applied sciences

Article A Study on the Stall Detection of an Axial through Analysis

Haoying Chen 1,† ID , Fengyong Sun 2,†, Haibo Zhang 2,* and Wei Luo 1,† 1 Jiangsu Province Key Laboratory of Power System, College of and Power Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing 210016, China; [email protected] (H.C.); [email protected] (W.L.) 2 AVIC Aero-engine Control System Institute, No. 792 Liangxi Road, Wuxi 214000, China; [email protected] * Correspondence: [email protected] † These authors contributed equally to this work.

Received: 5 June 2017; Accepted: 22 July 2017; Published: 28 July 2017

Abstract: In order to research the inherent working laws of nearing stall state, a series of compressor experiments are conducted. With the help of fast Fourier transform, the amplitude–frequency characteristics of at the compressor inlet, outlet and blade tip region outlet are analyzed. Meanwhile, devices imitating inlet distortion were applied in the compressor inlet distortion disturbance. The experimental results indicated that compressor blade tip region pressure showed a better performance than the compressor’s inlet and outlet pressures in regards to describing compressor characteristics. What’s more, compressor inlet distortion always disturbed the compressor pressure characteristics. Whether with inlet distortion or not, the pressure characteristics of pressure periodicity and amplitude frequency could always be maintained in compressor blade tip pressure. For the sake of compressor real-time stall detection application, a detection algorithm is proposed to calculate the compressor pressure correlation coefficient. The algorithm also showed a good monotonicity in describing the relationship between the compressor surge margin and the pressure correlation coefficient.

Keywords: stall state; inlet distortion; pressure characteristics; detection algorithm

1. Introduction With the expansion of the advanced envelope, aero propulsion has put forward higher requirements for the performance and stability of compressors. During aircraft super maneuver operation processes, compressor inlet conditions badly deteriorate. The worsening inlet airflow could shrink compressor surge margins and lead the compressor to rotating stall and surge. Meanwhile, compressor stall and surge are the main influencing factors that cause inherent aerodynamic instabilities in the compressor operational envelope [1,2]. A large number of studies have been carried out on the model of surge and rotational stall. Due to their complexity, it is difficult to establish an accurate real-time mathematical model. At present, most research is aimed at single compressor parts. In 1980s, the United States carried out computer simulation research of the whole engine surge, and published a research report [3,4]. Also, a NASA report pointed out that the T700 engine adopts active stability control to control the compressor, but the technical details are unknown [5]. Wadia identified the same problem [6,7]. As is well known, the compressor characteristics map of pressure ratio versus mass flow rate could reflect the compressor working performance. In other words, the inlet pressure and outlet pressure of the compressor could reflect compressor performance, to a certain extent. In order to investigate the relationship between the compressor pressure and performance, the study of the compressor requires massive numerical simulations and experiments [8,9].

Appl. Sci. 2017, 7, 766; doi:10.3390/app7080766 www.mdpi.com/journal/applsci Appl. Sci. 2017, 7, 766 2 of 14

As the pressures are easily observed or have been stored in other engine control sub-systems, pressures monitored at the inlet and outlet of the compressor are apparently the first choices for compressor performance analysis. In fact, inlet and outlet pressures on the compressor have played an important role in the engine and nozzle throat area control system. However, the compressor’s inlet pressure is easily disturbed by the inlet air conditions, such as compressor inlet distortion. As a result, the application of compressor potential performance needs more accurate estimations of compressor surge margins. Traditional compressor safety protections are restricted in the compressor potential performance application. Therefore, studies on the information at compressor blade tip region, including pressure, have been gradually emphasized. The references written by Li, Shi and Brand [10–12] researched the working principal of compressor blade tip performance, which is difficult to apply in the engine compressor control system. The references written by Dhingra, Liu and White [13–15] studied the pressures at the compressor blade tip region, and found some interesting laws about the relationship between blade tip pressures and compressor surge margin. Nevertheless, compressor inlet distortion disturbances are neglected, which the papers written by Dong, Lesser, Seo and Gunn [16–19] verified are significant impact factors in the compressor working performance. In this paper, the research is focused on estimating compressor stability through examining the compressor pressure signals under different compressor inlet aerodynamic conditions, including inlet distortion influences. A series of experiments were conducted to research the laws that affect how the compressor inherently works near stall state. The experiments approached the compressor from normal operating state to near stall state by controlling the flow of the compressor, while at the same time simulating the compressor’s inlet distortion flow field. In order to discover the stability boundary of the compressor, the experiments measured the total pressure at the inlet and outlet of compressor under different speeds, and forced surge tests. In addition, the experiments also captured the compressor surge boundary under the condition of inlet distortion. Experiments on inlet-forced surge tests were conducted by adding a distortion simulator to the inlet section of the compressor. There are two kinds of distortion simulators used in these experiments. One simulated 90 degrees of a circumferential sole distortion device, and the other is 90 degrees of circumferential symmetrical distortion device. The fast Fourier transform (FFT) method enabled the comparison of inlet conditions, as well as the analysis of compressor inlet pressure, outlet pressure and blade tip region pressure. The compressor pressure amplitude–frequency characteristics were discussed with the FFT method [20,21]. At last, a new compressor stall detection is proposed, and blade tip region pressure is applied with the algorithm. In the first section of this paper, the experiment facility and process will be briefly introduced. Then, FFT method principals are mentioned, and the pressures collected in the experiments are analyzed. Finally, a compressor pressure signal analysis algorithm is proposed and applied to compressor stability analysis.

2. Compressor Experiment Facilities The compressor experiments were conducted within the low speed compressor facilities of Nanjing University of Aeronautics and Astronautics. Different compressor working conditions were realized with the auxiliary of an air mass flow control valve. In the case of given compressor revolutions per minute (RPM), the compressor’s geometric structure and the actuating mechanism of the control system are fixed during the experiments. As the airflow control valve turns down, working conditions get closer to the surge limit line for the compressor. Revolutions of 600 RPM, 800 RPM, and 1000 RPM are separately experimented under three inlet conditions. The inlet conditions are: without inlet distortion, with sole inlet distortion, and with symmetrical inlet distortion. Figure1 shows the compressor experiment facility structure. It mainly contains four parts: the air inlet unit, the compressor body, the air outlet unit, and control devices. On the inner wall of the compressor, three sensors are separately arranged at the compressor inlet on the first level of the compressor rotor and outlet, which are both marked as “9” in Figure1. These sensors are used to judge Appl. Sci. 2017, 7, 766 3 of 14

