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Experimental investigations of on-axis discrete frequency fan noise. Leggat, Lennox John 1973

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Cl EXPERIMENTAL INVESTIGATIONS OF ON-AXIS DISCRETE FREQUENCY FAN NOISE by Lennox John L e g g a t B. Eng., Royal M i l i t a r y C o l l e g e o f Canada A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE ,i,n .the J).ep.ar.tiTient o f M e c h a n i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA October-, 1973 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver 8, Canada Date 9 C U o L r rf73 ABSTRACT The thesis describes experimental techniques used and results obtained in the investigation of the pure tone components of sound radiation from a commercial 19 inch axial flow fan. The causes and extent of the discrete tone sources were investigated by several methods: cross-correlation of fan surface pressure fluctuations with far field sound, spectral analysis of surface pressure, and examination of surface pressure waveforms. A unique feature involved the design of an apparatus for detecting and transmitting fan-borne pressure fluctuations off the rotating blades. "Causality Correlations" with the on-axis far field sound rendered dipole source strength distribution functions over a span wise line at 15 per cent chord from the leading edge of the fan blade and around a circumferential ring on the motor support strut at a fan radius of 89 per cent. Results indicate that the on-axis discrete tones are a result of source mechanisms causing force fluctuations on the blades and struts which in turn lead to sound radiation which is dipole in nature and is most intense on the axis of the fan. These mechanisms include ingestion of a concentrated vortex, modulation of the clearance between the blade tips and the fan shroud, flow separation around the inlet bell mouth, and fluctuations in the inflow velocity due to the proximity of the fan to the wedged wall of the Anechoic chamber. Crude integral approximations of source strength distributions over the surfaces of the blades and the struts indicated that sound radiation at the blade passage frequency from th two contributors to the overall sound would be about equal, although more sound radiation is expected to originate at the rotor. ACKNOWLEDGEMENT This work was conducted under the supervision of Dr. T. E. Siddon on whose guidance, good humor, and experience the author relied. Thanks go to summer students, K. F. Phoon for assistance in the construction of the anechoic chamber, and to R. Moore for helping with data reduction and presentation. This research was funded under Defense Research Board of Canada grant No. 9611-03. iv NOTATION c ambient speed of sound db- decibels f. local surface stress p f f far-field acoustic pressure fluctuating part of surface pressure P acoustic pressure amplitude P surface pressure amplitude s R - fan radius r0 " r0 = ^ ~ ^  distance from source point to far field microphone r - fan radial co-ordinate S - surface t - time < t - retarded time = t-- r /c o u - component of velocity in axial direction u.j - velocity vector u n - normal surface velocity U - fan inlet flow velocity x . - space co-ordinate (often indicating the point of sound detection in 1 the far field) y.,- >y. - space co-ordinate used in source region 9 - angle between surface normal and far field direction <f> - phase angle of filtered correlation functions p - ambient density V v - maximum thickness of blade T - time delay between two realization of fluctuating variable x - retarded time delay for sound travel from source to far-field point T•. - viscous stress tensor to - rotational frequency - a dot over a symbol indicates derivation with respect to time. Overbar denotes time avera.ge of statistically stationary quantity. vi TABLE OF CONTENTS I INTRODUCTION 1 1 . 1 Background and Motivation 1 1.2 Scope of Present Work 5 II THEORETICAL FORMALISM 7 2.1 Application of Curie's General Aerodynamic 7 Noise Equation 2.2 Causality Formalism - 9 2.3 Periodic Correlation Functions 10 2.4 Accounting for Phase 11 III EXPERIMENTAL METHOD 13 3.1 Apparatus 13 3.