5&9 WIHllIHIIIIHIHIHIIHHHIWNWIWIIWIHIHIHJI “15813 This is to certify that the thesis entitled AN EXPERIMENTAL STUDY OF BLADE-TO-BLADE STATIC PRESSURE DIFFERENCES AND OPERATING CHARACTERISTICS OF A CENTRIFUGAL COMPRESSOR presented by NEIL WHITBECK has been accepted towards fulfillment of the requirements for M.S. MECHANICAL ENGINEERING degree in Majo rofessor Date 0" " 0" “ 3‘} 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution iiiiiiiiiiiiii LIBRARY ~ Michigan State University PLACE IN RETURN BOX to romovo thin checkout from your record. T VOID FINES return on or botoro duo duo. DATE DUE DATE DUE DATE DUE IT ll IE;J| i: II III I ll l V—II I! MSUI. AnAfiirmut oActIo qunE uoIO pportunity lnotitutio WMH‘ AN EXPERIMENTAL STUDY OF BLADE-TO-BLADE PRESSURE DIFFERENCES AND OPERATING CHARACTERISTICS OF A CENTRIFUGAL COMPRESSOR By Neil Glenn Whitbeck A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Mechanical Engineering 1994 ABSTRACT AN EXPERIMENTAL STUDY OF BLADE-TO-BLADE PRESSURE DIFFERENCES AND OPERATING CHARACTERISTICS OF A CENTRIFUGAL COMPRESSOR By Neil Glenn Whitbeck A centrifugal compressor with a 10+10, radial-outlet impeller and vaned diffuser was run at de=10,000 rpm, 12,000 rpm, 14,000 rpm, and 16,500 rpm. Measurements of shroud-side static pressures were obtained, together with temperature and pressure readings at rotor outlet and stage exit for several operating points for both normal and unsteady operation. Characteristic performance data for the normal operation were plotted to show variations in stagnation pressure rise and efficiency for the rotor and the stage. Stable operation was also characterized by plotting blade-to-blade pressure oscillation amplitudes against flowrate and meridional position. SuCh plots provided convenient formats for possibly tracking the extent of reverse flow through impeller passages. In addition, unstable operation was characterized according to instability type (rotating stall or surge), stall zone number, and stall velocity. ACKNOWLEDGMENTS From February to August 1993, I participated in a student exchange between the Institutfiir S tro'mungsmaschinen , Universitr'it Hannover (Hannover, Germany) and Michigan State University's Department of Mechanical Engineering (E. Lansing, Michigan, USA). This thesis grows out of the work I performed in Germany. I thank Dr. A. Engeda and Dr. J. Lloyd for facilitating the student exchange. I especially thank Prof. Dr.-Ing. M. Rautenberg for his invitation to me to study at the Institut and for his gracious hospitality once I arrived. I also thank Dipl.-Ing. U. Seidel, who acted as guide and counselor through my entire tenure at the Institut. Without his patience and guidance, this work could never have been produced. Most of what I know about flow instabilities in centrifugal compressors, I learned from him. Thanks also go to Dr.-Ing. D. Jin and Dr.-Ing. U. Haupt. Dr. J in offered valuable instruction on the experimental detection and characterization of rotating stall and surge. Dr. Haupt helped deepen my conceptual understanding of these phenomena. Messrs. Seidel, Weber, Clevenot, and Wichmann gave me hands on training with data acquisition and analysis equipment. Mr. Tanneberg ran the compressor rig. I thank them all. I wish to thank my thesis examiners: Drs. A. Engeda, J. McGrath, and M. Koochesfahani. I also appreciate the support of the German Research Association (DFG) for the support of this research. iii TABLE OF CONTENTS LIST OF TABLES ............................................................... v11 LIST OF FIGURES .............................................................. viii NOMENCLATURE ............................................................... xi CHAPTER l-lNTRODUCTION 1 1.1 Scope of Work ................................................................ 1 1.2 Rotating Stall and Surge in Centrifugal Compressors 2 1.2.1 Rotating stall .......................................................... 2 1.2.2 Surge ..................................................................... 11 1.3 Relation between Reverse Flow and Rotating Stall .............. 13 CHAPTER 2--EXPERIMENTAL EQUIPMENT AND MEASUREMENT 18 2.1 Compressor Test Facility ................................................. 18 2.1.1 Rotor ..................................................................... 19 2.1.2 Diffuser ................................................................. 20 2.2 Data Collection System ..................................................... 21 2.2.1 Flowrate measurement .............................................. 21 2.2.2 Rotor speed measurement .......................................... 21 2.2.3 Pressure measurement ............................................... 23 2.2.4 Temperature measurement ......................................... 25 2.2.5 Blade vibration measurement ..................................... 25 iv Semen Page 2.3 Data Analysis Equipment .................................................. 25 2.3.1 Time-domain analysis equipment ................................ 27 . 2.3.2 Frequency-domain analysis equipment .......................... 27 CHAPTER 3--EXPERIMENTAL ANALYSIS PROCEDURES 29 3.1 Data Processing .............................................................. 30 3.2 Analysis of Steady Operation ........................................... 32 3.2.1 Pressure ratio and efficiency ......................................... 32 3.2.2 Blade-to-blade pressure difference ............................ 34 3.3 Analysis of Unsteady Flow/Operation .............................. 38 3.3.1 Analysis of the time domain .................................... 38 3.3.2 Analysis of the frequency domain ............................ 39 CHAPTER 4--RESULTS AND DISCUSSION 47 4.1 Stage and Rotor Performance .......................................... 47 4.2 Surge Characteristics ...................................................... 49 4.2.1 Surge at Nred=10,000 rpm ....................................... 51 4.2.2 Surge at Nred=12.000 rpm ...................................... 56 4.3 Rotating Stall Characteristics ........................................... 73 4.3.1 Event A ................................................................. 73 4.3.2 Event B ................................................................. 80 4.3.3 Event C .................................................................. 92 4.3.4 Event D ................................................................. 96 4.3.5 Other Events ........................................................... 105 4.4 Blade-to-Blade Pressure Characteristics for Stable Operation 106 4.4.1 Pressure variation with mass flow rate ....................... 111 4.4.2 Pressure variation with meridional location ................. 113 4.4.3 Pressure variation with impeller type ......................... 114 Section Bag: CHAPTER 5--CONCLUSIONS & RECOMMENDATIONS 117 5.1 Conclusions ................................................................... 117 5.2 Directions for Future Work ............................................ 118 APPENDIX A--EQUIPMENT .............................................. 120 APPENDIX B--DERIVATION OF EQUATIONS FOR ANALYSIS 124 APPENDIX C--EXPERIMENTAL DATA ........................... 131 APPENDD( D--PLOTS OF NORMALIZED BLADE-TO-BLADE PRESSURE DIFFERENCE ............................................. 141 APPENDIX E--MISCELLANEOUS GRAPHS ...................... 145 APPENDIX F--RESULTS OF ANALYSES OF UNSTEADY EVENTS 149 LIST OF REFERENCES ...................................................... 165 LIST OF TABLES Title Reported rotating stalls (vaneless diffusers) Reported rotating stalls (vaned diffusers) Geometric data for compressor rotors Natural blade modes for impellers used Parameter values for diffuser geometry Measured quantities Derived quantities Blade passing frequencies of interest Rotating stalls in surge at de=10,000 rpm Comparison of calculated blade vibration peaks with measured blade vibration peaks Comparison of calculated blade vibration peaks with measured blade vibration peaks Rotating stalls in surge at Nred=12,000 rpm . Analysis of Event B, Nrcd=l4,000 rpm Explanation of blade vibration peaks due to different stall modes Rotating stalls found for different impeller and diffuser configurations, A=l.15 for all Amplitude of pressure signal at blade passing frequency--raw data Amplification coefficients used in recording experimental measurements Amplitude of pressure signal at blade passing frequency—-amp1ification accounted for Amplitude of non-dimensionalized pressure (=Pb/P2) at blade passing frequency Amplitude of pressure coefficient at blade passing frequency 10 19 21 22 29 35 54 66 67 73 87 89 106 131 133 135 137 139 ° [5 Ff???“ H000 \l O‘Ut-hUJNI—A w w NNN-~ H N H «kn-its) w w #m PP??? mNHam PP? own-h LIST OF FIGURES Rotating stall pattern with m=-3 Continuous and intermittent rotating stall Propagation of stall cell in axial compressor Sequence of passage stall for an unshrouded impeller Influence of rotor speed on critical stage element Simplified surge paths and their variation with connected discharge volume Velocity pattern of Rossby waves together with vortices highs (H) and lows (L) Pressure-time signals for various flowrates Blade-to-blade pressure variation with flow, x/s=0.7 Compressor test rig Characteristic curves for test compressor Measurement sites in the diffuser Data processing pathway for analysis of unsteady pressure and blade vibration signals Data processing pathway for use of Hewlett-Packard FFI‘ analyzer Sawtooth signal recorded by pressure transducer in shroud wall Signals produced by two circumferentially-spaced transducers Harmonics produced by principal pressure fluctuation at 35 Hz Effect of pressure unsteadiness on blade vibration Peaks in blade vibration spectra Characteristic curves for rotor and stage Gould plot of surge train, Nred=10.000 rpm First event in surge train, de=10,000 rpm Third event in surge train, de=10,000 rpm Phase angle analysis for Nwd=10,000 rpm Blade vibration spectra of first section of surge (top) and middle section of surge (bot) ... .....g n w m n m w u m m w m n 46 ‘48 50 52 52 53 55 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.31 4.32 4.33 4.34 4.35 i r ' l Pressure and phase angle spectra for surge, de= 10,000 rpm Pressure-time Signals for surge, Nred=12.000 rpm Pressure-time signal for section A, de=12,000 rpm Pressure-time Signals for section B, de=12,000 rpm Pressure and phase spectra for section B, Nrcd=12.000 rpm Blade vibration spectra for section B, Nred=12,000 rpm Pressure-time signals for section C, de=12,000 rpm Blade vibration spectra for section C, Nrcd=12,000 rpm Pressure-time signals for section D, Nrcd=12,000 rpm Phase angle analysis for surge, de=12,000 rpm Blade vibration spectra for section D, Nred=12.000 rpm Pressure signal at Nred=14,000 rpm, x/s=0.74 Pressure-time signals for event A, de=14,000 rpm Pressure and phase spectra for first rotating stall in event A, Nrcd=14,000 rpm Blade vibration spectra for first rotating Stall in event A, Nred=l4,000 rpm Blade vibration spectra for second rotating Stall in event A, Nrcd=l4,000 rpm Pressure-time Signals for event B, Nrcd=14,000 rpm Pressure and phase Spectra for event B, Nred=14.000 rpm Blade vibration spectra for event B, Nred=14,000 rpm Pressure-time signals for event C, Nrcd=l4,000 rpm Pressure and phase spectra for first segment of event C, Nrcd=14,000 rpm Blade vibration spectra for first segment of event C, Nred=14,000 rpm Pressure-time signals for event D, Nrcd=14,000 rpm Pressure spectra for individual signals (Single-Signal FFTS) for event D, Nred=14,000 rpm Pressure and phase spectra for event D (Cut #1), Nrcd=14,000 rpm Pressure and phase spectra for event D (Cut #2), Nrcd=14,000 rpm Blade vibration spectra for event D, de=14,000 rpm Blade-to-blade pressure variation with flowrate and meridional position (Nrcd=10,000 rpm, 90 deg. impeller) Blade-to-blade pressure variation with flowrate and meridional position (N red=12.000 rpm, 90 deg. impeller) ix 57 58 61 61 62 68 68 69 70 71 74 75 77 77 79 81 82 85 93 95 95 97 99 100 101 103 107 108 D2 D3 D4 El E2 E3 E4 Eigurelitle Blade-to-blade pressure variation with flowrate and meridional position (de=l4,000 rpm, 90 deg. impeller) Blade-to-blade pressure variation with flowrate and meridional position (Nred=16,500 rpm, 90 deg. impeller) General variation in blade-to-blade pressure difference with mass flowrate over last section of impeller Blade-to-blade pressure variation with flowrate and meridional position (de=12,000 rpm, 60 deg. impeller) Schematic representation of compressor test stand Key components of centrifugal compressors Basic diffuser configuration parameters Schematic of Kulite XCQ-080 dynamic pressure transducer Absolute and relative reference frames Signals produced by two circumferentially-spaced transducers Graphical method for determining lobe number Non-dimension. blade-to-blade pressure rise, Nred=10.000 rpm Non-dimension. blade-to-blade pressure rise, Nrcd=12.000 rpm Non-dimension. blade-to-blade pressure rise, Nrcd=14,000 rpm Non-dimension. blade-to-blade pressure rise, Nrcd=16,500 rpm Pressure & phase spectra for rotating Stall, Nred=10.000 rpm Pressure & phase spectra for surge, de=12,000 rpm Pressure & phase spectra for second rotating stall in event A, Nrcd=l4,000 rpm Pressure & phase spectra for second segment of event C, Nrcd=14,000 rpm 109 110 112 115 120 121 122 123 125 128 130 141 142 143 144 145 146 147 148 NOMENCLATURE S' 'f' |' Area ratio Diffuser channel throat aspect ratio Impeller blade height (hub to tip) Average impeller width Absolute velocity Diameter Diffusion factor l—H wlms Z . s - wl,rms Frequency Enthalpy Diffuser charmel width Axial length of blade Diffuser blade length Length to width ratio LWR=—L— h4 Number of stall cells Mass flowrate Reduced mass flowrate mrcd=[TK/288K]-m Shaft rotational speed Reduced shaft speed Nrcd=[288K/TK]0-5-N Static Pressure w V b ]+[1+ lag] Wl,rrns [In] [In] [m/Sl [m] {-l [H2] [Id/kg] [ml [III] [ml {-1 {-l [kg/s} [kg/S] [rev/min] [rev/min] [Pal '1"! U) ascgaam G'WN DE 87313 a D. . . Blade-to-blade static pressure difference [Pa] Stagnation Pressure [Pa] Flow coefficient (Mizuki, 1976) [~] = (9-) 11 2 Pressure ratio [-] Volumetric flowrate [m3/s] Radius [m] Mean radius of curvature [m] Blade length along tip [-] Temperature [K] Period (1 If) [s] Stagnation Temperature [K] Blade velocity [m/s] Relative velocity [m/s] Distance from blade leading edge along blade tip [m] Number of impeller blades {-1 Blade angle or relative fluid angle [deg] Flow coefficient 4V 4) _ [ND3U2] Circumferential position of transducer Phase angle between two pressure Signals Efficiency Diffuser radius ratio Pressure ratio Fluid density Slip factor Rotational speed Rotational velocity Shaft rotational speed {-1 [deg] [deg] {-1 {-1 mwm MM] mM] MM] S' 'E' Ii Blade-to-blade pressure coeff. {-1 2p 91% Subscripts and Superscripts abs "'6 ‘O‘ a ”a at rel/abs Utc§UJNH in the absolute frame atmospheric average of the blade(s), of the blade passes isentropic of settling chamber midway between hub and shroud of the pressure radial component in the relative frame of the relative frame with respect to the absolute frame root-mean-square average at shroud of the shaft of the rotating stall total or stagnation value at rotor inlet at rotor exit at leading edge of diffusor vanes at diffuser vane channel throat at trailing edge of diffusor vanes W Characterizing machine operation beyond simple performance curves can prove difficult to investigators interested in developing a deeper understanding of flow phenomena and operational characteristics of centrifugal compressors. The following Study seeks to characterize the operation of a centrifugal compressor running at de=10,000, 12,000, 14,000, and 16,500 rpm during both normal and unstable operation. Over the normal operating range--from the choking limit to the point where significant instabilities are felt--blade-to-blade Static pressure oscillations at the Shroud are evaluated to determine if they provide a reliable means for tracking reverse flow in impeller channels. At the instability limits, FFI‘ analyses are performed using both a bench top analyzer and Signal analysis software to determine the character of instabilities felt. Blade-to-blade Static pressure difference data were obtained using a bench top FFI‘ analyzer for several positions along the meridional extent of the shroud for several operating points. These data were then processed and displayed three-dimensionally as blade-to-blade static pressure difference amplitudes versus both flowrate and meridional position. This provided a convenient way of detecting trends in blade-to-blade pressure differences and assessing the possibility of tracking reverse flow along the shroud wall by means of its effect on these pressure differences. 