A statistical approach to the analysis of the surge phenomenon

Energy 124 (2017) 502e509

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A statistical approach to the analysis of the surge phenomenon R. Bontempo, M. Cardone, M. Manna*, G. Vorraro
degli Studi di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy Dipartimento di Ingegneria Industriale, Universita

a r t i c l e i n f o

a b s t r a c t

Article history: Received 24 March 2016 Received in revised form 16 January 2017 Accepted 6 February 2017 Available online 10 February 2017

The paper presents an innovative data processing methodology for the analysis of the surge phenomenon occurring in a compressor. Since the dynamic of the surge cycle does not have a deterministic character, its proper description can only be obtained through a statistical approach. To this aim, the temporally resolved traces of the pressure and mass flow rate signals are processed through a phase averaged decomposition technique. Furthermore, the shape of the oscillating surge cycle is detected and quantified by introducing the joint probability density function of the aforementioned signals which are reported in the pressure ratio versus mass flow rate plane. This probabilistic approach offers two significant advantages over the conventional deterministic approach, namely the possibility to quantify the time of residence of all individual unstable states in a statistical sense, as well as the possibility to carry out a proper code-to-experiments or experiments-to-experiments comparison of such an unstable phenomenon. In this paper, the proposed statistical approach is used to process the experimental data related to the surge phenomenon occurring in a small-sized free spool centrifugal compressor for automotive applications. However, the methodology can be applied both to numerical and experimental surge data from either centrifugal or axial compressors. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Surge Compressor Turbocharger Turbocharger test rig

1. Introduction Nowadays, the reduction of the engine displacement is one of the most widespread and successful technique used to reduce the fuel consumption and the pollutant emissions of internal combustion engines (ICE). However, in order to preserve or even augment the delivered power, the ICE has to be charged, for example through a turbocharger (TC) [1e5]. In such a way the intake air density, the mass flow rate and consequently the power output are raised while retaining a small engine size. Further combustion advantages can be gained by turbocharging the ICE, such as an improved fuel atomization process [6] and a shorter fuel jet penetration length [7]. In spite of the aforementioned benefits, some drawbacks also exist. First of all, there are a few well-known shortcomings associated to the poor quality of the transient response of turbocharged engines [8e11]. These problems are mainly associated to the mechanical inertia of the TC which induces significant delays in the charging effect during those maneuvers requiring a rapid increase of the delivered power. Another

* Corresponding author. E-mail address: [email protected] (M. Manna). http://dx.doi.org/10.1016/j.energy.2017.02.026 0360-5442/© 2017 Elsevier Ltd. All rights reserved.

drawback can be caused by the occurrence of the critical surge phenomenon. Operating the compressor in surge regimes is not at all recommendable since it induces a significant drop down in the compressor efficiency, a probable failure of the TC mechanical components, undesirable noise, and, finally, a reduction of the vehicle driveability due to the oscillating power output. From the previous considerations, it is clearly understood that a proper characterization of the TC operating in the unstable surge regime is very important. This is witnessed by the large amount of research papers dealing with this issue. For instance, in Ref. [12] the authors described a test bench specifically designed for the characterisation of automotive TCs and used it to define a sound criterion for the surge limit definition. An experimental investigation of the effects of an inlet swirl generator to enlarge the surge margin is reported in Ref. [13]. Galindo et al. [14] developed a surge model in which the fluid inertia effects are taken into account. The model is validated against data measured in a specifically designed facility. Andersen et al. [15] proposed a standardized measurement setup for the definition of the compressor surge limit. The effects of a pulsating flow at the compressor outlet are analysed in Ref. [16] by experimental means. Specifically, the effects of the amplitude and frequency of the pressure oscillations upon the surge line have been described. The authors found that, for the typical frequencies

R. Bontempo et al. / Energy 124 (2017) 502e509

Nomenclature f f0 fs m_

frequency fundamental frequency sampling frequency mass flow rate

m_ N Nc NDS Ns Ns;T p pm; _ p Pr S T

long time averaged mass flow rate rotational speed number of surge cycle number of samples falling in a grid cell total number of samples number of samples in a surge cycle static pressure probability density function probability _ pÞ subset of the plane ðm; period of a surge cycle

