Stator Loading Measurements Behind a
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Stator Loading Measurements Behind a Fan with Trailing Edge Blowing by Margarita C. Brito S.B. Aeronautics and Astronautics, Massachusetts Institute of Technology (1997) Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the Massachusetts Institute of Technology September 1999 @ 1999 Massachusetts Institute of Technology. All rights reserved. MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEC 2 8 1999 LIBRARIES Author Department of Aeronautics and Astronautics August 28, 1999 / Certified by cToessor Ian A. Waitz Director, Aero-Environmental Research Laboratory Thesis Supervisor Accepted by v Professor Nesbitt W. Hagood Associate Professor of Aeronautics and Astronautics Chairman, Department Graduate Committee Stator Loading Measurements Behind a Fan with Trailing Edge Blowing by Margarita C. Brito submitted to the Department of Aeronautics and Astronautics on 28 August 1999 in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics Abstract The effects of trailing edge blowing on stator unsteady loading were investigated through a set of experiments on a trailing edge blowing fan. Flow field measurements and stator unsteady loading measurements were taken at five radial locations. Reductions in the relative wake harmonics were seen at all spans for the first two multiples of blade passing frequency. The reductions ranged from 59% to 95% for the 1*BPF harmonic and from 19% to 84% for the 2*BPF harmonic. Trailing edge blowing was seen to have significant effects on both the longitudinal and transverse harmonics. The largest reduction (73%) of the 1*BPF transverse harmonic was seen at 37.5% span, while the largest reduction (99%) of the 1*BPF longitudinal harmonic was seen at 75% span. Changes in the stator unsteady loading ranged from -15dB to +7dB at different points along the chord and span. The changes did not correlate well with changes in the wake harmonics. The most notable lack of correlation occurred at 50% span, where the stator unsteady loading increases while the largest overall reductions in wake harmonic amplitude are seen. Two-dimensional steady state analysis of the free stream and wake (maximum velocity deficit) conditions suggests that the effects of the longitudinal and transverse gusts partially cancel each other in the no blowing case at 50% span. Thus, it is likely that trailing edge blowing disturbs the established balance resulting in an unsteady loading increase even though the wake harmonics are reduced. The flow field measurements were used in conjunction with the BBN/PW V072 noise prediction code to obtain stator unsteady loading predictions with and without trailing edge blowing. The predictions correlate to the changes in the wake transverse harmonics and fail to agree with the stator unsteady loading measurements. Because the V072 code only models the effects of transverse gusts and because trailing edge blowing has strong effects on both transverse and longitudinal gusts, the lack of agreement between the predictions and the measurements is understandable. Thesis Supervisor: Dr. Ian A. Waitz Title: Associate Professor of Aeronautics and Astronautics Director, Aero-Environmental Research Laboratory Associate Director, Gas Turbine Laboratory ACKNOWLEDGEMENTS I would like to thank my advisor Prof. Ian Waitz for the opportunity to work on this project and for his guidance, patience and encouragement. I would also like to thank Prof. Nick Cumpsty for all his help with the design of the new set of throttle plates, and Prof. Jack Kerrebrock for answering being always willing to offer helpful suggestions and for answering many questions about the BDC. Thanks also to Dr. Envia of NASA Glenn for all his help with V072. Many thanks to Victor Dubrowski, Bill Ames and James Letendre for always helping me when things broke down. Without them I would have been unable to keep the facility running. I am also grateful to Dr. Gerry Guenette who on many occasions took the time to help me track down problems with the facility. And of course, many thanks to Lori Martinez who knows or can find the answer to anything I needed to know about how things work around here. I am grateful to J.B. for all the moral support and for helping me out long after he thought he was free of the BDC. Thanks to Brian for patiently waiting his turn and for coming down to help me whenever I needed help. Thanks to Chris, Dan and Rory for helping me out on various occasions. Thanks to my officemates, Ken, Sanith, and May (and Brian) and thanks to Torrey, Staci, Tan and Ernest. Finally, I would like to thank my family for their support and encouragement throughout my life. This work was funded by NASA Glenn Research Center. Thanks are given to technical monitor Brian Fite for his support. The support of Rolls Royce and Allison Engines through the funding of the Sir Frank Whittle Fellowship is gratefully acknowledged. CONTENTS 1 Introduction 2 3 17 1.1 Motivation and Objectives ........................ 17 1.2 Previous Research ....... 19 ..................... 1.2.1 Airfoil Response to Unsteady Gusts . ........... 1.2.2 Trailing Edge Blowing Research . ................ . . 20 Experimental Setup 23 2.1 Blowdown Compressor Facility . .................. 2.2 Instrumentation ................... Four-way Probe ................ 2.2.2 Instrumented Stator 2.2.3 Other Instrumentation . .................. 2.2.4 Data Aquisition System Fan Stage Test Geometry 2.4 Blowing System ............. ... . 2.2.1 2.3 .. ....... 25 ........ . .................. 25 .... 27 ... ................... ......... 23 27 .. 29 .............. 30 ............. . Modifications to Blowing Distribution 3.1 19 Parametric Studies ................... 35 ....... 7 31 . 36 4 5 6 3.2 Momentum Thickness Calculations ................... 3.3 Loss Calculations ................... 3.4 Throttle Plate Design ................... 3.5 Results of Throttle Plate Modifications . ................ 37 ....... . . .. ...... 38 . 39 40 Flow Field Measurements and Stator Unsteady Loading Predictions 43 4.1 Overview of Flow Field Measurements 4.2 Flow Field Measurements 4.3 V072 Noise Prediction Code . .................. 4.4 Unsteady Stator Loading Predictions . ................. ................. ...... ........ 43 .. ..... 44 .... 63 64 Stator Loading Measurements 5.1 Mean Pressure Envelope ................... 5.2 Differential Pressures ................... 75 ...... 75 ........ 76 Discussion 95 6.1 Discarded Hypotheses 6.2 Wake Cancellation Hypothesis ................... ................... ..... . 95 ... . . 96 7 Conclusion 105 A Wake Identification Method 107 B Four-way Probe Measurements 111 C Instrumented Stator Measurements 127 LIST OF FIGURES 2-1 Blowdown compressor facility . . . . . . . . . . . . . . 24 2-2 Four-way probe ................. ... . 26 2-3 Four-way probe cross-section with fin . . . . . . . . . . 27 2-4 Instrumented stator blade transducer locations . . . . . 28 2-5 Schematic of instrumented stator blade . . . . . . . . . 28 2-6 Test section layout in blowdown compressor . . . . . . 31 2-7 Trailing edge blowing blade, stagger view . . . . . . . . 32 3-1 Fraction momentum thickness filled at 1.5c . 4-1 Relative Mach number data, 25% span . . . . . 45 4-2 Wake harmonic data, 25% span . . . . . . . . . 47 4-3 Relative Mach number data, 37.5% span . . . . 48 4-4 Wake harmonic data, 37.5% span . . . . . . . . 49 4-5 Relative Mach number data, 50% span . . . . 50 4-6 Wake harmonic data, 50% span..... . . . . 52 4-7 Relative Mach number data, 75% span . . .. 53 4-8 Wake harmonic data, 75% span . . . . . . . . . 54 9 4-9 Relative Mach number data, 87.5% span . . . . . . . . . . 55 . . . . . 57 . . . . . . 59 4-12 Longitudinal harmonic amplitudes vs. span . . . . . . . . . . . . . . 60 4-13 Transverse harmonic phases vs. span . . . . . . 61 . . . . 62 4-15 Stator harmonic amplitude predictions, 25% span . . . . . . . . . . . 65 4-16 Stator harmonic phase predictions, 25% span . . . . . . . . 66 4-17 Stator harmonic amplitude predictions, 37.5% span . . . . . . . . . . 67 4-18 Stator harmonic phase predictions, 37.5% span . . . . . . . . . . . . . 68 4-19 Stator harmonic amplitude predictions, 50% span . . . . . . . . . . . 69 4-20 Stator harmonic phase predictions, 50% span . . . . . . . 70 4-10 Wake harmonic data, 87.5% span . . . . . . . . .. 4-11 Transverse harmonic amplitudes vs. span . . . . . . . . . . . . . . . . 4-14 Longitudinal harmonic phases vs. span . . . . . . . . . . . . . . . 4-21 Stator harmonic amplitude predictions, 75% span . . ......... 4-22 Stator harmonic phase predictions, 75% span . . . . . . 71 . . . . . 72 4-23 Stator harmonic amplitude predictions, 87.5% span . . . . . . . . . . 73 4-24 Stator harmonic phase predictions, 87.5% span . . . . . . . . . . . 74 5-1 Stator mean pressure envelope, 25% span . ........... 5-2 Stator mean pressure envelope, 37.5% span . .......... 5-3 Stator mean pressure envelope, 50% span . ........... 5-4 Stator mean pressure envelope, 75% span . ........... 5-5 Stator mean pressure envelope, 87.5% span . .......... 5-6 Harmonic amplitudes of stator differential pressure, 25% span 5-7 Harmonic phases of stator differential pressure, 25% span . . 10 . 5-8 Harmonic amplitudes of stator differential pressure, 37.5% span 5-9 Harmonic phases of stator differential pressure, 37.5% span ...... . . . 85 86 5-10 Harmonic amplitudes of stator differential pressure, 50% span . . . . 87 5-11 Harmonic phases of stator differential pressure, 50% span ...... . 88 5-12 Harmonic amplitudes of stator differential pressure, 75% span . . .. 91 5-13 Harmonic phases of stator differential pressure, 75% span ....... 5-14 Harmonic amplitudes of stator differential pressure, 87.5% span 90 . . . 92 5-15 Harmonic phases of stator differential pressure, 87.5% span ...... 93 6-1 Gust impinging on stator at 50% span . ................ 97 6-2 Gust impinging on stator at 25% span . ................ 99 6-3 Gust impinging on stator at 37.5% span 6-4 Gust impinging on stator at 75% span 6-5 Gust impinging on stator at 87.5% span . ............... 100 . ................ 101 . ............... 102 A-1 Example of wake that is easy to identify ................ 108 A-2 Example of wake that is hard to identify . ............... 109 B-i Absolute Mach number and flow angles at 1.5c, 25% span ....... 112 B-2 Components of Mach number at 1.5c, 25% span . ........... 113 B-3 Pressures at 1.5c, 25% span .............. ... . . .. 114 B-4 Absolute Mach number and flow angles at 1.5c, 37.5% span ...... 115 B-5 Components of Mach number at 1.5c, 37.5% span . .......... 116 B-6 Pressures at 1.5c, 37.5% span ................... B-7 Absolute Mach number and flow angles at 1.5c, 50% span ....... 11 ... 117 118 B-8 Components of Mach number at 1.5c, 50% span . . . . . . . . . . . 119 B-9 Pressures at 1.5c, 50% span . . . . 120 . ...... ........... B-10 Absolute Mach number and flow angles at 1.5c, 75% span .. . . . . 121 B-11 Components of Mach number at 1.5c, 75% span . . . . . . . . . . . 122 B-12 Pressures at 1.5c, 75% span . . . . 123 . ................. . B-13 Absolute Mach number and flow angles at 1.5c, 87.5% span . . . . . 124 B-14 Components of Mach number at 1.5c, 87.5% span . . . . . . . .... 125 B-15 Pressures at 1.5c, 87.5% span . . . . . 126 ................ C-1 Suction surface harmonic amplitudes, 25% span . . . . . . . . . . . 128 C-2 Pressure surface harmonic amplitudes, 25% span . . . . . . . . . . . . 129 C-3 Suction surface harmonic phases, 25% span . . . . . . . . . . . . 130 C-4 Pressure surface harmonic phases, 25% span . . . . . . . . . . . . 131 C-5 Suction surface harmonic amplitudes, 37.5% span . . . . . . . . . . . 132 C-6 Pressure surface harmonic amplitudes, 37.5% span . . . . . . . . . . . 133 C-7 Suction surface harmonic phases, 37.5% span . . . . . . . . . . . . . . 134 C-8 Pressure surface harmonic phases, 37.5% span . . . . . . . . . C-9 Suction surface harmonic amplitudes, 50% span . . . . . . . . . . . 136 . 135 C-10 Pressure surface harmonic amplitudes, 50% span . . . . . . . . . . . . 137 C-11 Suction surface harmonic phases, 50% span . . . . . . . . . C-12 Pressure surface harmonic phases, 50% span . . . . . . . . . . . 138 .. 139 C-13 Suction surface harmonic amplitudes, 75% span . . . . . . . . . . . 140 C-14 Pressure surface harmonic amplitudes, 75% span . . . . . . . . . . . 141 C-15 Suction surface harmonic phases, 75% span . . . . . . . . . . . . 142 C-16 Pressure surface harmonic phases, 75% span . ............. 143 C-17 Suction surface harmonic amplitudes, 87.5% span . .......... 144 C-18 Pressure surface harmonic amplitudes, 87.5% span ........... 145 C-19 Suction surface harmonic phases, 87.5% span . ............. 146 C-20 Pressure surface harmonic phases, 87.5% span . ............ 147 14 LIST OF TABLES 4.1 Transverse Mach number harmonic amplitudes . ............ 56 4.2 Transverse Mach number harmonic amplitudes . ............ 58 4.3 Longitudinal Mach number harmonic amplitudes . .......... 58 4.4 Longitudinal Mach number harmonic amplitudes . .......... 58 6.1 Steady state loading difference ...................... 98 16 CHAPTER 1 INTRODUCTION 1.1 Motivation and Objectives The problem of aircraft noise pollution around airports has become increasingly important as those areas have become more densely populated. Currently, the removal of older noisier aircraft from operation is reducing noise levels around airports [2]; however, with air traffic projected to increase by about 5% over the next decade the number of commercial aircraft operating in the world is expected to be about 17,700 by the year 2007 [1]. To keep noise levels around airports from increasing as a result of traffic increases, it is important to investigate new methods of noise reduction. The main sources of aicraft noise are airframe noise and engine noise with the engine being the largest contributor. In many high-bypass-ratio turbofans, the total perceived noise is dominated by fan noise [15]. One of the major components of fan noise is rotor-stator interaction noise. This type of noise results from the interaction of the stator row with the unsteady gusts produced by the rotor. Rotor-stator interaction produces two types of noise- tonal noise and broadband noise. Tonal noise stems from stator interaction with the harmonic components of gusts produced by the rotor wake. This type of noise appears in discrete tones which correspond to multiples of blade passing frequency. Broadband noise is a result of stator interaction with gusts produced by turbulence in the flow. Typical methods for reducing rotor-stator interaction noise include choosing appropriate blade-to-vane ratios to cut off tones with the most energy, and increasing blade-to-vane spacing to allow greater mixing of the wake. More recently new methods for rotor-stator interaction noise reduction have been investigated. These have included studies on the effects of leaning and sweeping of the stator vanes [8] [14] as well as investigations of wake management techniques. This thesis addresses the latter category. Wake management refers to techniques, such as trailing edge blowing and boundary layer suction, which are designed to reduce the magnitude of the wake through addition or removal of fluid. Preliminary studies by Waitz et al. [22] indicate that noise reductions can be obtained through either trailing edge blowing or boundary layer suction, but suggest that trailing edge blowing is more attractive because it is relatively easier to implement. Subsequently, three-dimmensional rig experiments by Brookfield [3] and Brookfield et al. [4], have shown significant reductions in the wake harmonics as a result of trailing edge blowing. However, Brookfield [3] found that changes in stator unsteady pressure measurements did not always correlate well with changes in the wake harmonics. He suggested that further investigations be conducted. The objective of this work is to provide a better understanding of the effects that trailing edge blowing has on stator unsteady loading. This is done by presenting flowfield and stator loading data from experiments conducted with and without trailing edge blowing. Additionally, computational data from the BBN/PW V072 rotor-stator interaction noise prediction code and from the viscous cascade code MISES [6] is used to help interpret the experimental results. In the next section a brief overview of previous research in the area of rotor stator interaction and trailing edge blowing will be given. A description of the experimental facility is given in Chapter 2. Chapter 3 describes modifications that were made to the trailing edge blowing distribution. In Chapter 4 the flow field measurements are presented. Stator loading measurements are presented in Chapter 5 and discussed in Chapter 6. Finally, conclusions and recomendations are given in Chapter 7. 1.2 Previous Research Because this thesis focuses on the stator unsteady loading response to changes in the wake harmonics due to trailing edge blowing, it is appropriate to provide a brief overview of research regarding airfoil response to unsteady gusts as well as an overview of research on trailing edge blowing. Section 1.2.1 deals with airfoil response to unsteady gusts, while Section 1.2.2 discusses trailing edge blowing research. 