2 Using a bench top FFI‘ analyzer to capture and analyze instabilities at part load operation proved much more difficult. Surge events and instances of intermittent rotating stall occur for very brief periods (approximately 125 rotor rotations) before dying out. Analyzing these events using a bench top FFI‘ analyzer required the investigator to correctly guess the advent of stall and activate analyzer scanning within a very narrow time window to produce meaningful results on the analyzer. This method proved cumbersome and difficult. Therefore, in addition to analyses using the bench top analyzer, static pressure and blade vibration signals were digitized and analyzed using signal analysis software. The software approach offered a convenient way to conduct analyses into the character of the specific instabilities encountered. The resulting characterizations of rotating stall found at 14,000 rpm extended the findings of Seidel, et al. (1991b) and revealed the presence of instabilities giving rise to unusual blade vibration characteristics. O O 0 xi? i‘ 5. ii' "I ‘I ..‘5. IN". Rotating stall is a flow phenomenon characterized by rotating circumferential distortions in the flow field. Such distortions are marked by equidistant rotating zones (stall cells) of low flow surrounded by zones of relatively high flow, as Shown schematically in Figure 1.1. [Note: In Figure 1.1, cell rotational sense is indicated for rotation of cells in a coordinate frame rotating with the shaft.] In rotating stall, flow in impeller passages takes turns stalling, then recovering. Specific instances of rotating stalls are usually characterized by the number of stall cells they contain D Region of normal flow Region of low (stalled) flow Fig.1.l. Rotating stall pattern with m=-3 (m), the rotational sense of these cells (m<0 against impeller rotation; m>0 with the impeller rotation), and their propagational speed (msdfl). In contrast to surge, which can be marked by massive system flow reversals, the time-mean mass flow through the compressor does not drop when the compressor operates under rotating stall (Fringe & Van Den Braembussche, 1983). At a set flowrate, rotating stall may emerge as an intermittent series of local, low frequency static pressure oscillations or it may occur continuously. Figure 1.2 schematically illustrates the difference between these two modes of rotating stall. Static pressure patterns for the normal flow show only sawtooth signals produced by blade passes. However, rotating stall produces the roughly sinusoidal pressure oscillations shown. This investigation found instances of intermittent rotating stall for operation at Nred=14.000 rpm. Intermittent rotating stall often precedes continuous rotating stall or surge. fr! _.' I‘M-X) revolutions Static time (a) continuous rotating stall stall / normal / flow 15> , _.l I 100 revolutions time (b) intermittent rotating stall Fig. 1.2. Continuous and intermittent rotating stall The precise physical mechanisms instigating and controlling rotating stall in centrifugal compressors are not well known. For axial machines, authors most frequently explain the propagation of stall cells around the inlet annulus as arising from boundary layer separation and excessive incidence at the leading edge of blade leading edges. According to this model, perturbations in incoming flow approaching the leading edges of inducer blades at excessive incidence cause a group of blades to stall, as depicted in Figure 1.3. This stall acts to block the incoming flow and divert it to nearby flow passages. As a result, flow incidence with the blades on one side of the blocked cell increases; while on the other side, incidence drops. Blades with the increased incidence will tend to stall, while the previously stalled blades will tend to recover. In this way, the stall cell moves to a new location in the direction 5 for which blade incidence was increased. Cells always propagate at speeds less than the rotational speed of the rotor. Experimental evidence suggests that rotating stall in centrifugal machines is much more complex than that occurring in axial machines (Pampreen, 1993). Although the exact mechanisms controlling the inception and character of rotating stall remain largely unexplained, it appears that rotating stall in centrifugal compressors can result from destabilization of flow in either the rotor or the diffuser. The former is called impeller rotating stall; the latter is called diffuser rotating stall. For impeller rotating stall, pressure fluctuations occur throughout the entire meridional extent of blade channels. Kammer & Rautenberg (1985) report maximum pressure fluctuations occurring at x/s=0.8. Direction of rotation Direction of propagation Fig. 1.3. Propagation of stall cell in axial compresso (from Pampreen, 1993) 6 Authors usually suggest that impeller rotating stall results from boundary layer separation either at the inducer inlet, along impeller blades, or along either the hub or shroud walls (Chen, et al., 1989). Flow separation serves to block the forward flow of fluid, thereby producing cells of stalled flow. When boundary layer separation occurs progressively as flow rate is reduced, the resulting stall is called progressive Stall. Progressive stall is usually marked by relatively mild velocity fluctuations and smooth variation in velocity fluctuation amplitude with flowrate (Fringe & Van Den Braembusche, 1983). In contrast, abrupt stall occurs much more abruptly and is marked by relatively strong velocity fluctuations. Lennemann & Howard (1970) provided experimental evidence of how boundary layer separation can produce stall in impeller passages. They used the hydrogen bubble technique to visualize stall patterns produced in pump passages with the pump operated at part load. The pattems drawn in Figure 1.4 in four passages reflect the sequence of events occurring in a single passage during impeller stall. First, boundary layer separation occurs on the pressure side of the blade with subsequent backflow strongly supported by eddying (1). It appears that clearance flow passing over the blade to the adjoining suction side helps stagnate flow on the pressure side, leading to boundary layer separation. Relative eddies then block flow through the passage (2) causing flow to move out of the passage into the inlet (3). Hence, over part of the cycle, the passage acts briefly as a turbine passage. During recovery, the suction side may separate briefly (4). For shrouded impellers, Lennemann & Howard found the patterns to differ from that described above. However, both patterns showed the occurrence of flow separation, followed by blocked flow and regurgitation into the Fig. 1.4. Sequence of passage stall for an unshrouded impeller, (from Lennemann & Howard, 1970) impeller inlet. Pressure ratio usually rises as flowrate drops in centrifugal turbomachines. As flowrate drops, pressure gradients increase until a point is reached where boundary layers separate. ‘ Diffuser rotating stall has been explained as resulting from the interaction between unsteady boundary layers along diffuser walls and the inviscid core flow. The boundary layers presumably provide perturbations that induce a hydrodynamic instability in the diffuser core flow. (Fringe & Van Den Braembussche, 1983; Kammer & Rautenberg, 1985). In vaneless diffusers, stall is always associated with a reversal in the radial component of diffuser flow and with three-dimensional boundary layer separation. However, no one knows how rotating Stall is initiated from the separation ring. For vaned diffusers, conditions in the semi-vaneless space appear to initiate stall. In this area, both increasing static pressure recovery and increasing diffuser vane incidence with decreasing flowrates have been 8 implicated in the initiation of stall. Also, rotating stalls initiated in vaned diffusers rotate opposite to rotor rotation (Pampreen, 1993). The location of rotating stall inception appears related to the operating conditions of a compressor. Fringe & Van Den Braembussche (1983) found that initiation of impeller rotating stall will completely suppress diffuser rotating stall. However, diffuser rotating stall does not automatically suppress impeller rotating stall arising from critical inducer incidence. Kammer & Rautenberg (1985), taking inducer incidence angle and diffuser inlet flow angles as stall criteria, constructed Figure 1.5. As illustrated in the figure, they predict that at low rotational speeds, the inducer determines stall limit. As speed increases, the diffuser load increases until it eventually becomes the critical component. '3 2% :10,% ~ 74 drffuserstall “an ’2, a: . . 5 20 ”trig-”1 1} =060 § mducerstall g 16"% \q =0.65 .\ E 1% D =0.7i g T 20, II, \\\V\‘ 0.75 15 \\\\ 0’V’\ I’ 0 "s .:‘::: g 10/////////// 0”/’/"’l””: to... a as "$63 15 Inducer incidence angle, [deg] Fig. 1.5. Influence of Rotor Speed on Critical Stage Element (from Kammcr & Rautenberg, 1985) 9 Table 1.1 Reported Rotating Stalls (Vaneless Diffusers) Lobe Authors 11.2.1111le Number 91219. AtttihutedJn Kubo & 30.7 +1 0.25-0.3 Murata (1976) ‘ Fringe & 43.5-130.5 +4, +5 0.15 Rotor Van Den 43.5-130.5 +1, +2, +3 0.25-0.3 Rotor Braembussche 43.5-130.5 +1 (with 0.5-0.8 Rotor (1983) harmonics of +2 & +3) 43.5-130.5 +2 0.13-0.16 Diffuser 43.5-130.5 +3 0.17-0.21 Diffuser Ariga, et al. 54.2 -1, -2, -3 0.435 Rotor (1986) 54.2 -3, -4 0.625 Rotor 54.2 -4 0.667 Rotor 54.2 -1 0.333 Diffuser Mizuki, et a1. 60.8 048-10 (1978) Ligrani, et al. 136 2 0.23 (1982) Kammer & 293 2 0.44 Rotor Rautenberg (1982) Kammer & 293 (varied) 0.89 Rotor Rautenberg 314 +3 0.128 Diffuser (1985) 335 +3 0.155 Diffuser Haupt, et al. 335 -2 0.039 (1988) 335 +3 0.159 10 Table 1.2 Reported Rotating Stalls (Vaned Diffusers) Authors Roth (1992) Haupt, et al. (1990) Abdel-Hamid, et al. (1987) Seidel, et al. _ (1991a,b) Haupt, et a1. (1988) 146 168 168 189 189 226 226 293 304 262 226-283 304 251 251 251 25 1 251 251 251 293 293 293 293 293 293 335 335 260-283 283-304 272-304 226-262 226-272 Lobe Number min 2, 3 +5 0.015 +6 0.035 +5 0.021 +6 0.035 +4 0.01 +5 0.02 -2 0.22 -2 0.15 -3 0.06 -3 0.04-0.06 -2 0.1 1-0. 17 -3 0.026029, 0.047, 0.067 +4 0.052 +5 0.0680084 +6 0.050, 0.097 -2 0.129, 0.146 -4 0.013 +7 0.03009 -2 0129-0231 -3 0.020 -4 0.013 +4 0.05 +5 0.014 +6 0.0420092 -2 0.098, 0.18 +5 0.034 -3 0.04006 -2 0.15-0.17 -2 0157-0214 -3 0061-0096 -4 0.01-0.02 Diffuser Geomotu Cambered Airfoil Twisted Vane Twisted Vane Twisted Vane Twisted Vane Twisted Vane Twisted Vane Twisted Vane Cambered Airfoil Straight Channel Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Cambered Airfoil Straight Channel Straight Channel Straight Channel 11 Experimental investigations have revealed the existence of rotating stalls of varying character, including stalls of different lobe number occurring in series at a single operating point (Haupt, et al, 1986, 1988). Investigators have reported rotating stalls composed of from one to seven cells occurring in centrifugal compressors. Generally, stall cell speed lies well under the rotational speed of the impeller, particularly with high lobe numbers. For centrifugal compressors outfitted with vaneless diffusers, Haupt, et al. (1988) have also established the occurrence of non-rotating pressure oscillations occurring at the same point where rotating stalls have occurred. Tables 1.1 and 1.2 list rotating stalls reported by researchers. 1.2.2.8.urgo In contrast with rotating stall, surge produces significant flowrate fluctuations in the entire system. The amplitude of flowrate fluctuations can vary. In deep surge, the pressure differences between compression system inlet and system outlet are sufficiently great to force the fluid in the reverse direction through the machine. Compressor surging sometimes causes the entire compression system and foundation to vibrate and can result in serious damage. Whereas most axial compressors manifest rotating stall behavior before surge occurs, centrifugal compressors often start surging without preliminary rotating stall. This is particularly true for centrifugal compressors operating at high speeds (Wachter & Rohne, 1984). Surge occurs in a cycle, which includes a breakdown in pressure rise and reduction in mass flow through the compressor, followed by a phase of pressure recovery with an increase in mass flow up to the initial point of departure. The cycle then begins again. The operating point for a compressor in surge thus describes a hysteresis loop such as those 12 Steady-state characteristic ———————— Surge; very small volume; stalled flow ._ _. _ .. Deep surge; small volume - — Deep surge; large volume Fig. 1.6. Simplified surge paths and their variation with connected discharge volume, (adapted from Wachter & Rohne, 1984) illustrated in Figure 1.6. The Size of these hysteresis loops gives some indication of the intensity of particular instances of surge. When flowrate variation is dramatic, the operating point traces a large loop as shown. In contrast, surge may be so mild that the operating point merely circles around the top of the performance curve. Generally, surge intensity increases with increases in stage pressure ratio (Cumpsty, 1989). The frequency of flow fluctuations associated with surge usually lies below those for velocity fluctuations associated with rotating stall. The time scale associated with rotating stall depends on the propagational speed of stall cells. However, the time scale associated with surge depends on the size of the compressor exhaust volume. The larger the discharge volume of the compressor system, the larger the time scale for surge (i.e., the lower the surge frequency). Figure 1.6 shows the influence of discharge volume on operating point behavior under surge. 13 Surge usually occurs due to flow instabilities when the compression system is operating near maximum pressure ratios for a given rotor speed. Two such instabilities include (1) abrupt stall and (2) progressive stall. Surge resulting from abrupt stall generally produces violent flow reversals and is audible. Abrupt stall results in a sudden, apparently discontinuous drop in the compressor pressure rise and efficiency. It appears that single cell rotating stall patterns correlate with the occurrence of abrupt surge. Altemately, surge due to progressive stall is relatively mild and frequently inaudible. It gradually reduces stage pressure ratio and efficiency with decreasing flowrate. It appears that multi-cell rotating stall patterns correlate with the occurrence of surge due to progressive stall (Pampreen, 1994). Studies concerning the nature of centrifugal compressor surge have demonstrated that surge consists almost entirely of rotating stall events of m=+l (J in, et al., 1992b). Brief periods of other modes of rotating stall may immediately precede surge but not in every case. For example, I in, et al. (1992b) report finding m=+5 and +6 rotating Stalls immediately preceding surge events at Nrcd=10,800 rpm and 8,000 rpm respectively and m=-2 stalls preceding surge events at Nred=14.000 rpm and 14,500 rpm. However, for operating speeds between 8,000 and 14,000 rpm they found no instances of rotating stall preceding surge. {':H_r"."‘r 1" ‘ l’r'eil {iz'r' -. Chen, et al. (1987; 1989; 1991a,b,c; 1992) has proposed that rotating stall be explained in terms of Rossby waves, which link baroclinic instabilities through secondary reverse flows in impeller channels. According to this model, and verified by Haupt, et al. (1987b), reverse flow travels as vortex filaments from the impeller outlet along the suction l4 surface/shroud side comer. At the inlet, it turns over the leading edge of the blade in the direction of the impeller rotation and into the adjoining impeller channel. There it joins the forward flow, traveling along the pressure surface/hub side comer. A free-swirl flow field arising on the suction surface of the blade in the rotating stall cell then allows the pressure gradient at the impeller outlet to bend fluid exiting from the pressure/hub comer over the blade trailing edge. This fluid then travels back down the adjoining impeller passage as the secondary reverse flow, as explained. Briefly, rotating stall occurring in machines with vaned diffusers (as in the present investigation) is explained as follows. As a result of flow reversal at the outlet plane of the impeller channel, the flow in the semi- vaneless annular space between impeller outlet and diffuser vane inlet has non-uniform temperature and velocity fields. The same occurs at the impeller inlet, where reverse flow meets the low temperature/low entropy incoming flow. These temperature non-uniforrnities result in a baroclinic wave for each of these regions. These two baroclinic waves are linked together by rotating Rossby waves through the impeller channels. Karman vortices as lows and highs reside on the flanks of the Rossby waves. The Karman vortex "lows" travel with the Rossby waves and represent the active cells of rotating stall. Figure 1.7 shows the Rossby wave pattern, together with vortex lows and highs (cyclones and anticyclones). The occurrence and character of rotating stall patterns does appear to correlate with the existence and character of reverse flow in some cases. During the occurrence of rotating stall in a compressor with vaned diffuser, Haupt, et al. (1988) conducted oil injection experiments and verified the existence of reverse flow originating near the impeller outlet. 