Greek symbols pressure ratio long time averaged pressure ratio

p p

characterising the pulsating flow in turbocharged engines, a surge margin enhancement is possible. Guillou et al. [17] carried out PIV measurements in the proximity of the centrifugal compressor (CC) inlet, both in stable and unstable regimes. In Ref. [18] a properly designed test bench is used to point out the dependence of the surge margin from the piping configuration upstream and downstream a CC. Finally, the design and prototyping of a new highly flexible hot gas generation system is reported in Ref. [19], while in Ref. [20] the collected experimental data are manipulated to estimate the effect of the thermal losses on the compressor efficiency, and to analyse the surge phenomenon. As proven by the above literature review, up to now the surge phenomenon has always been studied through a deterministic approach based on the single cycle characterisation. Conversely, in this paper a new and more advanced data processing methodology is proposed. In more detail, based on the fact that the surge cycle is not deterministic in nature, the analysis is conducted through an original statistical approach relying on the processing of the temporally resolved traces of the pressure and mass flow rate signals. The statistical description of the phenomenon is two-fold. Firstly, a spectral analysis of the collected signals is carried out in order to build the phase locked averaged quantities offering the appealing opportunity to properly characterise the intrinsic surge unsteadiness. Secondly, the shape of the oscillating surge cycles set is detected and quantified by introducing the joint probability density function of the aforementioned signals which are reported _ plane. This stain the pressure ratio (p) versus mass flow rate (m) tistical approach, which as far as we are aware has never been proposed before, allows to quantify the time of residence of all individual unstable states, an information of the utmost importance for the evaluation of the global aerodynamic loads affecting the rotor dynamics. It further offers the possibility to compare, in a quantitative fashion, calculations with experiments and/or experiments with experiments, a task that can not be properly accomplished using a conventional deterministic approach based on the single cycle characterisation. In fact, because of the intrinsic chaotic nature of the surge phenomenon, measurements based on a single cycle (or few cycles) realization do not allow to properly validate surge models. Similar drawbacks arise when comparing results of

f

〈f〉 ~ f f 0 f DS

503

generic quantity phase averaged quantity modulation long time averaged quantity perturbation area of the grid cell

Subscripts D delivery ref reference quantity S suction Acronyms BST best straight line CC centrifugal compressor FFT fast Fourier transform FS full scale FSO full scale output ICE internal combustion engine PDF probability density function TC turbocharger

different experimental campaigns using a conventional deterministic approach. Instead, processing the data with statistical tools, like the phase-average technique and the joint probability density function, offers the possibility to take advantage of the information buried in a large number of surge cycles, each of which has stochastic character. By so doing, a more reliable representation of this complex phenomenon is attained. Therefore, new or existing surge models are more exhaustively validated through the phaseaveraged surge cycle and the associated probability density function. The same is true if the results of different experimental campaigns have to be compared. In this paper, the proposed processing strategy is applied to study the surge phenomenon in a small-sized free spool CC for automotive applications. The study is carried out by a specifically designed test bench, described in section 2, which has been equipped with fast response pressure and mass flow rate sensors. Then, the main features of the surge phenomenon are studied by phase-locked averaging the collected signals (see x3.1) and by _ pÞ inspecting their joint probability density function in the ðm; plane (see x3.2). Note that, although the proposed methodology has been applied to the experimental study of the surge in a small-sized CC for automotive applications, it can be generally applied to both axial and radial compressors and to experimental and numerical results. 2. Experimental apparatus Fig. 1 shows a schematic view of the experimental apparatus employed to characterize the unsteady behaviour of the tested turbocharger. As shown in this figure, the mass flow delivered by the centrifugal compressor is discharged at ambiance through a backpressure valve which is remotely operated to span the whole characteristic map in a semi-automated manner. The CC is driven by a centripetal turbine which is fed by a hot gas generator consisting of a 2:5 l diesel engine. A Borghi&Saveri FE 350SA eddy current dynamometer is used to operate the engine both in steady and variable rpm regimes. In order to properly span the compressor map, the total amount of exhaust gas is directly sent to the test

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Fig. 1. Schematic description of the test bench layout.