-2 -Approach 15 IV RESULTS AND INTERPRETATION 17 4.1 Inflow Separation 18 4.2 Geometric Anomalies in the Fan 19 4.3 Tip Clearance Modulation 19 4.4 Inlet Velocity Distortions 21 4.5 Inlet Vortex 23 4.6 Motor Support Struts 25 4.7 Integral Check on Source Strength 27 (Rotor/Strut) V CONCLUSIONS 30 5.1 Recommendations for Further Work 32 REFERENCES 34 APPENDIX A 35 APPENDIX B AND C 37 FIGURES 38 vii LIST OF FIGURES Figure 1 Periodic Noise Generation Mechanisms 2 Broad Band Noise Generation Mechanisms 3 Typical Antisymmetric Cross-Correlation Function 4 Cross-Correlation Function of Filtered Signals 5 Anechoic Chamber Showing Fan Installation 6 Experimental Fan Rig 7 Instrumented Fan Blade 8 Relative Phase Shift-Microphone/Transducer Telemetry System 9 Schematic of Apparatus and Analysis Instruments 10 Unfiltered Cross-Correlation Function Showing Strong Harmonic Content 11 Far Field Noise Spectrum 12 Blade Surface Pressure Spectrum 13 Blade rms Pressure 14 Fan Noise Forward Directivity 15 Flow Visualization of Intake Velocity Field 16 Circumferential Blade Pressure Fluctuation 17 Spanwise Source Strength at 15% Chord 18 Clearance Between Fan Tip and Shroud .19 . Autocorrelation.Functions Showing Doubl-e-frequency «at Fan Circumferential Angle of 270 Degrees 20 Effect of Ingested Vortex on Blade Lift Characteristics 21 Strut Surface Pressure Spectrum 22 Strut Source Strength Distribution at r/R = .89 23 Strut Circumferential Pressure Distribution at r/R = .89 24 Vibrating Piston Example of Negative Source Strength 25 Theoretical Results From Piston Example 26 Chordwise Approximation of Source Strength Distribution / I. INTRODUCTION 1.1 Background and Motivat ion Noise produced by j e t a i r c r a f t engines is pr imar i ly a resu l t of the unsteady aerodynamic phenomena generated in the exhaust j e t , the i n l e t fan and compressor, and the turb ine. In e a r l i e r pure-turbojet engines such as the Prat t and Whitney JT3C, the overa l l noise was mainly caused by the exhaust je t and compressor. Noise from more modern high bypass ra t io turbofan engines i s dominated by the i n l e t fan , espec ia l l y in the forward arc d i r ec t i ons , unless specia l types of absorptive duct l i ne rs are employed. Although much of the benef i t of these new high by-pass engines rests in the improved aerodynamic performance, an equal ly important acoust ical advantage resu l ts from the inherent decrease in exhaust je t ve loc i t y . Jet flow noise in tens i t y i s known to 8 »vary .as <U.., where ..LJ „is .the.. Oiet*.exit...»v<e.l,0c.ity.. A .decrease 1n ,the .exi t ve loc i t y then w i l l have a s i gn i f i can t e f fec t on the acoustic.power l e v e l s . Noise generated by fans increases approximately l i k e U^, thus, changes in flow rate through the fan w i l l not produce as s i g n i f i c a n t an e f fec t on the sound power l e v e l . Presently the noise from fans i s often the most dominant of the various component contr ibutors to j e t engine no ise. Noise generated aerodynamically by fans can be separated into d iscre te tone components superimposed on an underlying spectrum of broad-band energy (Figure l l ) . The tendency for d iscre te tone noise to stand out above the broad-band energy helps to determine the annoyance f ac to r , and depends to a great extent on the blade dens i ty , t i p speed, and flow rate for which the fan i s designed. Discrete tones produced by an iso la ted fan rotor with no obstruct ions 2 either upstream or downstream are caused by mutually interfering rotating blade pressure distributions, as predicted by Gutin for a freely rotating 5 14 propeller and later by Tyler and Sofrin for a ducted rotor. The periodic acoustic field may have many harmonic components of the blade-pass frequency i f the blade solidity is low. The directivity, however, will always show a nulle at the on-axis position (theoretically) because of the axisymmetric nature of the pressure field on that line. Should obstructions such as stator vanes or struts exist in the flow, upstream or downstream of the rotor, the periodic interaction of wakes * from one blade row with a downstream stage will introduce periodic changes of pressure and total blade load due to incidence and wake velocity modulations. These force modulations lead to strong interaction tones which have a complicated directivity but generally radiate dominantly in the on-axis direction. In this way, the periodic passing of rotor wakes over downstream obstructions results in discrete tones being produced at the surface of the struts with characteristic frequencies at multiples of the fundamental wake-cutting (blade passage) frequency. Simultaneously, potential field distortions in front of the obstructions interact with the upstream moving rotor causing discrete tones to be generated by the modulating force field on the fan blades at multiples of the strut passage frequency. Where the number of struts and blades are unequal, the fundamental frequencies of blade passage and strut passage will be different. The former of these two mechanisms usually dominates over the latter except in cases where the rbtor/stator separation is very small. This is 3 because the viscous (and turbulent) blade wakes persist for many blade thicknesses downstream, while the upstream potential effects are only felt for a few diameters