Appl. Sci. 2017, 7, 766 3 of 14 compressorAppl. Sci. 2017 stall, 7, and766 measure compressor pressure signals. In order to reduce the sensor installation3 of 14 volume,compressor the sensors rotor areand embedded outlet, which directly are both into marked the probe as “9” head. in Figure 1. These sensors are used to compressorjudgeThe signal compressor rotor measurement and stall outlet, and system measurewhich are in compressor theseboth marked experiments pressure as “9” signals.includesin Figure In steady 1.order These to state sensors reduce measurement arethe used sensor to and dynamicjudgeinstallation measurement.compressor volume, stall the The andsensors steadymeasure are embedded state compressor measuring directly pressure systeminto thesignals. probe includes In head. order a rotation to reduce speed the measuringsensor instrument,installationThe asignal pressure-measuring volume, measurement the sensors system are system, embedded in these a steady experidirectly pressurements into theincludes probe,probe steady head. and a state signal measurement storage processor, and dynamicThe signalmeasurement. measurement The steady system state in these measuring experiments system includes includes steady a rotation state measurementspeed measuring and which is mainly used to get steady compressor pressure signals under different inlet conditions. dynamicinstrument, measurement. a pressure-measuring The steady system, state measuringa steady pressure system probe,includes and a arotation signal storagespeed measuringprocessor, The total of pressure-measuring points are set in the compressor inlet and outlet. The dynamic instrument,which is mainly a pressure-measuring used to get steady system,compressor a steady pressure pressure signals probe, under and different a signal inlet storage conditions. processor, The measuringwhichtotal of is pressure-measuring system mainly includesused to get a steadypoints dynamic arecompressor set pressure-measuring in the pressure compressor signals inlet instrument, under and outlet. different a The dynamic inlet dynamic conditions. pressure measuring The sensor, and atotalsystem signal of pressure-measuringincludes storage a processor, dynamic pressure-measuringpoints which are is mainlyset in the used compressorinst torument, obtain inlet a adynamic dynamic and outlet. pressure pressure The dynamicsensor, signal and measuring and a signal judge the compressorsystemstorage includes stall.processor, The a dynamic dynamicwhich ispressure-measuring pressure-measuringmainly used to obinsttainrument, points a dynamic area dynamic set inpressure the pressure compressor signal sensor, and inlet,and judge a outletsignal the and the compressorstoragecompressor processor, stall. first The stage. which dynamic In is these mainly pressu experiments, re-measuringused to ob thetain points Programmable a dynamic are set in pressurethe Quad compressor Bridgesignal inlet,and Amplifier outletjudge and (PQBA)the signal-acquisitioncompressorthe compressor stall. modulefirst The stage. dynamic of In the these pressu LMS experiments,re-measuring signal acquisition the points Programmable systemare set in is theQuad adopted. compressor Bridge The Amplifier inlet, highest outlet (PQBA) sampling and frequencythesignal-acquisition compressor of the LMS first module stage. dynamic Inof thesethe signal LMS experiments, acquisitionsignal acquisition the systemProgrammable system can getis Quadadopted. up toBridge 200The kHz,Amplifierhighest and sampling (PQBA) the digital analoguesignal-acquisitionfrequency conversion of the LMS accuracymodule dynamic of is the 16 signal bit.LMS The signalacquisition dynamic acquisition system pressure-measuring system can get is adopted.up to 200 instruments The kHz, highest and adoptedthe sampling digital in this test arefrequencyanalogue Copal conversion Electronicsof the LMS accuracy Companydynamic is 16signal P-2000bit. The acquisition dynamicdynamic systempressure-measuring pressure can sensors. get up to instruments 200 kHz, and adopted the digital in this analoguetest are Copal conversion Electronics accuracy Company is 16 bit. P-2000 The dynadynamicmic pressure-measuring pressure sensors. instruments adopted in this test are Copal Electronics Company P-2000 dynamic pressure sensors.

Figure 1. Compressor experiment facility. Figure 1. Compressor experiment facility. Figure 1. Compressor experiment facility. In order to simulate the inlet distortion that happens in super maneuverability flight or other air inletIn order Indisturbance, order to simulate to simulate a distortion-imitating the the inlet inlet distortion distortion device thatthat was happenshappens installed in in super closely super maneuverabil maneuverabilitybehind the fairing.ity flight flightTwo or otherkinds or other air of air inletinlet disturbance, disturbance,distortion a distortion-imitatingare a distortion-imitating simulated in these device device experiments: waswas in installedstalled sole closely closelyinlet distortionbehind behind the the andfairing. fairing. symmetric Two Two kinds inlet kinds of of inletinletdistortion. distortion distortion Figure are simulatedare 2 showssimulated inthe these device in these experiments: imitating experiments: sole sole inlet inletsole distortion, distortioninlet distortion and and Figure symmetric and 3 showssymmetric inlet the device distortion.inlet Figuredistortion.imitating2 shows symmetrical Figure the device 2 shows inlet imitating the distortion. device sole imitating inletAlthough distortion, sole the inlet sole distortion, and inlet Figure distortion and3 showsFigure and 3 the symmetricalshows device the imitatingdevice inlet symmetricalimitatingdistortion inlet symmetricalboth distortion.have an effectinlet Although distortion.on inlet conditions, the Although sole inlet only the distortion the sole sole inlet inlet and distortion distortion symmetrical conditionand symmetrical inlet is distortionconsidered inlet both havedistortionin an this effect article. both on inlet have conditions, an effect on inlet only conditions, the sole inlet only distortion the sole inlet condition distortion is condition considered is considered in this article. in this article.

Figure 2. Sole inlet distortion-imitating device. Figure 2. Sole inlet distortion-imitating device. Figure 2. Sole inlet distortion-imitating device. Appl. Sci. 2017, 7, 766 4 of 14 Appl. Sci. 2017, 7, 766 4 of 14

Figure 3. Symmetrical inlet distortion-imitating device. Figure 3. Symmetrical inlet distortion-imitating device.