article through a thermally insulated pipe so that the highest enthalpy content is made available at the turbine inlet. This entails that the ICE is no longer turbocharged and thus it has been implemented an external supercharging system (see Ref. [20]) whose main objective is to ensure the largest possible operating envelope to the test article. The TC lubrication is provided by a properly designed closed loop oil circuit consisting of a 5 cc gear pump, a 20 l tank and a remotely controlled valve for the mass flow regulation via a by-pass system. Moreover, a heat exchanger and an heater are used to control and set the appropriate oil temperature value. Finally, all signals are collected and managed through a high speed data acquisition system and real-time controllers. Coming now to the measurement systems, the test article is fully equipped with several pressure, temperature and mass flow rate sensors (see Fig. 1). In particular, the steady state mass flow rate is acquired with a Rosemount 3095 MFA low-frequency response meter equipped with an Annubar primary element sensor (see Table 1 for technical specification). To properly investigate the surge phenomena a pair of two opposite mounted high-frequency response hot-film mass-flow meters Bosch HFM-5 MFA are employed. All temperature measurements are carried out with K-type thermocouples flush mounted on the compressor suction and delivery pipes. Finally, the slow and fast pressure signals are collected through strain gauge piezo-resistive transducers whose technical specifications are

Table 1 Technical specifications of the measuring instruments.

Rosemount 3095MFA Bosch HFM-5 MFA Druck PTX 1400 Druck PTX 1000 Kulite XTEL-190 M

Measurement range

Units Uncertainties Frequency response

[60, 900]

kg=h ±0:9%

[-50, 480] [-1, 1.6] [0, 5] [0, 5]

kg=h barG barG barA

±3:0% ±0:15% BSL ±0:15% BSL ±0:10% FSO BSL

e 100 Hz e e 76 kHz

Fig. 2. Compressor pressure ratio during deep surge: raw and filtered signals.

listed in Table 1. Specifically, the Druck PTX and the Kulite XTEL190 M are used for steady and unsteady pressure measurements, respectively. The pressure signals from the Kulite XTEL-190 M sensors are characterized by a significant level of high frequency background noise, as it can be seen from Figs. 2 and 3. For this reason a properly designed low-pass filter has been adopted to post-process the aforementioned signals. Preliminarily, the pressure and mass flow rate data have been Fourier transformed in order to analyse the energy content of the different frequencies. The FFT results systematically reveal the presence of a dominant frequency in the range 14  18 Hz corresponding to the surge leading frequency, while the second harmonic is in the range 28  36 Hz. For this reason a cutoff frequency of 50 Hz has been considered to be comfortably large to remove the high frequency

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Fig. 3. Spectra of the pressure signals reported in Fig. 2.

noise without compromising the characteristics of the base signal. The adopted filter is of the Butterworth type. This filter has a very flat frequency response in the passband so that it is also referred as a maximally flat magnitude filter. A high order transfer function has been employed to obtain a very high roll-off in the stopband, i.e. a twelfth order function which corresponds to an attenuation of 240 dB per decade. In order to show how the filter works, the raw and filtered signals of the instantaneous pressure ratios in typical surge operation are reported in Fig. 2. The corresponding spectrum, obtained by fast Fourier transforming the discrete data set, is shown in Fig. 3. As it can be easily inferred from the figure, thanks to the flat frequency response of the filter in the passband, the spectra of the two signals are almost identical till the cutoff frequency. Conversely the filter rapidly attenuates all high frequency components because of the high order transfer function adopted. Finally, all signals are routed to a digital acquisition system based on a National Instrument PCI-6133 DAQ and on a cFP-1808 Programmable Automation Controller. A Labview Virtual Instruments code handles in real-time mode all the available data and stores them with a sampling rate that can be defined by the user.

3. Results This section deals with the testing of a small size single stage centrifugal compressor typically employed in diesel engine turbocharging. The steady state performance map of the compressor is presented in Fig. 4 reporting, in dimensionless terms, the pressure _ m_ ref ) for ratio (p=pref ) as a function of the mass flow rate (m= different rotational speed (N=Nref ) of the turbo shaft. All data are classified and therefore they have been normalised. The dashed line denotes the surge line which has been estimated from the occurrence of some unsteadiness in the recorded pressure and mass flow rate signals, and, as such, they are representative of incipient surge conditions. To give some confidence in the quality of the collected data, the measurements uncertainties have been quantified and reported on Fig. 4 through vertical and horizontal errors bars for N=Nref ¼ 1:0. As it can be easily understood with the help of the magnifying window, the effects of the uncertainties on the presented results are very small, that is the shape and

505

Fig. 4. Compressor steady state performance map.