1.2.1 Airfoil Response to Unsteady Gusts The response of airfoils to unsteady gusts has long been the object of study. In 1941, Sears [20] developed an analytical model for the unsteady lift of a flat plate under transverse gusts. In 1968, Horlock [9] looked at the effects of longitudinal gusts on a flat plate and determined that the unsteady lift response could be significant, and in some cases greater than the response caused by transverse gusts, at high angles of attack and high lift. By combining his results with the Sears model, Horlock obtained an expression for the unsteady lift response of a flat plate to a general gust. The effects of camber were first considered by Naumann and Yeh in 1973 [16]. In 1976, Goldstein and Atassi [7] formulated a complete second order theory for the unsteady lift which includes the effects of longitudinal and transverse gusts, the effects of angle of attack, camber and thickness as well as all of the coupling effects. One of the elements included in this theory is the distortion of the gust by the steady-state airfoil response. This distortion proves to have a significant impact on the unsteady lift response. Furthermore, it introduces nonlinearities which prevent the effects of thickness, camber and angle of attack from being considered separately and then superposed. 1.2.2 Trailing Edge Blowing Research Early experiments with trailing edge blowing demonstrated the ability to reduce the mean wake deficit [5] [17] [18]. Later, two-dimensional cascade experiments by Sell [21] investigated the effects of adding different amounts of mass as well as the effects of different injection port geometries. Noise reduction estimates were made based on amplitude reductions of the wake profile spatial harmonics. The noise estimates showed the greatest reductions when momentumeless wakes were produced and injection was done at the deviation angle. The results also showed that not fully eliminating the momentum deficit produced larger harmonic reductions than exceeding the momentum deficit by the same amount. Experiments by Leitch [12] (see also Ref. [13]) showed that trailing edge blowing can be used to effectively reduce radiated noise generated by stator wake-rotor interaction. Trailing edge blowing was applied to four inlet guide vanes located upstream of a rotor and tests were conducted at 40%, 60% and 88% of the design speed. For all cases, acoustic far-field measurements showed reductions in the overall sound pressure level. Reductions in the blade passing tone ranged from 2.6dB at 88% speed to 8.9dB at 40% speed. Finally, an existing fan design was modified to incorporate trailing edge blowing and tested by Brookfield in a realistic three-dimensional environment [3] (see also Ref. [4]). Flow field measurements were taken at 0.1 and 1.5 rotor chords downstream of the the rotor. These locations correspond to just downstream of the rotor trailing edge and just upstream of the stator leading edge. The flow field measurements showed that both the wake harmonic amplitude and the wake harmonic phase can be manipulated. Up to 80% reductions in the wake harmonic amplitudes were seen at 1.5c and the harmonic amplitudes at 0.1c with blowing were found to be up to 40% smaller than those without blowing at 1.5c. Shifts of approximately 180 degrees were seen in the harmonic phase when the wake was overfilled. The stator pressure measurements showed that changes in the stator harmonics did not correlate well with changes in the wake harmonics and further study was recommended. Finally, due to changes in the radial mode content, the duct wall acoustic measurements were inconclusive. 22 CHAPTER 2 EXPERIMENTAL SETUP This chapter describes the experimental setup. First a description of the blowdown compressor facility will be given. This will be followed by a description of the instrumentation. Next, the test section geometry will be discussed, and finally, a brief description of the wake management system will be given. 2.1 Blowdown Compressor Facility The experiments were conducted in the blowdown compressor facility in the Gas Turbine Laboratory at MIT. The facility was developed by Kerrebrock, and details of the theory and development of the facility can be found in [11]. The basic facility consists of a supply tank(100 ft3 ) and a dump tank(300 ft3 ) connected by a tube 2 ft in diameter (23.25" inside diameter) and approximately 5 ft long. As seen in the schematic diagram in Figure 2-1, the front part of the connecting tube allows for removal of the casing boundary layer and the aft part of the tube contains the test section. Finally, the supply tank is separated from the test section and dump tank by a fast acting valve. A full description of the valve's design and operation can be found in [23]. The basic procedure used to conduct a test in the blowdown compressor is as follows: 1) the entire facility is brought down to vacuum (less than 200 milliTorr) Figure 2-1: Blowdown compressor facility with the fast acting valve closed, 2) the supply tank is filled with a gas mixture of 61.7% CO 2 and 38.3% Ar by mass fraction, this mixture was chosen to match, at the test conditions for this study, the specific heat ratio of air, 3) an electric motor is used to bring the fan to a speed higher than the desired test speed, 4) the motor is turned off and the fan spins freely with the speed slowly decaying due to frictional forces, 5) when the fan reaches the target speed, the fast acting valve opens and the data acquisition system begins to take data. During the test, the speed of the rotor decreases as it does work on the flow. The rate of decay of the rotor speed depends on the inertia of the rotor and the amount of work done on the flow. At the same time, the pressure and temperature in the supply tank decay as the gas in the supply tank expands isentropically. By proper matching of the initial supply tank pressure to the rotor inertia for a given operating point, the change in speed of sound can be matched to the change in rotor speed to within 1% resulting in. constant Mach numbers and flow angles. The test lasts approximately 300 milliseconds from the time when the valve is opened until the data acquisition system stops taking data. However, the time during which the Mach number and flow angles remain constant is about 80 milliseconds. This time is equivalent to about 8 rotor revolutions or 200 flow through times. For flow phenomena on the time scale of blade passing this condition corresponds to steady-state. The time during which the facility is in steady-state and the measurement probes are in place is about 60 milliseconds, in this study the equivalent of 6 rotor revolutions or 96 blade passing periods [11]. 2.2 Instrumentation This section describes the instrumentation and the data acquisition system used in this study. The main sources of data were the four-way probe described in Section 2.2.1 and the instrumented stator described in Section 2.2.2. The rest of the instrumentation used is briefly described in Section 2.2.3. The data acquisition system is described in Section 2.2.4. 2.2.1 Four-way Probe Flow field measurements behind the rotor were made using a probe instrumented with four flush-mounted Kulite differential pressure transducers (XCQ-093-25D) with vacuum reference. The transducers are thermally compensated and the probe includes water cooling to help prevent thermal drift from the transducers heating up in vacuum. The four transducers are arranged on the probe such that the total and static pressures as well as the radial and tangential flow angles can be determined. From these four quantities the flow Mach number and its components (radial, tangential and axial) can be determined. As seen in Figure 2-2, the probe head is an elliptical cylinder with the tip cut off at a 45 degree angle. Detailed drawings of the probe can be found in Reijnen [19]. Transducer 1 faces the flow, transducers 2 and 3 are at + 45 degrees in the tangential direction, and transducer 4 is at 45 degrees in the radial direction. Not shown in Figure 2-2 is a permanent fin which was attached to Tubes 0 Position of Diaphragm I---- -1.20" Tubes Shidden behind Solder Pads Wire Channel Solder Pads Figure 2-2: Four-way probe the back of the probe to reduce errors due to unsteady vortex shedding as explained in Brookfield [3]. A schematic of the probe cross-section with the fin attached is shown in Figure 2-3. The probe was calibrated at Boeing in a 1" free jet facility. Errors were found to be +1 degree in flow angles and ±1% in Mach numbers and total pressure over the normal operating range. Detailed explanations of the calibration process and the data reduction procedures can be found in Reijnen [19]. The probe was mounted on a translator which traveled in the radial direction and was actuated pneumatically. The actuator was connected to a timer circuit which delayed firing of the probe into the flow to prevent damage to the transducers during tunnel start-up. The final position of the probe was set by stoppers made of 1" OD rubber tubing and calibrated in length to position the probe at the desired radial location. To determine the time history of the probe position, a linear potentiometer was connected to the probe translator. When measurements were taken closer to the hub than 25% span, the pneumatic actuator was not used and the translator was I \IFin Figure 2-3: Four-way probe cross-section with fin clamped in place in order to prevent the probe head from hitting the hub when fired. 2.2.2 Instrumented Stator Stator loading measurements were taken using a stator blade instrumented with 13 flush-mounted Kulite differential pressure transducers (XCQ-093-15D) with vacuum reference. As shown in Figure 2-4, there are seven transducers on the suction side and six transducers on the pressure side. The instrumented blade was made extra long and fitted with a detachable extension equal to 50% of the stator span. These features allow the row of transducers to be positioned at any point along the stator span. A schematic of the instrumented stator blade is shown in Figure 2-5. A more detailed description of the instrumented stator design can be found in Brookfield [3]. 2.2.3 Other Instrumentation Pressure transducers Absolute pressure transducers were used in the supply and dump tanks as well as in the hub. A 35 psi differential pressure transducer was used to measure the total pressure of the wake management tank. Figure 2-4: Instrumented stator blade transducer locations Thermal Compensation 70 -, -~--------- . "9 - - -- -- -- -- -- ---- 5 M 4 - - --. 6.-------- - -1 - - : ;,10 - -- " :: -2- - - - - - - - - - - - - - - - - - - - - - - - - - - - Vacuum Reference Plenum Wires Along Channels Under Vac. Ref. Plenums to Thermal Compensation Figure 2-5: Schematic of instrumented stator blade Wiring Socket Gauges and thermocouples Absolute pressure gauges were used to measure pressures in the supply tank, the dump tank, and the vacuum reference system. A gage pressure pressure transducer was used in the wake management tank. Thermocouples in the supply tank were used to measure the temperature in the supply tank at the beginning of each run. Optical encoder An optical shaft encoder which outputs a 400 pulse per revolution signal was used to determine the speed of the rotor. Additionally, the encoder produces a one pulse per revolution index signal which was used to ensure the data analyzed for each run was always with the rotor in the same location. 2.2.4 Data Aquisition System The data acquisition system used consists of a DELL 450DE 80486 32 MB RAM EISA with three 12-bit 8 channel ADTEK A/D boards. The A/D boards accept signals in the range of ±10 volts. The data was sampled at a rate of 333kHz. Except for the 6 pressure side transducers on the stator blade and the supply and dump tank transducers, all transducers were driven by 10 Pacific Instruments model 3210 transducer conditioning amplifiers. The excitation voltage was set at 15 volts DC and the gain was set to maximize the A/D input range. The signals were filtered through 50kHz low-pass filters internal to the amplifiers. The 6 pressure side stator transducers were driven by Pacific Instruments model 8650, F2, J transducer amplifiers. The signals were filtered through a separate 25kHz low-pass filter bank. The excitation voltage was set at 15 volts DC except for transducer eleven. The gain and zero offset were set to maximize the filter input signal range which is ±5 volts. The excitation voltage for transducer eleven was initially set at 15 volts but was changed to 13 volts mid-way through the testing due to thermal drift problems. As stated in Brookfield [3], the linearity of the transducers was checked up to one atmosphere pressure difference. The microphone and stator transducers were not linear over one atmosphere and correction factors had to be applied during data reduction. The transducers were calibrated on a daily basis by calculating the slope from zero pressure differential to one atmosphere pressure differential. The slope variation during the testing was less than one percent. The calibrations were also compared to calibrations taken more than one year earlier and were found to be consistent to within one percent. 2.3 Fan Stage Test Geometry The test section used in this study was designed by Brookfield and first used in the studies presented in [3] [4]. The engineering drawings and a full description of the test section design can be found in [3]. As in the Brookfield experiment, the stator leading edge is located 1.7 midspan rotor chords behind the rotor trailing edge and a choke-plate is located two stator chords behind the stator trailing edge. See Figure 2-6 for a drawing of the test section layout. The test fan is 22 inches in diameter and has a hub to tip ratio of approximately 0.45. It features 16 wide chord blades with 40 degrees of twist from hub to tip. The outer blade geometry is a scaled version of the 17 inch Pratt and Whitney Advanced Ducted Propulsor but, as part of the wake management design, has a modified trailing edge. The inner blade geometry incorporates five passages- one for every 20 percent of the span. The flow through each of the five passages can be managed using a throttle plate placed at the base of the blade over the inlets to each of the passages. Each passage ends in seven discrete injection ports that open to the suction surface of the blade. Additionally, each passage has two internal vanes to help turn the flow and provide structural support. A stagger angle view of the blade is shown in Figure 2-7. The stator row used in the tests consists of 40 blades which are uniform along Instrumentation window (4-way probe ports) 0.5c 1.5c Bearing housing 'Actuated face seal Figure 2-6: Test section layout in blowdown compressor the span. The airfoil of the stator blades is the same as the midspan airfoil of the stator designed for the ADP fan but with a slightly modified leading edge. 2.4 Blowing System This section provides a brief overview of the system used to provide the gas for trailing edge blowing. More details can be found in [3]. Like the main gas flow, the gas used for trailing edge blowing was a mixture of CO 2 and Ar. It was held in a cylindrical tank with approximately 356 cubic inches of effective volume. The flow was initiated by a single fast acting valve which led the gas through a 1" diameter pipe to a settling chamber of approximately 73 cubic inches. From the settling chamber, eight 1/2" copper tubes connected to wake management tubes located at 45 degree increments along the circumference of the tunnel. The wake management tubes led the flow through the outer tunnel casing and the outer part of the motor/bearing housing to the area under the hub. This is illustrated in Figure 2-6. The gas then flowed under the hub to the back face of the rotor where it fed into the blades. To minimize leakage through the gap between the rotor back face and the hub, a graphite face seal was Figure 2-7: Trailing edge blowing blade, stagger view 32 used (see Figure 2-6). The seal was mounted on eight miniature pneumatic actuators and was held back while the rotor was brought up to speed. This was done to prevent the seal from overheating. When the main flow through the tunnel was initiated, the seal was seated. Subsequently it was pulled back after the tunnel unchoked. 