The inlet system includes a flared tube, fairing, an inlet duct, and a distortion simulator (includingThe inlet sole system distortion includes and a flaredsymmetric tube, fairing,distortion an inletsimulators, duct, and which a distortion are mainly simulator composed (including of soleskeleton, distortion based and mesh, symmetric and mesh, distortion as shown simulators, in Figures which 2 and are 3). mainlyThe exhaust composed devices of skeleton,include volute, based mesh,the exhaust and mesh, passage, as shown throttle in Figuresand the2 anechoicand3). The ch exhaustamber. The devices power include systems volute, are thecontrol exhaust components passage, throttleand DC and motor, the anechoicwhose rated chamber. power The is power200 kw. systems The signal are control measurement components system and DCis constituted motor, whose of ratedsensors, power signal is processor 200 kw. The and signal storage. measurement The compress systemor has is two-stage constituted of axial of sensors, flow, which signal includes processor a andtwo-level storage. stator The and compressor a two-level has rotor. two-stage The main of axialdesign flow, parameters which includes of the compressor a two-level are stator as follows. and a two-levelThe compressor’s rotor. The outside main diameter design parametersis 0.9 m, and of its the hub compressor ratio is 0.6. areThe as design follows. points The of compressor’s rotate speed, outsidepressure diameter ratio, efficiency is 0.9 m, and and flow its are hub 1500 ratio RPM, is 0.6. 1.035, The 0.88% design and points 25 kg/s, of rotate respectively. speed, pressureTable 1 shows ratio, efficiencythe designand parameters flow are of 1500 the RPM,compressor 1.035, rotor 0.88% and and the 25 stator kg/s, blade. respectively. Table1 shows the design parameters of the compressor rotor and the stator blade. Table 1. Relevant design parameters of the compressor blade. Table 1. Relevant design parameters of the compressor blade. Blade Position Blade Parameters First-Stage Rotor First-Stage StatorBlade Second-Stage Position Rotor Second-Stage Stator Blade Parameters Type First-StageNACA-65-010 Rotor NACA-65-010 First-Stage Stator Second-StageNACA-65-010 Rotor Second-StageNACA-65-010 Stator Chord length/mm 130 106 130 117 Type NACA-65-010 NACA-65-010 NACA-65-010 NACA-65-010 ChordNumber length/mm 19 130 22 106 18 130 11720 Radial Numberclearance/mm 1.3 19 1 22 1 18 20 1 Radial clearance/mm 1.3 1 1 1 3. Experiment Analysis 3. Experiment Analysis Compressor experiments are always designed under the restrictions of compressor characteristics. FiguresCompressor 4 and 5 show experiments a compressor are always characteristic designed map under without the restrictions inlet distortion. of compressor With given characteristics. compressor Figuresrevolutions4 and per5 show minute, a compressor the compressor characteristic pressure map ra withouttio will increase inlet distortion. while the With compressor given compressor air mass revolutionsflow is decreasing. per minute, However, the compressor excessive reduction pressure ratioof compressor will increase air mass while flow the compressorwould lessen air compressor mass flow iscompressing decreasing. ability, However, as shown excessive in Figure reduction 4. Meanwh of compressorile, the efficiency air mass flowof the would compressor lessen is compressor gradually compressinglessening with ability, the reduction as shown of incompressor Figure4. Meanwhile, air mass flow, the as efficiency the compressor of the compressor experiment is facility gradually duct lesseningwould block with mass the reduction flow in the of compressor experiment, air as mass is shown flow, as in the Figure compressor 5. Figures experiment 6 and facility7 show duct the wouldcompressor block characteristic mass flow in the map experiment, with sole asinlet isshown distortion, in Figure and5 Figures. Figures 86 andand 79 showshow thethe compressor compressor characteristic mapmap withwith sole symmetrical inlet distortion, inlet anddistortion. Figures 8When and9 showthe compressor the compressor works characteristic in the sole mapdistortion with symmetricalsituation, the inlet inlet distortion. is influenced When by stal thel compressor flow, and the works surge in margin the sole of distortion the compressor situation, ought the inletto move is influenced towards the by bottom stall flow, right, and theoretically. the surge margin Although of the the compressor measuring ought point to of move compressor towards inlet the bottompressure right, is set theoretically.behind the distortion-imitating Although the measuring device, point thereof is compressorlittle difference inlet in pressure the surge is margin set behind the thebetween distortion-imitating inlet with distortion, device, and there the inlet is little withou differencet distortion. in the However, surge margin when the compressor between inletoperation with distortion,is close to its and surge the inlet margin, without the distortion.stall flow of However, compressor when inlet compressor distortion operation is obviously is close different to its surgefrom margin,the situation the stall without flow ofdistortion. compressor As the inlet compressor distortion isflow obviously decreases, different the pressure from the ratio situation increases without and the operating efficiency gets higher; when the flow reduces to a certain degree, the pressure ratio and efficiency both go down. Appl. Sci. 2017, 7, 766 5 of 14 distortion. As the compressor flow decreases, the pressure ratio increases and the operating efficiency Appl. Sci. 2017, 7, 766 5 of 14 getsAppl.Appl. higher;Sci. Sci. 2017 2017,when 7,, 7766, 766 the flow reduces to a certain degree, the pressure ratio and efficiency both go down.5 of5 of 14 14

1.020 1.0201.020

1.015 1.0151.015

1.0101.010 RPM 1.010 RPM RPM 600 600 600 700 700 700 800 Pressure Ratio 1.005 800 Pressure Ratio 800 1.005Pressure Ratio 1.005 900 900 900 1000 1000 1000 1100 1100 1100 1.0001.000 1.000 51015 5101551015 m(kg/s) mm(kg/s(kg/s) ) FigureFigure 4. 4. Compressor Compressor characteristic characteristic of of pressure pressure ratio ratio vers versusus mass mass flow flow rate rate with with no no inlet inlet distortion. distortion. FigureFigure 4. 4.Compressor Compressor characteristic characteristic of of pressure pressure ratio ratio versus versus mass mass flow flow rate rate with with no no inlet inlet distortion. distortion.

0.8 0.80.8

RPM RPM RPM 600 600 600 700 0.70.7 700 700 0.7 800

Efficiency 800 800 Efficiency

Efficiency 900 900 900 1000 1000 1000 1100 0.6 1100 1100 0.60.6

6 9 12 15 18 66 9 9 12 12 15 15 18 18 mm(kg/s(kg/s) ) m(kg/s) Figure 5. Compressor characteristic of efficiency versus mass flow rate with no inlet distortion. FigureFigureFigure 5.5. 5.CompressorCompressor Compressor characteristiccharacteristic characteristic ofof of efficiencyefficiency efficiency versusversus versus massmass mass flowflow flowrate rate ratewith with withno no noinlet inlet inletdistortion. distortion. distortion.

1.016 1.0161.016

1.012 1.0121.012 RPM RPM RPM 600 600 600 700 1.008 700 700 1.0081.008 800 800 800 900

Pressure Ratio 900 900 Pressure Ratio

Pressure Ratio 1000 1000 1000 1.004 1100 1100 1.0041.004 1100

51015 5101551015m(kg/s) m(kg/s)m(kg/s)

FigureFigure 6. 6.Compressor Compressor characteristic characteristic of of pressure pressure ratio ratio versus versus mass mass flow flow rate rate with with sole sole inlet inlet distortion. distortion. FigureFigure 6. 6.Compressor Compressor characteristic characteristic of of pressure pressure ratio ratio vers versusus mass mass flow flow rate rate with with sole sole inlet inlet distortion. distortion. Appl. Sci. 2017, 7, 766 6 of 14

Appl. Sci. 2017, 7, 766 6 of 14 Appl. Sci. 2017, 7, 766 6 of 14 Appl. Sci. 2017, 7, 766 6 of 14 0.80

0.80 RPM 0.800.75 600 700 Efficiency 800 RPM 900 0.75 6001000 700 Efficiency RPM 1100 0.750.70 800600 900700 Efficiency 1000800 1100 6 8 10 12 14 900 16 0.70 1000 m(kg/s) 1100 0.70 6 8 10 12 14 16 Figure 7. Compressor characteristic of efficiencym( kg/sversus) mass flow rate with sole inlet distortion. 6 8 10 12 14 16 m(kg/s) Figure 7. Compressor characteristic of efficiency versus mass flow rate with sole inlet distortion.