15 Fig. 1.7 Velocity pattern of Rossby waves together with vortices highs (H) and lows (L), (adapted from Chen, ct al., 1991) They found that for a 2-cell pattern, reverse flow extended to the leading edge of the splitter blades. With 3-cell rotating stall, the reverse flow extended all the way to the inducer inlet and mixed with the forward flow there. As evidence of reverse flow associated with the inception and occurrence of rotating stall, Chen, et al. (1988) present blade-to-blade pressure variation data extracted from Mizuki, et al. (1976) for x/s=0.7. Figure 1.8 represents the pressure-time traces presented by Chen, et al. (1988) for four different flowrates and operation at N=4150 rpm. Pressure-time data for the highest flowrate (the design flowrate) shows sharp pressure pulses residing along the suction sides of the signal. Chen, et al. interpret this to represent the high-pressure fluid from the outlet annulus passing through the core of the reverse flow vortex tube. As flowrate drops, the sharp pressure pulse disappears. Instead, the average pressure increases, and the blade-to-blade pressure differences diminish. Chen, et al. interprets this as an indication that the vortex tube, formerly restricted to the shroud/suction side comer for (pm=0.330, widens over the 16 Fig. 1.8. Pressure-time signal for various flowrates, (adapted from Chen, et al., 1988) phi=0.330 phi=0.165 phi=0.330 phi=0.l 10 17 entire surface of the Shroud. Figure 1.9 Shows how blade-to-blade pressure differences vary as flowrate drops for this data. As flowrate drops, reverse flow not only widens, but also penetrates further upstream, apparently triggering rotating stall once it reaches the blades' leading edges (Haupt, et al.,1988). The linkage between reverse flow and blade-to-blade pressure difference variations is not conclusive. Nevertheless, Chen, et al.'s interpretation of Mizuki's data suggests that under conditions of reverse flow, the blade-to-blade static pressure rise will drop as flowrate is reduced. Furthermore, their analysis indicates that as flowrate drops and reverse flow intensity increases, the influence of the reverse flow should be felt further and further upstream in the impeller passages. If this occurs, then it should be possible to track reverse flow from the rotor exit along the shroud wall by tracking the meridional positions over which a drop in blade-to-blade static pressure difference occurs. 100 /o— 90 /j 80 / 70 I .0 / .../3 0.0 0.1 0.2 0.3 0.4 Flow coefficient diff. (% of phi=0.330 value) Blade-to-blade press. Fig. 1.9. Blade-to-blade pressure variation with flow, x/s=0.7 (adapted from Chen, et al. 1988) Pressure measurements were taken for a single-stage compressor with the basic dimensions shown in Figure 2.1. The compressor was driven by a 1350 kW DC-motor coupled to a gear box with a shaft speed ratio of 1:162. Readers unfamiliar with centrifugal compressors are encouraged to view the contents of Appendix A. A Transducers at x/s = 1.00! (for 90 deg. impeller) H- Two 25 deg Pressure ’ probes at___ g ‘ x/s=0.74 {A ‘ .. _‘__ _ - _ '6. 4: 80 ¢'I A Fig. 2.1 Compressor Test Rig Figure 2.2 gives compressor characteristic curves obtained for this investigation and also shows the measuring points for each speed line. Chapter 4 contains more complete characteristic curves for both the stage and the rotor. Surge formed the instability limitation for part-load 18 19 2.4 ‘ —'— 10,000rpm 23' —v— 12,000rpm 4.: . —°_ 14,000rpm 5.: 2'0 —-— 16,500rpm g l =- 18‘ O I 60 a 1.6* KN ‘0 . 1.4~ "Hm-...” 1.2‘I'V‘I'l't'r' 2 3 4 5 6 7 8 9 Mass flowrate,red. [kg/s] Fig. 2.2 Characteristic curves for test compressor operation at de=10,000 and 12,000 rpm. However, intermittent rotating stall events with m=-3, m=+5, and m=+4 limited part-load operation at Nred=14.000 rpm. At Nrcd=16,500 rpm, the compressor was not run to the instability limit in order to avoid machine damage. 2.1.1—Rotor This investigation employed a 20-bladed radial outlet rotor with every other blade cutback to x/s=0.25. For purposes of comparison, Table 2.1 Geometric Data for Compressor Rotors 90-degree ISO-degree Impeller Imuollor [32:90 deg. [32:60 deg. Blm=27 deg. Blm=27 deg. Zi=10+10 Zi=10+10 D2=400 mm D2=400 mm D15=28O mm D13=280 mm D1h=90 mm D1h=90 mm lax=130 mm lax=130 mm =26 mm =26 mm 20 blade-to-blade static pressure difference measurements were also obtained for both the radial outlet rotor mentioned and a 20-bladed backswept impeller with every other blade cutback to x/s=0.34. Table 2.1 gives further information on the geometries of both impellers. Previous testing at the Institutue of Turbomachinery (University of Hannover) found the blade vibration characteristics for the impellers used in this investigation. Table 2.2 presents these data. Table 2.2 Natural Blade Modes for Impellers Used Blade 90-degree ISO-degree Mods. Imuollor Imuollor I. 1300 Hz 1300 Hz 11. 3305 Hz 2600 Hz 111. 4300 Hz 3950 Hz IV. 5450 Hz 4400 Hz These values represent approximate values for the impeller blades as a set. In actuality each blade has its own natural vibration frequencies, which may deviate from those given above. Also, the vibration of other blades is transmitted through the hub to any blade under consideration. Consequently, under the experimental conditions of this investigation, vibration measurements from one blade will Show not only its own distinct blade vibration frequency but also vibration frequencies from the other blades. This produces fairly wide frequency band (say, of 60 Hz) for vibrations due to excitation of natural vibration modes, instead of one distinct vibration frequency for each mode. LlLlliffusor A vaned diffuser fitted with nineteen cambered airfoil vanes was used for all tests. Table 2.3 gives the various geometric configuration 21 Table 2.3 Parameter Values for Diffuser Geometry A3=l .15 LWR=2.37 [33:27 deg. AR=1.45 [35:37 deg. AS=0.61 parameters for the placement and orientation of diffuser blades. Appendix A contains a schematic representation of diffuser blade geometry and orientation. LLDataJlollootionflstom Results of this investigation are based upon measurements of flowrate, temperature, and pressure taken for several operating points, illustrated in Figure 2.2. Table 2.4 gives further information regarding measured quantities for this investigation. Stagnation temperature and pressure readings were read and recorded manually. Analog voltage-time signals representing pressure history of operation at the different operation settings were recorded on 14 channels on magnetic tape. Transducer output was calibrated so that one bar of pressure corresponded to 1 volt of received output, with no offset. WW Flowrate was measured using a venturi-type flow meter located far downstream of the compressor exit. Throttle valves located downstream of the flow meter allowed for fine control of flowrate. Wont A tachometer measured Shaft rotational speed. In addition, rotor speed could be obtained by identifying a peak in the blade strain frequency spectra corresponding to blade excitation due to the presence of the system exit. 22 882538 8:095 2958 8822-5 Aeneas E095 25 a. sine... Ea 582: 88258 822.5 a 8.2.22 25 . Loamxctxanfimk 58805. 258m 35583 3003 25 a bias... 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Static pressures were routed to mercury manometers with a resolution of 1 mm. Figure 2.3 shows measurement sites in the diffuser. Measurements were also read and displayed using pre-calibrated software. Unsteady pressure measurements along the shroud wall were performed by means of several Kulite XCG-080-050 high-frequency response pressure transducers flush-mounted into the shroud wall. Appendix A contains further information on these transducers. The transducers resided at meridional positions in such a way as to follow the blade edge contour of the 60-degree impeller mentioned previously. This contour deviated slightly from that of the 90-degree impeller. Meridional position of the transducers for both rotors was determined by hand using a Stiff wire. Figure 2.1 indicates these transducer positions for the blade contour of the 90-degree impeller. In order to allow phase analysis determination of the character of rotating stall events, a second transducer at x/s=0.74 was placed circumferentially 125 degrees from the first. For the 60-degree impeller, unsteady pressure measurements were taken along the shroud line at x/s=-0.02, 0.15, 0.4, 0.55, 0.70, 0.80, 0.95, and 1.03. 24 ‘1) Measurement plane: Diffuser blade entrance, D/D2=1.10. 6 Measurement plane: Diffuser blade channel throat. (6‘ Measurement plane: Diffuser blade exit, D/D2=1.55. El Total pressure midway between difl’user walls. 0 Static pressure along diffuser wall. 0 Total temperanne midway between diffuser walls. Fig. 2.3 Measurement sites in the diffuser 25 LLLIomoeratueroasuromont Temperature measurements allow for calculation of stage efficiencies. Total temperatures were read in the settling chamber located upstream of the impeller inlet. Also, total temperature measurements were obtained for several locations in the diffuser and at the stage outlet located just past the collector exit. Figure 2.3 shows the sites of temperature measurement in the diffuser. 2 2 5 B] I '1 |° | Blade vibration measured simultaneously with shroud side static pressure gives insight into the character of unstable flow. This study used blade vibration data from a single strain gage mounted on a rotor blade at the site indicated in Figure 2.1. Previous tests and calculations on a 28- bladed radial impeller ([32:90 deg.) determined that this is the zone of maximum stresses for vibrations in the I. and II. blade modes for a 28- bladed radial impeller used in earlier investigations (Haupt, 19853, 1985b). Vibrating blades flex, thereby elongating mounted Strain gages. In this way strain gages prove useful for measuring blade vibration. In the present investigation, the mounted strain gage transmitted its vibration- dependent blade strain Signals through a FM-telemetry system. A telemetry transmitter resided in the hollow impeller shaft and received power from an inductive power supply consisting of a coil system located between the gear box and the compressor. Transmitted signals were picked up by a permanently installed receiver near the test rig and then routed to data recording equipment. 2 3 D | i I . E . | This investigation analyzed unsteady pressure signals in both the frequency and time domains and blade vibration signals in the frequency 26 domain. Digitizing data converted it into a form digestible to computer programs, useful in the detailed analysis of some signals. Electronic filters were used only to block very high frequencies (above 96,000 Hz) from recorded data during playback of that data. Figure 2.4 shows the signal processing pathway for unsteady blade vibration and shroud-side pressure signals. Time signals were analyzed for evidence of pressure instability and provided the means for identifying problems in data recording and playback. In addition, time signal displays helped the investigator identify specific instances of pressure unsteadiness so that these could be classified as either rotating stall or surge. Time signals were analyzed using a bench top FFI‘ signal analyzer and a signal analysis software package. These allowed the investigator to V VI ,, IOU—t t . F~l> [15] m Amplifier — . Filter Magnetrc Pressure Tape Transducer V . . . AID e - Converter Gould 8,3533% Computer System J Fig. 2.4. Data processing pathway for analysis of unsteady pressure and blade vibration signals 27 determine peaks in pressure and blade vibration spectra, as well as phase transfer angles between unsteady pressure signals taken at two different circumferential positions. 2 3 l I. _ I . I . . | Two principal tools were used to visualize pressure and blade vibration signals in the time domain: (1) an electrostatic recorder and (2) analog oscilloscopes. This investigation employed Gould Electronics' model ES2000 electrostatic recorder for visualizing several pressure signals simultaneously. This recorder consisted of an acquisition and control unit, a plotter, and a display screen. It received and displayed analog signals. Users can select individual signal amplification and arrangements for the display. Analog oscilloscopes used were of the usual type and were equipped with trigger and amplification settings. 2 3 2 E _ I . l . . | Analysis of signals in the frequency domain provided a means for characterizing rotating stall regimes encountered and measuring the rms averaged blade-to-blade pressure difference at particular speed and flowrate settings. Conversion from the time domain to the frequency domain was performed via FFI‘ analyses using (1) a Hewlett-Packard model 3582A spectrum analyzer and (2) DIA/DAGOT”, a software package specifically designed for signal analysis. Both instruments converted pressure time signals to pressure-frequency signals. When two signals were analyzed and compared, both instruments could also provide phase angle spectra. However, only the HP analyzer could provide Coherence readings. The Hewlett-Packard model 35 82A spectrum analyzer accepted analog signals in the time domain, performed an FFI‘ analysis on these signals and displayed the amplitude and frequency of oscillations embedded 28 in the original analog signal. Users could specify frequency ranges of interest for display (max: 0-25 kHz). For two channel FFT analysis, the bench top analyzer also provided information on amplitudes of Coherence (a Statistical measure of the power in one signal caused by that of a reference signal) and phase shift between the two signals. Appendix A contains further technical details for this device. In addition to a bench top FFI‘ analyzer, this investigation made extensive use of DIA/DAGOT”, a signal analysis software package for use on IBM compatible microcomputers. After converting digitized data to a format compatible with the software, it could be analyzed using the specific procedures dictated by the software. By this means any portion of the digitized signal could be displayed in the time domain. For further analysis, this software provided a means for performing either single signal or double signal FFT analyses to determine frequency characteristics of the recorded signal. In addition to providing the location and amplitude of discrete signal peaks in the frequency domain, the software also displayed the phase transfer angle for each frequency under consideration. However, it provided no information on coherence. Terminal displays could be saved to memory and/or printed. Both the bench top analyzer and the software package allowed the user to Specify passband windows for use in the FFT analysis. All FFI‘ analyses in this study used a Hanning passband window. HAPT R -- AT Y I Analyzing measured quantities listed in chapter 2 allowed for (1) determination of characteristic curves Showing pressure and efficiency variation with flowrate, (2) determination of variation in blade-to-blade pressure differences with both flowrate and meridional position, and (3) identification of the character of instabilities occurring at the part-load operation limit. These three results are covered in chapter 4. This chapter details how collected data were analyzed to produce the results presented in chapter 4. Table 3.1 shows the most important derived quantities. Table 3.1 Derived Quantities Parameter Sxmhol Erotn Analxsis Pressure frequency fp FFT analysis Phase angle A¢st FFI‘ analysis Blade vib. frequency fb FFI‘ analysis Blade-to-blade Static pressure difference pb FFI‘ analysis Shaft frequency f5 fs=N/60 Blade passing freq. fbp fs/Z Lobe number m m=(Aostik-21t)/A¢g OI m=(fb+8'fp)/fs Propagational speed cost/Q msdfl=fpl(fs-m) Tom] pressure ratio 150 TCO=P02IP01 lsentropic efficiency Tlisen niscn=[1ro(Y-1/D-l ]/(t—1) 29 30 Wine Careful records were kept for each operating point to keep track of pressures, temperatures, flowrate, amplification factors used to boost the transducer signals, etc. Appendix C shows these data. Temperature and pressure values were entered by hand into a computer; pressure ratios and efficiencies were then computed using an in-house program. Determining the character of the instabilities forming the limit to part- load operation required the use of both analog and digitized signals. The bench top analyzer can perform FFT analyses on analog signals routed directly from the tape player. But, in order to more readily visualize the signals, the output from the magnetic tape player was routed first to the Gould visualization system , then to the FFT analyzer. The Gould visualization system displayed several signals at once and was easier to see and manipulate than oscilloscopes. However, an oscilloscope was also connected to the benchtop analyzer to provide a means of checking the Amplification=l.0 t Block f>96,000 Hz No offset adjusunent I . 