significance of the data is barely altered by them. No significant differences appear for the remaining rpm iso-lines. In the following, two surge states (see Table 2) have been characterised with standard statistical tools. These two surge states have been obtained by simply throttling the back pressure valve starting from the last stable operating point at N=Nref ¼ 0:6 and N=Nref ¼ 1:0, respectively. For this reason, the two states have been respectively named S0.6 and S1.0, where S stands for surge while 0.6 and 1.0 are the turbo shaft normalised rotational speed in the corresponding incipient surge conditions. As reported in Table 2, the long time averaged mass flow and pressure _ m_ ref ; p=pref ) for S0.6 and S1.0 are (0.100,0.688) and ratio pair (m= (0.277,1.057), respectively. These two long time averaged operating points are also reported as triangles in Fig. 4 both for the S0.6 and S1.0 surge states. It is interesting to observe that while at N=Nref ¼ 0:6 the pressure ratio of the surge point is similar to the incipient surge value, it considerably drops at N=Nref ¼ 1. Only these two operating points are analysed because the structural damaging occurring during the unstable cycles limits the extent of the data acquisition time and of the experimental campaign. Moreover, given the scope of the present work, which is focused on an innovative surge data processing methodology, a more extended data set would not bring any additional information. 3.1. Phase averaged analysis In order to investigate the time evolution of the relevant statistics during the surge oscillating period through a phase averaged decomposition technique, the leading frequency f0 of the surge phenomenon has to be evaluated first. To accomplish this task the filtered pressure ratio and mass flow rate signals were Fourier transformed. Figs. 5 and 6 show the frequency spectrum of the normalised pressure ratio and mass flow rate filtered signals relative to the S0.6 and S1.0 surge states. Table 2 Description of the surge states analysed.

S0.6 S1.0

N=Nref

_ m_ ref m=

p=pref

f0 ½Hz

0.6 1.0

0.100 0.277

0.688 1.057

16.5 14

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Before starting the discussion let us observe that the shape of the S0.6 and S1.0 spectra is similar, although they show some scatter that could be smoothed out using the composite spectrum approach. The amplitude difference of about half an order of magnitude for the pressure ratio looks nearly uniform over the whole frequency band. For the mass flow rate, the energy content of both signals is similar at low frequencies (f < 10Hz), while at higher frequencies some differences appear. The normalised pressure ratio (mass flow rate) oscillation amplitude of the leading harmonic increases from 0.027 (0.367) to 0.162 (0.968) moving from S0.6 to S1.0. As it can be easily understood from the aforementioned figures, the mass flow rate and pressure ratio frequency spectra have the same fundamental frequency. Some small size frequency shifts are also appreciable between the S0.6 and S1.0 cases. In agreement with the experimental results reported in Ref. [12], the surge frequency decreases as the rpm increases. Specifically, a drop in the leading frequency f0 from 16 Hz (S0.6) to 14 Hz (S1.0) occurs increasing N=Nref from 0.6 to 1.0. Once the leading surge frequency has been detected, the unsteady characterization of the surge phenomenon can be completed. The sampling frequency fs is set to 1024 Hz. On account of the signals analysis reported in Figs. 5 and 6, the period T of each of the Nc oscillating cycles is set equal to 1=f0 , while the number of samples Ns describing the in-cycle variation is obviously Ns;T ¼ fs T. As reported before, the long-time average of the generic quantity f is denoted with an overline (f) and evaluated through the following relation:

f¼

Ns 1 X fðiÞ; Ns i¼1

(1)

where Ns is total number of samples. The phase averaged quantities will be denoted with angle brackets (〈f〉) and evaluated by means of the following expression:

hfðkÞ i ¼

Nc   1 X f k þ ði  1ÞNs;T for k ¼ 1; …; Ns;T : Nc i¼1 0

(2)

The prime symbol (f ) is used to indicate the deviation of the

_ m_ ref (down) for S0.6 case. Fig. 5. Spectra of p=pref (top) and m=

_ m_ ref (down) for S1.0 case. Fig. 6. Spectra of p=pref (top) and m=

instantaneous values from the phase averaged quantities, i.e.

f’ ¼ f  hfi;

(3)

while the changes within the period, i.e. the modulation in the oscillating cycle, are computed as the difference between phase and long-time averaged quantities 

f ¼ hfi  f:

(4)

_ hpS i, and hpD i within Figs. 7 and 8 show the variation of 〈p〉, 〈m〉, the oscillating cycle. With the proposed phase average approach, all information buried within the Nc surge cycles are put forward and summarised through a single plot. By so doing, a global characterization of a chaotic-like phenomenon can be more properly carried out. In particular, the processed data show that, although all quantities

Fig. 7. Phase average of the collected signals (S0.6).