34 CHAPTER 3 MODIFICATIONS TO BLOWING DISTRIBUTION The trailing edge blowing distribution used in this study differs from the distributions used by Brookfield. Brookfield tested two different trailing edge blowing distributions, a tip-weighted case and a midspan-weighted case. In the tip-weighted case the wake was momentumless at about 80 percent span but was overfilled at the tip and underfilled at the hub. The midspan-weighted case was underfilled at both the tip and the hub regions and overfilled at 50% span. The tip-weighted distribution resulted when throttle plates were placed at the base of the blades. The midspanweighted distribution was obtained when no throttle plates were used [3]. The blowing distribution in the experiments presented in this thesis is a compromise between the two Brookfield distributions. The present blowing distribution was obtained by using a set of throttle plates designed with the aid of data from Brookfield's experiments as well as data from a set of experiments which will be described shortly. The goal of the throttle plate modification was to achieve a spanwise uniform momentumless wake. Although this was not achieved, the resulting distribution has less spanwise variation than either of the distributions presented in Brookfield [3]. In the following sections, the methods used to design new throttle plates are described. Section 3.1 details the parametric studies which were carried out to gather data needed for the throttle plate design. In Section 3.2, the metric used to evaluate the wake reduction is explained. Section 3.3 explains how losses in the blowing system were estimated. This is followed by a description of the throttle plate design method in Section 3.4. Finally, the resulting blowing distribution is presented in Section 3.5. 3.1 Parametric Studies Data from the pressure transducers in the wake management tank and the hub, in combination with four-way probe data, provided the opportunity to better estimate the conditions needed for a momentumless wake while eliminating the need to estimate the pressure losses incurred from the wake management tank to the hub. To expand on the information provided by Brookfield's data, a set of experiments using Brookfield's midspan-weighted blowing distribution was carried out. The midspanweighted distribution was chosen because it does not incorporate throttle plates. Flowfield measurements were taken at 1.5 midspan rotor chords downstream of the rotor trailing edge at the following radial locations: 15%, 25%, 50%, 75% and 87.5% of span. At each location, measurements were taken with increasing initial pressures in the wake management tank until a "flat" or an overfilled wake was obtained. For this reason, the number of runs at each location varied. The parametric experiments provided four major pieces of information. First, they showed that momentumless wakes could be achieved at all the spanwise locations where measurements were taken. Second, the experiments proved that the wake management system had the capacity to provide the hub pressures needed to obtain momentumless wakes at each span. Third, injection was found to be off-center at locations near the hub, i.e. 15% and 25% span, resulting in an increased 2*BPF harmonic when a momentumless wake was achieved. At these locations, the highest reductions in wake harmonics were achieved at a hub pressure close to that needed for a momentumless wake at 87.5% span. Finally, the parametric studies showed that the hub pressure rate of decay was not matched well to the main supply tank pressure rate of decay. During the length of the usable data window, the hub pressure to supply pressure ratio changed by close to 60% resulting in wakes that were not uniformly filled in time. By opening the wake management tank 100 msec earlier to allow time to fill the hub before the flow through the tunnel was initiated, the hub pressure to supply pressure ratio variation was reduced to about 17%. Because the wake variation during the run was found to be comparable to that found in the cases without blowing, efforts to further reduce the hub pressure to supply pressure ratio variation were not pursued. 3.2 Momentum Thickness Calculations The metric used to measure wake reduction is the fraction of momentum thickness filled. The changes in temperature and density between the free stream and the wake were small so speed of sound and density were assumed constant. Thus the momentum thickness equation was reduced to: 0 M(1 )dy (3.1) where 0 is momentum thickness, M indicates Mach number, and the oo subscript indicates free stream values. Due to the unsteadiness inherent in the flow, equation 3.1 was only applied to the portion of the flow containing the wake as indicated by the integral limits b and e. The method used to identify the wakes is described in Appendix A. The free stream Mach number was calculated by mass-averaging the Mach number of the flow outside the wake limits. To determine the fraction of momentum thickness filled, the momentum thickness of the wakes with trailing edge blowing was compared to the momentum thickness of wakes with no trailing edge blowing. For the parametric studies, the no blowing measurements taken by Brookfield at 25%, 50%, 75%, and 87.5% span were used. Because Brookfield did not include measurements at 15% span, measurements without blowing were taken at 15% span during the parametric studies. 3.3 Loss Calculations During the design of the initial set of throttle plates, Brookfield estimated the losses in the blowing system to obtain pressure values at the hub and at the base of the blades. The need to estimate the losses from the wake management tank to the hub was eliminated once experiments were conducted because pressure measurements at the hub were taken. However, the pressure losses incurred from the hub to the base of the blade passages still had to be estimated. Two types of losses were considered in the estimate. The first were turning losses resulting from a 90 degree turn into the blade passages, the second were losses introduced by the throttle plates at the base of the blades. The losses through the blade were not considered because hub pressure measurements and flow field measurements were available. It was assumed that matching the conditions at the base of the blade passages would result in matching the conditions at the exit of the blade passages. Before estimating the turning losses it was necessary to calculate the Mach number at the base of each blade passage. The total pressure of the flow before it turned into the blade passages was assumed to be equal to the pressure measured at the hub, the mass flow was set equal to the amount of mass needed to fully eliminate the momentum deficit, and the following equation was solved numerically for the Mach number: h = PtMA RTt (1 + 2 2 M 2 ) 2(--1) (3.2) where ri is mass flow, Pt is total pressure, 7y is the specific heat ratio, R is the gas constant, Tt is total temperature, M is Mach number, and A is area. Once the Mach number was computed, Equation 3.3 was used to compute the total pressure after losses. Pt 2 = Pt1 1 Y2 (138+ 38 (3.3) (2- ) Ptl and Pt2 are the total pressures before and after the turning loss is applied. As indicated equation 3.3, the turning loss was assumed to be equal to the difference between total and static pressure. To estimate the throttle plate losses, the flow was modelled as flow from one infinite area to another through a beveled orifice facing the flow direction, and the ratio of orifice thickness to hydraulic diameter was estimated as greater than 0.16. In such a case, the loss coefficient is given as =0.18 [10]. ( is defined as the pressure loss over the dynamic pressure of the jet, ( = 6 Pt/qjet. Since the pressure loss needed was prescribed, the following equations could be solved simultaneously to determine the orifice area needed. Ao rh MPtjet qjet= RTt y (1 + 22 P MetM - et(11 +- -y- 1 2 M2) 2 2(-1) MJ t)) (3.4) (3.5) The total pressure of the jet was assumed to be equal to Pt2 from Equation 3.3. As before, rh represents mass flow, but in this case it was set equal to the mass flow needed for each individual passage. 3.4 Throttle Plate Design To obtain a new blowing distribution, a modified set of throttle plates was designed. Information from the parametric studies described in Section 3.1 as well as from Brookfield's experiments was used to aid in the design of the new throttle plates. The parametric studies indicated that a momentumless wake at 15% span resulted in an increase of the 2*BPF harmonic. Furthermore, it was seen that the largest reductions in the 1*BPF and 2*BPF harmonics were seen at a hub pressure similar to that needed to achieve a momentumless wake at 87.5% span. For the reasons just mentioned, the passages responsible for the 0-20% and the 80-100% sections of span were left unthrottled. The process followed to determine the size of the throttling holes for the middle three passages is described in the following paragraphs. First, the pressure needed at the base of each blade passage was established. Using data from the parametric studies, the hub pressures needed to produce momentumless wakes at each spanwise section was established. Then, turning losses were calculated, as described in Section 3.3, to provide an estimate for the total pressure required at the base of each blade passage. As previously mentioned, the throttle plate losses were not considered at this point because the data used for this purpose was taken without throttle plates. The next step was to establish the design hub pressure. Since the passage responsible for the 80-100% section of span was left unthrottled, the design hub pressure was set to be that which produced a momentumless wake at the 87.5% span location. Once the hub pressure was established, turning losses were once again calculated and the "feed" pressure at the base of each passage was determined. Finally, the difference between the feed pressure and the required pressure was used to establish the throttle plate hole sizes. Losses through the throttle plate were calculated as described in Section 3.3. The size of each hole was set to produce the pressure drop needed to obtain adequate pressures at the base of each blade passage. 3.5 Results of Throttle Plate Modifications Figure 3-1 shows the blowing distribution achieved with the new set of throttle plates along with the two distributions tested by Brookfield. The thicker line marked with asterisks represents the new distribution. The lines marked with circles and crosses represent the tip-weighted and mid-weighted distributions respectively. Although the new distribution did not achieve a spanwise uniform reduction in momentum thickness, the spanwise variation was reduced. I 1 j 0 .9 . .... ............. .. . . ........... .. ................. ......... 0.8 . ...... 0 .7 . .... ........ .... ..... 0 .6 . ............ 0.5 F 0.41- ....... 0.3 F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 .2 k ........... . Fraction momentum deficit added Figure 3-1: Fraction momentum thickness filled at 1.5c. Modified distribution(*), tipweighted distribution(o), mid-weighted distribution(+) 42 CHAPTER 4 FLOW FIELD MEASUREMENTS AND STATOR UNSTEADY LOADING PREDICTIONS This chapter is divided into two main parts, the first part (Sections 4.1 and 4.2) presents flow field data with and without trailing edge blowing. The data presented illustrates the flow field changes caused by trailing edge blowing. The second part (Sections 4.3 and 4.4) presents stator unsteady loading predictions based on the measured wake data that were calculated using the noise prediction program BBN/PW V072. The unsteady loading predictions will later be compared with the stator measurements presented in Chapter 5. 4.1 Overview of Flow Field Measurements Flow field measurements were taken using the four-way probe described in Chapter 2. Measurements were taken at 1.5c downstream of the rotor trailing edge at the following five radial locations: 25%, 37.5%, 50%, 75% and 87.5% span. All data is presented as an ensemble average on blade passing period and is shown along with 95% confidence intervals. For the cases without blowing, the average consists of one run with 96 blade passing periods. For the cases with blowing, two runs with 96 blade passing periods were averaged. For the blowing case at 37.5% span the runs averaged contained only 80 blade passing periods. For each radial location, two sets of figures are presented. The first is used to illustrate the degree to which trailing edge blowing reduced the wake, the second provides information more directly relevant to understanding the stator response. The first set of figures shows the rotor relative Mach number, the relative Mach number blade passing frequency (BPF) harmonics, and the rms of the non-harmonic component of the relative Mach number. The latter is largely a measure of the turbulence intensity; although it also includes other disturbances not harmonic on the blade passing period such as those caused by blade-to-blade differences. The second set of figures shown for each radial location will present the harmonic amplitudes of the axial, tangential, longitudinal and transverse Mach number components. The components of the absolute Mach number (axial, tangential, radial), the flow angles, and the static and total pressures are presented in Appendix B. 4.2 Flow Field Measurements 25% span As seen in Figure 4-1, the no blowing wake width exceeds 60% of the rotor pitch and the maximum velocity deficit is greater than 15% of the freestream value. The relative Mach number in the trailing edge blowing case has a velocity excess on the pressure side of the wake and a velocity deficit on the suction side. This indicates that the blowing mass addition did not occur at the center of the wake, but rather toward the pressure side. The velocity deficit is equal to about 6% of the freestream value and the velocity excess is about 4%. At this spanwise location, reductions in the relative Mach number harmonics are only seen for the first two multiples of BPF (Figure 4-1b). At 1*BPF a reduction of close to 60% is seen. At less than 20%, the reduction at 2*BPF is more modest. Changes in the axial and longitudinal Mach number harmonics (Figure 4-2a,c) follow a) Mean Profile: Relative Mach number I I I I I I I ! 0.55 E 0.5 ... . . 0.45 . . .. .. ... . . . .. . . .... .. . . . .... . I. ... . ...... . .. 0.4 " 0.35 . .. . -'''''I'''' 0.3 0 '' I I~ '''''' I' ' ' . . . I.-.. . . . . . . . . [ . . . . . . . . . .I . . . . . . . . . . r . . . . . . . . . .I . . . . . . . . . . f . . . . . . . . . .I . . . . . . . . . . I. . . . . . . . . . "1. . . . . . . . . 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Harmonic Amplitudes: Relative Mach number 0.08 . 0.06 E . 0.04 - - - E S0.02 - 0 0 - 1 2 3 4 Multiples of blade passing 5 c) Turbulence Intensity: Relative Mach number 0.12 -! C, E 0.1 ID0.08 I -I - cc 0.02 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fraction pitch Figure 4-1: Relative Mach number data at 1.5c, (- -)w/ blowing 25% span. (-)w/o blowing, the same trend as the changes in the relative harmonics. However, in the tangential and transverse harmonics, reductions are seen at each of the first five multiples of blade passing frequency. It is necessary to note, however, that there is a strong overlap in the confidence intervals of the higher harmonics. 37.5% span At 37.5% span, the unaltered wake has a maximum velocity deficit equal to about 11% of the free stream value. In the blowing case, mass was added near the center of the wake resulting in a velocity excess with velocity deficits on either side (see Figure 4-3). Each of the velocity deficits and the velocity excess is equal to about 2% of the freestream value. The relative harmonics show reductions of 90% and 87% for the first two multiples of BPF respectively. The 3*BPF harmonic increases by over 80%. The 4*BPF and 5*BPF harmonics also increase. As in the relative harmonics, the longitudinal harmonics show strong decreases in the first two multiples of BPF and an increase in the 3*BPF harmonic. The transverse harmonics, however, also show an increase in the 2*BPF harmonic (see Figure 4-4). 50% span The 50% span case without blowing has a maximum velocity deficit of about 10% of the freestream value (see Figure 4-5). In the blowing case, the maximum velocity deficit is reduced to about 1% of the freestream value; however, a jet component with a velocity excess of about 2% of the freestream value is also present in the wake. This indicates that the mass addition was slightly off-center. Large reductions in the relative Mach number harmonics are seen in the blowing case. The 1*BPF harmonic is reduced by almost 95% and the 2*BPF harmonic is reduced by close to 85%. The 3*BPF and 4*BPF harmonics are reduced by over 60% and 40% respectively. Reductions of about 80%, 75%, 70% and 55% are seen for the a) Harmonic Amplitudes: Axial Mach number 0.045 b) Harmonic Amplitudes: Tangential Mach number riA r 0.04 0.035 0.030.025 . 0.02 1 2 3 4 5 1 c) Harmonic Amplitudes: Longitudinal Mach number 0.045 0 .04 .. . . . . . . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . 0.035 0.03 3 4 5 d) Harmonic Amplitudes: Transverse Mach number 0.045 0 .04 .. 2 - ... . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . 0 .0 35 .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . ... . . . . . - 0.03 .....- ...... 0.025 - . .. .................. ........ 0 .02 5 .. . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . ... . . . . 0.02 0 .02 - ... . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. 0 .0 15 . ............................ 0 .0 1 ....... 0 .0 15 . . . . . : . . . . . ..... . . . . ... . . . . . ... . . . . 