33 m p g — Filter Magnetic Amplifier & Tape Offset Adjust. Hewlett-Packard Gould FFI‘ Analyzer System Fig. 3.1. Data processing pathway for use of Hewlett- Packard FFl‘ analyzer 31 signal the analyzer received. Figure 3.1 shows the data processing set up used when using the FFI‘ analyzer. In addition to using the FFT analyzer for characterizing instabilities, DIA/DAGOT”, a signal analysis software package, was also used. However, to use this software, portions of the analog signal recorded on magnetic tape had to be digitized and archived in computer memory or on floppy disks. To do this, analog signal output from the tape recorder was routed to the Gould system for visualization purposes, then to a digitizer, where the analog signal was digitized at a sampling rate of 33474 Hz and recorded in computer memory. Figure 2.5 shows this data processing pathway. A pre-written computer program managed data storage and digitizer control. To digitize a section of the analog signal, the section was first observed on the Gould system. Next, investigators decided how large a section of the signal was of interest and what kind of resolution the investigation required. Because this investigation concerned surge and rotating Stall, with frequencies below 200 Hz, investigators determined that digitizing 15,000 points with the tape run at 1/4 normal Speed would adequately capture each event of interest with sufficient resolution. Thus, 1.04 seconds (1.04 seconds = [15,000 pts/3600 pts. per second] X 1/4)]) of each event of interest were digitized and recorded. To more easily visualize signals for digitizing, voltage-time signals from the tape recorder were manipulated to have large amplitudes before they were digitized. This was accomplished by adjusting amplification and offset settings on the amplifier located between the tape player and the Gould system. Signals from the tape recorder were adjusted to give maximum signal values near but not exceeding 9 Volts. At the same time, minimum signal values were adjusted to be near but below -1 Volts. 32 After digitizing the data, investigators checked to make certain that signal maximum and minimum values all resided within the window required by the digitizer (-1V to 9 V). The digitized signal was then checked visually to make certain that it was continuous and resembled the analog signal. If so, then the digital data stored in computer memory was transferred to floppy disks and reloaded in a computer equipped with the signal analysis software. The digitized data, existing in ASCII format was then converted to a format required by the signal analysis software and analyzed according to the rules and procedures of the software. The bench top FFI' analyzer was used to detennine the blade-to-blade pressure difference values over the normal operating range. The data processing stream was identical to that shown in Figure 3.1. 3 2 i I . [SI i Q |° 3 2 l E |° I [Ii . Determination of pressure ratio and isentropic efficiency was straightforward. The stage and rotor total pressure ratio compares the total pressures recorded at the stage exit and rotor exit, respectively, with the total pressure recorded in a settling chamber upstream of the impeller inlet. As such, they are P atom“, =—3-'2— and (3-1) Po,K P 7 “cause = 1%. Where (3'2) 0 P03 is the impeller exit total pressure, Po,7 is the stage exit total pressure, and P0,}: is the total pressure in the settling chamber. 33 lsentropic efficiency can likewise be calculated for both the rotor and the stage exits. Efficiency is a ratio of actual work compared to work done in an ideal process. For compression between states 1 and 2, this can be expressed as a ratio of the isentropic work (representing the ideal process) and the real work. In terms of enthalpy, this becomes . h - —h 1‘Iisen = wrsen = 0,266“ 0’1 (3'3) wreal h0,2 - h0,1 For an ideal gas, the relation dh=cp- ((11) can be used to rewrite equation (3- 3) in terms of temperature. m... = wise“ = Tm“ _ T” (34) Wren] To,2 — T0,1 For an isentropic process, pressure and temperatures are related 7 P02 {1.232. )[7’1] T0,1 according to . Therefore, substituting into equation 0.1 (3-4), the isentropic efficiency for a compression process between states 1 and 2 can be written as (E) [P02 J 7 _ 1 P0,] T 0,2 _ 1 To,1 (3-5) 1’lisen = For this investigation, equation (3-5) can be used to find values for the isentropic efficiency for the rotor and for the stage. The appropriate expressions are 34 [1?] . . . (no.2 ) — 1 Rotor rsentroprc efficrency “om = I 1 (3-6) 0.2 T [E] 7 . . . (“0,7 ) T 1 Stage rsentroprc efficrency nomge = 1: 1 . (3-7) 0.7 _ Values for rotor and stage isentropic efficiencies were computed for each measuring point. For the normal operating range, a transducer mounted on a compressor shroud wall will give a pressure signal similar to that represented in Figure 3.2. The signal has a sawtooth nature due to the passing of the impeller blades. Pressure builds up in an impeller channel from the suction Side to the pressure side. The pressure reaches a maximum as thepressure side of a blade passes, then drops rapidly when the blade passes the transducer and the transducer senses pressure on the suction side of the blade. Pressure then rises again, dropping when the next blade passes. The blade passing frequency gives the number of pressure peaks produced by the passing of the impeller blades per unit time. For a single blade pass, fbp=1/I‘b. Blade passing frequency is always much higher than the frequencies associated with rotating stall and surge. Blade-to-blade static pressure differences can be determined by performing a FFT analysis of a recorded signal and observing the magnitude of the resulting pressure spike at the blade passing frequency. This blade passing frequency can be determined using the rotational speed using the equation 35 f hp = j, where N is given in revolutions per minute. (3-8) A g T 4 " - " “ 3: 3:5 5 Nde— ' time > Pb = blade-to-blade pressure rise 5 = mean pressure Tb = blade pressure rise period Fig. 3.2. Sawtooth signal sensed by pressure transducer in shroud wall Since we investigated operation at 10,000 rpm, 12,000 rpm, ' 14,000 rpm, and 16,500 rpm, the blade passing frequencies listed in table 3.2 were of interest TABLE 3.2 Blade Passing Frequencies of Interest Speed Before Splitter After Splitter 1mm] Jim W 10,000 1,667 Hz 3,333 Hz 12,000 2,000 Hz 4,000 Hz 14,000 2,333 Hz 4,667 Hz 16,500 2,750 Hz 5,000 Hz Once blade passing frequency was determined, bench top analyzer settings were adjusted to display the expected blade passing frequency and the recorded signal was sampled and averaged by the FFT analyzer using a 36 32-sample RMS mode with a Hanning passband window. The last portion of the recorded signal for the measurement point corresponding to the lowest flowrate at de=12,000 rpm contained surge events, and a 32-sample average could not be used for this point. Instead, l6-sample RMS averaging was used. The amplitude of the blade-to-blade pressure differences appeared as spikes in the pressure Spectra near the calculated blade passing frequency. Because shaft speed varied slightly at each operating point, it was necessary to set the range setting to 0-5000 Hz. Selection of the frequency range played a critical role in obtaining useful values for blade-to-blade pressure rise. At any measuring point, rotor speed fluctuates slightly. This, in turn, makes the blade passing frequency fluctuate slightly. If investigators use a small frequency range in their investigation, the analyzer resolution becomes small enough to detect each of these variations in rotor speed. On the analyzer display, they will observe several peaks occurring in a small frequency band (e.g., three major peaks between 1669 and 1674). Since this investigation used RMS averaging, pressure peaks occurring at non-identical frequencies affect the amplitude of each other. For example, suppose the first sample picked up a pressure peak occurring at 1670 Hz with an amplitude of 55 mV. Now, what happens if the second sample picks up a pressure peak at 1674 Hz with a Similar amplitude? The analyzer computes new RMS averages for both 1670 Hz and 1674 Hz. Since the peaks did not occur at identical frequencies, the RMS average amplitudes drop for both frequencies. To avoid this problem, the frequency range must be set to produce a sufficiently grainy resolution so that minor rotor speed variations do not affect the amplitude of the pressure spike occurring at the blade passing frequency. 37 Readings of blade-to-blade pressure amplitude for several meridional positions for each measuring point (a compressor operation point at which measurements were taken) were recorded by hand in measurement charts. Since transducer Signals were amplified before being recorded on magnetic tape, the values obtained for blade-to-blade pressure rise from the FFT analysis still retain the influence of this amplification. To find the true value measured by the transducers, these raw blade-to-blade values were divided by the appropriate amplification coefficients. For example, suppose a transducer registers a pressure rise corresponding to an output of 4.2 mV. Suppose further that before being recorded this was amplified by 8 (i.e., amplification coefficient=8.0). Then, the blade to blade pressure difference detected by the bench top analyzer would be 4.2 mV X 8=33.6 mV. To get back to the true value of 4.2, the blade-to-blade pressure value obtained from the FFT analyzer (viz., 33.6) must be devided by the amplification coefficient (viz., 8). This procedure was performed for all measurement points for all working probes. Appendix C contains the values of both the raw and adjusted pressure rise data and the values of the amplification coefficients used. As one might expect, blade-to-blade pressure difference amplitudes for operation at high speeds exceed those of lower speeds. Two means were used to account for the influence of blade speed on blade-to-blade pressure difference to make the data more comparable with one another. First, blade- to-blade pressure values were non-dimensionalized using the rotor exit static pressure. These non-dimensionalized values were then plotted against both meridional position and mass flowrate. Appendix D contains the resulting graphs. A second means to account for the effect of operating speed on 38 blade-to-blade pressure rise data consisted of converting these data into pressure coefficients using the following formula: vb =[ 281,2]. _ (3-9) PK '112 This strategy successfully collapsed the data into the same approximate range while retaining the overall trends observed in the unadjusted data. Blade-to-blade pressure coefficient data were plotted against both meridional position and flow coefficient using Mathematicam, a mathematics software package. Chapter 4 contains these results. To convert the pressure coefficient data into a form digestible to Mathematica, data were first plotted and interpolated using CricketGraphTM (a software package for creating 2-D plots). Values needed for Matlrematica were then read from these graphs visually, manually recorded, then transferred to Mathematica. JJEI'HIIIEIIQ I' Determination of the specific character of unsteady operation required analysis of unsteady pressure and blade vibration data in both the time and frequency domains. 3 3 l i I . I II |° I . Unsteady pressure-time Signals were analyzed in the time domain by first printing hard copies of the signals, then measuring distances corresponding to the wavelengths of principal frequencies present. Hard copy representations of signals of interest were obtained using either the Gould system plotter or the signal analysis software together with a laser quality computer printer. Events were classified as either rotating stall or surge according to how their time histories resembled those of rotating stall and surge events from past investigations. 39 3 3 2 i I . I II I] I . Most insights into the nature of unsteady flow in this investigation occurred through FFT analysis, which converts signals in the time domain to signals in the frequency domain. _ Rotating stall in centrifugal compressors can be characterized in terms of stall cell (lobe) number, rotational speed, and rotational sense. Two types of analysis are commonly used to measure the stall propagation and lobe number (1) Analysis of pressure measurements taken from two pressure transducers placed at different circumferential, but identical radial positions, and (2) Analysis of pressure signals along the shroud wall, together with blade vibration frequencies. The following explains these two methods. W The first method finds the lobe number by comparing the phase angle between pressure signals of two peripherally placed transducers. Figure 3.3 shows two such pressure signals and indicates the phase difference between them. Lobe number can be obtained by applying the following expression: m = (”8‘55 ° 2”), k = o,1,2,3,... (3-10) 3 Here, A¢st is the angular phase difference between the two pressure signals and Aog is the physical angle separating the two circumferential spaced transducers. The direction of rotation is found by noting which pressure signal leads the other. Appendix B shows the derivation of this equation. Proper placement of the pressure transducers allows for accurate, distinct determination of lobe number. The present investigation makes use of transducers placed at (pg: 0 degrees and ¢g= 125 degrees. Accordingly, B /\/ \/‘ Transducer A Fig. 3.3. Signals produced by two circumferentially- spaced transducers mpg: 125 degrees, and a m=+3 rotating stall can produce a phase angle of 15 degrees [i.e., 3=(15 deg/125 deg)=(375 deg/125 deg)]. Since Aog is fixed, it follows from equation (3-10) that finding the lobe number for a rotating stall event only requires the determination of phase angle. The only phase angles of interest are those corresponding to pressure pulses produced by rotating stall events. However, the pressure spectra may contain several peaks, not all of which are produced by rotating stall events. To distinguish peaks that may correspond to rotating stall from those peaks that do not requires the use of the coherence function. Coherence is a statistical function relating the amount of power in one measured signal caused by the other measured signal. If an FFT analysis of two measured static pressure signals produces peaks at the same frequency (fp) and the Coherence at this frequency is high (0.95 p m p one.» .33 .83.. ..8 8:3 331399.30 A... .3."— 000.~— 80.3 H39: 3226. n. 0 coo“? 000.3. E9 00mg: ... mmmz m b ’ v — 59 80.9 000.2 no.0 .000 30.0 .1050 .350 “00.0 .000 00.0 Ll ‘uasr 96335 36215 ‘on 0 0 m. H39: 3826.... man: 0 m. w n I A. e p . r _ . p . 1.4.00.3 _ .— .— 83 P .— P b ) 69. 08.3 0 m w m 10101 ‘uas!LL 1010) 01L 49 Figure 4.1 shows that total pressure at rotor exit decreased slightly for operation at 10,000 rpm as flowrate was decreased. At 12,000 rpm and 14,000 rpm it generally increased slightly. In contrast, total pressure gains in the rotor at 16,500 rpm, increased boldly as flowrate dropped. Rotor isentropic efficiency partly explains the behavior of total pressure in the rotor. Efficiencies for both 10,000 rpm and 14,000 rpm gradually decline as flowrate drops. The unusual efficiency value for the second highest flowrate at 14,000 rpm agrees with recorded values. Therefore, it probably stems from an incorrectly recorded experimental datum. At 12,000 rpm, the sudden drop in efficiency at incipient surge produced a corresponding drop in total pressure rise. Rotor isentropic efficiency at 16,500 rpm increased significantly over the entire recorded range as flowrate was reduced. Figure 4.1 also shows stage performance. Losses in the diffuser produce stage pressure ratios and efficiencies below those for the rotor. Low efficiencies at high flowrates serve to decrease the total pressure available at the stage exit. Hence, stage pressure ratios tend to assume their lowest values at high flow operation and generally increase as flowrate drops. Again, the dramatic decrease in isentropic efficiency at incipient surge corresponds to a decrease in total pressure ratio for that point. I 2 5 [II | . |° Surge forms the instability limits for operation at both 10,000 rpm and 12,000 rpm for the compressor under investigation. This investigation confirmed earlier findings that a rotating stall with m=+l forms significant portions of surge events in centrifugal compressors. In addition, an interesting form of rotating stall--forming an initial surge event--was 50 En.