser passage experience a local flow breakdown which quickly brings the entire compression system into surge. At supersonic impeller inlet tip conditions, 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. Since instability may originate in either the impeller or diffuser, application of range extension techniques to multiple components may be necessary to achieve range extension through the compressor map for high-speed centrifugal compressors.

Furthermore, the relationships between the surge mechanism, static pressure rise characteristic, impeller leading edge tip relative Mach number, and inlet recirculation were examined with experimental and computational data. The surge mechanism observed in the present study follows the criterion provided by Camp and Day [1] for axial compressors where spike-type disturbances tend to dominate for compressors experiencing instability on the negatively sloped side of static pressure rise characteristic, and modal waves exist prior to instability if the compressor stalls on the positive slope of the characteristic.

The presence or absence of inlet tip recirculation is shown to be critical to the impeller, and by extension stage, stability. At subsonic impeller tip relative Mach numbers, inlet recirculation damps transient disturbances associated with rotating instabilities. The perturbations grow with decreasing mass flowrate until they become large enough to overcome the damping effects of the recirculation and global instability is encountered. Inlet recirculation is drastically reduced, if not eliminated, by the discontinuity of an impeller leading edge shock at supersonic impeller tip relative Mach numbers. The associated broadband disturbances associated with inlet recirculation are also removed, and the resulting organized inlet flow is beneficial for stability. However, removal of inlet recirculation also entails loss of the damping properties of the recirculation region at the impeller leading edge. The loss of damping is both in terms of dynamic damping of small transient disturbances as well as bulk adjustment of the flow at different operating conditions via blockage to provide more favorable incidence at the inducer. The increased instability of the impeller due to the loss of inlet recirculation can be observed in the more positively sloped static pressure rise characteristics at supersonic impeller tip relative Mach numbers.

The interaction of the inducer leading edge shock and impeller inlet recirculation was shown to be the cause of the “kink” in the surge line often observed in high-speed centrifugal compressors due to mild surge events that occur at transonic impeller tip relative Mach numbers [4,5,8]. Modal waves develop as the stage nears the mild surge condition which interrupts the incipient shock formation at the impeller leading edge. As the shock formation is disrupted, recirculation is reasserted along the impeller shroud, and the recirculation damps the growing disturbances before global backflow. The stage then temporarily reattains stable operation, and the process repeats. During the mild surge cycles, the diffuser stabilizes the system which prevents global instability.

Finally, the analysis of the steady static pressure rise characteristics showed the potential of using stage and component characteristics in predicting surge mechanisms as well as the destabilizing component. The loss of the damping effect of inlet recirculation at supersonic impeller tip relative Mach numbers can be explicitly observed and quantified by the change in shape and slope of the impeller, inducer, and exducer characteristics. Static pressure characteristics coupled with knowledge of the impeller inlet conditions may be used to explore effective surge suppression techniques, circumvent impeller instability at transonic operating speeds, and extend a centrifugal compressor’s operating range throughout the compressor map.

## 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 in data interpretation. The authors would also like to thank Mr. Matthew Fuehne at the Purdue Compressor Research Laboratory for his 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

• $m˙$ =

mass flowrate

•
• D =

diameter

•
• P =

pressure

•
• $P¯$ =

power

•
• T =

temperature

•
• U =

wheel speed

•
• Nc =

corrected speed

•
• ρ =

density

•
• Φ =

flow coefficient

•
• Ψ =

pressure rise coefficient

### Subscripts

• 0 =

housing inlet

•
• 1 =

impeller inlet

•
• 2 =

impeller exit

•
• 3 =

diffuser inlet

•
• 4 =

diffuser throat

•
• 5 =

diffuser exit

•
• 6 =

deswirl exit

•
• s =

static

•
• t =

stagnation properties

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