0.005 0.01 1 . 1 at 1.5c, 25% ... .. 0.005 2 3 4 5 Multiples of blade passing Figure 4-2: Wake harmonic data (open)w/ blowing . . . . . .. . . . . . ... . . .. . ... . . . . .. span. ...... 2 3 4 5 Multiples of blade passing (shaded)w/o blowing, a) Mean Profile: Relative Mach number i i ! I ! I I I I 0.6 E 0.55 c 0.5 . S0.45 rr 0.4 .............. 0.35 S 0.1 .......... 0.2 ........ 0.3 .............. 0.4 0.5 . 0.7 0.6 . . . 0.8 . . . . . . r 0.9 1 Fraction pitch b) Harmonic Amplitudes: Relative Mach number 0.08 _ 0.06 E C I . ......... .. .. .. . . . . . .. . . . . . . .. . . ... . .. . . I. . .......... . . . . .. . . . .. ..... .. .. ~ ~ .~ .~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ~E 0.04 cc " 0.02 0 1 2 3 4 Multiples of blade passing ) c) Turbulence Intensity: Relative Mach number 0.12 C, :....................... .... ............. E 0.1 I........ 0.08 E = 0.06 Oc . . .. . ... .. .. ... .. .. .S. .. .. . ........... ....... .. .. . .. ... . . .. .... ................. .......... ,. . . ........ ................... . ...... . .. . . .. .. . . I 0.04 - 0.02 0) 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 Figure 4-3: Relative Mach number data at 1.5c, 37.5% span. (- -)w/ blowing 0.8 0.9 (-)w/o blowing, a) Harmonic Amplitudes: Axial Mach number b) Harmonic Amplitudes: Tangential Mach number 0.0451 U.U4: ............ 0.04 ....................... .. ....... 0.0315 .....................:..................... 0.02 .......................................... 0.025 .......................................... 0.02 ........ . ...... I ....... I . ..... ....... - 0.0155 2 . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . .. ........ ..... ..... . . ...... ...... AAI5.i .: LL : ~ l 0.014~ -0.005 1 2 3 4 J 5 1 c) Harmonic Amplitudes: Longitudinal Mach number 1 I I I I I 0.045, 2 3 4 5 d) Harmonic Amplitudes: Transverse Mach number 0 nAR 0 .04 .. . . . . . .. . . . . . . .. . . . . .. .. . . . . . . . . . . . . .. . . . .. 0.035 0 .03 ................... . . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . .. 0 .02 5 .. . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . ... . . . . . 0 .0 2 .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 .0 15 .. . . . ..-. . . .. . . . . . . . . . . . .... .. . . . ... .. . . . .. 0.01 0.005 1 2 3 4 5 Multiples of blade passing Figure 4-4: Wake harmonic (open)w/ blowing data 1 2 3 4 5 Multiples of blade passing at 1.5c, 37.5% span (shaded)w/o blowing, a) Mean Profile: Relative Mach number . - 0.65 0.6 -"~'' ;''''~ " ":' 0.55 " '- ~--'' -- . ~~~' - 0.5 . '' '~ '__'' - - '5- 0.45 04 v. SI 0 0.1 I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Harmonic Amplitudes: Relative Mach number 0.08 n 0.0 E -3 C 4 E 0.0 rrO. 2 - 1 0 2 3 4 Multiples of blade passing 5 6 c) Turbulence Intensity: Relative Mach number 0.1 2 C,) E 0.1 ......................... 0.08 E - 0.06 . ............................. . ..... .... ..................... .......... ....... ................... ............ .. ........ . . . c 0.04 - 0.02 00 03 -II 0.1 . 0.2 .. .. .... 0.3 . 0.4 0.5 . 0.6 ... 0.7 0.8 0.9 Fraction pitch Figure 4-5: Relative Mach number data at 1.5c, (- -)w/ blowing 50% span. (--)w/o blowing, 1,2,3 and 4*BPF longitudinal harmonics (see Figure 4-6). For the transverse harmonics, the first two multiples of BPF show reductions of 47% and 80% respectively but slight increases are seen in the higher harmonics. 75% span At 75% span the wake without trailing edge blowing has a maximum velocity deficit equal to about 10% of the freestream value. In the trailing edge blowing case the deficit is reduced to a little over 2% of the freestream value. However, as seen in Figure 4-7a, there is a slight (about 1%) velocity excess on the suction side of the wake. The relative Mach number harmonics seen in Figure 4-7b show significant decreases in the first four multiples of BPF. The 1*BPF and 2*BPF harmonics were both reduced by about 74% while the 3*BPF and the 4*BPF harmonics were reduced by about 63% and 47% respectively. Reductions in the longitudinal harmonics are similar to those in the relative harmonics except for the 1*BPF harmonic where a reduction of about 98% is seen. In the transverse harmonics, reductions of about 43% and 80% are seen in the first two multiples of BPF but increases are seen in the higher harmonics (see Figure 4-8). 87.5% span At 87.5% span the wake deficit was reduced from about 10% of the freestream value in the case without blowing to a little over 3% in the case with blowing (see Figure 4-9a). Unlike the wakes measured at the other radial locations, the wake at 87.5% span does not have a component with a velocity excess. However, the wake appears to be more filled-in on the suction side indicating that, like the case at 75% span, the blowing mass was most likely injected toward the suction side of the wake. In the blowing case, reductions in the relative Mach number harmonics of 72% and 57% are seen in the first two multiples of BPF (see Figure 4-9). An increase of about Harmonic Amplitudes: Tangential Mach number a) Harmonic Amplitudes: Axial Mach number 0.04 0.035 0.03 U) E 0.025 - o 0.02 0.015 0.01 1 2 3 4 1 5 c) Harmonic Amplitudes: Longitudinal Mach number 0.045 .... ...... 5 d) Harmonic Amplitudes: Transverse Mach number 0.045 ... .... .... 0 .0 35 ....... : 4 0.04 . . . . . . .. . . . . .. . . . . . .... . . . . . .. . . . . 0 .0 4 .. -. 3 2 ........................ . 0.035 ....... .. .. ..... .... . .. ............ 0 .0 3 . . .. . . . . . . . . .. . . . . . . . .. . . . . . . .. . . . . . . . . . 0.03 0 .0 2 5 .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . 0.025 ;... . ...... . . . . . .. . . . . . .. . . . . . .. . . . . . . . . . . . . .. . . . . . ... . . .. . ... . . . . . ... . . . . . . 0 .02 0.015 . .. .. .... . . . . ... . ... . .... .. . .. 0 .015 . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . .. 0 .01 0.01 .... 0.005 0 0.02 1 0.005 0 5 4 3 2 Multiples of blade passing Figure 4-6: Wake harmonic (open)w/ blowing data 2 1 3 4 5 Multiples of blade passing at 1.5c, 50% span (shaded)w/o blowing, a) Mean Profile: Relative Mach number 0.75 . . 3 0.7 E 5 0.65 ... ............. . -: L.... . i.... ...... I ... .......... . ......... ... -s C: 0.6 0.55 0.5 ) 0C 0.1 0.2 0.4 0.3 0.5 0.6 0.7 0.8 1 0.9 Fraction pitch b) Harmonic Amplitudes: Relative Mach number o 0. E .0. E rr 0. 3 Multiples of blade passing c) Turbulence Intensity: Relative Mach number 0.12 - -! E 0.1 m 0.08 E = 0.06 -. -- U0.04 . .. . . . . . . .. . . . .. . .. . . . i5---i--- t_ ~-~~~S--- Z 0.02 C I I I I I 0.1 0.2 0.3 0.4 0.5 0.6 I I I 0.7 0.8 0.9 Fraction pitch Figure 4-7: Relative Mach number data at (- -)w/ blowing 1.5c, 75% span. (-)w/o blowing, b) Harmonic Amplitudes: Tangential Mach number 0.045 a) Harmonic Amplitudes: Axial Mach number 0.045 0.04 0.035 0.03 0.04 0 .0 3 5.. .................... :.......;..... ..........- 0 .0 3 .. . . . . ... . . . .. . . . . . ... . .. . ... . .......................................... 0.025 0.02 . ... . .. . . . . . .. . ... . .. . . ... ... . . .. 0.025 ....... 0.02 ... ....! _...................... ! 0.015 .... 0.01 .. . . . . 0.01 0.005 ............. 0.005 0 2 1 3 4 0 5 c) Harmonic Amplitudes: Longitudinal Mach number 0.045 0 .0 3 5 ........ ....... ...... 0 .0 3 .... 1 5 0.01 .... .. 0.005 .... 0 2 3 4 5 Multiples of blade passing data .................. 0 . ...... ....... ................... .. .. .. .. ............... .. 0 .0 .0 1155 .. . . . . .. .. ............ . . . .. . .. . . ... . .. . . ... . . . . . .. Figure 4-8: Wake harmonic (open)w/ blowing ... 0 .0 2 .. . . . . . . . . . . ... . . . . . . . . . . . . ... . . . . . ... . . .. . . . . . . . .. . . . .. .. .. . . . 0.005 4 0 .0 2 5 .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..- ... 3 d) Harmonic Amplitudes: Transverse Mach number 0.045 0.03 ........... 0 .025 .. .. .. .. . . . .. .. . . .. . .. . . . . . .. .. . . . .. . ... . 0 .0 1 2 .. .... ... . . ... ... . . . . . ... . . . . . . . .. . . .. 0 .0 15 ... ... 1 0 .04 .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. . . . . . . .. . . . 0 .0 4 .. . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . 0 .02 . at 1.5c, 1 75% 2 3 4 5 Multiples of blade passing span (shaded)w/o blowing, a) Mean Profile: Relative Mach number I I I I 1 I 1 .... .......... 0.75 E .......... i ...... ........................ i.......... i. ..... ..........! . ........ ......... .......... . S 0.7 I ......... ............ .. . .. ....,. ..... ...... ........ ... ........ ......--.-.- . ,...........,..................... ... ............................ - 0.6 . -. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . ..I . . . . . . . . . ... . . . . . .. . . ... . . . . . . . .. I . . . . . . . . . . I. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . ... 0.55 0.502 . ; ''''' ''' " ' ' ' - 0.3 0.2 0.1 0 ; ''''' 0.4 0.5 0.7 0.6 0.9 0.8 1 Fraction pitch b) Harmonic Amplitudes: Relative Mach number 0.08 . 0.06 E oC -E 0.04 $ 0.02 0 2 1 0 5 4 3 Multiples of blade passing c) Turbulence Intensity: Relative Mach number 0.12 -! -. . .. . .. . .. . . a) -0 . . . . . .. . . . . . .. . . . . .. . . . . .. . . . . 0.08 E = 0.06 ca0.04 -L -00.02 00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch Figure 4-9: Relative Mach number data at 1.5c, 87.5% span. (- -)w/ blowing (-)w/o blowing, Without Blowing 25% span 37.5% span 50% span 75% span 87.5% span With Blowing 25% span 37.5% span 50% span 75% span 87.5% span Table 4.1: BPF .0149 .0094 .0070 .0148 .0117 BPF .0121 .0025 .0040 .0084 .0071 2*BPF .0090 .0050 .0037 .0047 .0063 2*BPF .0059 .0062 .0007 .0010 .0039 3*BPF .0033 .0025 .0019 .0011 .0020 3*BPF .0023 .0017 .0021 .0020 .0011 4*BPF .0014 .0027 .0011 .0007 .0009 4*BPF .0007 .0008 .0011 .0014 .0005 5*BPF .0006 .0026 .0011 .0004 .0003 5*BPF .0003 .0004 .0010 .0008 .0006 Transverse Mach number harmonic amplitudes at 1.5 chord for cases with and without trailing edge blowing 35% is seen in the 3*BPF harmonic. For the longitudinal Mach number harmonics, the blowing case shows decreases of 89% and 63% for the first two multiples of BPF. The transverse Mach number harmonics show reductions in the first five multiples of BPF. In particular, the 1*BPF and 2*BPF harmonics are reduced by about 40% and 38% respectively. Summary of Wake Harmonics The transverse and longitudinal harmonic amplitudes are tabulated in Tables 4.1 and 4.3. Additionally, the harmonic amplitudes with trailing edge blowing are shown as fractions of the amplitudes without blowing in Tables 4.2 and 4.4. The first four multiples of BPF are also plotted versus span in Figures 4-11 and 4-12. Note that with blowing the 1*BPF harmonic is lower at all radial locations for both the transverse and the longitudinal Mach numbers. The 2*BPF harmonic was reduced at all spans for the longitudinal Mach number and at four out of five locations for the transverse Mach number. For completeness, the phases of the transverse and longitudinal Mach numbers are plotted versus span in Figures 4-13 and 4-14 for the first four multiples of BPF. b) Harmonic Amplitudes: Tangential Mach number 0.045 a) Harmonic Amplitudes: Axial Mach number 0.045 . . ... 0.04 0.04 0.035 0.035 0.03 I I 0.025 0.02 0.02 0.015 0.015 0.01 0.01 0.005 0.005 1 2 3 4 . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . .. . . . . . . , . . . . . . ...... ..... .. . 0.03 I 0.025 0 . .. 1 0 5 c) Harmonic Amplitudes: Longitudinal Mach number 0.045 2 ....... 3 4 5 d) Harmonic Amplitudes: Transverse Mach number 0.045 0 .0 4 - . ... . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . .. 0 .04 ....... ............... 0 .0 3 5 ................................ 0 .035 ........ ....... ....... ....... ........ 0 .03 .. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.03 . . . .... .. 0.025 0 .025 .. .. . . .. . . .. . .. . . .. . . . . . . . .. . .. . . .. . . . . ... 0 .0 2 . ... . . . . . . .. . . . . . ... . . . . . . .. . . . . . .. 0 .0 2 ... .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . . .. . . . . . .. 0 .0 15 . . . . . . .. . . .. . . .. . . . . .. .. . . . . .. . . . . . .. 0.025 - -- 0.01 . . - 0 .0 15 ....... 0 .0 1. . . . 0.005 0 ......... . . . ...................... ............................. -- 0.005 1 0 2 3 4 5 Multiples of blade passing Figure 4-10: Wake harmonic data (open)w/ blowing at 1.5c, 87.5% 1 2 3 4 5 Multiples of blade passing span (shaded)w/o blowing, 25% span 37.5% span 50% span 75% span 87.5% span Table 4.2: BPF .81 .27 .56 .57 .60 3*BPF .68 .66 1.13 1.78 .58 4*BPF .48 .29 1.06 1.89 .49 5*BPF .57 .16 .89 2.19 2.17 Transverse Mach number harmonic amplitudes with blowing as fractions of harmonics without blowing Without Blowing 25% span 37.5% span 50% span 75% span 87.5% span With Blowing 25% span 37.5% span 50% span 75% span 87.5% span Table 4.3: 2*BPF .66 1.24 .19 .21 .62 BPF .0347 .0227 .0158 .0141 .0267 BPF .0147 .0024 .0031 .0002 .0030 2*BPF .0061 .0074 .0075 .0154 .0117 2*BPF .0055 .0004 .0018 .0038 .0043 3*BPF .0015 .0028 .0067 .0079 .0025 3*BPF .0020 .0032 .0020 .0037 .0030 4*BPF .0012 .0017 .0033 .0030 .0007 4*BPF .0015 .0012 .0015 .0019 .0011 5*BPF .0005 .0015 .0014 .0011 .0001 5*BPF .0008 .0008 .0011 .0009 .0005 Longitudinal Mach number harmonic amplitudes at 1.5 chord for cases with and without trailing edge blowing 25% span 37.5% span 50% span 75% span 87.5% span BPF .42 .10 .19 .13 .11 2*BPF .89 .05 .24 .25 .37 3*BPF 1.31 1.16 .30 .48 1.18 4*BPF 1.24 .68 .45 .63 1.66 5*BPF 1.77 .56 .80 .84 5.83 Table 4.4: Longitudinal Mach number harmonic amplitudes with blowing as fraction of no blowing harmonics a) BPF b) 2*BPF 0.01 0.02 0.018 .. . . . . . 0.009 . 0.016 - 0.008 . . . . . . . . .. . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 0.014 0.007 . . .... . 0.012 0.006 0.01 0.005 ..... ....................... .. 0.008 0.004 ... .. . . . . . . . . . . . . . . . . .. . .. 0.006 0.003 . . . . ... . . . . . . i. I . . . . . 0.002 0.002 0.001 0 5 0.2 0.4 0.6 0.8 0 c) 3*BPF x 10 - 3 ..J.. .. .... .. 0 1 . -r . 0.004 I x 10 0.2 0.4 0.6 0.8 d) 4*BPF -3 4 .5 ....... 43.5 - 32.5 ....... 21.5 ....... 1 -- - -- 10.5 ....... 00 0.2 0.4 0.6 0.8 1 0 Fraction span 0.2 0.4 0.6 0.8 Fraction span Figure 4-11: Transverse Mach number harmonic amplitudes vs. span, first four multiples of BPF. (shaded)w/o blowing, (open)w/ blowing 59 1 a) BPF b) 2*BPF 0.04 0.02 0 .0 18 .................. 0.035 0 .0 16 .. . . . . . . ... . . . . . . ... . . . . . . . 0.03 . . . . . . . .... 0 .0 14 .. . . . . . .... . . . . . . ... . . . . . . . 0.025 . . . . . . . . . . ... . 0.012 0.02 . 0.01 ).015 ...... . . . . . . . ... 0.008 . 0.006 .... 0.01 .. . . 0.004 -. 0.005 . " 0.002 0 0 3 0.2 0.4 0.6 0.8 1 c) 3*BPF ....... 0 x 0.01 .. 0.2 10- 3 - 0.4 . ..... 0.6 ... 0.8 d) 4*BPF 0.009 0.008 0.007 i 0.006 .0 E c 0.005 1 - 2 0.004 0.003 - 0.002 - 0.001 0 0 0.2 Figure 4-12: 0.4 0.6 Fraction span 0.8 1 0 0.2 0.4 0.6 0.8 Fraction span Longitudinal Mach number harmonic amplitudes vs. span, first four multiples of BPF. (shaded)w/o blowing, (open)w/ blowing a) BPF b) 2*BPF 1 1 ! 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 ................. ... .....\ . ........... ...... . 13 .4 I 0.4 0.4 0.3 0.1 0 0 -100 0 u 100 o. ............ .. .. ..... ... .... 100 .I 0.9 0.8 . .. * N. 0 d) 4*BPF 1 0.8 0.7 0.6 -N ........................................ . . - 0.6 - -.. 0.5 0.5 0.4 0.4 0.3 -100 c) 3*BPF 1 0.7 I 0.2 0- 0.1 0.9 . .. .... ....i • 0.3 -El 0.2 .. .... . . . . . .. -- - IN "I NI. -d , / -:- 0.3 0.2 0.2 0.1 0.1 0 0 -100 0 100 -100 Phase Angle 0 100 Phase Angle Figure 4-13: Transverse Mach number harmonic phases vs. span, first four multiples of BPF. (-)w/o blowing, (- -)w/ blowing 61 ' - a) BPF b) 2*BPF .0.6. c 0.5 ' & 0 .7 .... 0 ... i .. . 0 ............... 0 -100 c) 3*BPF ............. 0 100 d) 4*BPF 1 I 0 .9 ..... ....................... ....... ........ 0.8 - .. ....... ...................... 0.8 . a . 0.5 .- ... .. . . .. 0.4 zcc 0.4......... .......... 0.3 0.1 0 .r.-. . ..-. 0.4 00.4 ............. '- 0.3- -. 0 .2 .... . . . .-.... . . . . ........................ 0.2 ........................ 0.1 - -100 Figure 4-14: 0 Phase Angle . 0.1 ............................... ......... 100 1 0 .9 .. ........... 0 .2 .. 00.1 .- ..................................... .. .... -100 ........ ..... . ... ... ....... .. ... . 0.3 - ... .................. .................... 0 -.. .. . . . .... 0.4. 0.4 .. . 0 .~ :~- - -~- : - -- - ----------- 0.3 0 .2 .. ......... 0.5 - 0.4 L 0.4 . 0.7 ...... - . 0.. ... ..... r ... . ...... ............. 0 .8 ........ 