— 000.3n8. Z .59: owesm .3 8:. 2.50 .N... .wE DEE omssard 51 measured at de=10,000 rpm. The following provides details regarding surge encountered in this investigation. Maul—13mm Figure 4.2, obtained from the Gould recorder, shows the surge events occurring at Nred=10.000 rpm. Analysis of the time signal reveals that each event occured for about 0.6 seconds and resembled the others in that they all show a general decline in mean pressure followed by pressure recovery. Pressure/Phase analysis using the bench top analyzer revealed the presence of stall with m=+l occurring within each instance of surge. For a clearer picture, we digitized pressure and blade vibration signals for the first and third events depicted in Figure 4.2. Figure 4.3 shows the first of the recorded instabilities in the surge train for machine operation at 10,000 rpm. Here two pressure-time signals taken simultaneously for different circumferential positions at x/s=0.74 are juxtaposed to ease comparison. Both show a general drop in mean pressure with the oscillating rotating stall signals superimposed. AlthOugh both signals are similar, they are not identical. This is normal. Signals obtained from different circumferential positions reflect the continually changing unsteady nature of real physical flows as they respond to different boundary conditions. For example, it is well known that the presence of a volute exit produces a circumferential non-uniformity in pressure signals. The remaining surge events more closely resembled that shown in Figure 4.4. Figure 4.4 shows that for both circumferential probes at x/s=0.74, the mean pressure begins to drop for the first 0.13 seconds. This drop in pressure is followed by a general rise in pressure until clear rotating stall ceases. This pressure pulse indicates the presence of reverse flow in Pressure x/s = 0.74 e = 125 deg x/s = 0.74 q: = 125 deg 52 v , . 0'13 0.?) 07:3 1 Time [sec] Fig. 4.3. First event in surge train, Nred=10,000 rpm ' l ' ' T'T’i . I 0 0.3.3 0.5: 0.75 1 Time [sec] Fig. 4.4. Third event in surge train, Nred=10,000 rpm 53 impeller passages during surge (Pampreen, 1993). After this, the pressure drops over the rest of the surge, especially when a second clear rotating stall emerges. After the surge event, the mean pressure recovers before the compressor enters surge again. ' The surge event illustrated in Figure 4.4 appears to have three distinct sections. The first section is characterized by distinct oscillations which die out abruptly at about t=0.2 seconds. After this comes the middle section, which lasts about one-quarter of a second (about 42 rotor revolutions). Parts of this middle section also appear to contain pressure oscillations. The final section resembles the first in that it contains very distinct oscillations which end abruptly at the end of the surge event at about t=0.6 8. After the surge event, no distinct pressure oscillations occur and normal flow resumes with a recovery in the mean pressure. Analysis using both the bench top analyzer and signal analysis software reveals that the first instance of surge depicted in Figure 4.2 is 14o m§-2 ‘-5 +5 +1] 0 lst Event 0 3rd Event 7:3 E. § § 0 i 100 l l ‘ 100 120 140 Angle of Separation, 4); [deg] Fig. 4.5 Phase Angle Analysis for Nred=10,000 rpm. 54 composed entirely of m=+1 rotating stall with speed wsdfl=0.33. It also reveals that m=+1 rotating stall causes the clear pressure oscillations at the beginning and ending sections of the surge event depicted in Figure 4.4. Figure 4.5 shows the results of pressure/phase analyses for both events. Note that the phase analysis reveals several possible modes of rotating stall. Blade vibration analysis provided a better indication of the lobe number. Table 4.1 shows the results of the analyses. Full results are given in appendix F. Table 4.1. Rotating stalls in surge at Nred=10,000 rpm Event 'PLressure iobe fil‘ropagation Number Frequency Number Speed fp m (oer/Q 1 56.3 Hz +1 0335 3 54.4 Hz +1 0324 Interestingly, both pressure/phase angle analysis and blade vibration analysis showed no clear evidence of rotating stall in the middle section of surge events resembling event 3. Figure 4.6 compares blade vibration signals for the first section of the surge event with the middle section. The blade vibration spectra for the first section reveals distinct blade vibration peaks at 117 Hz and 233 Hz. Both peaks are caused by pressure oscillations. Comparison with pressure spectra data reveals that a rotating stall with m=+1 causes the 117 Hz blade vibration peak. Contrasted to this, the blade vibration spectra for the middle section of the surge signal shows no clear blade vibration peaks except for the blades' 1. and H. vibration mode. Other than these, blade vibration remains fairly flat. A more complete description of a surge event will be undertaken for surge at Nred=12,000 rpm to illustrate the distinct character of each section of surge. Blade Vlb. strain Blade vib. strain Almlgl H7Hz 33HZ Ll 2 J 55 I. Blade Mode ll. Blade Mode r———I 7—1 LAWAV T Y T 1000 2000 3000 4000 Frequencylel ‘ W MW“ V’M,’A~"M\ ' ’ ' I ' l f T7 1000 2000 3000 4000 Frequencyle] Fig. 4.6. Blade vibration spectra of first section of surge (top) and middle section of surge (bot.) 56 The pressure/phase angle analysis for the rotating stalls occurring in surge events at Nred=10.000 rpm represents a good case where the same event will produce several peaks in the pressure spectra. Figure 4.7 shows the pressure spectra and phase angle readings for the third instability in the surge train. Here, as recorded in Table 4.1(b), we have three well-defined pressure peaks at 54, 109, and 161 Hz with corresponding phase angles (M’st) of 118, -128, and -5 degrees, respectively. The analytical procedures explained earlier for determining if pressure peaks arise from the same source reveals that the same source produces all three peaks. The bench top analyzer detected multiple peaks also, with frequency and phase angle information similar to those represented in Figure 4.6. However, it was difficult to establish to which surge event these readings pertained. Coherence for each peak was approximately 1.0. Appendix F gives more complete information. 4.2-Wm A surge event recorded at the instability limit for Nred=12.000 rpm is given in Figure 4.8. Chen, et al. (1994) have analyzed the character of mild, progressive stall before surge at Nred=12.000 rpm. Surge at Nred=12,000 rpm looks substantially like that occurring at Nred=10.000 rpm. Both have what appears to be fairly distinct instances of rotating stall separated by a region of undefined character which appears to contain some periodic pressure fluctuations. Further, both occur for approximately 0.6 seconds. The surge occurring at Nred=12,000 rpm shows more prominent mean pressure fluctuations than occur at Nred=10.000 rpm, indicating stronger reverse flow. At 12,000 rpm operation, the mean pressure rises gradually until shortly after the end of the first apparent rotating stall. It then shows a E... Sqinai .033 ..8 «58% 29:“ 3.23 a. 2385 S6 .wE 0mm _ HNIH>ocmscoLu 00" on . _ fil- O .6 S H 2 . _ > _ _xooHu _ use mm_- _womn T _ _1O _ .om may m- _ ow _— w r /////\\ _ u o m _ioofi ., _ _ _ _ emu I lilrllulrll « _ . com _ ooh _ _ no Izrrrt. _ /L\\_ _ . _ m _ _ I .l _ _ , Z I H _ _ . _ . ZH V'VS [63p]aseud aJnssaJd 58 EB cccfiuatz awe—a ..8 £2»? 250.2385 .06 .wE 33. we; 96 m9 n e 5.0 " 3x d r 8 S S m 8 own 0 u e 0') \ X V5.0 u 59 marked drop until approximately the midpoint of surge, after which it rises until the beginning of the second rotating stall. With the onset of the second instance of rotating stall, the mean pressure again declines quickly, ending its descent with the termination of the second rotating stall. The mean pressure then recovers until the next surge event is triggered. As with surge occuning for Nred=10.000 rpm, the surge events recorded at different circumferential positions for Nred=12.000 rpm look similar, but are not identical. The mean pressure behavior preceding surge at both positions differ radically. At ¢g=0 degrees, a short rise in mean pressure occurs, followed by an even sharper drop. Throughout this spike in mean pressure, blade-to-blade pressure oscillation amplitudes at the shroud line appear to diminish some, hinting that over this period, energy transfer is breaking down in the impeller. The sharp rise in mean pressure indicates the presence of strong reverse flow in the impeller channels (Pampreen, 1993). At approximately the same time that the 0 degree transducer is recording a sharp rise and fall in the mean pressure, the 125 degree transducer records a slight decrease in mean pressure, then an abrupt reduction in blade-to-blade pressure rise. Again, it appears energy transfer largely breaks down as the compressor enters surge. Both pressure/phase angle and blade vibration analyses using the bench top analyzer indicate the presence of m=+1 rotating stall in surge events at Nred=12.000 rpm. However, the question remains: "Does the m=+l rotating stall occur over the entire surge event, or only for discrete sections?" Signal analysis software provides a means for conveniently examining the details of each section of the surge event, whereas the logistics of capturing these details using the bench top analyzer prove cumbersome. To locate the actual occurrence of rotating stall with m=+1 in 60 the surge event, this investigation examined four sections of the surge signal shown in Figure 4.8. For convenience, these are labeled a, b, c, and d, as shown. W Section A, which lasts from t=0.225 seconds to t=0.4 seconds, is shown in more detail in Figure 4.9. It immediately precedes the first large pressure fluctuations, includes the sites where blade-to-blade pressure rises fall rapidly, and appears to contain some periodic pressure fluctuations. Analysis of section A shows mild pressure fluctuations in the 60 to 70 Hz range, but no identifiable rotating stall. W In contrast with section A, section B, which roughly corresponds to t=0.38 to 0.5 seconds, is composed of apparent rotating stall. Figure 4.10 shows the pressure-time signals, while Figure 4.11 shows the corresponding pressure and phase spectra obtained by performing a two channel FFI‘ analysis on these two signals. Both the pressure-time and the pressure spectra reveal that pressure fluctuations for this section occur at varying frequencies. Due to variable oscillation frequency and short sample period (giving poor resolution), the pressure spectra show pressure peaks extending over wide frequency ranges. For example, the frequency peak which shows a maximum of 62.1 Hz has a base which extends from 36 Hz to 75 Hz. Nevertheless, we can use phase angle data to detennine whether or not each of the pressure spectra peaks are caused by the same event. One should note, however, that although the same event causes all of the pressure spectra peaks, this fact is determined by analyzing the phase angle data near the fp=89 Hz peak using that near the 62 Hz peak and by Pressure 61 x/s = 0.74 o = 0 deg Pressure x/s = 0.74 o = 125 deg L41 Time [sec] Fig. 4.9. Pressure-time signal for section A, Nredz 12,000 rpm 0.4 0.425 0.45 Time [sec] Fig. 4.10. Pressure-time signals for section B, Nred=12,000 rpm 0.475 62 E... ogfiuaaz .m 5598 .50 «58% «mafi— a 9:585 .Sé .wE ENI_>ucm:ooLm cc“... of 2: . cm . . . . . _ imwg on _ - ".187. 3a m- 7187 . _iomi T. ;noc “neon _-00~ fliflil T ' i rifrir [fiapleseud aJnSSBJd 63 analyzing the phase angle data near the fp=137 Hz peak using that near 45 Hz. Because the pressure peaks in the frequency domain vary so much and phase angles vary widely as well, we turn to blade vibration data for characterizing the stall for section B. Figure 4.12 shows the blade vibration spectra for section B of the surge. Neglecting peaks associated with the first mode, mild yet distinct blade vibration spectra peaks occur at 144 Hz, 766 Hz, 828 Hz, 1094 Hz, 1236 Hz, 1265 Hz, and 1408 Hz. The peaks at 828 and 1236 Hz are dismissed as harmonics of the shaft frequency (fs=205 Hz). Analyzing the other peaks, and comparing the results with phase analysis results, we find three distinct possibilities regarding lobe number for the rotating stall under scrutiny: m=+1, m=+4 or m=-5. A comparison between these possibilities and those embedded in the pressure/phase analysis shows that of these three possible lobe numbers, results most closely confirm the m=+1 pattern. However, the imprecise nature of the empirical results argue for continued analysis to more conclusively establish the lobe number. I in, et al. (1992a) showed that blade vibration peaks not directly associated with rotating stall can occur due to circumferentially asymmetric rotating stall. This gives a means to narrow the possibilities found earlier for rotating stall of section B. According to J in, et al. (1992a), circumferentially asymmetric rotating stall can induce distinct blade vibration peaks at any frequency given by the following equation: fb=M°[(m'fsifp)+N'fs], (3'12) where M and N are natural numbers. Since it appears that rotating events occurring between 45 and 62 Hz are responsible for all the interesting E... gaineez .m .8303 ..8 958% .8028.» ova—m .Nfié .w_..._ on: 00m; 00m: . _ . _ Ft zH 90l7l .rlL one: ova—m ._ HNIH>ocoacoLn 000~ 00m. 000 0 » t h L 00m H L ZHVVj 012.118 014 30918 65 peaks in the pressure spectra, then we explore possible blade vibration spectra peaks from equation (3-12) using 45, 50, 55, and 62 Hz for fp. Tables 4.2(a) and 4.2(b) show blade vibration peaks calculated from (3-12) which lie within 10 Hz of measured blade vibration peaks. Both tables reflect results obtained for -3$MSS and -10$N $10, which appears to be the important range for these constants (J in, 1992a). Two tables were created to investigate variations brought about by small changes in shaft speed. Results shown in Tables 4.2(a) and 4.2(b) show that m=+l best accounts for all of the blade vibration peaks measured. This confirms that the first rotating stall of the surge events for operation at 12,000 rpm is composed of a one-cell rotating stall rotating in the same direction as the rotor rotation. This also agrees with the results reported in J in, et al. (1992b). Reporting results obtained from the same machine operated under a different configuration, I in, et al. (1992b) indicated that all rotating stall found to occur during surge have one cell and rotate in the same sense as rotor rotation. In contrast to our findings, however, they also report rotating stall occurring just before surge (in the present investigation, we labeled this region A). W Section C, shown in Figure 4.13, fonns the middle part of the surge event and corresponds to the pressure signal between t=0.5 to 0.82 3. (see Figure 4.8). It appears that this section contains distinct pressure fluctuations measured (from the time signal) to occur with a frequency of approximately 79 Hz. FFT analysis shows static pressure fluctuations at 82 Hz. Although a phase analysis reveals several possible modes of rotating stall occurring in this section, the blade vibration analysis indicates that no rotating stall occurs over section C. This result is found by noting from a... 3.8.. :82...» 3a: 8.28.8 a 82:35 .3 N... 35; Ne: .23 N v as: NNN_ e N NNN_ 82 _ a- 82 _ ONE N _ 82 NNNN N- e NNNN N a. 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N NNNN NNNN N NNNN N NNNN N NNNN NNNN N N- NNNN N N NNNN N N NNNN NNN 83 NNN NNN N- N- NNN N- N NNN N N NNN NNN N- NNN N NNN N NNN. NNN N- N- NNN o N NNN N N NNN NNN N . NNN NPN 8N NNN N NNN N- NNN N SN .28.: z 2 .28.: z .28: z 2 .85.: .28.: z .28.: z .28: 2 82...: WE: H+uE mfiE v+nE ~+uE a: Ne": ...-N 2: an: .5: 3: N- N. :8: N. N. 8: _oNNN N N NNNN NNNN N- N NNNN 2 N- 3: N- 3: N N No: NNNN N N- NNNN N N NNNN N N NNNN NNNN N NNNN N NNNN N N NNNN 52 N- N 82 NNNN N N. NNNN NNN N N- NNN 52 o 82 N- NNNN e N NNNN E N N NNN a NNN N N NNN NNN N N NNN o N E N N NNN. NNN N N. NNN N: N N N: N- N N: o N 3N N: N N: N- N: o N SN .28. z 2 .28.: 2 .28.: z 2 88.5: .28.: z 28%: z .28.: 2 .85.: Mr":— 3 H+HE . MINE V..." H+NE 2: RA: .3: 2: 8...... ...-N N: SN": 38: 8:8...» 2.2.. 8:8... 5:. 38.. 8:82» 2.2.. 8328 a 82.855 .5 N... 55.... 68 x/s : 0.74 ¢ - 0 deg 4 E 8 d‘: ‘i‘ - i l 'l 'y l ‘- ll | i ' i I ' X/S'0.74 ll “ i . I ill" ‘1 '- il 0-1250eg: ‘. I ‘l I ‘ ,I - - ,' -' I I ‘i ! . 