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507

dispersion, can be reduced to a single deterministic curve, which can be properly used for experiments-to-experiments or code-toexperiments validation. For the sake of clarity, the compressor steady-state map (see Fig. 4) has also been reported. Once again, the two upper triangles _ m_ ref ; p=pref Þ of the surge represent the long time average values ðm=

Fig. 8. Phase average of the collected signals (S1.0).

have a similar oscillating pattern with identical fundamental frequency, some differences appear in terms of signal amplitude and phase. First of all, the m_ and p phase averaged signals seem to be almost in-phase, while pS and m_ are in quadrature. Moreover, the outlet static pressure pD traces are characterised by a lower phase shift in comparison with the mass flow rate. In terms of signal amplitude, the data clearly show that the static pressure oscillation at the compressor outlet is greater than that at the inlet, especially for high rpm values. In more detail, the hpS i=pref oscillation is roughly equal to 0.1 (resp. 0.2) for the S0.6 case, while the static pressure oscillation at the outlet grows up to z0:2 (resp. 0.9). All amplitudes become greater as the rpm increase. For example, the mass flow rate oscillation doubles moving from S0.6 to S1.0, while the hp=pref i oscillation increases from z0:6 to z1:5. A very interesting representation of the surge phenomenon can _ pÞ plane. Fig. 9 shows the phasealso be obtained in the ðm; averaged surge orbits for both S0.6 and S1.0 cases. Once more, the several individual orbits characterised by a remarkable

_ pÞ plane. Fig. 9. Phase average quantities in the ðm;

cycles. As can be seen, in the S1.0 case, the long time average is located outside the surge orbit. This is because, as shown in the next subsection, the time of residence of the surge points in the _ pÞ area. _ pÞ region is greater than that in the low ðm; high ðm; Although the scope of this paper is to present a general data processing procedure which can be applied to both numerical and experimental results, an analysis of the measurement errors propagation in the phase averaging process has also been carried out, to gain some confidence on the quality of the collected data. The analysis is based on the assumption of independent and random uncertainties. In Fig. 9, the uncertainties have been represented through classical horizontal and vertical error bars just for few surge points. A magnifying window has also been introduced for the sake of clarity. As can be easily understood, the effects of the measurements uncertainties on the presented results are very small in the whole measurement range. Fig. 10 reports the modulation of the pressure ratio versus the modulation of the mass flow rate for all cases detailed in Table 2. It can be appreciated that the span of the mass flow rate S0.6 case is nearly 800% of the long time averaged value. In other words the maximum positive and minimum negative mass flow rates, which are roughly speaking equal, differ from m_ by nearly ±400%. On the other side, the pressure ratio shows a reduced cycling variation adding up to z 10% in a global sense (largest minus smallest value). Increasing the rpm from 60% to 100% of the reference velocity induces a considerable variation in the pressure ratio modulations (see Fig. 10), a result that agrees well with those reported in Ref. [12]. Specifically, p and m_ vary in the range [-15%,20%] and [-500%,300%], respectively. 3.2. Joint probability density function analysis A further insight into the main features of the surge

Fig. 10. Modulation of the mass flow rate and of the pressure ratio.

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phenomenon can be gained representing the time variation of the _ p) plane. To this aim it is operating point on the characteristic (m; convenient to introduce the joint probability density function _ pÞ defined such that the probability of the compressor pm; _ p ðm; _ pÞ plane is operating point to fall in the subset S of the ðm;

Z PrðSÞ ¼

_ pÞdm_ dp: pm; _ p ðm;

(5)