0 100 -100 0 Phase Angle 100 Longitudinal Mach number harmonic phases vs. span, first four multiples of BPF. (-)w/o blowing, (- -)w/ blowing 62 4.3 V072 Noise Prediction Code The BBN/PW V072 rotor-stator interaction noise prediction program was developed by Pratt and Whitney under NASA funding. This code is a modification of two previously existing programs- the GE/NASA semi-empirical rotor wake/vortex model, and the BBN/NASA rotor-stator interaction noise prediction code. The V072 code can be broken down into two parts. In the first part, a model of the rotor wakes is calculated; in the second, the wake model is used to calculate stator noise response. The rotor wake calculation section comes from a program originally developed by General Electric under NASA funding. It divides the annulus into strips and then unwraps those strips to form two-dimensional infinite cascades. This allows flow in the circumferential and axial directions but not in the radial direction. The flow across the rotor is assumed to be incompressible and the mean flow is analytically calculated along each streamline. The flow perturbations due to the rotor wake are calculated separately and superimposed on the mean flow. The perturbations are calculated using empirical data from existing fans. Once the wake velocity perturbations and mean flow are combined the upwash velocity at the stator leading edge is obtained. When obtaining the upwash velocity, it is assumed that the mean flow passes directly through the stator row producing no upwash. It is also assumed that the mean flow does not interact with the wake perturbations. The noise calculation comes from a section originally developed by Bolt, Beranek, and Newman. Initially, the unsteady pressure distributions on the stator are found using two-dimensional strip theory. Once the chordwise pressure distributions have been found, the annulus is reformed. This results in an annular duct with spanwise and chordwise pressure distributions. Using the pressure distribution, the interaction with the duct acoustic modes is calculated and power levels for the circumferential and radial propagating modes can be found. Total noise power is given as a sum of these modes. For the studies in this thesis, the majority of the rotor wake calculation section of V072 was bypassed. Instead of using the wake calculated by the program, the upwash was calculated using experimental wake measurements at 25%, 37.5%, 50%, 75% and 87.5% span. The results were then interpolated to 41 spanwise locations and input into the noise calculation part of the program. The stator unsteady pressure distributions calculated in this second part of the program are presented in the following section. 4.4 Unsteady Stator Loading Predictions The stator unsteady pressure distributions calculated using the V072 program are found in Figures 4-15 through 4-24. The amplitudes and phases are plotted against stator chord and are presented for the first three harmonics of BPF. The solid lines represent the no blowing case while the blowing case is represented by dashed lines. Reductions in the amplitude of the first two harmonics of BPF are predicted at every spanwise location. For the 1*BPF harmonic, reductions of about 10dB are seen at the 50%, 75% and 87.5% span locations. A 15dB reduction is seen at 37% span while a 5dB reduction is seen at 25% span. Reductions of 2-3dB for the 2*BPF harmonic are seen at 25% and 37.5% span. The 87.5% span location shows a reduction of about 5dB, and reductions of 10-15dB are seen for the 50% and 75% locations. For the most part, the harmonic reductions follow the trend set by the reductions in the transverse harmonics. Slight discrepancies can most likely be attributed to interpolation of the data. The flow field measurements at the five measuring locations were interpolated to produce 41 sets of input for the V072 code. The predictions seen here were calculated using the interpolated upwash and not the actual measurements. Finally, note that at all of the locations the amplitude changes and the phase shifts are essentially uniform along the chord. It will be seen in Chapter 5 that the same does not hold true for the experimental measurements. a) Amplitude of differential pressure: 1*BPF 175 170 165 ..."... ...... ......... ........... .............. .. . ......... ....... .... 155 - " ' . . .- 150 ' 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 a) Amplitude of differential pressure: 2*BPF 160 155 150 145140 135 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 a) Amplitude of differential pressure: 3*BPF 145 140 135 m 130 125 120115 0 0.1 Figure 4-15: 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 Stator unsteady loading predictions: harmonic amplitudes at 25% span. (-)w/o blowing, (- -)w/ blowing 65 a) Phase differential pressure: 1*BPF 200 150 100 -.... 50 -- .................... .. ................. .. ...........i. ...... ....... .................. -50 -100 . . . . .. i -150 -200 . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . i 0.1 0 0.2 0.3 I I . . . . . . . . . . . . . . . . . . . . . . . . . . . .-. . . . . . . . . . .-.. . . . . . . . . I 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 a) Phase differential pressure: 2*BPF 200 150 . .................................. . ........... . ............. I I .............. .. . .. I ......... ......... I ...... ......... ... II ..... ..... ....... .. .. ...... S100 . ................ .................................................... S .......................... I.. 50 S 0 S I -50 0 .I CL. -100 -150 -200 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 a) Phase differential pressure phase: 3*BPF " ... 20C ) 150 p J g loc 3 a) 5 a 3 ) -Sc C, 3 -50 3: -10 W -150 -200 SI 0 0.1 0.2 I I 0.3 0.4 I I 0.5 0.6 Fraction span Figure 4-16: Stator unsteady loading predictions: (-)w/o blowing, (- -)w/ blowing 66 I I I 0.7 0.8 0.9 harmonic phases at 25% span. 1 a) Amplitude of differential pressure: 1*BPF 170 160 155 . . .. . . .. . . . . . .. . . .. . . . . . .. . . .. . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . ......... .. . . .. ......... m 15 0 ........... 145 140135 130 0 I 0.1 I I I 0.2 0.3 0.4 I I 0.5 0.6 Fraction span I I I 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 a) Amplitude of differential pressure: 2*BPF 160 155 150 m 145 140 135 130 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 a) Amplitude of differential pressure: 3*BPF 140 135 M 130 125 120 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 Figure 4-17: Stator unsteady loading predictions: harmonic amplitudes at 37.5% span. (-)w/o blowing, (- -)w/ blowing 67 a) Phase differential pressure: 1*BPF 200 150 100 50 0 -50 -100 -150 -200 C0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span C).7 0.8 0.9 1 0.7 0.8 0.9 1 0.8 0.9 1 a) Phase differential pressure: 2*BPF 200 150 100 50 0 -50 -100 -150 -200 ) 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span a) Phase differential pressure phase: 3*BPF 200 150 100 50 0 -50 -100 -150 -200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction span Figure 4-18: Stator unsteady loading predictions: (-)w/o blowing, (- -)w/ blowing 68 harmonic phases at 37.5% span. a) Amplitude of differential pressure: 1*BPF 170 130120 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 0.8 0.9 0.8 0.9 1 a) Amplitude of differential pressure: 2*BPF 155150 145 140 , 135 130 125 1201150 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 a) Amplitude of differential pressure: 3*BPF 145 135 130 125 120 0 0.1 Figure 4-19: 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 Stator unsteady loading predictions: harmonic amplitudes at 50% span. (-)w/o blowing, (- -)w/ blowing 69 1 a) Phase differential pressure: 1*BPF 200 150 -' .. ....... . . . . ... . . . . . ... . . . . . . . . .. . . . . . 100 . . . .\ . . . . . . . . . 50 .. . . . 0 -50 . . . . . . .i. . . . . . . . . . . . . . -100 -150 I I I I I 0 0.1 0.2 0.3 0.4 -200 I I 0.5 0.6 Fraction span 0.7 0.8 0.9 1 a) Phase differential pressure: 2*BPF 200 150 100 50 0 -50 - -100 I I .. . . . ..-. .. . . . ... . . .. . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . .. . . . .. . . -150 . . . . . . . . . . .. . . . . . . . . . . . . . ..-. I . . ... . .. . . . . . . .I . . . . . . .. . . . . . . . . . . . . . . . . . . . -3nn -- f-.*%J V 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 a) Phase differential pressure phase: 3*BPF r"1rl Cu 150 - a, 100 a, 50 -- 0 -m -50 = -100 -150 I -200 0 0.1 0.2 .~ 0.3 ~ I I 0.4 0.5 ~ I I I 0.6 0.7 0.8 .I 0.9 Fraction span Figure 4-20: Stator unsteady loading predictions: (-)w/o blowing, (- -)w/ blowing 70 harmonic phases at 50% span. a) Amplitude of differential pressure: 1*BPF 165 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 0.8 0.9 1 a) Amplitude of differential pressure: 2*BPF 155 150 145 140 m 135 130 125 120 115 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 a) Amplitude of differential pressure: 3*BPF 150 145 140 135 130 125 ..................... 120 ...... ,-, .... I 115 0 0.1 Figure 4-21: 0.2 . ......... I 0.3 I 0.4 ....................................- ........ . .. . . . . . . . . . . . .. . . .. . .... ........... ..... I 0.5 0.6 Fraction span 0.7 0.8 0.9 Stator unsteady loading predictions: harmonic amplitudes at 75% span. (-)w/o blowing, (- -)w/ blowing 71 1 a) Phase differential pressure: 1*BPF 200 150 c 100 W 50 i 0 .. . . . . . . . . . . . . .. o A C- a , -50 = -100 a. -150-200I 0 0.1 0.2 I 0.4 0.3 I 0.7 I I 0.5 0.6 Fraction span I 0.9 I 0.8 1 a) Phase differential pressure: 2*BPF 200 I . I I. . . . . . 150 S. . . . . . . . . . . . . 100 50 0 -50 S. . ... ... ................ ........... ............................... -100 .......... -150 ......... II -200 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 0.8 0.9 1 0.8 0.9 1 a) Phase differential pressure phase: 3*BPF 200 150 100 -- 50 . .. I ' I: .......i.... .............. . .... .... ..i. . . . . . 0- . . .. . ... . .. . . . .i -50 - ! -100 - . . . - .. . .. ... .... ... ... . ... ..... . ... ... ..... ... ... . ... . . . . . .. . . . -...... .. I . I I 0.3 0.4 - . - - . . . . . . . . . . . . . : - - . - - - . : . -150 -200 I 0 0.1 0.2 0.5 0.6 0.7 Fraction span Figure 4-22: Stator unsteady loading predictions: (-)w/o blowing, (- -)w/ blowing harmonic phases at 75% span. a) Amplitude of differential pressure: 1*BPF 170 16 5 . . . . . . . .... . . . . . . . . ... . . . . . . . ... . . . . . . . . ... . . . . . . . . .... . . . . . . . ... . . . . . . . . ... 160.. 155 150 130 0 I 0.1 II I 0.2 0.3 0.4 I 0.5 0.6 Fraction span II 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 a) Amplitude of differential pressure: 2*BPF 155 150 145 140 135 130 125 120 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 a) Amplitude of differential pressure: 3*BPF 140 135 130 125 120 115 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction span 0.7 Figure 4-23: Stator unsteady loading predictions: harmonic amplitudes at 87.5% span. (-)w/o blowing, (- -)w/ blowing 73 a) Phase differential pressure: 1*BPF 200 150 100 50 0 -50 -200 L 0 0.1 0.2 0.3 I 0.4 I I I 0.5 0.6 Fraction span 0.7 0.8 0.9 1 a) Phase differential pressure: 2*BPF ofAIII o3 100 .................................................. 50 50.............. - 5 0 .. . . . . . . . . .. . . . .. . . .... . . .. .. . . . .*. . .. . . .. .. . . -100 -150 I .. .. -200 0 0.1 0.2 0.3 I 0.4 I 0.5 0.6 Fraction span I 0.7 I 0.8 0.9 a) Phase differential pressure phase: 3*BPF 200 .......... 150 ........... 100 a) 50 0 a . ......... C -50 c) ................................................. a-S- 10 0 . ............... -150 -200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fraction span Figure 4-24: Stator unsteady loading predictions: (-)w/o blowing, (- -)w/ blowing harmonic phases at 87.5% span. 1 CHAPTER 5 STATOR LOADING MEASUREMENTS This chapter presents stator loading measurements taken using the instrumented stator described in Chapter 2. Measurements were taken at the same five radial locations where flow field measurements were taken (i.e. 25%, 37.5% 50%, 75%, 87.5% span). As in Chapter 4, all data presented is an ensemble average on blade passing period and is shown along with 95% confidence intervals. At each radial location, the same number of runs were averaged in the blowing and the no blowing cases. For the 50%, 75% and 87.5% span locations 9 runs with 96 blade passing periods each were averaged. Due to time restrictions, the data presented for the 25% and 37.5% span locations is the average of 5 runs and 3 runs respectively. The mean pressure envelopes are presented in Section 5.1. In Section 5.2, the amplitudes and phases of the differential pressure harmonics are presented. The amplitudes and phases of the stator pressure and suction side pressures can be found in Appendix C. 5.1 Mean Pressure Envelope In order to show the general behavior of the flow field, the stator mean pressure envelopes are presented in Figures 5-1 through 5-5. The coefficient of pressure is defined as Cp = (Pocai - Pupstream)/(Pt- P)upstream. Upstream values were obtained from the four-way probe measurements in Appendix B. The case without blowing is shown as a solid line while the case with blowing is shown as a dashed line. The dashed-dot envelopes represent the minimum and maximum pressures seen over the ensemble-averaged period. Note that while the general shape of the curves does not change much with blowing, a slight increase in stator loading is seen. This increase is attributed to the changes in axial Mach number and tangential flow angle seen as a result of the blowing mass addition. This is a feature of the experimental facility, in which the throughflow is throttled by passing through a fixed area choke plate downstream of the test section. 5.2 Differential Pressures The pressure difference across the stator was calculated from the pressures measured on the pressure side and suction side of the stator. The amplitudes and phases of the first three harmonics of the ensemble-averaged differential pressure are plotted along the stator chord for each spanwise location in Figures 5-6 through 5-15. The dashed and solid lines represent the blowing and no blowing cases respectively. Amplitudes are given in dB (dB = 20*loglo(P,m/2 * 10-5)) while phases are given in degrees. 25% span Figures 5-6 and 5-7 show the stator harmonic amplitudes and phases, respectively, at 25% span. The 1*BPF harmonic exhibits a significant reduction in amplitude ranging from about 5dB at the leading edge to about 15dB at the trailing edge and a fairly uniform phase shift of about -80 degrees along the entire chord. The 2*BPF harmonic amplitude is virtually unchanged, and although there appears to be a slight increase in the amplitude of the 3*BPF harmonic, it cannot be resolved within the 95% confidence intervals. A phase shift ranging from about -50 degrees at the leading and trailing edges to about -20 degrees at the midchord is seen for the 2*BPF harmonic. The 3*BPF harmonic phase has a shift ranging from about zero Mean pressure envelope: no injection 0.4 0.2 C _ 0 o o H D -0.2 i_ -0.4 H -0.6 -0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 0.9 Fraction chord Mean pressure envelope: injection 0.4 ".. 0.2 .... ....... . .... . . . . . . . .. 3* ... _. .-'. . '.-.. . ..' . . . . . . :" C ............................... 0 .... .. ..- . . . . . . .. . . . . . . . . . . ... . . . . . . . . . .. . . . . . . . . . ...--- ........... .......... _ _--- 0 S -0.2 : .......... : ......... ........... . . . . . ,..-. -. . .. ': . .:.. . . . . . .. . . . . .. . ....................... ............... ... . . ..-. . . . -0.4 -0.6 . . . . . . . . . .. . . . . . . . ... -OR ". 0 . . . . . . . . . .. . . . . . I I I I [ 0.1 0.2 0.3 0.4 . . . .I 0.5 0.6 0.7 I I 0.8 0.9 1 Fraction chord Figure 5-1: Stator mean pressure (- -)w/ blowing envelope at 25% span. (-)w/o blowing, Mean pressure envelope: no injection i . ...... ..............: - . . ........:. .. ...... . ............................ . 0.2 ......... ..... ..... ......... . . . . . . . .•.-..... . . . . . . . -0.2 . .. . . . . . . . . . . .•.. . . . . . . . . .. .. .. .. . .. ,.. . . . . . ,. . . . .. . . . . . . .. . . . . . .. . . . . . . . . . •.. . . . . . . . .. . . . . . . . . . . . . . . . .I . . .. . . . . . .. .. . .. . .. . . . . .. .. -0.4 ........................... I .... .. ........... -0.6 -0.8 3 0C 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fraction chord Mean pressure envelope: injection I V F F .....- ...... -.. .. . r I . . -.- -..- n -.. - - . 0.2 ... . . .. . . . C .. .. ... . . .I! ... . . ..... .. ... .. ... .. . .. . .. . .. . 0o o . 0- • .. . ... . . .. .... . . . ./ . ... .-.. -........ .... q/ , :. , -0.2 W-0.2(f) a) . . . .. . .. .. . ... . .. . .. . ..... . .. . .I .. .. . . .. .... E -0.4-0.6 k . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . -n ni ' I 0 Figure 5-2: 0.1 0.2 0.3 0.4 Stator mean pressure (- -)w/ blowing 0.5 0.6 Fraction chorc envelope at 37.5% 0.7 span. 0.8 0.9 1 (-)w/o blowing, Mean pressure envelope: no injection Fraction chord Mean pressure envelope: injection -c- -8' -.- -- 0.2 - .. ... ... .. .. ... .. ~ -r . .. ... . . . . . . . . . .. . . . . ~ ~~ ~ ~ . . .. .. . .. ... . .. .. . . . . . -0.2 - -Q~ - - - . . . . . . . . . . . . . . . .. . . . .. . . .. . . . . - --. ....... >i... ........... .......... .~ - -. " ............... - ............. ;- -0.4 .............. ............. -0.6 . -0/ .. I I . . . . . ni I 0 Figure 5-3: 0.1 Stator 0.2 mean (- -)w/ blowing 0.3 0.4 pressure 0.5 0.6 Fraction chord 0.7 envelope span. at 50% 0.8 0.9 1 (-)w/o blowing, Mean pressure envelope: no injection T ...... I . 