FigureFigure 7. 7.Compressor Compressor characteristic characteristic1.016 of of efficiency efficiency versus versus mass mass flow flow rate rate with with sole sole inlet inlet distortion. distortion.

1.016 1.012 1.016 RPM 600 700 1.012 800 RPM 900 1.008 1000 1.012 600 7001100

Pressure Ratio RPM 800600 900 1.008 700 1000800 1.004 1100

Pressure Ratio 900 1.008 51015 1000 1100

Pressure Ratio m(kg/s) 1.004 Figure 8. Compressor characteristic51015 of pressure versus mass flow rate with symmetrical inlet 1.004 m(kg/s) 51015distortion. m(kg/s) FigureFigure 8. Compressor 8. Compressor characteristic characteristic of pressure of pressure versus vers massus flow mass rate flow with rate symmetrical with symmetrical inlet distortion. inlet Figure 8. Compressor characteristic of pressuredistortion. vers us mass flow rate with symmetrical inlet distortion.

0.8

0.8 0.7 RPM 600 0.8 700

Efficiency 800 0.7 RPM 900 0.6 6001000 1100 RPM 700

Efficiency 0.7 800600 900700

Efficiency 0.6 1000800 51015 1100 m(kg/s) 900 0.6 1000 1100 Figure 9. Compressor characteristic51015 of efficiency versus mass flow rate with symmetrical Figure 9. Compressor characteristic of efficiencym(kg/s ve)rsus mass flow rate with symmetrical inlet inlet distortion. 51015 distortion. m(kg/s) Figure 9. Compressor characteristic of efficiency versus mass flow rate with symmetrical inlet TheThe compressor compressor experiment experiment design design fully fully utilizes utiliz thees compressor the compressor characteristics. characteristics. The control The control valve distortion.Figure 9. Compressor characteristic of efficiency versus mass flow rate with symmetrical inlet adjusts the compressor air mass flow in order to let the compressor get into stall or surge state. valvedistortion. adjusts the compressor air mass flow in order to let the compressor get into stall or surge state. InTheIn this this compressor paper, paper, the the collected experimentcollected pressure pressure design signals signalfully aresutiliz are pre-processed pre-processedes the compressor by by the the followingcharacteristics. following function, function, The control valve adjusts the compressor air mass flow in order to let the compressor get into stall or surge state. The compressor experiment design fullyCp = utiliz(P − Pes0)/ Pthe0 compressor characteristics. The control(1) Cp = (P − P0)/P0 (1) valveIn adjusts this paper, the compressor the collected air pressure mass flow signal in orders are topre-processed let the compressor by the getfollowing into stall function, or surge state. whereInP isthis the paper, monitored the collected pressure, pressure which signal isCp filtered =s ( areP − by Ppre-processed0 a)/P low-pass0 filter by the with following any convenient function, cut-off (1) frequency, and P0 is the compressor inlet pressure.Cp = (P Therefore, − P0)/P0 Cp is a dimensionless variable, which(1) is called the pressure coefficient in this paper. Appl. Sci. 2017, 7, 766 7 of 14

where P is the monitored pressure, which is filtered by a low-pass filter with any convenient cut-off Appl.frequency, Sci. 2017, 7and, 766 P0 is the compressor inlet pressure. Therefore, Cp is a dimensionless variable, 7which of 14 is called the pressure coefficient in this paper. The tested pressures are always disturbed by unsteady environmental factors and other unavoidableThe tested measurement pressures are disturbances. always disturbed Therefore, byunsteady in order environmentalto research the factors laws andby otherwhich unavoidablecompressors measurement work, the pressure disturbances. characteristics Therefore, should in order be topre-analyzed. research the lawsIn this by paper, which compressorsthe pressures work,are mainly the pressure calculated characteristics by fast Fourier should transform be pre-analyzed. (FFT). With the In thisFFT paper,method, the the pressures experiment’s are mainly results calculatedwould be byanalyzed fast Fourier through transform the comparison (FFT). With of the the sensor FFT method,location theat the experiment’s compressor resultsinlet, blade would tip beregion, analyzed and throughcompressor the comparisonoutlet. In this of experiment, the sensor location the main at useful the compressor signal frequency inlet, blade is no tip more region, than and500 compressorHz. In order outlet. to improve In this experiment, the signal–noise the main ratio useful and signalreduce frequency the noise issignal no more interference, than 500 Hz. the Indynamic order to pressure improve measurement the signal–noise data ratiohas been and filtered reduce at the a cut-off noise signalfrequency interference, of 500 Hz. the dynamic pressure measurement data has been filtered at a cut-off frequency of 500 Hz. Pressure Analysis Results Pressure Analysis Results In order to research the developing laws of compressor pressure under different compressor In order to research the developing laws of compressor pressure under different compressor conditions, two patterns of compressor working states are experienced. The compressor working conditions, two patterns of compressor working states are experienced. The compressor working patterns are: normal working conditions (where the compressor surge margin is 14.2%), and stall patterns are: normal working conditions (where the compressor surge margin is 14.2%), and stall working conditions (where the compressor surge margin is 1.5%). Under both of these compressor working conditions (where the compressor surge margin is 1.5%). Under both of these compressor working conditions, the compressor is analyzed through the FFT method [19,20]. In this way, working conditions, the compressor is analyzed through the FFT method [19,20]. In this way, the the pressure signal obtained in the time domain can be transferred into the frequency domain. pressure signal obtained in the time domain can be transferred into the frequency domain. The analysis The analysis of the compressor pressure signal in the frequency domain is to study the influence of of the compressor pressure signal in the frequency domain is to study the influence of different inlet different inlet conditions on the characteristics of the pressure signal. Because the rotational speed conditions on the characteristics of the pressure signal. Because the rotational speed doesn’t affect the doesn’t affect the purpose of this experiment, this paper takes the compressor experiment at 600 RPM purpose of this experiment, this paper takes the compressor experiment at 600 RPM randomly within randomly within examples to analyze the pressures. The experienced compressor contains 19 blades, examples to analyze the pressures. The experienced compressor contains 19 blades, so the compressor so the compressor blade frequency with the compressor rotor at 600 RPM is 190 Hz. blade frequency with the compressor rotor at 600 RPM is 190 Hz. Figure 10 shows the variation of compressor inlet pressure with no inlet distortion at a surge Figure 10 shows the variation of compressor inlet pressure with no inlet distortion at a surge margin of 14.2%, and Figure 11 shows the variation of compressor inlet pressure with sole inlet margin of 14.2%, and Figure 11 shows the variation of compressor inlet pressure with sole inlet distortion. As is shown in Figure 10, the pressure periodicity is hard to maintain, but the spectrogram distortion. As is shown in Figure 10, the pressure periodicity is hard to maintain, but the spectrogram indicates that the compressor inlet pressure still holds the pressure frequency characteristic. indicates that the compressor inlet pressure still holds the pressure frequency characteristic. However, However, with the impact of compressor inlet distortion, the compressor inlet pressure periodicity is with the impact of compressor inlet distortion, the compressor inlet pressure periodicity is further further decreased, and the pressure frequency characteristic is obviously destroyed. In comparison decreased, and the pressure frequency characteristic is obviously destroyed. In comparison to one to one another, it can be concluded that the compressor inlet pressure is not the best choice to describe another, it can be concluded that the compressor inlet pressure is not the best choice to describe the the compressor’s working characteristics. compressor’s working characteristics.