S

The discrete equivalent of (5) is computed with the help of a two _ pÞ plane. Then the dimensional background grid covering the ðm; discrete joint probability density function is evaluated from the number of samples NDS falling into each cell of area DS ¼ Dm_ Dp. The discrete joint probability density function (PDF) is simply the ratio NDS =Ns divided by DS. Figs. 11 and 12 show the shaded con_ pÞ=maxfpm; _ pÞg for the surge tours of the function pm; _ p ðm; _ p ðm; states, S0.6 and S1.0, respectively. We begin the analysis from the deep surge S0.6 case shown in Fig. 11. Firstly the PDF has a clear asymmetric ring-like shape with a large inner area with nearly zero joint PDF values. This means that _ pÞ pairs falling into this region are unlike to appear during those ðm; the oscillation cycle. Moreover, the tight shape of the grey stripe reveals a strong statistically coherence of the surge cycle signal with a clear tendency towards negative flow rate values and small pressure ratios (see the dark region around (0.35,0.66)). Incidentally, let us note that the darker area corresponds to a longer time of residence, which has to be considered as a feature of the whole data set rather than that of a single cycle. Looking now to the positive flow rate range, the PDF contours have a clear double pressure ratio path in this zone. The lower branch of this path corresponds to increasing flow rates, while the upper one, which is also characterised by a sudden pressure ratio drop near m_ ¼ 0, corresponds to decreasing flow rates. The shape of this loop is related to the dynamical phenomena occurring in the compressor and in the circuit. The PDF of the S1.0 case, shown in Fig. 12, is even more interesting. The surge cycle signature is very neat on the positive flow rates half-plane and characterised by a rather complex shape with a fairly large extent. On the negative flow rates side the joint PDF

Fig. 12. Normalised joint probability density function for S1.0 case (scale up of Fig. 4).

contours are more smeared, and, unlike the S0.6 case, the most likely events appear to be those occurring at the highest pressure ratios. More than half of these states take place beyond the incipient surge line and there are formidable coherent variations of the measured quantities. Overall, this cycle is ridden counter-clockwise and two sudden pressure ratio variations are seen to occur on the positive flow rate branches. Again the particular shape of the loop is dictated by the previously mentioned dynamical effects. Unlike the S0.6 case, there seem to be a clear tendency towards positive flow rates values with high pressure ratios (see the dark region around (1.0,1.25)). Here the dark area, corresponding to longer time of residence, is characterised by the largest m_ and p values at the right hand of the surge limit line.

4. Conclusions

Fig. 11. Normalised joint probability density function for S0.6 case (scale up of Fig. 4).

The paper has presented a new statistical approach to the study of the surge phenomenon. The proposed methodology has been applied to analyse the unsteady flow characteristics of a free spool centrifugal compressor operated under surge flow conditions. The analysis, based on a set of experimental data acquired with high frequency response transducers, has been carried out on a highly flexible turbocharger test bench consisting of a hot gas generator feeding the test section. The rig offers the possibility to easily drive the compressor into surge by operating a backpressure valve located on the delivery branch of the compressor piping. Preliminarily, the stable operating points have been determined. After that, two unstable regimes have been investigated at two rotational speeds. These regimes have been qualified with the help of standard statistical tools. Specifically, pressure ratio and mass flow rate signals were processed to determine the dominant oscillating frequency used to carry out a phase averaged decomposition. To this aim the fundamental frequency f0 of the surge phenomenon has been evaluated first, processing the signals of the fast response pressure and mass flow rate transducers. The associated spectral analysis of the signals also allowed to ascertain the effect of the rotational speed on the fundamental frequency shift. The unstable states were characterised in terms of the modulations, that is, the deviation of the phase lock averaged quantities from the long time

R. Bontempo et al. / Energy 124 (2017) 502e509

average of the pressure ratio and mass flow rates in phase space. All analysed cases exhibited huge mass flow rates variations with moderate pressure ratio changes. Moreover, the effect of the compressor rotational speed has been documented to be impressive. In fact, the overall variation of the phase-averaged mass flow rate increased by a factor three, increasing the compressor rpm from 66% to 100% of the reference velocity. Furthermore, the incycle variation occurring under surge regimes have been quanti_ pÞ operating fied with the help of a probabilistic approach in the ðm; plane. The analysis has allowed the identification of the most likely to occur instantaneous states in the unstable envelope. The two deep surge regimes were documented to be characterised by longer time of residences in different quadrants of the characteristic plane, a fact that has a major impact on the shape of the anomalous aerodynamic load applied to the rotor. Acknowledgements The technical contribution provided by Rosario Moreschi to process the experimental data is greatly acknowledged. Salvatore De Cristofaro and Gennaro Stingo provided a tangible support to assemble the rig components.

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