0.41 H C 0.2 . .. .. .. . . . . . . . . . . . .. . .. . O . . -0.2 . .. . . . . . " . .. .. ,-' ". -0.4 H '- -0.6k - - /-* _.. - I I I I , -0.8 I I 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 Mean pressure envelope: injection . . .. . . .. . . . -. . ..-. . 0.2 ~ . . . -0.2 - .... . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . ". . . :. . . . . . . .".. . ...... . . . . .... . . . ... . . . . . . . . -. . -. . . -. .. . . . . . . . . . -. . . . . ... - . . . .. . . . . . .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . ...... • • / . . .. . . / i~ / L. K-/ -0.4 - . .K"/ . . .. . .. . . . . .. .. . . . . \\ -. c- - _ . . . ., -0.6 F -0.8L 0 Figure 5-4: . , .. . . . . i- - .- . .. . .. . .. " . . . I I I i 0.1 0.2 0.3 0.4 Stator mean pressure (- -)w/ blowing . . . . :. . './/..... . . . . . . . . . . . . . . . . 0.5 0.6 Fraction chord 0.7 envelope span. at 75% .. .. . . .. . . .. . . . 0.8 . . . . . . . . . . . 0.9 (-)w/o blowing, Mean pressure envelope: no injection 0.4 . ........ I ' I II" 0 .2 ........ -0.2- ./ ........ ........... ..... . ...... ..... ............. : ; ...... :iL ........L.. -0.4 -0.6- ........ .. . .. ..:.. ....... :....... ,,\ .. . . .. : .. ................:....... . . ] I . Ii _A - 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 . 0.8 0.9 1 0.8 0.9 1 Fraction chord Mean pressure envelope: injection 0.4 ... . ........... ...........:..........:. ...... .. ...... -4 0.2 ..... . . . . .: . . . - ------T.--.- --' .:.-----.- .................... ............ . ... . . . . . . . . . .... . . . . . . . . .. . . . . . . . . . ... . . . . . . . . .i.. . . . . . . . . .. . . . -0 .2 ........... -0 .4 ...........-. . . . . . . . . . . . . . .N-.. . . . . . .. . . . . . . . . -0.6 ..... -0.8 0 0.1 .. ... .. .. . .....:..........:. ................. .. ' .~~~ " \ ., ....: .. 0.2 0.3 '""tt _ \', . .~~ 0.4 . 0.5 0.6 Fraction chord Figure 5-5: Stator mean pressure envelope (- -)w/ blowing . . . . . . .. . . . . . . ........ at 0.7 87.5% span. (-)w/o blowing, Amplitude of differential pressure: 1*BPF 16( E 4I S155 ... o 15C . . .. az o 145 . 14C 0 .. .. . . . .. ...... 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 Amplitude of differential pressure: 2*BPF T-I ............0 0.1 0.2 0.3 0.4 .... - . 0.5 0.6 Fraction chord .. 0.7 .. .. . .I. ... .. .. .. 0.8 0.9 0.8 0.9 1 Amplitude of differential pressure: 3*BPF E 14 0 m 11 " 121 0 0.1 0.2 Figure 5-6: Harmonic 0.3 0.4 0.5 0.6 Fraction chord amplitudes of stator (-)w/o blowing, (- -)w/ blowing differential 0.7 pressure at 25% span. Phase of differential pressure: 1*BPF I I I I I I 150 100 ........ ... ... .I ...-- - ..... 50 ........... ..................... ...........i.......... 0 . C (c -50 a) Ca-100 C. SI -150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Phase of differential pressure: 2*BPF 150 100 I 50 5 0o 0 0 -50 CO-100 -150 -. 0 C .. 0.1 I . 0.2 0.3 0.4 i......... ........... ............ ....... ... ... 0.5 0.6 Fraction chore 0.7 0.8 0.9 1 0.8 0.9 1 Phase of differential pressure: 3*BPF 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Figure 5-7: Harmonic phases of stator differential pressure at 25% span. (-)w/o blowing, (- -)w/ blowing 83 degrees at the leading edge to about -100 degrees at the trailing edge. At this same spanwise location, reductions of about 5dB and 3dB were predicted for the 1*BPF and 2*BPF harmonic amplitudes (see Figure 4-15) and uniform shifts of about +30 degrees and -20 degrees (see Figure 4-16) were predicted for the phases of the 1*BPF and 2*BPF harmonics. While it may be said that there is rough agreement between the predicted amplitude reductions and the experimental measurements, the same cannot be said for the phase shifts. 37.5% span In contrast to a predicted reduction of about 15dB in the 1*BPF harmonic amplitude at 37.5% span (see Figure 4-17), measurements show a slight decrease at the stator leading edge and a slight increase at the trailing edge but these changes are not discernible within the 95% confidence intervals (see Figure 5-8). Likewise, there seems to be little agreement between the predicted phase shifts and the phase shifts in the experimental measurements (see Figures 4-18 and 5-9). 50% span The stator harmonic amplitudes at 50% span are shown in Figure 5-10. An increase in amplitude, ranging from about 2dB to about 7dB, is seen along the entire chord. The largest increase occurs in the midchord section. At 2*BPF and 3*BPF no significant changes are seen. For the harmonic phases, shifts ranging between -50 and -120 degrees are seen for the first three harmonics of BPF, (see Figure 5-11). The changes in the stator harmonics at 50% span do not agree with the data presented in Chapter 4. At 50% span the longitudinal and transverse Mach number 1*BPF harmonic were reduced by about 80% and 45% respectively and a reduction of about 10dB was predicted for the stator 1*BPF harmonic. A possible reason for this inconsistency will be presented in Chapter 6. Amplitude of differential pressure: 1*BPF J^^ 'I~ill IWv I I 155 * .. ...... ... ... ............. .................... .................. ................ . .. ........." 150 ........ 145 .. .. . . 140 L 0 0.1 . . . 0.2 .... ... ... . ... .. . .I 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 Fraction chord Amplitude of differential pressure: 2*BPF 140 . 130 120 ca 110 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Amplitude of differential pressure: 3*BPF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction chord Figure 5-8: Harmonic amplitudes of stator differential (-)w/o blowing, (- -)w/ blowing pressure at 37.5% span. Phase of differential pressure: 1*BPF -I - 150 I I ! ............. ..... 100 S50 .... ........ 0 - C ..................... -50 C, -100 ............ 0057 - ......... a .................... ......... ............ 1__ -150 ..................... 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 37.5% span. Phase of differential pressure: 2*BPF 150 e 100 -50 CD a 0 -50 a) Cz-100 CL 0.--is -150 - --- --- - -. III 0 0.1 0.2 0.3 0.4 0.5 0.6 I 0.7 Fraction chord Phase of differential pressure: 3*BPF I ------ - 150 a) 100 50 (D 0 c, C Cz -50 cz -100 ---Cl iso I . .... . . . . . .. . . ..- C Figure 5-9: 0.1 . . . . . 0.2 ... . . . .. ... . . . . . . . 0.3 0.4 0.5 0.6 Fraction chorc Harmonic phases of stator differential (-)w/o blowing, (- -)w/ blowing 86 0.7 pressure at Amplitude of differential pressure: 1*BPF 55 I i 45 . I " ..... 40 1 3G 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Amplitude of differential pressure: 2*BPF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction chord Amplitude of differential pressure: 3*BPF .... 140 . .. ...... . . . . . . . . II D 130 o - 120 k. m 110 "D 0 0.1 0.2 I I 0.3 0.4 I 0.5 0.6 0.7 I I 0.8 0.9 1 Fraction chord Figure 5-10: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing differential pressure at 50% span. Phase of differential pressure: 1*BPF .I 150 - C, CD 100 - I I I I I - 50 C a, I - - -50 a) C, CO-100 S-150 .I - 0 0.1 0.2 0.3 0.4 I 0.5 0.6 Fraction chord I I 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 Phase of differential pressure: 2*BPF 150 - U, _ 100 50 CD z . __ . ...... .. ~ 0 -50 a) U, Ca-100 . ... . . -150 .. . . ... I I 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chor( 0.7 Phase of differential pressure: 3*BPF c, , 150100 S50 4 C am 0 -50 ca -100 -150 0 0.1 Figure 5-11: 0.2 0.3 0.4 0.5 0.6 Fraction chord Harmonic phases of stator differential (-)w/o blowing, (- -)w/ blowing 0.7 pressure at 50% span. 75% span At 75% span the 1*BPF harmonic amplitude is reduced mostly at the midchord (by 3dB) and the trailing edge (by 5dB) while virtually no change is seen in the harmonic phase, (see Figures 5-12 and 5-13). Reductions along the entire chord are seen in the 2*BPF harmonic amplitude, although the reductions along the midchord are not altogether discernible within the 95% confidence levels. A reduction of about 15dB in the 3*BPF harmonic amplitude is seen at the leading edge of the stator, but no change is seen at the trailing edge. In contrast, the stator loading predictions presented in Chapter 4 show close to uniform reductions in amplitude along the entire chord for the first three harmonics of BPF. Reductions in amplitude of approximately 9dB are predicted for the first and third multiples of BPF, while a reduction of about 12 dB is predicted for the second harmonic. The predicted phase shifts are uniform along the chord, whereas in the stator measurements shifts in harmonic phase vary along the chord. Strong shifts in the 2*BPF harmonic phase are seen at the leading and trailing edges but shifts at the midchord section cannot be distinguished within the confidence intervals. The 3*BPF harmonic phase exhibits a shift of about +150 degrees at the leading edge and decreases along the chord to a shift of about -60 degrees at the trailing edge. 87.5% span Figures 5-14 and 5-15 show the stator harmonic amplitudes and phases at 87.5% span. The 1*BPF harmonic amplitudes are reduced by about 2dB toward the leading edge and about 7 dB toward the trailing edge while a reduction of about 10 dB was predicted (see Figure 4-23). The front half of the stator shows reductions of about 7dB in the 2*BPF harmonic amplitudes, while the 3*BPF amplitudes remain virtually unchanged. Stator loading predictions showed a 5dB reduction and a 3dB increase in amplitude for the 2*BPF and 3*BPF harmonics respectively. Phase shifts of about -50, +50 and -100 degrees are seen along the entire chord for the 1*BPF, 2*BPF and 3*BPF respectively. There is a strong disagreement with the predicted phase shifts Amplitude of differential pressure: 1*BPF 155 I 150 . 145 140 1 0 I ", 0.1 0.2 0.3 I 0.4 I 0.5 0.6 0.7 0.8 0.9 0.8 0.9 0.8 0.9 Fraction chord Amplitude of differential pressure: 2*BPF E14 II 013 0 o 12 m 11 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Amplitude of differential pressure: 3*BPF E 11 II E 0 r .) o , o v Ml 0 0.1 Figure 5-12: 0.2 0.3 0.4 0.5 0.6 Fraction chord Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 90 0.7 differential pressure at 75% 1 span. Phase of differential pressure: 1*BPF 0 0.2 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 i i 1 Fraction chord Phase of differential pressure: 2*BPF (D I 150 I I I I i 100 . . S50 .. a) 0 ........... r -50 . ... ....... .................... ........... .............................. i......... . ............................ ..........................................i...................... a) . . . .. . . . . . . ................ c -100 a-- I 0.1 . . . .. . . . . . I . . . 0.2 . 0.3 0.4 . .. . .. . . . . . .. . . .. . . . . . -150 0 . .. . . ...... I 0.6 0.5 0.7 0.8 0.9 1 Fraction chord Phase of differential pressure: 3*BPF Ci 150 a 100 cD 50 (D 0 . . ..... . . . . .. . .... ..... .......... ........... ....... -50 a) C -100 -150 ............... F 0 0.1 , 0.2 0.3 0.4 0.5 I I 0.6 0.7 I 0.8 0.9 1 Fraction chord Figure 5-13: Harmonic phases of stator differential (-)w/o blowing, (- -)w/ blowing pressure at 75% span. Amplitude of differential pressure: 1*BPF 155 I SI I I I I ....... d difeenia .. pre sur:. IBP 150 ....... .................. .. . . I . 40 ....... .................................... 1 135 0 0.2 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Amplitude of differential pressure: 2*BPF I I 0 0.1 I I 0.2 I 0.3 I I 0.4 I 0.5 0.6 Fraction chord . 0.7 . . 0.8 0.9 0.8 0.9 1 87.5% span. Amplitude of differential pressure: 3*BPF 0 0.1 Figure 5-14: 0.2 0.3 0.4 0.5 0.6 Fraction chord Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing differential 0.7 pressure at Phase of differential pressure: 1*BPF 0) e0 v0) a) CD r.. 0) C -1 C a - 0.1 0 0.2 0.3 0.4 0.5 0.7 0.6 0.8 0.9 . .. .. .. .. .. . ..... 0.8 0.9 1 Fraction chord Phase of differential pressure: 2*BPF I I I I I I I 150 ? 100 50 (D 0 r c -50 S. .. .. .. .. .... . .. .. .. . .. ... .. ..... .... .. .... .. ... .. a -100 - 1111 -150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 Fraction chord Phase of differential pressure: 3*BPF -! 150 -- a) 100 -/ ......... .......... S50 ... -1 0 0 a -50 a) CO a -100 -150 .7 . ... . .. -_. 0 0.1 ........................... I I III 0.2 0.3 0.4 0.5 ..--........................ I 0.6 ..... ..........- ............ . I 0.7 . . - I 0.8 0.9 1 87.5% span. Fraction chorc Figure 5-15: Harmonic phases of stator differential (-)w/o blowing, (- -)w/ blowing pressure at which ranged from about zero to 10 degrees, (see Figure 4-24). Summary of stator loading measurements There is some weak agreement between the harmonic amplitude reductions measured at the 25% and 87.5% span locations and the predicted changes. However, the same cannot be said for the other radial locations. For the first harmonic of BPF, amplitude reductions are seen at 25% span and 87.5% span. the amplitude is seen. At 50% span, an increase in Changes in the 2*BPF harmonic amplitude could not be distinguished at the 25%, 37.5% and 50% span locations. At 75% and 87.5% span amplitude reductions are seen, particularly for the front half of the stator chord. CHAPTER 6 DISCUSSION As seen in Chapter 5 there was a lack of correlation between changes in the stator harmonic amplitudes and changes in the wake harmonic amplitudes. Several possible hypotheses to explain the stator measurements were investigated and eliminated. These hypotheses are briefly discussed in Section 6.1. It was determined that wake cancellation may be responsible for the discrepancy between the stator measurements and the flow field measurements. This possibility is discussed in Section 6.2. 6.1 Discarded Hypotheses Possible problems with the experimental facility, the data acquisition system, and the data reduction process were investigated first because the lack of correlation between the wake harmonic reductions and the changes in the stator harmonics was unexpected. The raw data traces of the instrumented stator transducers and the four-way probe pressure transducers were checked to ensure that the transducers were responding properly. To check the noise level in the data acquisition system, data was taken at constant conditions with all the instrumentation on. After the data was reduced, the noise level was found to be an order of magnitude less than the unsteady signals being measured. The manner in which the data was averaged and in which the wake harmonics were computed was investigated to ensure that the results were not artificial. The data was averaged and the fourier transforms were computed with various methods and the end results were found to be in agreement with each other. A final concern was the possibility that the data was being affected by blade vibrations. To investigate this possibility, an accelerometer was attached to the instrumented stator blade and vibration tests were conducted. The natural frequency of the blade was found to be close to 2*BPF. The pressure transducers, however, were not in phase as would be expected if the blade was vibrating. 