No inlet distortion 1.5 No inlet distortion

0.0002 1.0 Cp

0.0001 0.5 Amplitude (mV) Amplitude

0.0000 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 time (s) Frequency (Hz)

FigureFigure 10. 10.Compressor Compressor inlet inlet pressure pressure with with no no inlet inlet distortion distortion at at a a surge surge margin margin of of 14.2%. 14.2%. Appl. Sci. 2017, 7, 766 8 of 14 Appl.Appl.Appl. Sci.Sci. Sci.2017 2017 2017,,7 ,7 ,7, 766 ,766 766 88 of8 of of 14 14 14

Sole inlet distortion 1.5 Sole inlet distortion 1.5 Sole inlet distortion Sole inlet distortion 1.5 Sole Sole inlet inlet distortion distortion 0.0000 0.00000.0000 1.0 1.0 -0.0002 1.0 -0.0002

Cp -0.0002 Cp Cp 0.5 -0.0004 0.50.5 -0.0004-0.0004 (mV) Amplitude Amplitude (mV) Amplitude Amplitude (mV) Amplitude

-0.0006 0.0 -0.0006-0.00060.0 0.2 0.4 0.6 0.8 1.0 0.00.00 100 200 300 400 500 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 0.0 0.2time 0.4 (s) 0.6 0.8 1.0 0 100Frequency 200 (Hz) 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) Figure 11. Compressor inlet pressure with sole inlet distortion at a surge margin of 14.2%. Figure 11. Compressor inlet pressure with sole inlet distortion at a surge margin of 14.2%. FigureFigure 11. 11.Compressor Compressor inlet inlet pressure pressure with with sole sole inlet inlet distortion distortion at at a a surge surge margin margin of of 14.2%. 14.2%. Figures 12 and 13 show the variation of compressor outlet pressure with no inlet distortion and FiguresFigures 12 12 and and 13 13 show show the the variation variation of of compresso compressorr outlet outlet pressure pressure with with no no inlet inlet distortion distortion and and sole inletFigures distortion 12 and at 13 a showsurge themargin variation of 14.2%, of compressor respectively. outlet It is pressurenot hard to with find no out inlet that distortion the pressure and solesole inlet inlet distortion distortion at at a a surge surge margin margin of of 14.2%, 14.2%, respec respectively.tively. It It is is not not hard hard to to find find out out that that the the pressure pressure periodicitysole inlet distortion at the compressor at a surge margin outlet ofis 14.2%, not well respectively. held whether It is not the hard compressor to find out experiences that the pressure inlet periodicityperiodicity atat thethe compressorcompressor outletoutlet isis notnot wellwell heldheld whetherwhether thethe compressorcompressor experiencesexperiences inletinlet distortionperiodicity or at thenot. compressor With the amplitude outlet is not of well the held compressor whether thepressure compressor coefficient experiences suddenly inlet increased, distortion distortiondistortion oror not.not. WithWith thethe amplitudeamplitude ofof thethe cocompressormpressor pressurepressure coefficientcoefficient suddenlysuddenly increased,increased, theor not.later Withpressure-signal the amplitude processing of the compressordifficulty in pressure compressor coefficient stall detection suddenly is increased, raised. However, the later thethe laterlater pressure-signalpressure-signal processingprocessing difficultydifficulty inin compressorcompressor stallstall detectiondetection isis raised.raised. However,However, thepressure-signal compressor processingoutlet pressure difficulty frequency in compressor characteristic stall detectionis well kept. israised. However, the compressor thethe compressor compressor outlet outlet pressure pressure frequency frequency characteristic characteristic is is well well kept. kept. outlet pressure frequency characteristic is well kept.

0.003 No inlet distortion 30 0.003 No inlet distortion 30 No inlet distortion 0.003 No inlet distortion 30 No No inlet inlet distortion distortion 24 24 0.002 24 0.0020.002 18 1818 Cp Cp

0.001Cp 0.001 12 0.001 1212 Amplitude (mV) Amplitude

Amplitude (mV) Amplitude 6 0.000 (mV) Amplitude 66 0.0000.000 0 0.0 0.2 0.4 0.6 0.8 1.0 00 100 200 300 400 500 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 0.0 0.2time 0.4 (s) 0.6 0.8 1.0 0 100Frequency 200 (Hz) 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) Figure 12. Compressor outlet pressure with no inlet distortion at a surge margin of 14.2%. FigureFigureFigure 12.12. 12. CompressorCompressor Compressor outletoutlet outlet pressurepressure pressurewith with withno no noinlet inlet inletdistortion distortion distortionat at at a a a surge surge surge margin margin margin of of of 14.2%. 14.2%. 14.2%.

0.004 Sole inlet distortion 20 0.004 Sole inlet distortion 20 Sole inlet distortion 0.004 Sole inlet distortion 20 Sole Sole inlet inlet distortion distortion

15 1515 Cp

0.002Cp 10 Cp 0.0020.002 1010

5 Amplitude (mV) 5 Amplitude (mV) 5 Amplitude (mV)

0.000 0 0.0000.0000.00.20.40.60.81.0 00 100 200 300 400 500 0.00.20.40.60.81.0 0 100 200 300 400 500 0.00.20.40.60.81.0time (s) 0 100Frequency 200 (Hz) 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) FigureFigure 13. 13. CompressorCompressor outlet outlet pressure pressure with with sole sole inlet inlet distortion distortion at surge margin of 14.2%. FigureFigure 13. 13. Compressor Compressor outlet outlet pressure pressure with with sole sole inlet inlet distortion distortion at at surge surge margin margin of of 14.2%. 14.2%. Appl.Appl. Sci. Sci. 2017 2017, ,7 7, ,766 766 99 of of 14 14