4 ' 1 | - - l f " ‘f i ’* *ii0 a ,.... a 7 l 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Time [sec] Fig. 4.13. Promure-time signals for section C, Nred=12,000 rpm I. Blade Mode C '5: L H 0') 2 > O.) '0 l S ' . an AM A A M 'j'XNAVWij T I r l ' I 1 _fi 0 250 500 750 1000 1250 1500 1750 Frequency [Hz] Fig. 4.14. Blade vibration spectra for section C, Nred=12,000 rpm 69 EN... :8.NNu§z .Q .8508 .5. 2:58 «Es-c.5895 .mfiv .wE 382 NE; 00.0 . 0N00 N . . . p _. N8 NNN .. N v3.80. 1 amssard awn o a e and .. m\x l'l‘l'l‘f‘lTl‘T 70 Figure 4.14, that for this section no notable blade vibration peaks occur, except at those frequencies associated with the rotor's I. vibration mode. W Figure 4.15 shows the pressure-time signal for section D of the surge signal shown in Figure 4.8. Like section B, section D contains large amplitude pressure oscillations. The pressure and phase angle spectra for this section show that a very notable pressure peak occurs at 75.6 Hz. The peak is fairly wide, with its base extending from 62 to 88 Hz, due to the course resolution resulting from the small time scale of the analyzed section. For this peak, the phase angle lies in the 115 degree range and this can correspond to a number of modes of rotating stall as indicated in Figure 4.16, which presents the results of pressure/phase angle analysis for the entire event, for section B and for section D. ““ .0.- Es +5 M 9 O Entire event —be'nchtop analyzer .— 0 9 Section B 2" 0 Section D ”W“? ... . analyszs 3 Q Entire event '50 5 O E 100 I l ‘ 100 120 140 Angle of Separation, A03 [deg] Fig. 4.16. Phase angle analysis for surge, Nred=12,000 rpm. 71 con; . EE 892...?2 G 5:03. ..8 3.8% .8395? 25m .2... .3..— 3.: 3825: 00m: 82 can. 000 can _ p > b _ _ 2H VLZ FIIL one: ova—m ._ ZH {'Lil UIBJIS 'QM GDBIQ 72 Blade vibration spectra give more information concerning which type of rotating stall was encountered in section D. Figure 4.17 shows that prominent blade vibration peaks occur at 137 Hz and in the frequency range corresponding to the first vibration mode. Analyzing these data gives the result that a rotating stall of m=+1 produces the oscillating pressure patterns of section D. Appendix F contains complete analytical results for the surge event pictured in Figure 4.8. Knowing that m=+1, a review of Figure 4.16 shows how much more accurately the bench top analyzer captured the appropriate phase angle for an entire event than did the software. This may stem from the fact that probably a different surge event in the surge train was analyzed using the bench top analyzer than was analyzed using the software. In summary, each surge event at both Nred=10,000 rpm and de= 12,000 rpm is composed of two segments of clear rotating stall separated by pressure unsteadiness of largely indeterminate character within which reasonably clear pressure oscillations reside. Within these intermediate sections, no rotating stall was detected. Comparing the results of analysis for the section as a whole with those obtained for its sub-sections reveals a dramatic variation in pressure, phase angle, and blade vibration spectra which occurs, depending on the portion of the recorded signal analyzed. Table 4.3 summarizes these results for de=12,000 rpm. Despite the differences, phase analysis did indicate possible modes of rotating stall; blade vibration analysis specifically showed which of these was the actual one. Blade vibration signals provided the most accurate means for determining the character of pressure oscillations recorded. 73 Table 4.3. Rotating stalls in surge at Nred=12,000 rpm Sect'on Frequency Number Speed 1 TD m (on/Q Entire 62 Hz +1 0.302 A 60-70 Hz -- -- B 50-62 Hz +1 0244-0302 C 82 Hz -- -- D 76 Hz +1 0.371 In contrast with operation at 10,000 rpm and 12,000 rpm, the compressor was not run to surge at Nred=14,000 rpm. Instead, intermittent rotating stall formed the limit to low flowrate operation. This investigation recorded four of these events, as shown in Figure 4.18. For convenience, these events are labeled A, B, C, and D. Using the software approach explained earlier, it was found that multiple modes of rotating stall occurred within each event. Rotating stalls with m=-3, m=+4, and m=+5 were definitely detected. In addition, it appears that in two instances,a weak =-2 rotating stall may have occurred simultaneously with a m=-3 rotating stall. Highly irregular blade vibration spectral patterns were encountered. The following presents the details of the experimental findings regarding rotating stall at Nred=14,000 rpm. mm Figure 4.19 shows the pressure-time trace of the first prominent instability recorded for Nrcd=14,000 rpm. The entire event appears to contain at least two, possibly three different rotating stalls and lasts for approximately 0.55 seconds (130 shaft rotations). Analysis of the time signal indicates that the pressure fluctuations forming the initial section of 74 Q o "m a a I. h c \x ER. 25 31322:“ .mcwfi 9:58.:— .w~.v .mE 65:239. 258 8:83. 33 75 0.: En.— 25.3"..22 .4. E96 ..8 £23.." «Eton—58.5 .36 .wE H82 2:; or O .—‘ O mac v.0 md UITrTT l r*r* ‘lrl‘ 1T7—T I 9% mm_ a e 3.0 a 3x amssord 3o 0 a e 3.0 u 2x 76 the event begins with mild amplitude and variable, but low frequency. They then quickly increase in both amplitude and frequency up to t=0.28 s., at which point a new type of rotating stall appears to emerge. This new mode of rotating stall occurs with large pressure fluctuations and comparatively high frequency. IJIIEI ||° III The initial section of event A was investigated using a phase angle and blade vibration spectral analysis to determine the presence and character of any rotating stalls present. Figure 4.20 shows the pressure and phase angle spectra for this section of event A. A phase angle analysis performed using software revealed two possible modes of rotating stall here: m=+3 and m=-3. To pinpoint the character of the first rotating stall occurring in event A, we turn to a blade vibration analysis. Figure 4.21 shows the blade vibration response for the 0.1 $350.28 3. section of event A depicted in Figure 4.21. This interval corresponds to approximately 40 rotor rotations. Several prominent peaks appear in the blade vibration spectra; however, most of these (viz., 718, 952, 1191, and 1430 Hz) can be accounted for as multiples of the shaft frequency (fs=239.6 Hz) and can be dismissed as not resulting from rotating stall. After these peaks are dismissed, only one unexplained prominent peak remains: that at 753 Hz. This peak corresponds to m=-3. Since this agrees with one of the possibilities uncovered by the phase analysis, the investigator can justifiably conclude that the first rotating stall in event A had three lobes (cells) and rotated in a direction opposite to that of the rotor. Applying equation (3-13) reveals that for this mode of rotating stall msdQ=0.048. Interestingly, this mode of 77 342Hz Pressure r --Jh-‘——‘—-———— J 4 J Phaseldegl 9 50 100 150 200 Frequency [Hz] 4.20. Pressure & phase spectra for first rotating stall in event A, Nred=l4,000 rpm N I n In N N I .. N IE] 5‘ In . adeHode (U- :4 O ' ' :3. I N m 7 N 0 f . I K o g «0‘ to ..E N F‘ O; '—o '91:: >" n n V“ 0‘ N N ’3 "U“ .. _ (U (D r ' r T r ' f - I f r ‘ O 23) 3X) ‘Km to“) 123) 15“) 17m) Frequency [Hz] Fig. 4.21. Blade vibration spectra for first rotating stall in event A, Nred=l4,000 rpm 78 rotating stall did not greatly excite blade vibrations at the rotor's I. vibration mode. W The second rotating stall of event A begins at approximately t=0.28 s., as represented in Figure 4.19. Measurements of wavelength from the time signal indicate that pressure oscillated with a frequency of 116 Hz in this section, while the pressure spectra for this section shows a clear peak occurring at fp=116.5 Hz with a corresponding phase angle of -105 degrees. Again, phase angle analysis reveals several possible modes for this rotating stall: m=+5, m=+2, and m=-1. Figure 4.22 shows the blade vibration spectra for the second rotating stall of event A. Unlike the first rotating stall of event A, the second rotating stall does not show a number of prominent peaks in blade vibration spectra over a wide range of frequencies. Instead, this rotating stall excites prominent blade vibrations at 1087 Hz, 1238 Hz, and those frequencies associated with the blades' 1. Mode. Dismissing the 1. Mode frequencies and performing a blade vibration analysis, we find that the 1087 peak can correspond to rotating stalls with either m=+5 or m=-4. Comparing this with results obtained from the phase analysis suggests that the second rotating stall in event A had m=+5. For this mode of rotating stall, we find msdfl=0.098. The source of the 1238 Hz peak is unknown. This peak does not correspond to a multiple of the shaft frequency, a multiple of the system noise frequency (50 Hz), or a result of a circumferentially asymmetric rotating stall. Sometimes vibration peaks lying near those of the I. Mode are amplified due to their proximity to vibration frequencies of the I. Mode. Possibly, the prominence of the 1238 Hz peak results from its 79 ES Soiustz .< .53 E :53 ”5.39. 6:88 .8.— abqum .5295? ova—m .mné .wE smug ccn_ ommz r » HNI_>ucosooLu coo“ can con _ 5 W P } .‘l‘l’u’.a\}\(\<(’|\l§/.l. com l\(\(/\I|l\r\(ll\|] p 2H 8231 FIL one: mum—m ._ ZH L801 UlBJIS'QlA*999l8 80 proximity to the 1. Mode. However, with the given data, no conclusive determination of its origin can be established beyond identifying this possibility. Nevertheless, the fact that this peak lies 151 Hz from the principal blade vibration peak is significant. As it turns out, this sort of extraneous peak shows up in blade vibration signals for the other events recorded for Nrcd=14.000 rpm, too. Signal analysis software proves very useful for rapidly changing occurrences such as event A. Analysis conducted using the bench top FFT analyzer produced results only for the second rotating stall, as can be seen from Appendix F. However, once the existence of the m=-3 rotating stall was established using a software approach, it was possible to find this rotating stall with the bench top analyzer. Nevertheless, this required several trials and the operator had to activate the analyzer at precisely the correct moment to detect this mode of rotating stall. This illustrates the usefulness of the software approach over the bench top approach for investigating these very brief events. W The pressure-time signal for event B, pictured in Figure 4.23, shows that this event appears to consist of a mode (or modes) of rotating stall giving somewhat varying frequencies in pressure oscillations. It turns out that the character of the rotating stall(s) occurring in event B is very difficult to conclusively establish. Figure 4.24 shows the pressure and phase angle spectra for event B. Shown are three distinct pressure peaks centered at 48 Hz, 83 Hz and 129 Hz, respectively. Analysis using the bench top analyzer revealed a strong peak at 45 Hz, with weaker peaks at 85 Hz and 131 Hz. Each had a coherence reading of 0.98 to 1.0. The weakness of the 83 Hz and 129 Hz 81 QC EB Seiueez . .m «:96 ..8 2.2—Em «55-9—38.5 .mné .wE 30$ 05:. v.0 md U“:- o‘ lTlrl ' l moo mm: «e v50 ... m\x m w m. moo o no v50 .... m\x -...t (\l I 82 5.... 25.3"..an .m Ease ac «558 «we ..8 958% 82:— on 9:58.:— éNé .uE HNIH>ocoscoan w: on. on; OS ms _ on 8 p p t b L _ t r t h r 7 on? 32.. r toot .to use R . o _ too 0 1 e 2 _ toe . 8.0 n2 _ _ BE 0.: on; mm” 2: _ no 8 mm _ _ r p _ . — P P h r _ . . 9 t C. s H T Z Y [69p]eseud aJnSSBJd 83 peaks motivates us to ignore them for now and to concentrate on the 48 Hz oscillation. Focusing on the 48 Hz peak, we notice that the phase angles recorded for this peak vary dramatically over its base from 98 degrees to -10 degrees. For transducers spaced 125 degrees apart, it follows from equation (3-10) that rotating stalls can only give phase angles as follows: lml lAfstl 7 155 6 3o 5 95 4 140 3 15 2 110 1 125 Since no rotating stalls occur for phase angles between 30 and 95 degrees and since the phase angle represented at different frequencies will actually be correct only for those locations corresponding to rotating stall, then we can neglect the portion of the 48 Hz peak with phase angles located in this range. Thus, we can neglect the area between 35 and 45 Hz. Noticing that below 35 Hz the amplitude of the pressure peak is low, we turn our attention to those portions of the peak between 45 and 50 Hz. It appears that this section of the peak most likely represents the effects of rotating stall. A phase analysis for the sections of the 48 Hz peak where rotating stall may occur reveals that several possible modes of rotating stall can correspond to pressure oscillations with this frequency: m=-3, m=+3, m=-5, and m=-2. In order to narrow the field of possible rotating stall modes, a comparison between the results of the phase analysis and results obtained from a blade vibration analysis is helpful. 84 Before moving to the blade vibration spectra, we first determine if the 83 Hz and 129 Hz pressure peaks are related to the 45 Hz peak in the pressure spectra. Recall that this can be done by examining the phase angles involved and noting if the phase angles of the higher frequency peaks are the appropriate multiple of the phase angles of the lower frequency. As noted, for this event analysis must focus on the portion of the 48 Hz peak between 45 Hz and 50 Hz. In this range, the 48 Hz peak contains phase angles of between -15 to 30 degrees. Calculating for the 83 Hz peaks we find that in order for the two peaks to be related, the 83 Hz peak must contain a phase angle between -28 and 57 degrees. Since the 83 Hz peak does not contain a phase angle reading in this range, we conclude that the 83 Hz peak and the 48 Hz peak are not directly caused by identical physical events. Similar procedures reveal that the 129 Hz peak is not directly caused by the same event as causes the 48 Hz peak. It appears, then, that three distinct pressure fluctuations were detected which are not directly caused by the same event. Figure 4.25 shows that the blade vibration strain spectra for event B contains several distinct peaks. Of these, the peak at 157 Hz may be dismissed as a "false" peak arising as an aliased signal of the blades' 11 Mode. The 1204 Hz and 1682 Hz peaks can be dismissed also. These arise as harmonics of the shaft frequency (239 Hz). To avoid false peaks in signal analysis, digitizing must conform to the sampling theorem: fsaZZfsi, where fsa is the sampling frequency and fsi is the frequency to be analyzed. In this investigation, fsa=3474 Hz. Under the conditions of this investigation, any peaks residing in blade vibration spectra between 1737 Hz (fsa/2) and 3474 Hz will be reflected back and show up as "false" peaks in the blade spectra. In our case, only one 85 2H 3891 EE Seinei .m «:96 ..8 «.5on .8255? mum—m .mué .wE E: 3533.: cog coma 000— can com com . p s p c r p . b P ZH I702! ZH SI ll 2H 171.01 2H 886 2H 609 zH 6LZl ZH916 zH 99L. ..IIL «no: ova—m ._ 2H LSl l ' UIBJIS 'QlA 30218 86 significant peak occurred in this frequency range: the vibrations near 3320 Hz associated with the blades' 11 mode. The difference between these frequencies shows up as the false peak at 157 Hz (i.e., 3474-3320:154). An FFI‘ analysis of the digitized signal between t=0.l s. and t=0.26 s, which corresponds to the section wherein significant pressure oscillations first begin, shows no peaks near 157 Hz. Blade response for this section only shows excitation of frequencies corresponding to multiples of the shaft frequency and excitation of blade vibration near fb=745 Hz. Given fps 40 Hz, fb=745 Hz probably corresponds to an emerging m=-3 rotating stall. This m=-3 rotating stall produced the fb=766 Hz peak in Figure 4.27. We leave the explanation of the remaining blade vibration strain spectra peaks until later. Several possibilities emerge for explaining the causes of the three peaks shown in Figure 4.25. Of these, the following are investigated: (1) All three pressure spectra peaks are caused by distinct physical events (e.g., rotating stall) operating in series. (2) Distinct physical events occurring concurrently produce the 48 and 83 Hz pressure spectra peaks and produce the 130 Hz peak as an artifact. (3) Distinct physical events cause the 48 and 130 Hz pressure spectra peaks, while the 83 Hz pressure peaks is produced as an artifact of these two peaks. ”2] E .1.