6.2 Wake Cancellation Hypothesis As hypotheses were investigated, the focus was placed on the 50% span data because the stator and flow field measurements were in most obvious disagreement at that location. Figure 6-1 is a graphical representation of the gust impinging on the stator at 50% span. The solid line represents the freestream Mach number, the dashed line represents the wake (maximum deficit) Mach number, and the bold line represents the gust. Notice that in the no blowing case the wake is characterized by a drop in Mach number and an increase in angle of attack. Figure 6-1 suggests that the disturbance caused by the no blowing wake may be lower than would be expected due to the combination of Mach number and angle of attack changes. In other words, the increase in loading caused by the higher angle of attack is partially offset by the decrease in loading caused by a lower dynamic pressure. It would then be possible that when trailing edge blowing is applied the balance between the two effects could be diminished in such a way that although the gust is reduced the loading changes are increased. To determine the plausibility of this theory, a very simple analysis was conducted using MISES, a two-dimensional, steady, viscous cascade code [6]. At each radial location, the force coefficients were calculated for four different conditions using MISES. Cases were run at the free stream and the wake conditions for both blowing and no blowing. Once the force coefficients were obtained, the actual loads were calculated using the dynamic pressure at each condition. The unsteady No blowing 0.5 0.45 0.4 A 0.35 2 0.3 0.25 S 0.2 0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 axial direction -- > 0.5 0.6 0.7 0.5 0.6 0.7 Blowing 0.5 0.45 0.4 A 0.35 0 0.3 5 0.25 ' S0.2 , 0.15 0.1 0.05 0) 0 0.1 0.2 0.3 0.4 axial direction -- > Figure 6-1: Gust impinging on stator at 50% span. (-)freestream, (- -)wake, ( 97 )gust radial location 25% span 37.5% span 50% span 75% span 87.5% span Table 6.1: "I 7.46 2.34 1.58 0.60 0.52 Loading difference with blowing as a fraction of loading difference without blowing loading was then estimated by taking the difference between the freestream condition and the wake condition. At 50% span, the loading difference with blowing was 1.58 times that without blowing. The loading difference results for all radial locations are shown in Table 6.1. This simple analysis predicts the trend seen in the data for the three outer locations (50%, 75%, 87.5%) but not for the inner two locations (25%, 37.5%). However, it is important to note that the wakes at 25% and 37.5% have velocity excess and deficit components which are of roughly the same magnitude. Thus, a two point analysis such as the one being discussed cannot be expected to represent the situation accurately. For completeness, graphical representations of the points used in this analysis at the 25%, 37.5%, 75% and 87.5% span locations are shown in Figures 6-2 through 6-5. The results from the above analysis clearly indicate that for this stage the stator unsteady response is dependent on both the transverse and longitudinal gust components. This dependence explains why the predicted stator loadings do not agree with the stator measurements. V072 only predicts the unsteady response caused by the upwash of the wake. Thus, the longitudinal component of the gust, first determined by Horlock [9] to have significant effects on the unsteady stator response, is completely ignored. Furthermore, because no interaction between the mean flow and the gust is allowed and because the mean flow is assumed to pass through the stator without producing any effect, the gust distortion effect determined by Goldstein and Atassi [7] to have important effects on the unsteady loading does not appear in the predictions. No blowing 0.5 0.450.4 0.35 A C 0 0.3 S0.25 - C 0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 axial direction -- > 0.5 0.6 0..7 0.5 0.6 0 .7 Blowing 0.5 I 0.45 0.4 0.35 A S0.25 S0.2 Cz +0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 axial direction --> Figure 6-2: Gust impinging on stator at 25% span. (-)freestream, (- -)wake, (-)gust No blowing 0.5 0.45 0.4 A 0.35 I 0.3 c 0.25 S0.2 C ' 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 axial direction -- > 0.5 0.6 0.7 0.5 0.6 0.7 Blowing 0.5 0.45 0.4 A 0.35 I o 0.3 0.25 5 0.2 c0 "- 0.15 0.1 0.05 0.1 Figure 6-3: 0.2 0.3 0.4 axial direction -- > Gust impinging on stator at 37.5% span. (-)freestream, (- -)wake, (-)gust 100 No blowing 0.5 0.45 0.4 A 0.35 2 0.3 0.25 . c 0.2 Co S0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 axial direction -- > 0.5 0.6 0. 7 0.5 0.6 0..7 Blowing 0.5 , 0.45 0.4 A 0.35 0 0.3 0.25 A 0.2 0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 axial direction -- > Figure 6-4: Gust impinging on stator at 75% span. (-)freestream, (- -)wake, (-)gust 101 No blowing 0.5 0.45 0.4 0.35 A o 0.3 5 0.25 S0.2 C5 _c 0.1 0.05 0 0 0.1 0.2 0.3 0.4 axial direction -- > 0.5 0.6 0.7 0.5 0.6 0.7 Blowing 0.5 5 0.455 0.4 A I 0.355 o 0.3 0.25 c 0.2 - 0.15 0.1 0.05 0.1 Figure 6-5: 0.2 0.3 0.4 axial direction -- > Gust impinging on stator at 87.5% span. (-)freestream, (- -)wake, (-)gust 102 It is possible that analysis which incorporates all of the effects considered by Goldstein and Atassi [7] into a cascade setting could predict the experimental results. Unfortunately, time did not allow for such an analysis. However, the simple analysis performed does indicate that wake cancellation is a plausible explanation for the lack of correlation between the wake harmonics and the changes in the stator harmonics. Furthermore, the results highlight the importance of using prediction tools which include the effects of longitudinal and transverse gusts and the effects of the steadystate response when analyzing changes caused by trailing edge blowing. 103 104 CHAPTER 7 CONCLUSION The effects of trailing edge blowing on the stator unsteady loading harmonics were investigated. Experiments using a new blowing distribution were conducted on Brookfield's [3] trailing edge blowing fan. Flow field and stator pressure measurements were taken with and without trailing edge blowing. Additionally, the experimental wake measurements were input into the BBN/PW V072 noise prediction code and stator unsteady loading predictions were computed. The new blowing distribution filled the wake with less spanwise variation than previously tested distributions. A momentumless wake was produced at 50% span and was over 70% filled elsewhere. Reductions in the first two BPF harmonics of the relative Mach number were seen at all radial locations. However, it was seen that reductions in the relative harmonic amplitudes did not dictate reductions in the harmonic components parallel to and normal to the stator chord. For the 1*BPF harmonic, reductions ranging from 58% to 90% were seen for the longitudinal component, while reductions from 11% to 95% were seen for the transverse component. The 2*BPF harmonic underwent reductions ranging from 20% to 44% in the longitudinal component. The transverse component was reduced from 19% to 44% except at the 37.5% span location where an increase of 24% was seen. Correlating well with the wake harmonic reductions, the stator loading predictions showed reductions at all spans for the first 2 harmonics of BPF. 105 The stator unsteady loading measurements did not correlate well with the wake harmonic reductions. The strongest disagreement was seen at 50% span for the 1*BPF harmonic. At this location an increase in the harmonic amplitude of up to 7 dB was seen along the chord while the longitudinal and transverse wake harmonics were significantly reduced. Graphical representations of the gusts suggested that the effects of the longitudinal and transverse gust components could be partially cancelling each other. A simple two-dimensional analysis was done to determine the steady-state loading at the freestream and wake conditions. At 50% span, the difference in loading between the freestream and the wake was higher when trailing edge blowing was used. This result suggests that wake cancellation effects could account for the lack of correlation between the stator and wake harmonics. The V072 stator loading predictions did not agree with the stator measurements. The discrepancy is most likely present because V072 only considers the effects due to transverse gusts. The wake measurements show that trailing edge blowing affected both the longitudinal and the transverse harmonics. Furthermore, in the set of experiments presented here, trailing edge blowing resulted in an increase of the steady-state stator loading. Because V072 models neither the effects of the longitudinal gusts nor the distortion effects of the steady-state loading, the unsteady loading changes caused by trailing edge blowing cannot be truly captured. If trailing edge blowing is to be used to reduce noise, it is important to understand the effects it has on the unsteady stator loading. To increase this understanding, the experimental wakes should be used in a stator loading prediction tool which can accurately capture all the changes caused by the blowing. The results will not only help to understand the effects of trailing edge blowing but may also increase the understanding of the airfoil unsteady response to gusts. 106 APPENDIX A WAKE IDENTIFICATION METHOD The edges of the wakes were identified using the same method employed by Sell [21]. The rms profile was examined from both ends for the point at which the value of the next point was larger by a factor of k. The result was checked visually, against both the rms and the mean profiles. If the edges did not appear reasonable, k was adjusted. Some wakes, such as the one seen in Figure A-1, were easy to identify. Others, especially those with trailing edge blowing, proved more difficult to identify (see Figure A-2). In such cases, the best judgement of the author was used to determine the edges of the wake. 107 a) Mean Profile: Relative Mach number 0.490.48 0.47 0.46 E - 0.45 cz r 0.44 0.43 0.42 0.41 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 0.8 0.9 b) Turbulence Intensity: Relative Mach number 0.055. I 0.05- 0.045 0.04 0.035 0.03 0.025 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 Figure A-1: Example of wake that is easy to identify 108 1 a) Mean Profile: Relative Mach number 0.51 0.505 . E 0.5 ....... .............. .. .. . . .. ........... ......... S 0.49 5 0.49 - 0.485 0 0.1 0.2 0.3 0.4 I 0.6 0.5 Fraction pitch I 0.7 I 0.8 I 0.9 0.8 0.9 b) Turbulence Intensity: Relative Mach number 0.038 0 0.1 0.2 0.3 0.4 0.6 0.5 Fraction pitch 0.7 Figure A-2: Example of wake that is hard to identify 109 1 110 APPENDIX B FOUR-WAY PROBE MEASUREMENTS The flow field varaibles that are not presented in Chapter 4 are presented here. These include the components of Mach number, the flow angles, and the pressures. As in Chapter 4 the data presented consists of the an ensemble average of one or two runs with 96 blade passing periods. Data is shown along with 95 111 a) Mean Profile: Absolute Mach number 0.65 0 0.6 E c 0.55 ................... I I I I .......... .......... . . . .. ... .. .. . . ... .. . . .. ............ 0.5 . 0.45 0.4 I I 0.5 0.6 II . I 0.1 0.2 0.3 0.4 0.7 0.8 0.9 0.8 0.9 1 Fraction pitch a) Mean Profile: Tangential flow angle I I ! I I I S50 o 40 -- ~ ............. .". ..... - . .. .... ....".. ... .: . .... .. . ... . ......... 30 C I 20 C I 0.1 0.2 III 0.3 0.4 0.5 0.6 0.7 Fraction pitch b) Mean Profile: Radial flow angle 15 10 5 0 -5 -10 .. ..- . . . .. -15 C:) Figure B-1: * . . . . . . . ~~ ~..-....... ~ . .. 0.1 0.2 0.3 0.4 ;...... .... ................. . .. . . .......................................... ....................... ........ 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 Absolute Mach number and flow angles at 1.5c, 25% span. (-)w/o blowing, (- -)w/ blowing 112 a) Mean Profile: Axial Mach number 0.55 .. ... .. . ...... ............ . ... ............. I.. .. ........... ...... ... ... ... . ......... . -. 0.5 0.45 0.4 0.35 - ............ ........ . .. .. . ....... . E---I- ..... . . - . ~ . -- . ... .. ...... . : E . . . . . .. . I......... . 0.3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Tangential Mach number 0.45 , .............................................. .... .......... I........... I. .. 0.4 E 2 0.35 - c 0 . . . . .- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 . . . . . .. I. . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . 0.3 D0.25 .. . . . .. Cu 0.2 0.1 0.2 0.3 . . . . .. . . . . .. . . . . . . .. . . . .. . ..-. 0 . ..- . . . 0.4 0.5 0.6 0.7 0.8 0.9 I I I 0.7 0.8 0.9 1 Fraction pitch . c) Mean Profile: Radial Mach number 0.15 M 0.1 E S0.05 0 16 -0.05 c -0.1 0 I I I I 0.1 0.2 0.3 0.4 i I 0.5 0.6 Fraction pitch 1 . Figure B-2: Components of Mach number at 1.5c, (- -)w/ blowing 113 25% span. (-)w/o blowing, a a) Mean Profile: Relative total pressure -1.25 c 0 1.2 1.15 . E-E -......... - CO) CO .. ....... .......... *...................... .... ..... .............. .. ......... 1.1 Q 1.05 -- 1 o .._2 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Absolute total pressure a a = 1.3 (0 I -' C ' 1.25 U CO I I ' - ' I I I ~~~~''''' : '' - : - ~ I ' 1.2 a) g 1.15 Cl) a).1.1 - " " " " " " " ~" " 0n .Q: 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.7 0.8 0.9 Fraction pitch ca 1.05 < (0 c) Mean Profile: Static pressure (n = 0.99 o "U0.98 -: a) 0.97 = 0.96 U) - S0.95 - ca0.94 .9 :--f '' '~' ' '~' ~~ ..i- U) C0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch Figure B-3: Pressures at 1.5c, 25% span. (-)w/o blowing, (- -)w/ blowing 114 1 a) Mean Profile: Absolute Mach number 0.7 .E 0.65 0.6 C- . 0 . .......... .......... .. ...... ........... .................... i l l 0.7 0.8 0.9 0.55 S0.5 l i 0.45 . . * . ) 0.1 0.2 l i l . 0.3 0.4 0.5 0.6 1 Fraction pitch a) Mean Profile: Tangential flow angle U, 0) %50 I -'540 C --F 30 . .. . .. . . I- 20 - 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fraction pitch b) Mean Profile: Radial flow angle 15 -1 10 5 . 0 . ... . . -5 .. . . . . . .. . . . . 0 .. . . . . . 0.1 . . . . 0.2 . . . . . . . . . . . . . . . . -10 -15 . .. . . .. . . . . . . . .. . . . . 0.3 0.4 . . . . . . . . . . . . . . . . . . .. 0.5 0.6 . . . . . . . . . . . . . . . . . . 0.7 . . . . . . . . . . . . . . . . . . 0.8 0.9 1 1.5c, 37.5% span. Fraction pitch Figure B-4: Absolute Mach number and (-)w/o blowing, (- -)w/ blowing 115 flow angles at a) Mean Profile: Axial Mach number 0.6 -] 0.55 ....... ........ ............. 0.5 -... I 0.45 0.4 0.35 0 0.1 0.2 I I 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Tangential Mach number 0r 5. III I I 0.45 E = 0.4 -C I. .. . .. .. O 0.35 6 C 0.3 ..... ......................-... ......... .... ..... . a. ....I ...... ...................... . .... i... r..... ............... ................................ ........ 0.25 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 c) Mean Profile: Radial Mach number ! I I I I I 0.1 E 0.05 - 0 S-0.1 -. =. ......... r-0.15 -...-0.15 = 00 Figure B-5: I . . .. ........ .. .. .. ........ . .. .. .. . ........ .. ... . i i I I 0.1 0.2 0.3 0.4 . . . ... . . ....... I . . . .. ......... . . I 0.5 0.6 Fraction pitch .I......... .. .. .. L I I 0.7 0.8 0.9 Components of Mach number at 1.5c, 37.5% span. (- -)w/ blowing 116 .. . . .. . .. .. 1 (-)w/o blowing, a) Mean Profile: Relative total pressure 5 C a . o 2 C. = 5 1.05 -'t- - - " - . .. ..-- . .. - ; . r.".. . .. . ..• .. . ,.. . . . . . . . . . . . . . .•.. . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . . 5 10 0.1 0.2 0.3 1. . ffl 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 b) Mean Profile: Absolute total pressure .......... 5 *-' 0.4 .......... .. ...... ...... . I........ .. ......... . . ...... ....... ......... ........- 1. 3 0 S1. S1.1 C 1.25 2 .... - - ... - - . .. . .. .... - _.. ... .. .. .. . . . 5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 c) Mean Profile: Static pressure C0.99 c 0.98 0 .5 0.97 . . . . . .I 0.96 . . ..-. . . .I . . . . . I... . . . . I I . . . . .I . . . . .. . . . . . I . . . . . . ..-. . . . . . . . .. . . . . . . . . . = 0.95 . 0.94 a ._O. 0.93 , 0 1 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 Figure B-6: Pressures at 1.5c, 37.5% span. (-)w/o blowing, (- -)w/ blowing 117 1 a) Mean Profile: Absolute Mach number 0 .7 5 . . .. .. .. . . .. .. .. .. .. .. . .. .. .. .. .. .. . ... .. E S0.65 ...... I ,, v 0.55 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 a) Mean Profile: Tangential flow angle 45 e 40 S30- a25 - 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction pitch b) Mean Profile: Radial flow angle 0 -10 -20 0 Figure B-7: 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 Absolute Mach number and flow angles at 1.5c, 50% span. (-)w/o blowing, (- -)w/ blowing 118 a) Mean Profile: Axial Mach number I I I I I I I 0.6 E 0.55 ---.......... H 0.45 ~ -~' ' .... .............. ...................... .......... : I I I'''''''~'~ ''''''''' ''''' I''''~''~~~' '' .0.4 0.35 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Tangential Mach number 0.5 2 0.45 E < 0.4 S0.35 0.3 -- ~_- := • I I I -r --- I I ' - 0.25 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.8 0.9 Fraction pitch c) Mean Profile: Radial Mach number 0.1 E 0.05 r r -0.05 0C 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction pitch Figure B-8: Components of Mach number at 1.5c, 50% span. (- -)w/ blowing 119 (-)w/o blowing, a) Mean Profile: Relative total pressure .. a 1.3 . .II .. .. .. .. I .. .. .. .. .. .l . . . . . .. . .... . ... ..........! .......... ......... I U, 0 1.25 1.2 1.15 U, I ..... ............. .. ........ .. ......... a.......... C, I.. 0 0.1 . 0.2 0.3 0.4 ...... . ... . .. . . . .. . 0.5 0.6 0.7 0.8 . . . 0.9 1 Fraction pitch 0 1.1 1.25 1.05 b) Mean Profile: Absolute total pressure a 2 1.35 I -i I I I I I I C o "-1.25 _1.15 S1.1 Cn I.. . .I . . .I. . . . . .I . . . . .I . ..-. .. . . . . . 0 0.1 0.2 0.3 0.4 0.5 0.6 I . . 0.7 . . . .. . . . . 0.8 0.9 1 Fraction pitch c) Mean Profile: Static pressure a -T S0.98 .- r----- ------ C .0.96 VA0.94 o .......... U)S0.92 - C ......... . . . .. . 0.1 0.2 ....... . 0.3 ...... . ...-. 0.4 ... . . .... [...... ... . ......... 0.5 0.6 Fraction pitch 0.7 . 0.8 0.9 Figure B-9: Pressures at 1.5c, 50% span. (-)w/o blowing, (- -)w/ blowing 120 a) Mean Profile: Absolute Mach number I I I I ' I..I I 0.7 .- 0.65 E =3 r -O 000 0.6 2 0.55 '''''' "" ' -. 0.5 -: ' ''''''''' I I. . ""~ 0.45 0.1 0 0.3 0.2 0.4 0.5 0.6 0.8 0.7 0.9 1 Fraction pitch a) Mean Profile: Tangential flow angle II c 50 I I I I I )45 .. ... .. .. .. .. ... .. .. ... .. .. .. .. . .. .. ... . . .. . .. .. ... .. .. .. .. .. . .. .. .. .. ... .. ... .. .. . .. .. .. .. .. ... .. .. ... .- a) 240 . .. .. .. . .. . . . .. . . . . . . . ... . . . . . .... . .. . . . . . a (.m35 g 30 o0 25 I-c ~ ~ ~ ~.. . .. . . .. ... . . ... . . . . . . . . . . . . -. . . . . . . . . ..- . . . . . . . . . ... . . . . , . . . . . . . . .. . . . . . . . ... . . . ... . . . . .. . . . . . . i . . .... . . . . . . . . . . . . . . . . . . - 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Radial flow angle II 15 10 5 0 ........ ............. -10 . -5 . . . . . . . . . .. . . . . .. .. .. .. . . . . . . . . . . . . . . . . .. .. .. ... . . -15 C:) . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 0.1 . 0.2 0.3 0.4 . . . .. . . . . . . . . . . . .. .. . . . . . . .. . . ... .. .. .. .. 