FiguresFigures 1414 andand 1515 showshow thethe variationvariation ofof compressorcompressor bladeblade tiptip regionregion pressurepressure withwith nono inletinlet distortiondistortion andand solesole inletinlet distortiondistortion atat surgesurge marginmargin ofof 14.2%.14.2%. ItIt isis nonott hardhard toto findfind outout thatthat bothboth thethe pressurepressure periodicityperiodicity andand frequencyfrequency characteristicscharacteristics areare wellwell kept.kept. TheThe compressorcompressor bladeblade tiptip regionregion Appl.pressurepressure Sci. 2017 signalsignal, 7, 766 integratesintegrates thethe advantagesadvantages inin compcompressorressor inletinlet andand outletoutlet prpressure.essure. Undoubtedly,Undoubtedly,9 of thethe 14 compressorcompressor bladeblade tiptip pressurepressure signalsignal isis thethe mostmost aappropriateppropriate pressurepressure signalsignal thatthat couldcould bebe usedused toto analyzeanalyze thethe compressor’scompressor’s workingworking characteristics.characteristics. FiguresSimilarSimilar 14conclusionsconclusions and 15 show alsoalso thecouldcould variation bebe deduceddeduced of compressor fromfrom thethe experimentalexperimental blade tip region compressorcompressor pressure pressurepressure with no underunder inlet distortionstallstall workingworking and conditions,conditions, sole inlet distortion asas shownshown at inin surge FiguresFigures margin 16–216–21. of1. WhetherWhether 14.2%. It thethe is not compressorcompressor hard to find isis workingworking out that withwith both inletinlet the pressuredistortiondistortion periodicity oror not,not, massivemassive and frequency low-frequencylow-frequency characteristics pressurepressure are signalssignals well existexist kept. inin The thethe compressor collectedcollected pressurepressure blade tip signalssignals region atat pressurecompressorcompressor signal inletinlet integrates andand outlet.outlet. the TheThe advantages collectedcollected pressure inpressure compressor signalssignals inlet atat thethe and compressorcompressor outlet pressure. bladeblade showshow Undoubtedly, thethe betterbetter thefrequencyfrequency compressor characteristic.characteristic. blade tip pressure signal is the most appropriate pressure signal that could be used to analyze the compressor’s working characteristics.

No inlet distortion 3535 0.00240.0024 No inlet distortion No No inlet inlet distortion distortion 3030

0.00160.0016 2525

2020 Cp Cp 0.00080.0008 1515

1010 Amplitude (mV) Amplitude (mV) 0.0000 0.0000 55

00 0.00.20.40.60.81.00.00.20.40.60.81.0 00 100 100 200 200 300 300 400 400 500 500 timetime (s)(s) FrequencyFrequency (Hz)(Hz) Figure 14. Compressor blade tip pressure with no inlet distortion at a surge margin of 14.2%. FigureFigure 14. 14.Compressor Compressor blade blade tip tip pressure pressure with with no no inlet inlet distortion distortion at at a a surge surge margin margin of of 14.2%. 14.2%.

Sole inlet distortion 20 Sole inlet distortion 20 Sole Sole inlet inlet distortion distortion

0.0020.002 1515

Cp 10

Cp 10 0.0010.001

5 Amplitude (mV) Amplitude 5 Amplitude (mV) Amplitude

0.0000.000 00 0.00.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 00 100 100 200 200 300 300 400 400 500 500 timetime (s)(s) FrequencyFrequency (Hz)(Hz) FigureFigureFigure 15.15. 15. CompressorCompressor Compressor bladeblade blade tiptip tip pressurepressure pressure withwith with solesole sole inletinlet inlet distortiondistortion distortion atat at aa a surgesurge surgemargin margin marginof of of14.2%. 14.2%. 14.2%.

Similar conclusions also could be deduced from the experimental compressor pressure under stall working conditions, as shown in Figures 16–21. Whether the compressor is working with inlet distortion or not, massive low-frequency pressure signals exist in the collected pressure signals at compressor inlet and outlet. The collected pressure signals at the compressor blade show the better frequency characteristic. Appl. Sci. 2017,, 7,, 766766 10 of 14 Appl.Appl. Sci. Sci.2017 2017, ,7 7,, 766 766 1010 of of 14 14

0.001 No inlet distortion 4 0.001 No inlet distortion 4 NoNo inletinlet distortiondistortion 0.001 No inlet distortion 4 No inlet distortion

3 0.000 3 0.000

Cp 2

Cp 2

Cp 2 -0.001-0.001 -0.001

1

Amplitude (mV) Amplitude 1 Amplitude (mV) Amplitude 1 Amplitude (mV) Amplitude -0.002-0.002 -0.002 0 0.00.20.40.60.81.0 0 0 100 200 300 400 500 0.00.20.40.60.81.0 0 100 200 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) Figure 16. CompressorCompressor inletinlet pressurepressure withwith nono inletinlet distortion at a surge margin of 1.5%. FigureFigure 16. 16.Compressor Compressor inlet inlet pressure pressure with with no no inlet inlet distortion distortion at at a a surge surge margin margin of of 1.5%. 1.5%.

Sole inlet distortion 10 Sole inlet distortion 10 SoleSole inletinlet distortiondistortion Sole inlet distortion 10 Sole inlet distortion 0.000 0.000 8 8

6

Cp 6 Cp -0.001-0.001Cp -0.001 4 4 Amplitude (mV) Amplitude Amplitude (mV) Amplitude

Amplitude (mV) Amplitude 2 -0.002-0.002 2 -0.002

0 0.0 0.2 0.4 0.6 0.8 1.0 0 0 100 200 300 400 500 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) Figure 17. CompressorCompressor inletinlet pressurepressure withwith solesole inletinlet distortiondistortion atat surgesurge marginmargin ofof 1.5%.1.5%. FigureFigure 17. 17.Compressor Compressor inlet inlet pressure pressure with with sole sole inlet inlet distortion distortion at at surge surge margin margin of of 1.5%. 1.5%.

0.004 No inlet distortion 15 0.004 No inlet distortion 15 NoNo inletinlet distortiondistortion 0.004 No inlet distortion 15 No inlet distortion

0.002 10 0.002 10 Cp Cp Cp

0.000 5 0.000 5 Amplitude (mV) Amplitude Amplitude (mV) Amplitude Amplitude (mV) Amplitude

-0.002-0.002 0 -0.0020.00.20.40.60.81.0 0 0 100 200 300 400 500 0.00.20.40.60.81.0 0 100 200 300 400 500 time (s) Frequency (Hz) time (s) Frequency (Hz) Figure 18. Compressor outlet pressure with no inlet distortion at a surge margin of 1.5%. FigureFigure 18. 18.Compressor Compressoroutlet outletpressure pressure with with no no inlet inlet distortion distortion at at a a surge surge margin margin of of 1.5%. 1.5%. Appl.Appl. Sci.Sci. 20172017,, 77,, 766766 1111 ofof 1414 Appl.Appl. Sci.Sci.2017 2017,,7 7,, 766766 1111 ofof 1414

Sole inlet distortion 20 Sole inlet distortion 20 SoleSole inletinlet distortiondistortion Sole inlet distortion 20 Sole inlet distortion

15 0.003 15 0.003 15 0.003 Cp Cp 10 Cp 10 10

0.000 0.000 5 0.000 (mV) Amplitude 5 Amplitude (mV) Amplitude 5 Amplitude (mV) Amplitude

00 0.00.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 0 00 100 100 200 200 300 300 400 400 500 500 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 timetime (s)(s) FrequencyFrequency (Hz)(Hz) time (s) Frequency (Hz) FigureFigure 19.19. CompressorCompressor outletoutlet pressurepressure withwith solesole inletinlet distortiondistortion atat aa surgesurge marginmargin ofof 1.5%.1.5%. FigureFigure 19.19. CompressorCompressor outletoutlet pressurepressure withwith solesole inletinlet distortiondistortionat ata asurge surgemargin margin of of 1.5%. 1.5%.