“ 5E] The first possibility to explore is that all three peaks in the pressure spectra are caused by distinct modes of rotating stall occurring in series. Table 4.4 presents the results of the pressure/phase angle and blade vibration analyses for this situation. It shows that a m=-3 rotating stall may cause the 48 Hz peak, no rotating stall causes the 83 Hz peak, and a m=+3, m=+6, or m=-2 rotating stall may cause the 129 Hz peak. 87 TABLE 4.4. ANALYSIS OF EVENT B, Nred=l4,000 rpm PHASE ANALYSIS DIA/DAGO DIA/DAGO 83 DIA/DAGO 129 FFT Analyzer 45 FFT Analyzer 85 FFT Analyzer131 18 133 50-100 4 154 128 Possible Annular: (94:12] W minutes m=-3 m=+3 m=+6 m=- =+1 m=+4 m=-5 m=+l m=+4 m=-2 m = - 3 =+3 m=+4 m=+7 m = - 2 =+1 m=+4 BLADE VIB. ANALYSIS ' Calculated W make: 609 -- 766 m=-3.00 916 m=+4.03 1334 I. Mode 1347 1. Mode 1368 m=+5.9l and 1. Mode 609 m=+2.09 766 -- 916 -- 1334 m=+5.9l and 1. Mode 1347 m=+5.96 and 1. Mode 1368 m=+6.06 and V I. Mode 609 m=-2.01 or m=+3.09 766 -- 916 -- 1334 m=-5.03 and I. Mode 1347 m=-5.08 and 1. Mode 1368 1. Mode 762 m=-3.01 88 The readings from the FFT analyzer recorded in Table 4.7 for 45 Hz and 131 Hz appear slightly more accurate than those obtained from the software. However, the phase angle (A¢st) for the 85 Hz peak disagrees strongly with the probable value. From consideration of the blade vibration spectra, the m=+6 pattern can be dismissed from consideration. It is well known that the 1. Mode will often amplify vibrations lying near it in the frequency domain. The fact that the blade vibration peak corresponding to m=+6 lies close to the I. Mode and shows mild amplitudes motivates dismissal of this stall pattern from the list of suspected rotating stalls. The prominence of the 1368 Hz peak likely results as a consequence of its being amplified by the nearby I. vibration mode of the blades. Further, the m=-2 and m=+3 modes of rotating stall correspond to a more distinct, larger peak in the blade spectra and, therefore, constitute more likely candidates. The above-mentioned modes of rotating stalls, if assumed to be circumferentially asymmetric, can account for all of the peaks encountered in the blade vibration spectra. Separately, no one mode of rotating stall explains all of the blade vibration peaks. Collectively, however, they do. Table 4.5 shows which peaks the different modes of rotating stall account for. The m=-2 hypothesis combined with an identified m=-3 rotating stall accounts for all of the observed blade vibration spectral peaks, whereas the m=-5 hypothesis does not. Although positing the occurrence of several distinct modes of rotating stall accounts for the pressure and blade spectra data, it appears that this scenario does not in fact occur. Examination of the pressure-time signal given in Figure 4.23 does not reveal three, or even two distinct rotating stalls at different frequencies occurring in series. Instead, what 89 Table 4.7. EXPLANATION OF BLADE VIBRATION PEAKS DUE TO DIFFERENT STALL MODES fp=48 Hz fp=129 Hz In ngak mz-z m:i§ m:-5 mz-z 609 x x ‘766 x x ' x 916 x x 1074 x 1101 x x 1115 x 1279 X 1292 x x x 1395 x x 1532 x x x appears are two pressure fluctuations with one clearly dominating the other and withthe weaker signal growing in strength as time elapses. This is what we would expect for distinct, simultaneous static pressure oscillations as may occur with the presence of concurrent rotating stalls. But, the complicated nature of pressure oscillations make time-domain analysis relatively infertile ground for producing meaningful results. ”22 E .1.“ EEZ The second possibility to consider posits that two pressure oscillations occur simultaneously, corresponding to the 48 and 83 Hz pressure spectra peaks, respectively. In acoustics, which deals with pressure waves, when two tones are produced simultaneously, the human ear will hear tones corresponding to their individual frequencies, a tone corresponding to the sum of their frequencies, and a tone corresponding to the difference of their frequencies. Using this as an analogy, possibility #2 proposes that the 129 Hz peak occurs as a by-product of the superimposed pressure oscillations at 48 and 83 Hz. However, FFT analysis of physical signals does not operate as does human hearing. All three pressure peaks which 90 show up in the FFI‘ analysis have direct sources in the physical signal. Therefore, possibility #2 must be rejected. ”23 E .1.“ 113 The third possibility to explore supposes that two modes of rotating stall occur simultaneously and that these two rotating stalls show up in the pressure spectra as peaks at 48 Hz and 130 Hz. According to this possibility, the 83 Hz signal occurs as a by-product of these two frequencies (83 Hz :13] Hz-48 Hz). As with possibility #2, possibility #3 derives from an analogy with acoustics and human hearing. Discussion from possibility #2 argues that we must abandon the notion that the 83 Hz peak derives from the others. i The time signal hints that two distinct pressure oscillations occur simultaneously. This agrees with both the pressure and blade vibration spectra data. Close examination of the pressure-time signal shows a 45 Hz oscillation dominating a superimposed 125 Hz oscillation. No oscillations at 83 Hz appear. The discussion of possibility #1 suggested that pressure oscillations giving rise to the multiple blade spectra peaks occur throughout the entire event. It also showed that only by assuming the m=-3 rotating stall and the =-2 rotating to be asymmetric could all of the blade peaks be accounted for. Asyrnmetries most often arise due to the influence of the compressor exit. The exit produces a circumferential distortion of the pressure field felt in the compressor and probably thereby influences the amplitude of pressure oscillations associated with rotating stall cells as these travel circumferentially. For simultaneous rotating stalls, the presence of the other rotating stall would represent a circumferential distortion in static pressure and would likely produce circumferential static pressure 91 amplitude variations for that rotating stall. Consequently, if two rotating stalls occur simultaneously, they both can be expected to be circumferentially asymmetric. 132 I R 'I'l'l Ell A fourth alternative simply dismisses the 83 and 129 Hz pressure peaks as insignificantly small. Under this assumption, the unexplained peaks in the blade strain spectra must be accounted for as resulting from either the m=-3 rotating stall with fp=48 Hz or as "false" signals arising from the non-linear nature of the system under analysis. Non-linear oscillations sometimes give rise to unusual peaks in frequency spectra which arise from the non-linearity of the system. This occurs when oscillations interact in such as way as to modulate each other. This can be illustrated by observing that A sin(x)-B sin(y)=(A-B/2)-[cos(x- y):l:cos(x+y)]. where A, B, and C are constants. This trigonometric identity shows how one oscillation (sin(x)) modulates a separate oscillation (sin(y)) and produces two superimposed oscillations which combine the frequencies of the original signals. In the system under investigation here, an oscillation at 157 Hz peak may have modulated one at 766 Hz, producing peaks at 766 Hz+157 Hz (913 Hz) and 766 Hz-157 Hz (609 Hz). Alternatively, these peaks may arise due to aliasing of vibrations occurring at frequencies higher than those explored here. In this case, the 157 Hz peak also arises as an aliased signal. In summary, the principal rotating stall found in event B had three cells and rotated counter to the rotor rotation with (1)/(2:0.067. Possibly, a much weaker m=-2 rotating stall rotating with (est/(2:027 occurs simultaneously with the m=-3 stall. However, such simultaneous rotating 92 stalls have not been reported in the literature. Consequently, the hypothesis of the sirnultaneity of stalls must be viewed with considerable skepticism. W Like event A, it appears that event C is composed of two distinct rotating stall patterns occurring in series. Figure 4.26 shows the pressure time signal obtained for this event from the two transducers at x/s=0.74. It shows that event C occurs for about 0.4 seconds (130 rotor revolutions). Analysis of the time signal shows that the first 0.15 seconds of the event contains pressure fluctuations oscillating near 48 Hz, while the rest of the event contains pressure fluctuations with frequencies near 21 Hz. The analysis of these two segments is straightforward. 13311? | ||° Ill Figure 4.27 shows the pressure and phase angle spectra for the first segment of event C and shows a fairly wide, prominent pressure peak with maximum amplitude at 48 Hz. For the majority of this peak, phase angle (A¢st) remains fairly level. A pressure/phase angle analysis reveals that this pressure peak is likely caused by one of three rotating stall patterns: m=+3, m=-3, or m=+6. Analysis of the blade vibration spectra helps determine which of these is correct. The blade vibration spectra are shown in Figure 4.28. Each of the prominent peaks in this Figure may be shown to correspond to the I. blade mode, a multiple of the shaft frequency, or the result of a circumferentially asymmetric rotating stall pattern with m=-3 or m=+6. Therefore, we narrow our considerations to the m=-3 and m=+6 modes of rotating stall. These correspond to prominent blade vibration peaks at fb=767 Hz for m=- 3 and fb=1382 Hz for m=+6. 93 EE ogiueaz .0 E96 .5. 2.33m 653-8565 .36 .mE 362 68; 'IYTY—T-‘T U T 7 ‘ I moo m9 u 9 Ed a 8x amssord own 0 u e v.50 u m\x 94 As already noted, the 1. mode of the rotor often amplifies signals lying near it in the frequency domain. Consequently, we can explain the prominence of the 1382 Hz peak--whose existence can be attributed to the circumferential asymmetry of the m=-3 stall mode--to its proximity to the 1. Mode of the blades. This, together with an examination of results obtained with the bench top analyzer (see appendix F) argues for the elimination of the m=+6 pattern from consideration. Therefore, it appears that the first rotating stall pattern has m=-3 and msdfl=0.067. W The pressure and phase angle spectra for the second pressure fluctuation occurring in event C shows a very clear peak occurs at fp=21 Hz. A pressure/phase angle analysis shows that the pressure peak was likely caused by a stall pattern with m=-2, m=+1 or m=+4. Comparison with the results of a blade vibration analysis confirms that the rotating stall has four cells rotating in the same direction as the rotor with cost/(2:0.022. Figure 4.27 shows the pressure and phase angle spectra for the m=-3 rotating stall. Note the difference between the recorded phase angles and the actual phase angle corresponding to the identified mode of rotating stall. According to equation (3-10), a m=-3 rotating stall should give rise to A¢st=-15 deg. However, the phase angle recorded here is A¢st=-l degree from the software and -7 degrees from the bench top analyzer. Furthermore, from Figure 4.27, it appears that for the pressure peak in question, the phase angle never reaches -15 degrees. Error in measuring A¢g could account for discrepancies between measured phase transfer angles and expected phase angles. If this were the case, however, the measured angle values would deviate from the expected values in a consistent way. For example, measured phase angles would always either Pressure phaseldeg] Blade Vlb. stratn 95 $ m V l 1 l J I * I I e , I ‘ L/ I ___ _. lo 100 150 1300 ‘,_____1 Ln __ _.__ ___-_. _____ 150‘| | A ‘l ./\/ \ 100~| l ‘ -1 50—. l deg \, 0.4 ~50“I 1ij —150 1 ~ t . - 1 50 100 150 200 Frequency [Hz] Fig. 4.27. Pressure & phase spectra for first segment of event C, N Ired:14,000 rpm I.BladeMode I H (x \D [x N l I N N CO NI N I ‘3 3311521: 0 0‘20 ‘33 " N 1W. 239 H2 8924 HZ % WM¢MLJJJ f, f ! ,, ..T.__ T 3:10 ()00 750 l 000 1250 l 500 Frequency [Hz] Fig. 4.28. Blade vibration spectra for first segment of event C, Nred=14,000 rpm 96 be lower than expected or higher than expected. However, this investigation reveals that measured phase angles do not follow these consistent patterns. Therefore, it appears that the deviation between recorded and expected values is not the result of error in determining Aog. The fact that examination of very slightly different sections of a signal produces significantly different pressure and phase angle spectra hints that the discrepancy between measured and expected values lies in the details of the FFT analysis. Note also that despite the fact that phase angle at the pressure spectrum peak corresponded most closely with m=+1, the actual mode of rotating stall was m=+4. This illustrates the imprecise nature of phase analysis for determining the character of rotating stalls encountered and the desirability of using several circumferentially-spaced transducers when using this method of stall detection and characterization. In summary, for event C, agreement between the two analyses shows that the first rotating stall in event C contained three cells and rotated in the opposite sense as the rotor with a speed (est/(2:0.067. The second stall had four stall cells, and rotated in the same direction as the rotor rotation with speed rust/9:0.022. M So far, the pressure-time trace obtained at ¢g=0 degrees and ¢g=125 degrees have looked substantially the same. However, with event D this changes. Figure 4.29 shows the pressure signals from the two transducers at x/s = 0.74 for event D. Here, the signal from ¢g=0 degrees appears to be dominated by low frequency (about 50 Hz) pressure fluctuations of approximately equal amplitude throughout the entire event. In contrast, the signal obtained from ¢g=125 degrees shows this low Ea. goinsi d 26.6 ..2 2.3»? app—5.6.5395 6N... .wE Sow. 68; 0.0 'Wfi—‘T’T’Tr V [\ 0 II (D \ X 98 frequency oscillation declining in amplitude, leveling off over the center section of the event, then increasing to its previous amplitude over the last of the event. Close inspection of this signal reveals that a clear 50 Hz signal appears to remain (with a lower amplitude), but each crest of this 50 Hz signal is separated by rapid oscillations which produce an unclear trace. This may indicate that we have pressure oscillations superimposed on one another. The ¢g=0 degree signal also shows these intermediate fluctuations; but, for this position they have very low amplitudes. Signal analysis software provides a means for clarifying the dominant frequencies of oscillations embedded in event D. Figure 4.30 shows pressure spectra obtained through FFT analysis of each signal separately. Although the same three frequencies show up at each circumferential position, they differ in amplitude. For ¢g=0 degrees, the peak at 45 Hz clearly dominates, followed by a peak at 89 Hz and one at 134 Hz. For ¢g=125 degrees, the peak at 134 Hz dominates, followed by the peak at 89 Hz and two peaks in the 40-50 Hz range. This unusual result does not resemble those obtained for the other rotating stall events investigated here. For all other events, the single-signal FFl‘s showed nearly identical pressure spectra for both signals. Figure 4.31 shows the pressure and phase angle spectra diagrams for the section of event D between t=0.1 and t=0.5. Figure 4.32 shows the same information, but for a slightly smaller section of event D (0.15 s.StSO.47 s.). Although the sections analyzed differed only slightly in size, their corresponding pressure/phase angle spectra diagrams differ significantly. Figure 4.31 shows greater resolution than Figure 4.32. The blade spectra analyzed comes from the same section represented by Figure 4.32. 99 En.— ¢¢¢.3ueo._z .9 E96 ..8 APE.”— Ecwfi 6&53 £23m 3:232: ..8 «566% 9.3.6.5 .cmé .wE ”NIL>oco:omaa com 09— 00‘ on t — t s . F" ~— .__‘_‘77 com cod God on > . h b fj Y moo mm. .... e who a 8x omssord moo o u e V5.0 n m\x ea. :8 .Eueez A; 39 Q «:96 ..8 5.566% 63.:— Q 2:86.:— ..um v .wE LNIL>oco3coan 100 com can con on t r Ten—I moo :T : LE: Afl/ L\_, r: o . Don 0Y1?” on an. ocoscoan 8m o2 9: cm. _ . _ _ _ , .09.. .32.. can: no: _ Toe. use o2 _ was. LE. _ _ com on. _ _ ....c 4\\)(\11 / ZH V68 4.. 7 —- i— '— Hilfil [63p]eseud GJOSSSJd 102 According to Figure 4.32, the phase angles corresponding to the 45 Hz peak vary dramatically over the entire base of the peak. However, it appears that the core of the peak has phase angles in the 0 to -35 degree range. A phase analysis reveals that this corresponds to rotating stall with m=-3. This agrees with the results found for the previous events at de=l4,000 rpm; however, this result should be checked with that obtained from a blade vibration analysis. Another possibility exists for the mode of rotating stall responsible for the 45 Hz peak. A phase angle of 95 degrees, which corresponds to m=- 5 takes place at approximately 42 Hz. However, this does not have the relatively flat phase angle distribution typically found for events formerly analyzed. For this reason, we suspect that the m=-3 hypothesis seems stronger than the m=-5 hypothesis. Figure 4.32 also shows prominent peaks at 89 Hz and 134 Hz. Analyzing the phase angles of the 89 Hz and 134 Hz peaks shows that these peaks are caused by a different event than causes the 45 Hz peak. The pressure spectra for event D looks very similar to that found for event B, where simultaneous stalls may have occurred. This observation also proves useful for explaining the data obtained for event D. Figure 4.33 shows the peak amplitude blade vibration spectra for event D. It appears that similar stall patterns produce the unusual blade vibration spectra for both event B and event D. The blade vibration spectra for both events resemble one another. This suggests that for event D, as in event B, simultaneously operating modes of rotating stall occurred. Equation (3-12) provides a means for explaining the peaks for both events. Supposing two simultaneous rotating stalls with fp=45 Hz and 134 Hz, almost every prominent peak can be explained as resulting from shaft 103 one L _ 5.: scineotz .9 «:96 .5. 