in front of the obstruction. (Figure 1) Broad band noise is the combined result of several possible aerodynamic mechanisms. Turbulence in the inlet air flow and shroud wall boundary layer causes localized, randomly occurring changes of angle of attack over the blade, resulting in random changes of pressure dist-ribution and consequently broad-band noise generation. Such sources would be expected to concentrate in the vicinity of.the leading edge or tip extremities of the blades. If the boundary layer on part of the blade is turbulent, the localized "slapping" of the surface also leads to the generation of broad-band noise. The blade wakes contain regularly occurring vortices and/or turbulent eddies of scales dependent on the thickness of the blade and on the angle of attack. These induce a fluctuating blade load concentration near the trailing edge believed to be associated with a time dependent adjustment of the wake centerline. High frequency broad-band noise is produced by the vortex shedding from the trailing edge. The vortex shedding frequency given by f ~ .211/(v + 26) varies continuously with U from a maximum relative velocity at the blade tip to a minimum at the root. If struts or stator vanes exist downstream, random pressure fluctuations and incidence changes in the turbulent rotor wakes interact with the strut or stator surfaces, again resulting in a source of broad-band radiation. Should the blade be operating at an excessively high angle of attack, or should local inflow velocity distortions create areas of high incidence on the blade, the resulting separated flow over the upper surface of the blade will produce intense broad-band noise sources. (Figure 2) In complicated machinery such as high-bypass ratio turbofans, or in low cost ventilating machinery, both periodic and broad-band mechanisms contribute in various degrees to the overall sound radiation. The foregoing notions on source mechanisms have led to considerable improvement in the design of fans over the past decade, or so. For example, the high-bypass ratio turbofan engines incorporate only one rotating stage on the main bypass unit. Inlet guide vanes have been eliminated and the outlet stators are well downstream and utilize blades which are both canted and swept back, in order to destroy coherence of rotor/stator interactions. Despite these measures noise levels are s t i l l high. Discrete frequencies which should have been minimized by the removal of obstructions .close .to .the fan are s.ti.ll very .evident. Efforts to reduce bread-band noise other than from the jet exhaust have been relatively unsuccessful. Clearly many of the mechanisms described earlier are only partially understood; their spatial extent and noise-producing potential cannot always be predicted. Their presence and importance may be dependent not only upon the design of the turbomachine, but also upon the environment and surroundings in which i t is operated. Recent work by Lowson^ has revealed other possible mechanisms such as large scale eddies and velocity distortions passing into the fan inlet. Many questions concerned with both broad-band and discrete-tone noise generation from axial flow fans s t i l l remain unresolved. Many of the noise reduction features being employed on modern engines are a result of trial and error testing wherein modifications were made to b specific components and then the change in overall sound level was noted. Of course this process has been supported by theoretical clues as to what the mechanisms might be, and how they might be modified, through semi-empirical applications of the classical aeroacoustic equations and source models. This indirect approach can often give rise to misleading observations. For example, a modification may reduce noise in one portion of the machine, but increase i t in another, resulting in l i t t l e net change in the overall sound level. In such a case, the modification would possibly be assessed as useless. A helpful technique would be one where the local effect of a design change could be evaluated in terms of the change in local contribution to the overall noise level. A source location method based on this concept has been used with apparent success in recent studies of surface-flow interaction 1^ and jet noise 6' 8' 1? Such a method -would be^exGeedi-ngly^useful in the-analysis of source ^mech'aniVsms for rotating machinery such as fans. 1.2 Scope of Present Work An initial facet of this work involved the development of a system by which fluctuating surface pressures could be detected on the upper and lower surfaces of the moving blades of an axial flow fan. By comparing the local fluctuating source signals with the composite far field sound, using real time cross-correlation, i