0.002 No inlet distortion 15 0.002 No inlet distortion 15 NoNo inletinlet distortiondistortion 0.002 No inlet distortion 15 No inlet distortion

1010 10 0.0000.000

0.000Cp Cp Cp

55 5 Amplitude (mV) Amplitude (mV) Amplitude (mV) -0.002-0.002 -0.002 00 0.00.0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 1.0 0 00 100 100 200 200 300 300 400 400 500 500 0.0 0.2 0.4 0.6 0.8 1.0 0 100 200 300 400 500 timetime (s)(s) FrequencyFrequency (Hz)(Hz) time (s) Frequency (Hz) FigureFigure 20.20. CompressorCompressor bladeblade tiptip pressurepressure withwith nono inletinlet distortiondistortion atat surgesurge marginmargin ofof 1.5%.1.5%. FigureFigure 20.20. CompressorCompressor bladeblade tiptip pressurepressure withwith nono inletinlet distortiondistortionat atsurge surgemargin margin of of 1.5%. 1.5%.

Sole inlet distortion 15 Sole inlet distortion 15 SoleSole inletinlet distortiondistortion Sole inlet distortion 15 Sole inlet distortion 0.0020.002 0.002

1010 10 Cp 0.000Cp Cp 0.000 0.000 55 5 Amplitude (mV) Amplitude (mV) Amplitude (mV)

-0.002-0.002 00 -0.0020.00.20.40.60.81.00.00.20.40.60.81.0 0 00 100 100 200 200 300 300 400 400 500 500 0.00.20.40.60.81.0 0 100 200 300 400 500 timetime (s)(s) FrequencyFrequency (Hz)(Hz) time (s) Frequency (Hz) FigureFigureFigure 21. 21.21. CompressorCompressor bladeblade tiptip pressurepressure withwith solesole inletinlet distortiondistortion atat aa surgesurge marginmargin ofof 1.5%.1.5%. Figure 21. CompressorCompressor bladeblade tiptip pressurepressure withwith solesole inletinlet distortiondistortionat ata asurge surgemargin margin of of 1.5%. 1.5%. Through simulation at a surge margin of 1.5%, the compressor experimental results indicated ThroughThroughThrough simulation simulationsimulation at atat a surgeaa surgesurge margin marginmargin of 1.5%,ofof 1.5%1.5% the,, thethe compressor compressorcompressor experimental experimentalexperimental results resultsresults indicated indicatedindicated that that inlet distortion severely influenced the inlet pressure amplitude–frequency characteristics. inletthatthat distortioninletinlet distortiondistortion severely severelyseverely influenced influencedinfluenced the inlet thethe pressure inletinlet pressurepressure amplitude–frequency amplitude–frequencyamplitude–frequency characteristics. characteristics.characteristics. In order In order to quantify the bad influence on the pressure, an amplitude–frequency index (Nam) is toInIn quantify orderorder toto the quantifyquantify bad influence thethe badbad on influenceinfluence the pressure, onon thethe an pressure,pressure, amplitude–frequency anan amplitude–frequencyamplitude–frequency index (Nam index)index is defined ((NamNam)) as isis defined as the sum number of the amplitude, which is greater than half of the amplitude at blade thedefineddefined sum numberasas thethe sumsum of thenumbernumber amplitude, ofof thethe amplitude, whichamplitude, is greater whichwhich than isis greatergreater half of thanthan the amplitudehalfhalf ofof thethe atamplitudeamplitude blade frequency atat bladeblade frequency within the region from zero frequency to the half-blade frequency. The bigger the Nam is, withinfrequencyfrequency the regionwithinwithin fromthethe regionregion zero frequency fromfrom zerozero tofrequencfrequenc the half-bladeyy toto thethe half-blade frequency.half-blade frequency.frequency. The bigger TheThe the biggerbiggerNam is, thethe the NamNam more is,is, the more low-frequency noise signals are mingled, and the more disturbances are generated to the low-frequencythethe moremore low-frequencylow-frequency noise signals noisenoise are signalssignals mingled, areare andmingled,mingled, the more andand disturbancesthethe moremore disturbancesdisturbances are generated areare generatedgenerated to the pressure toto thethe pressure amplitude–frequency characteristic. As is shown in Table 2, with inlet distortion, the inlet amplitude–frequencypressurepressure amplitude–frequencyamplitude–frequency characteristic. characteristic.characteristic. As is shown AsAs is inis shownshown Table2 , inin with TableTable inlet 2,2, distortion,withwith inletinlet distortion,distortion, the inlet pressure thethe inletinlet pressure amplitude–frequency characteristic is destroyed, and outlet pressure mingles with a large amplitude–frequencypressurepressure amplitude–frequencyamplitude–frequency characteristic characteristiccharacteristic is destroyed, isis destdest androyed,royed, outlet and pressureand outletoutlet mingles pressurepressure with minglesmingles a large withwith number aa largelarge of number of low-frequency noise signals. However, the blade tip Nam is continually kept at zero. The numbernumber ofof low-frequencylow-frequency noisenoise sisignals.gnals. However,However, thethe bladeblade tiptip NamNam isis continuallycontinually keptkept atat zero.zero. TheThe Appl. Sci. 2017, 7, 766 12 of 14

Appl. Sci. 2017, 7, 766 12 of 14 low-frequency noise signals. However, the blade tip Nam is continually kept at zero. The analyzed resultsanalyzed also results conclude also that conclude the compressor that the blade compressor tip region blade pressure tip showedregion apressure better performance showed a better than compressorperformance inlet than and compressor outlet on describing inlet and outlet the compressor on describing characteristics. the compressor characteristics.