0.5 0.6 Fraction pitch . . .. . . . . . . . . . . . .. ... .. 0.7 .. ... .. .. .. 0.8 0.9 1 Figure B-10: Absolute Mach number and flow angles at 1.5c, 75% span. (-)w/o blowing, (- -)w/ blowing 121 a) Mean Profile: Axial Mach number 0.6 0.55 0.5 0.45 0.4 0.35 I I 0.1 0.2 - 0 -I I I I I 0.3 0.4 0.5 0.6 . 0.7 0.8 0.9 1 Fraction pitch b) Mean Profile: Tangential Mach number 0.45 0.4 . E c 0.35 S0.3 c 0.25 0.2 0.2 0 0.I .I I . .I 0.1 0.2 0.3 0.4 .1 .I . . . 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Fraction pitch c) Mean Profile: Radial Mach number A J -.......... 0.15 .......... .......... .. ....... .......... !.........L. .... . 0.1 0.05 L 0 LL il-- -0.05 -0.1 0 0.1 Figure B-11: 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 Components of Mach number at 1.5c, 75% span. (- -)w/ blowing 122 (-)w/o blowing, a) Mean Profile: Relative total pressure Cn c 1.4 o 1.35 E 1.3 0 1.25 " 1.2 ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I I 1 Fraction pitch b) Mean Profile: Absolute total pressure CL1.15 = 1.4 I I I I I C .1.35 1.1 I I 0 0.1 0.2 I 0.3 0.4 0.5 I I I I 0.6 0.7 0.8 0.9 1 Fraction pitch -a 1.042 c) Mean Profile: Static pressure .......... I. ......... . ... ._ 1.02 . . L . . . . . . . .. _ -_-~ . .. .. t . . ...... .... . . .... 7~_~ 1 CO o , 0) cl) 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 Figure B-12: Pressures at 1.5c, 75% span. (-)w/o blowing, (- -)w/ blowing 123 1 a) Mean Profile: Absolute Mach number S0.65 c _ -...- - - -_- .- 0.55 S0.5 0.4 0.4 0 ....... ........ 0.1 0.2 ................ ......... 0.3 0.4 0.5 0.6 0.7 Fraction pitch 0.8 ..... ... 0.9 1 a) Mean Profile: Tangential flow angle Co 30 . .. . ... . ... 2 0 . .. .. .. . ... .S200 0.1 0.2 ... ... .. .. .. ... .. . ... .. .. .. ... .. .. . .. . .. .. .. .. ... .. . . ... . .. .. .. ... ... .. .. .. 0.3 0.4 0.5 0.6 Fraction pitch 0.7 0.8 0.9 1 b) Mean Profile: Radial flow angle 0 ........... " -1 0 0 0.1 Figure B-13: 0.2 0.3 0.4 0.5 0.6 Fraction pitch Absolute Mach number and flow (-)w/o blowing, (- -)w/ blowing 124 0.7 angles at .. 0.8 0.9 1 1.5c, 87.5% span. a) Mean Profile: Axial Mach number I. - 0.55 E I . I - S0.5 0.45 - 0.4 o --0.1.0.2.0.3.0.4.0.5.0.6.0.7.0.8.0.9 0.4 .. < 0.35 - . . . 0 0.1 0.2 0.3 . 0.4 . 0.5 . 0.6 0.7 . . . 0.8 0.9 I I I . . . 1 Fraction pitch b) Mean Profile: Tangential Mach number .. .. I I I • 0.4 E S0.35 0. 0.1 0. 0. 0. 0.1. . . C 0.3 60.25 -. ._ - -- a - 0.2 I 0.15 I 0.1 0 0.2 0.3 0.4 . . 0.5 0.6 0.7 0.8 0.9 1 Fraction pitch c) Mean Profile: Radial Mach number -I 0.15 ! I I ! .. I. .. . . 0.1 -. . E c 0.05 -• ca 0 . . .. .. . . . . . . . . . . . .. . . . . Ca 5 -0.05 .. -0.1 . 0 C ) . .. I 0.1 0.2 0.3 0.4 ... . 0.5 0.6 . . . 0.7 . 0.8 . . . 0.9 . 1 Fraction pitch Figure B-14: Components of Mach number at 1.5c, 87.5% span. (- -)w/ blowing 125 (-)w/o blowing, a) Mean Profile: Relative total pressure CL I I 0.3 0.4 I I I I ! 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 1.45 0 .5 1.4 . ...... .............. 1.35 US 1.3 a 1.25 .1.2 a, rr 0 0.1 0.2 Fraction pitch b) Mean Profile: Absolute total pressure a .. I I 0.3 0.4 I . I .I I co 1.35 1.3 2 1.25 g 1.2 00 C 1.15 0 ui 1.1 0 0.1 0.2 0.5 0.6 Fraction pitch 0.7 Q. c) Mean Profile: Static pressure -1.05 - 1.04 I I -7 I I I I I I 0.8 0.9 O 1.03 1.02 = 1.01 1 1 ( - -'''''''' -''''' ' 03 0.1 '~'''' I ''''''' ''' ' I ' S0.99 U) 0.2 0.3 0.4 0.5 0.6 Fraction pitch 0.7 Figure B-15: Pressures at 1.5c, 87.5% span. (-)w/o blowing, (- -)w/ blowing 126 1 APPENDIX C INSTRUMENTED STATOR MEASUREMENTS The harmonic amplitudes and phases of the stator pressure side and suction side are presented here. All data presented consists of an ensemble average as detailed in Chapter 5 and is plotted along with 95% confidence intervals. The no blowing data is shown by solid lines while the blowing data is represented by dashed lines. 127 Amplitudes of 1*BPF harmonics: suction surface 160 :-. - E . I ! __ 150 .i 140 .. .. . .. .. . I ... . . . . . . " . .. .. . . . .. . . . .. .. .. .. .. .. . . . . . 130 20 120 ................... .. S110 100 ........... 0 0.1 ........... 0.2 .......... 0.3 0.4 .............................. 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Amplitudes of 2*BPF harmonics: suction surface 16CJ E :).i 15C II 314C 3 o 13C 3 . 12C 0 3 S11C -I 77 -L €.n I0 1U 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Amplitudes of 3*BPF harmonics: suction surface 1:-n3 E 150 c1 II 140 I . .. . .I o 130 ID 120 . I.. . . . o .. 110 100 CI Figure C-1: 0.1 . . . . 0.2 .. . . . .. 0.3 . . . . .. 0.4 . . . .. . . . . 0.5 0.6 Fraction chord Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 128 suction 0.7 0.8 surface 0.9 at 25% span. Amplitudes of 1*BPF harmonics: pressure surface IbU E . 150 - S140 130 . 120 I .. ... . .- Cz .- . . ... .. ... .. . '110 m V3 I1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: pressure surface 1' 0 E c.%150 ......... .. . . . . . . . . . . . . . . . . . 140 . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . . . . . .. . . . . . . r 130 .. . 120 . . . . .. . . . . . . . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . U, -110 100 . . . . . . . . . .. . . . . . . . . . . . I . . . I I 0.2 0.3 . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I .... 0 0.1 0.4 0.5 0.6 Fraction chorc 0.7 0.8 0.9 1 25% span. Amplitudes of 3*BPF harmonics: pressure surface 1 0.5 Fraction chord Figure C-2: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 129 pressure surface at Phase of 1*BPF harmonics: suction surface S300 S200 CL 0 0.1 0 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 Phase of 2*BPF harmonics: suction surface L 300- o> 200 . Ut100 .. 0- 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Phase of 3*BPF harmonics: suction surface a300 "200 8 loo a. -- 00 Figure C-3: 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Harmonic phases of stator suction surface at 25% span. (-)w/o blowing, (- -)w/ blowing 130 Phase of 1*BPF harmonics: pressure surface T 3000 200 - ( 100 a 0- 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Fraction chord Phase of 2*BPF harmonics: pressure surface 2 300- "200 (U c 100 a. 00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction chord Phase of 3*BPF harmonics: pressure surface I ( !I . 300 .. . 2oo 200 ........ c- 0 0 0.1 ................. 0.2 0.3 .. . . ............ 0.4 0.5 0.6 Fraction chord . .................. 0.7 0.8 0.9 . 1 Figure C-4: Harmonic phases of stator pressure surface at 25% span. (-)w/o blowing, (- -)w/ blowing 131 Amplitudes of 1*BPF harmonics: suction surface 160 - I E z 150 II I I I I .. -. 140 - . . . . . . . . . . . .. . o130 . .2120 . . . . . , - . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . I.. . .. . - . . . . . . . . . . . . . . . . . . . . CO ... . 0 . . . . . O110 "o IUU 0 I I 0.1 0.2 . .. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: suction surface 1 0f I I I 150140130 120110IV 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 37.5% span. Amplitudes of 3*BPF harmonics: suction surface 16C E *iII 15C 14C r o 13C o S12C m "o 11 10C 0 I 0.1 0.2 Figure C-5: Harmonic 0.3 0.4 amplitudes 0.5 0.6 Fraction chore of stator (-)w/o blowing, (- -)w/ blowing 132 suction 0.7 surface at Amplitudes of 1*BPF harmonics: pressure surface 16C} I - E cO } I .. . . . . . . . .. . . . 15C . . . . . . . . .. . . . . . . . . . .. . . . . . . . . ) 14C } .. o 13C . . . . .. . .. . } 2 12C Cz Cn110 100 }. . 0 . . .i. .... . . . . .. . . . . . . 0.1 .. . . . . . . . . . 0.2 0.3 . . . . . . . . . .. . 0.4 . . . . . . . . 0.5 . . . . . . . . . .. . . . . . . . . . . .. 0.6 0.7 . . . . . . . . . .. . . . . . . . . . 0.8 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: pressure surface 16C ,.I E ., } 15C } 14C .. . .. . } 13C ... .. .. .. .. .... .. .. . R 12C . } C 110 1000 . . . . . 0.1 0 . 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fraction chord Amplitudes of 3*BPF harmonics: pressure surface 16C)- . E .i 15C )- 14C)o 13C 2 12C - 110 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Figure C-6: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 133 pressure surface at . 37.5% span. Phase of 1*BPF harmonics: suction surface 300 a, " 200 ........ - 100 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Phase of 2*BPF harmonics: suction surface 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Phase of 3*BPF harmonics: suction surface Fraction chord Figure C-7: Harmonic phases of stator suction surface at 37.5% span. (- )w/o blowing, (- -)w/ blowing 134 Phase of 1*BPF harmonics: pressure surface -Be--~ a 300 30 a 200 ....... ) 100 -. C0. .............. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Phase of 2*BPF harmonics: pressure surface -) ........ 300 .. .................... ................ .................... .. . ... ........ ... ... ... ... .. .... ") 0) a) / *./................ 200 . I Ca ca / S 100 Cz /1 •-...................... H 7 =h -CL_ ) 0.1 0.2 0.3 0.4 : /: 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Phase of 3*BPF harmonics: pressure surface -I -m 300 a) 0 0 "200 C cu ...................... 0 0.1 0.2 0.3 .......... 0.4 ... 0.5 0.6 Fraction chord ..... 0.7 ..... 0.8 .... 0.9 1 Figure C-8: Harmonic phases of stator pressure surface at 37.5% span. (-)w/o blowing, (- -)w/ blowing 135 Amplitudes of 1*BPF harmonics: suction surface 160 E "O150 S140 S130 - -o a) 120 0 -110 iU U 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: suction surface 16 0.@l SI I I E cII 150 140 S130 .~ 120 o 110 -li I 100 0 I 0.1 0.2 I I 0.3 0.4 I I 0.5 0.6 0.7 Fraction chord Amplitudes of 3*BPF harmonics: suction surface 160 E II I - 15C 14C . ..... .- ... o 13C .2 12( 0 11 . .. .................... . 4t . . . . . . ..- 100 - C Figure C-9: 0.1 . . . . . . . . . . . . .. .. . . 0.2 0.3 0.4 0.5 0.6 Fraction chord Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 136 suction 0.7 . .I . . .. . . . . 0.8 surface 0.9 at 50% span. Amplitudes of 1*BPF harmonics: pressure surface 160 I E - - ac 150 II I I - - -.-- - I -- - - I I . .. 140 o130 2 120 ........... ~"'"""""' --..................... ) C 110 'a I1 0 0.1 0.2 0.3 ......... 0.4 0.5 0.6 .................... 0.7 0.8 ....... 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: pressure surface 1: I I E 140 S130 . 120 CU 0 Cn 110 'a IU . . I I I. :. . .. .. .. ... .. .. .. .. .... . . .. . .. . .... . .. . . . . .. .. .... . .. . ... ... . .. . ... .. .. . .. ... .. . .. . .... . .. . .... . .. . . .. .. .. . . .. 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 Amplitudes of 3*BPF harmonics: pressure surface 10i0. E z 150 II ..................... 140 I . .. ... .. . 0 130 .T 120 Cu ....................... -. ........... . .. . . .. . ... . . . .. . . . . . . . . . .. . . . . . .. . . . .. .. . ... ... ... I.. .. . . . .................... o U 110 .. ...... ... .. .. I. 100 C3 0.1 Figure C-10: 0.2 I I 0.3 0.4 . .. ... .. . . 0.5 0.6 Fraction chorc Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 137 pressure 0.7 0.8 surface 0.9 at 50% 1 span. Phase of 1*BPF harmonics: suction surface I 300 . . !. - 300 - 200 IC100 0cz to 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Fraction chord Phase of 2*BPF harmonics: suction surface Fraction chord Phase of 3*BPF harmonics: suction surface - 300 200 r loo U 100 00 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Figure C-11: Harmonic phases of stator suction surface at 50% span. ( (- -)w/ blowing 138 )w/o blowing, Phase of 1*BPF harmonics: pressure surface 0 0.1 0.2 0.3 0.5 0.4 0.6 0.7 0.8 0.9 1 0.8 0.9 1 Fraction chord Phase of 2*BPF harmonics: pressure surface S30 20 0) 0 C - a- c1 CO, 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Phase of 3*BPF harmonics: pressure surface 30C 0 - 20 2C Ca C-- c1 0 . ......... ...... .... ......... 0 0 0.1 0.2 . . .-. . :- T.- . 0.3 0.4 7 - - - - ............ 0.5 0.6 Fraction chord 0.7 0.8 .......... 0.9 1 Figure C-12: Harmonic phases of stator pressure surface at 50% span. (-)w/o blowing, (- -)w/ blowing 139 Amplitudes of 1*BPF harmonics: suction surface 160 I E z 150 S I I 0.3 0.4 I I 140 o 130 - 2 120 -110 m "V IU 0 0.1 0.2 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Amplitudes of 2*BPF harmonics: suction surface 160 I! II E co150 II a_ a- 140 o 130 -o .ST120 Cz C) ' 110 m "'016 . . 1E IIvU 0 0.1 0.2 I I 0.3 0.4 0.5 0.6 Fraction chord 0.7 Amplitudes of 3*BPF harmonics: suction surface 16 I I I E a 150 II o_ 140 o 130 ...........- o 2 120 C) -I . .......... . ... .. .. ... .. .. ... .. . . o 110 100 - 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chore Figure C-13: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 140 suction 0.7 0.8 surface 0.9 at 75% 1 span. Amplitudes of 1*BPF harmonics: pressure surface 160 E c 150 II 140 r- 0 130 _ 120 o -110 Vc 0.5 4 Fraction chord Amplitudes of 2*BPF harmonics: pressure surface 160 - -I E 150 CO II ................ 140 o 130 . . . . . . . . .......... .......................... .. . .. -. ... ........ ...... . .. . ID 120 .......... ......... .- 0 C-110 ................ 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ... .. ... . 0.9 1 Fraction chord Amplitudes of 3*BPF harmonics: pressure surface 160 I ! E C 150 II 140 130 .. ............ . ...... . ..................... .......... .......... ...................................... 2 120 -110 100C) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Figure C-14: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 141 pressure surface at 75% span. Phase of 1*BPF harmonics: suction surface 300 a) ,)200 "a C t- (o 100 - Fraction chord Phase of 2*BPF harmonics: suction surface a 300 ",) a) 200 S100 a0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Phase of 3*BPF harmonics: suction surface 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Figure C-15: Harmonic phases of stator suction surface at 75% span. (- )w/o blowing, (- -)w/ blowing 142 Phase of 1*BPF harmonics: pressure surface I - I I S........... 0 300 () .................... 20C ............. ...... ........... 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 Phase of 2*BPF harmonics: pressure surface -\ 200 100 0 300 -\ S200 -\ 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0) Cz C- Phase of 3*BPF harmonics: pressure surface c-) 100 Cz a 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Figure C-16: Harmonic phases of stator pressure surface at 75% span. (-)w/o blowing, (- -)w/ blowing 143 Amplitudes of 1*BPF harmonics: suction surface 160 E C 150- e :-- - I_ M 140 C S130 ....... . 120 . . ........... . . . .. M . ...................... .................. .. 0 W110 ............. ...... ...... ........... m 1 II ' 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 Amplitudes of 2*BPF harmonics: suction surface 1I 0 E SIII 150 a c 140 o 130 . ............. 120 ... . ..... .. .. .. . . . ... . ....... . . .. . .... . ... .. .. ... .. .. .. ... .,...... ... . ... ... - 110 100 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chor( 0.7 0.8 0.9 1 87.5% span. Amplitudes of 3*BPF harmonics: suction surface 160E C 150II 140 o130. 120 110- V 1 0.5 Fraction chord Figure C-17: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 144 suction surface at Amplitudes of 1*BPF harmonics: pressure surface E M150 II 140 o 130 2. 120 o 0 u, 110 100 0.1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fraction chord Amplitudes of 2*BPF harmonics: pressure surface 160 - . . I . E M 150II . . I.. I. . .I ..................... 140- ...... ~~~~~~~ ....... ..... ~~~... .................. 0 130. o II 120. .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . S110100 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 Amplitudes of 3*BPF harmonics: pressure surface 160 E 150II 140- o 130. 120-0 110 rV 4 0.5 Fraction chord Figure C-18: Harmonic amplitudes of stator (-)w/o blowing, (- -)w/ blowing 145 pressure surface at 87.5% span. Phase of 1*BPF harmonics: suction surface Fraction chord Phase of 2*BPF harmonics: suction surface 3200 C200 01 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 Phase of 3*BPF harmonics: suction surface c- 100 0. 0 " "t 0.1 0.2 ! 0.3 0.4 0.5 0.6 Fractiont0chord Fraction chord 0.7 Figure C-19: Harmonic phases of stator suction surface at 87.5% span. (-)w/o blowing, (- -)w/ blowing 146 Phase of 1*BPF harmonics: pressure surface 300 a) 200 CL 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 0.8 0.9 1 0.8 0.9 1 0.8 0.9 1 Phase of 2*BPF harmonics: pressure surface 0 I 00 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fraction chord 0.7 Phase of 3*BPF harmonics: pressure surface O300 CY) - 5200 U 100 t-l 00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fraction chord Figure C-20: Harmonic phases of stator pressure surface at 87.5% span. ( )w/o blowing, (- -)w/ blowing 147 148 BIBLIOGRAPHY [1] Current Market Outlook, 1999. Boeing Aircraft Corporation, http://www.boeing.com/commercial/cmo. [2] Environmental Review, 1996. International Air Transport Association. [3] BROOKFIELD, J. Turbofan Rotor/Stator Interaction Noise Reduction Through Trailing Edge Blowing. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, June 1998. [4] BROOKFIELD, J., AND WAITZ, I. Turbomachinery Fan Noise". 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