866% .8385.» 82m .mmé .wE HNIL>oco3ooaa ZH 9L9 1; COD— Ommu Good can. ccn 6mm _ p — — r — 3 — \/\(/ 1111\ftr‘.\<..<:\lx\l/\c/\../\/.\ 020E .: 9:3on .L 230: 6:: 6 BEEBoc .E x8860 .: 85:65 .0 592:8 Locum A commoEEoQ Ewabbcou .w o>E> 630 .2 flag 8555 .x 09a 2365 a 09E couoam d use .25 Spa 121 2835—55 Ewébcoo ac Sagan—co mov— .N.< .wE 6.5395 23% SE 3.55 9525. Eng anemia—En 5. .. ES: 3 3.55 may 5 .2 ll E353: @882 8:53 33 «3.28% 3 328.. :2: 688:8 .__< 122 Fig. A.3. Basic diffuser configuration parameters 123 “003858 9538“” 283% owoéox 052M .8 ouaoaom .v.< .wfi 10:00: 22 am 3802 $0 a . 2 9.0 <0 wOZS .EwDOQZOJumF zmwo< a .2 9.0 (U wOZS .EwSOQZOJuw... WWI 259 m 1 30 h l fl, [K 5 oz: o> mm? mm «2,; 55. mm mOZS .vd Q 25. No mz.3m$nEm._. mmSm few I cmmcammms. mcom_Emc>u 0:: 30286 .2 I cm~co=amtcm9m ococ Emm I EE mmd mmcfi WEE o.~ 33062830 I :8..va 28:35.; 9:53.:— 2535—): mmzmngéoDmm—éDHSZHZ APPENDIX B--DERIVATION OF EQUATIONSFOR ANALYSIS APPENDIX B1--ANALYSIS OF ROTATING STALL USING BLADE VIBRATION CHARACTERISTICS Rotating stalls are characterized in part by the number of cells of which they are composed. The following derives a relation between measured pressure signals, blade vibration spectra peaks, and the number of cells in rotating stall. Maximum For centrifugal compressors, we must relate motions in two frames of reference: (1) the absolute frame, which corresponds to coordinate axes fixed to the earth, and (2) the relative frame, which corresponds to coordinate axes fixed to a rotor rotating with respect to the absolute frame. Figure 3.1 shows these two reference frames. From general kinematics, we can write (Dabs = (orel'l‘mabs/rel, 01' 0)rel = (Dabs‘i'mrel/abs, Where (B'l) (Dabs is rotational velocity in the absolute frame, (pm is rotational velocity in the relative frame, (Dabs/rel is rotational velocity of the absolute frame with respect to the relative frame, and (Drel/abs is rotational velocity of the relative frame with respect to the absolute frame. Now consider the rotation of the rotating stall cells. Following (B-l), we can write w'rel = w'abs+wre1/abs, (B-2) 124 125 where the prime designation is used to signify that we are talking of rotating speed of stall cells. Next, we note that in practice an impeller resides on and rotates around a fixed axis of rotation (fixed in both reference frames). In this case, (”rel/abs = (”rot = wshaft- (B-3) Y (Non-rotatin g) 4 2 Relative Frame (rotates with rotor) X Fig. 8.1. Absolute and relative reference frames. Noting from figure B.1 that the z and C axes are always parallel and employing equation (B-3) allows us to rewrite equation (B-2) in scalar form w'rel = E'm'abs+mshaft . where (B-4) 8 = +1, when (D'abs is in the same direction as (Oshaft and e = -1, when (D'abs is in the opposite direction as (Oshaft. Wes. Frequencies are related to rotational speeds by the relation f = 21m. Substituting into equation(B-4) allows us to write: f r.s.lrel = 8f r.s.labs 'f shaft- (B-S) Note that since f turd is a frequency, its value will always be positive; so, equation (B-S) should be rewritten 126 f r.s.lrel = ' 3fr.s./abs 'f shaft L (3'6) Next, we need to relate measured pressure and blade vibration frequencies with those of rotating stall. Note that the blade vibration arises from the frequency of rotation of the rotating stall in the relative frame. We must also account for the number of stall cells. 'We write, f blade: m'fr.s./rel , where m = number of stall cells. (B-7) Also, we should note that f puss/abs = m-fnsyabs. (B-8) Substituting into (B-6) and manipulating, we find that f blade = I e'fpress/abs ‘ nlfshaft '- (3'9) Here, we are confronted with three cases: Case 1: (e-fpress/abs - mf shaft)< 0; Case 2: (Efpress/abs - Inf shaft): 0; and Case 3: (e-fpress/abs - mf shaft)> 0. Since m 2 1 and since f shaft >fpress/abs. then only case 1 is of interest. Case 1 implies that f blade = '(e'fprcss/abs ' mfshaft)» (3'10) and this constitutes our final expression relating measured frequencies and rotating stall characteristics. APPENDIX B2--ANALYSIS OF ROTATING STALL USING PRESSURE AND PHASE SPECTRA DATA Instances of rotating stall are characterized in part by their lobe number. In addition to the method derived in appendix B1 for determining lobe number, we can also find this value by utilizing the pressure signal phase shifts in circumferentially spaced pressure transducers. The following, drawn from Kammer (1984), derives the relation expressing lobe number in terms of pressure signal phase shift. The lobe number of rotating pressure patterns such as rotating stall can be measured using two circumferentially spaced pressure transducers. Pressure signals for rotating pressure pattems are functions of both space and time and act essentially as pressure waves propagating in the circumferential position. The pressure signal will assume a sinusoidal character. For a signal of maximum amplitude, P, the pressure can be written p(t,A¢g)= P.sin(ms,t-mA¢g) (13-11) Here, cost is the rotational speed of the pressure pattern, Aog is the geometric angle separating the two transducers, and m is the number of cells of the pressure pattern. 127 128 When the pressure pattern rotates in the same direction as the rotor, then m assumes a positive value. For pattern rotation opposite that of the rotor, m is negative. Pressure signals from two pressure transducers located at circumferential position ¢g1 and ¢g2 sampling the Same rotating pressure pattern can be related as follows: P - sin(o)stt — ongl )= P - sin[o)_,,t (t + At) — ongz] (B-12) where at location ogz, the maximum pressure P arrives slightly later than at location ¢g1- This is time lag is accounted for by replacing t with t+At. This allows us to write m in terms of time, rotational velocity of the pressure pattern, and circumferential positions of the transducers, as follows: =(mstAtztk-21r) “ng — ¢gl) where k is any integer desired. Figure B.1 shows two signals produced by . (B-l3) two circumferentially spaced transducers. B \/ Transducer A Fig. 3.2. Signals produced by two circumferentially- spaced transducers 129 Next, we relate phase angle between pressure signals with the rotational speed of the rotating pressure pattem wstAt = 271‘; At = 134),, _ (13-14) St Here Tst is the average period of the measured pressure signals and A¢st is the phase angle difference between the pressure signals. Substituting (B-4) into (B-3), we find a useful relation for the lobe number: m: (Ad)st ik-er) A¢8 Here, A¢g=(¢g2-¢g1) and is the geometric angle separating the two (B-lS) transducers. Note that the value of A¢st can be negative. For example, for A¢st=15 degrees and A¢g=125 degrees, we get: m = (-0.26-21r)/(2.18) = -3. A graphical method provides an easy way to determine lobe number. Using equation (B-5) and plotting lines for m=-1, +1, -2, +2, -3, ..., -5, +5, we produce the diagram shown as figure B.2. To determine the lobe number, a user simply plots the point corresponding to a given transducer separation angle and a measured phase angle. The user can then read lobe numbers from the chart by noting by which m-lines cross «pg line in the area of the point. As an example, figure B.2 shows a reading for A¢st = -100 degrees and A¢g = 125 degrees, giving m=+5. To avoid ambiguous readings, at least three circumferentially-spaced transducers should be used when characterizing rotating stalls using this method. Phase Angle, Mm [deg] 130 180 \\ .1 ‘\‘ 480 l l 120 160 Angle of Separation, A¢g [deg] Figure 8.3. 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Non-dimension. blade-to-blade pressure rise, Nred 142 M / . 100 /; /\ .l— N 80 . /j¢j -‘p§> :3 {X104} “o ‘ // -/ ‘ o fil/ ...—4" / / ‘\ 4 3.5 \ / 5 ‘9 40 0 02 04 06 08 156 5.1",” X/s 6. / -\ \ \é ~100 ”// “ \‘fixi; 4 /,.. / .x/ ‘6‘ \ P P 4 sew I. l’ / / “R\— 20 6 mm :2. ;"’/W’ 5.56 \ / x ' ,5 vs!" lk\»0\B\\x ~-- \z/ 4 4.0 04,6» - 0.6 0.4 U 2 03 3.5 f6 X/s _ E I P*=AP’P2 *5 W4 Tb slim ET F > fblade=zxfs timC ° =12,000 rpm D.2 Non-dimension. blade-to-blade pressure use, NM Fig. . 60 ( x 10-4] # D. 0 00 BMW 420% \s\% 5 2 G 7 w .75” 7. w 6 p"‘=Ap/P2 Tb =1/fblade fbhde=z x fs 14,000 rpm Fig. D.3. Non-dimension. blade-to-blade pressure rise, Nred '- 1 I‘E“ 120 /§? . 4.. II=~P~~ $35 / / h:~\\ ‘ 75 P /éé &‘§§r~‘\~\‘\\\‘ 6O WW®‘§ 33 //’\\ZZ“'/" 7257 .O/\ N o \ In. P . O) m \1 \I 3% 6. 01 g qmmn ’ 7120 \:105 :90 ~75 P“ ‘5 H 45 1,“ ' F 30 s... 8 258.5 7 758 .\ , 5 . 7.5 ”$63; a £60 . — 7:; a .1. P*=AWVPE § “T 5 £15“— Tb =1/fblade - * r -—z x f tune blade" 8 Fig. D.4. Non-dimension. blade-to-blade pressure rise, Nred=16,500 rpm APPENDIX E--MISCELLANEOUS GRAPHS Pressure Phaseldeg] 145 N I H a In ‘ N ‘ I 4 I v. d | g . '- N 1 I j I A.\ Q ' .../J . \ ” u k» f T ' I- # "’ ' r 50 ‘ 100 am) < 1‘ __ .W. i, . .__. _ 150j I I IS dew t \ 100:: , afil z / W I , _5m‘ I r — 123 deg -' ~4afi: \ JKZwJ V —150‘ ‘ r r "r’ ““ “T” ” ‘fi fi 50 100 150 200 Frequencyle] Fig. E.l. Pressure & phase spectra for rotating stall, Nred=10,000 rpm Pressure Phaseldeg] 146 N I [x p. Q M W _ A r 1 r ' T 1I 100 150 200 lean-Ii 130m IT IlOdeg . 10mI I I 137/g A " ‘. ”I _/1 124deg e9 ‘ 50?. -5¢e9 V ' 0‘. 47 -5o-I 400‘: \- -1 l T ' 1 i T 50 100 150 200 Frequency [Hz] Fig. E.2. Pressure & phase spectra for surge, hired-=12,000 rpm Pressure Phaseldeg] 147 116.5 Hz A l A .L L L L ‘ 84 § / -105 deg l r l ' fl *— T 50 100 150 200 Frequency [Hz] Fig. E.3. Pressure & phase spectra for second rotating stall in event A, Nred=l4,000 rpm Pressure Phaseldeg] 148 N I 0‘ d N .: ' j | ‘ I I- .A. A. . - . | 50 100 150 an lar. RT 1001I 126 deg 50_| OEI -50«| -1oo~: -150dl f l V T ' f * ‘7 f a) 100 150 an FrequencyIHz] Fig. E.4. Pressure and phase spectra for second segment of event C, N red=l4,000 rpm APPENDIX F--RESULTS OF ANALYSES OF UNSTEADY EVENTS 149 $532 a: on 05 N823 533 :55 n 8 om- m- m2 OO»: 3:35.. on“- 2 2 T ONT «2 25 Sings v+uE fifiuaes ~+uE 8: W33 Nae $3 .285an “32 9 .88 8.?" 0mm Ammuaefl OO ova—m .— mPZmem >Gd 2:3: mhzmkm fiamhmZD kc m~m>d ova:— mhzm>m >Qd ova:— . _ < :E mhzm>m >G4 00::— .— Adda—h GZ—hflrcm ...—O m—m>.— 000:: . .— mEZm>m >GA 0: :00: 0.000% 05088. - 80 :m:-u..0$ 8.05 4:05 :0 0:: 0mmn.:00:: 80:0 6009. - hm: m-nE ma 0: o:- m: we 3n: 8:: 80.0: 300888 80:0?8 :05 820.3: :me lax: :05. 80205: :0::00m 03:000.: 8 03:80:: 02:0: :04: 0.04 0.: 0:050:30. ...—030:4 000::— .::> 0:00:— . mhzm>m >QA.E 303 E00: “0:: :0um:0:< :0::00m 03:08.: .0 20:08.: 00:0,. .00 000 e 0:00:05: 0:00 0: 000 .::> 000:: . _ < .E thEW >Ga-:: B03 B03 :05 :0N>:::< :0_:00m 03:08: ...: 03:80: 0mg: seq zed 0.: mam—0:0: 0:0: - . . :05: 000:: .0; 000:: .: 444.5 05.30.55: ...:0 m:m>.: 000:: . mEm>m >GM >G4 0:00:— .— mhznmkm >G 000:0 thH>m >QJ «ca:— mhzm>m >Gd 0:05 0:03:05: 000::— bum—05: :0::00m mhzmrwm— >Q4000 08:05:: 0.: u 00:20:00. 30 0:53 mm: mm: E :$:n.m0<0 V+HE Amsuaes 8 00:0: 30:00:00.: 30:3: 0: The -5000 3030: 50:: 003: 30:00: 0530:? 8: :naefl 00:35:: dam .:0 0.: u 85:200. as 0:: 8 E 80: 000.: 3:08:80 3029.5 3:: 30=_0>.E B02 302 E: 50:05: :0_:00m 0.:m030m 0.: 03:30:— 0M:::: 33: 3:8 0.: 03505: 33.» a: 000 . . S .:_> 00::— _ < :— 41—35 Elf—REC“ ,mO Ema—<72 LIST OF REFERENCES . LIST OF REFERENCES _ Abdel-Hamid, A. N., et al. "Unsteady Flow Characteristics in a Centrifugal Compressor with Vaned Diffuser," ASME Paper No. 87-GT-142, 1987. Ariga, I., et al. "Inducer Stall in a Centrifugal Compressor with Inlet Distortion," ASME Paper No. 86-GT-139, 1986. Chen, Y. N., et al. "On the Nature of Rotating Stall in Centrifugal Compressors with Vaned Diffusers. Part II. Karman Vortices as the Controlling Mechanism, " Proooooin ngs of tho 1282 Tokyo 1m.ion.l ..T.01 o 0 .To 0.1-.101”; ZQ-ZQ, 1282, JSME Paper No. 87-TOKYO— IGTC-23. Chen, Y. N., et al. "The Vortex-Filament Nature of Reverse Flow on the Verge of Rotating Stall," ASME Paper No. 88-GT-120. Chen, Y. N., et al. "The Vortex-Filament Nature of Reverse Flow on the Verge of Rotating Stall," WW, Vol. 111, October 1989, pp. 450-461. Chen, Y. N., et al. "Experimental Investigation of the Longitudinal- Vortex-Nature of Rotating Stall in Vaneless Diffusers of Centrifugal Compressors," ASME Paper 9l-GT-99, 1991(a). Chen, Y. N., et al. "The Rossby Waves of Rotating Stall in Impellers, Part 1: Theoretical Background of the Rossby Waves in Blade Channels," JSME Paper 91-YOKOHAMA-IGTA-9l(b). Chen, Y. N., et al. "The Rossby Waves of Rotating Stall in Impellers, Part 11: Application of the Rossby-Wave Theory to Rotating Stall," JSME Paper 9l-YOKOHAMA-IGTA-92 (c). Chen, Y. N., et al. "The Vortex Behavior of the Rotating-Stall Cell of a Centrifugal Compressor with Vaned Diffuser," ASME Paper 92-GT- 66. 165 166 Cumpsty, N. A. W, Essex, England: Longman Scientific & Technical, 1989. Fringe, P. and R. Van Den Braembussche. "Distinction between Different Types of Impeller and Diffuser Rotating Stall in a Centrifugal Compressor with Vaneless Diffuser," ASME Paper 83-GT-61, 1983. Haupt, U., K. Bammert, and M. Rautenberg. "Blade Vibration on Centrifugal Compressors-~Fundamental Considerations and Initial Measurements," ASME Paper 85-GT-92, 1985a. Haupt, U., K. Bammert, and M. Rautenberg. "Blade Vibration on Centrifugal Compressors--Blade Response to Different Excitation Conditions," ASME Paper 85-GT-93, 1985b. Haupt, U., et al. "Investigation of Unsteady Flow m a Centrifugal Compressor with Vaneless Diffuser," W ‘_..i..01 0“.‘o_11Wt'nln -' 0. , Cairo, Egypt, December 27-30,1986. Haupt, U., et al. "On the Nature of Rotating Stall in Centrifugal Compressors with Vaned Diffusers, Part I: Detection of Reverse Flow,"' 0 “1m. 0 ‘1': Tk In «.1111. , -, 11‘ l T r - l , JSME Paper No. 87-TOKYO-IGTC-23, 1987b. ‘ Haupt, U., et al. "Unsteady Flow in a Centrifugal Compressor with Different Types of Vaned Diffusers," ASME Paper No. 88-GT-22, 1988. Haupt, U., et a1. "Investigation on Rotating Stall Phenomenon of Multitudinous Stall Cells and Its Impact on Blade Excitation of Centrifugal Compressor Impeller," W, 1st International Congress on Fluid Handling Systems, Essen, Fed. Rep. of Germany, Sept. 10-12, 1990. J in, D., et a1. "Blade Excitation by Circumferentially Asymmetric Rotating Stall in Centrifugal Compressors," ASME Paper 92-GT-148, 1992a. J in, D., et al. "Excitation of Blade Vibration Due to Surge of Centrifugal Compressors," ASME Paper 92-GT-149, 1992b. 167 Kammer, N. and M. Rautenberg. "An Experimental Investigation of Rotating Stall Flow in a Centrifugal Compressor," ASME Paper 82- GT-82, 1982. Kammer,N. n arr 'o’mmn 1- -'o_i -. 1.1 mm, Doctoral Dissertation, University of Hannover, Hannover, Germany, 1984. Kammer, N. and M. Rautenberg. "A Distinction Between Different Types of Stall in Centrifugal Compressor Stage," ASME Paper No. 85-GT- 194, 1985. Kubo, T. and S. Murata. "Unsteady Flow Phenomena in Centrifugal Fans," Bulletin of the JSME, Vol. 19, No. 135, September 1976, pp. 1039- 1046. Lennemann, E. and J. H. G. Howard. "Unsteady Flow Phenomena in Rotating Centrifugal Impeller Passages," WW Journal of Enginooring for Eowor, January 1970, pp. 65-71. Ligrani, P. M., et al. "Rotating Stall Measurements in the Vaneless Diffuser of a Radial Flow Compressor," ASME Paper No. 82-GT-257, 1982. Mizuki, S., et al. "Reversed Flow Phenomena within Centrifugal Compressor Channels at Lower Flow Rate," ASME Paper No. 76- GT -86, 1976. Mizuki, S., et a1. "Investigation Concerning Rotating Stall and Surge Phenomena within Compressor Channels," ASME Paper No. 78-GT- 9, 1978. Pampreen, R. C. W, Norwich, Vermont: Concepts ETI, Inc., 1993. Roth, G. "Unsteady Pressure Measurements in a Rotating Centrifugal Impeller," ASME paper 92-GT-152. Seidel, U. et a1. "Experimental Investigation of Rotating Stall Behavior Influenced by Varying Design and Operation Parameters of Centrifugal Compressors, JSME Paper 91-YOKOHAMA-IGTC-93, 1991a. 168 Seidel, U., et al. "Rotating Stall Flow and Dangerous Blade Excitation of Centrifugal Compressor Irnpeller--Part l: Phenomena of Large- number Stall Cells," ASME paper 91-GT-102, 1991b. Wachter, J. and K.-H. Rohne, "Centrifugal Compressor Surge Behavior," ASME Paper No. 84-GT-91, 1984. nrcnran STATE UNIV. LIBRnRIEs WWI m IIII “I W I'll l1" “NIH ill" WI H IN WI 31293010220188