TableTable 2. 2.The The analyzed analyzed pressure pressure amplitude–frequency amplitude–frequency results results of ofNam Nam.. Working State Surge Margin of 14.2% Surge Margin of 1.5% Working State Surge Margin of 14.2% Surge Margin of 1.5% Position No DistortionSole Distortion No Distortion Sole Distortion Positioninlet No Distortion0 Sole Distortion 2 No Distortion 221 Sole Distortion730 inletoutlet 00 22 2216 7305 bladeoutlet tip 00 20 60 5 0 blade tip 0 0 0 0

4. Compressor Stall Detection Algorithm 4. Compressor Stall Detection Algorithm As is analyzed in the experimental pressure data, the compressor rotor blade is the best region for detectingAs is analyzed compressor in the experimental working conditions. pressure In data, order the to compressor predict the rotorcompressor blade is working the best regionconditions for detectingsuch as surge compressor margin, working a real-time conditions. stall detection In order algo to predictrithm is the proposed. compressor The workingcore ideaconditions of the algorithm such asissurge to utilize margin, the pressure a real-time periodicity, stall detection as is show algorithmn in Figure is proposed. 22. Figure The 22a core shows idea the of compressor the algorithm blade is totip utilize region the pressure pressure in periodicity, a stable condition as is shown and a in good Figure periodicity. 22. Figure Compressor 22a shows theworking compressor conditions blade in tipFigure region 22b pressure are in a in stall a stable state. condition The pressure and asign goodal shows periodicity. an obvious Compressor difference working when conditions conditions inare Figure stable. 22 b are in a stall state. The pressure signal shows an obvious difference when conditions are stable.

l l 0.004 l A A l 0.004 0.002 p p C C 0.000 0.000 B B time(s) time(s) 0.0040.00.10.20.30.40.5 0.00.10.20.30.40.5 0.004

0.002 p 0.002 p C C

0.000 0.000 time(s) time(s) 0.11 0.12 0.13 0.14 0.110 0.115 0.120 0.125 0.130 0.135 0.140 (a) (b)

FigureFigure 22. 22.Analysis Analysis of of correlation correlation at at steady steady (a (),a), and and stall stall working working conditions conditions (b ().b).

The calculation algorithm can be expressed as, The calculation algorithm can be expressed as, n n ()()PP−⋅ P− − P |(P −iaveiNaveP ) · (P − P )| = ∑inwnd=− i ave i−N ave Ct i=n−wnd (2) Ct = nn (2) s n 22n ((PP−⋅2 ))(()) P− − P 2 ( ∑(Pi −iavePave) ) · ( ∑ (P iNavei−N − Pave) ) i=n−inwnd=−wnd i= inwnd =−n−wnd

where Ct is the pressure correlation coefficient, wnd is the size of the correlation measure window, n where Ct is the pressure correlation coefficient, wnd is the size of the correlation measure window, n is is the index of the current pressure sample, Pi is the present pressure signal, Pave is the window the index of the current pressure sample, Pi is the present pressure signal, Pave is the window pressure pressure signal, and N is the sample number of the rotor rotational time delay between A and B. signal, and N is the sample number of the rotor rotational time delay between A and B. In order to verify the effectiveness of the stall detection algorithm, a dataset of compressor surge In order to verify the effectiveness of the stall detection algorithm, a dataset of compressor surge margin of 5.8% is added to the verification. Figure 23 shows the calculated results of compressor margin of 5.8% is added to the verification. Figure 23 shows the calculated results of compressor pressure correlation coefficients. Whether with compressor inlet distortion or not, the correlation pressure correlation coefficients. Whether with compressor inlet distortion or not, the correlation coefficient calculated at surge margin of 14.2%, 5.8%, and 1.5% all showed consistence in the value coefficient calculated at surge margin of 14.2%, 5.8%, and 1.5% all showed consistence in the value region. Although the compressor inlet distortion generated significant influence on the compressor region. Although the compressor inlet distortion generated significant influence on the compressor inlet inlet and outlet pressure characteristics of amplitude frequency and periodicity, the blade tip region and outlet pressure characteristics of amplitude frequency and periodicity, the blade tip region pressure pressure still kept a good characteristic of the amplitude frequency and periodicity. Therefore, still kept a good characteristic of the amplitude frequency and periodicity. Therefore, a relationship is a relationship is established between the pressure signal and the compressor surge margin. The results also showed that the stall detection algorithm kept a good monotonicity regarding surge margin versus the compressor pressure correlation coefficient. Appl. Sci. 2017, 7, 766 13 of 14 established between the pressure signal and the compressor surge margin. The results also showed that the stall detection algorithm kept a good monotonicity regarding surge margin versus the compressor pressureAppl. Sci. 2017 correlation, 7, 766 coefficient. 13 of 14

1.0 14.2% Surge Margin 0.9 No distortion Sole distortion 0.8 t

C 5.8% Surge Margin 0.7

0.6 1.5% Surge Margin

0.5 0.0 0.5 1.0 time(s)

FigureFigure 23. 23.Blade Blade tip tip pressure pressure correlation correlation coefficients coefficients at at 600 600 RPM. RPM.

5.5. Conclusions Conclusions The results showed that inlet distortion had a non-negligible influence on compressor working The results showed that inlet distortion had a non-negligible influence on compressor working conditions by experimenting the near stall test at different speeds under the condition of uniform conditions by experimenting the near stall test at different speeds under the condition of uniform inlet inlet and distortion inlet. Further, the compressor blade tip region pressure showed a better performance and distortion inlet. Further, the compressor blade tip region pressure showed a better performance than the compressor inlet and outlet on compressor characteristics, whether with inlet distortion or than the compressor inlet and outlet on compressor characteristics, whether with inlet distortion or not. not. With compressor pressure analysis through fast Fourier transform, the compressor blade tip With compressor pressure analysis through fast Fourier transform, the compressor blade tip pressure pressure could maintain more convincing information about the compressor in regards to working could maintain more convincing information about the compressor in regards to working conditions, conditions, such as pressure periodicity and frequency. A compressor stall detection algorithm is such as pressure periodicity and frequency. A compressor stall detection algorithm is proposed, which proposed, which showed a good monotonicity in describing the relationship between compressor showed a good monotonicity in describing the relationship between compressor surge margin and the surge margin and the pressure correlation coefficient. pressure correlation coefficient.

Acknowledgments:Acknowledgments:This This study study is co-supportedis co-supported by Researchby Research Funds Funds for Centralfor Central Universities Universities (No. NZ2016103)(No. NZ2016103) and Nationaland National Natural Natural Science Science Foundation Foundation of China of China (No. 51576096). (No. 51576096).

AuthorAuthor Contributions: Contributions:Haibo Haibo Zhang, Zhang, Fengyong Fengyong Sun and Sun Haoying and Haoying Chen conceived Chen conceived and designed and the designed experiments; the Wei Luo performed the experiments; Fengyong Sun analyzed the data; Haoying Chen wrote the paper. experiments; Wei Luo performed the experiments; Fengyong Sun analyzed the data; Haoying Chen Conflictswrote the of Interest:paper. The authors declare no conflict of interest.

ReferencesConflicts of Interest: The authors declare no conflict of interest.

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