t was anticipated that the distribution and character of the broad-band sources of noise might be evaluated. The unexpected presence of strong discrete tones in the fan noise spectrum at the on-axis position of the far field microphone necessitated investigations to determine the causes of this phenomenon. The scope of the thesis comprises a discussion of the theory used to determine source strength, a description of the apparatus designed to make these measurements possible, a presentation of the evidence 6 supporting the existence of certain noise generating mechanisms contributing to the on-axis discrete tones, and a discussion of the degree of suitability and limitations of the causality-correlation method as applied to the fan noise problem. 7 II. THEORETICAL FORMULATION 2.1 Application of Curie's General Aerodynamic-Noise Equation The noise produced by a rigid surface, free of vibration, and interacting with an unsteady flow is mostly dipole in nature. This statement is based on the experimental observation that the acoustic power output increases approximately as the sixth power of velocity for relatively low speeds and high Reynolds' numbers. The term "dipole" in this context implies a source associated with the force fluctuations which the surface imparts to the adjacent medium. If, further, the surface is small compared with the wavelength, i t is emitting as is sometimes called a "compact" dipole and will exhibit a so called "figure of eight" directivity pattern with strongest radiation in the direction normal to the surface element. In fans and other forms of turbomachinery, the noise produced is mainly a result of various forms of flow-surface interaction, as discussed in Section 1. Thus i t is usually observed that their sound power output increases as the sixth power of flow rate, provided that the flow maintains a state of dynamic similarity over the specific range of velocity, The acoustic radiation from a region of unsteady flow containing a 2 surface is given by Curie s generalized solution to the Lighthill equation The first two integrals are associated with noise generation between the fluid and the surface S which may deform with a velocity u . The quantity + Sx^ X j v j _4Trr0 The square brackets here denote evaluation at retarded time t (1) 8 f.j represents the loca l s t ress act ing at each point on the sur face. The v e c t o r ^ comprises both shear and normal s t ress components. The th i rd in tegra l i s the L i g h t h i l l volume integral for turbulence-generated quadrupole noise where T. . , the e f fec t i ve s t ress tensor i s given by: T i j = e V j + T i j + (P " c p , ) ^ i j In the geometric and acoustic far f i e l d ; r Q » S , r Q » A; the spa t ia l der ivat ives can be shown to become time der iva t ives and r Q = (x-y) - x such that : P( 4TTX J ( P U n ) d S + — 4 7 r x s n 4rrx < f i + P"l un> dS + x . x . f 1 J \ 9 2 T, U dV (2) 9t The quadrupole generated noise i s minimal, and so at tent ion i s d i rected to .,the.-two ..surface... integrals, . Eor-cases-whene the .fan-rotor -and i t s blades are essen t i a l l y r i g i d , and where a l l other obstruct ions to the f low are s i m i l a r l y r i g i d , the surface ve loc i t y terms u n and u. are zero causing a l l but the term involv ing the surface s t ress f.. to vanish. Experimental work has shown that for some types of turbulent f low over sur faces, the shear component of the s t ress i s subs tan t ia l l y smaller than 3 the normal component . Assuming th i s to be general ly t rue , a simple re la t i on between the rad ia t ion and the f luc tua t ing surface pressure resu l ts from equation (2) . Thus f . = p g which i s normal to dS. The angle 6 i s measured between the surface normal and the d i rec t ion of rad ia t ion x . p(x,t) - 4TTXC s COS 0 6t dS(y) (3) 9 2.2 Causal i ty Formalism If both sides of Equation (3) are mu l t ip l i ed by the rad ia t ion pressure at a new time t 1 , then taking a time average y i e l d s : 1 1 P ( t ) p ( t , ) * 4rk 1 c o s 9 (JO 6p~ ^ — p(x,t') (4) I f p and p s a re .s ta t ionary random var iab les then: P P O O 4iTxc x ^ cos 8 6? V ( T > dS(y.) T + — C (5) r e s t r i c t i n g our at tent ion to the mean square acoust ic pressure (T = 0) p'(x) = 4TTXC 8-1 Cos 6 T =X/C d S(y) (6) •T'hu«-«t-he^eontH-but4on--'to---the-''me'an "squ-are'-s'ound-pressure at a "far f i e l d point x_, a r r i v ing from the surface element dS(y) when p s i s being measured i s given by the integrand of (6). This quanti ty may be viewed as the strength of the acoust ic source at that po in t , and for the case where the d ipole sound rad ia t ion from the surface i s predominant, as described e a r l i e r , w i l l be ca l led surface dipole source st rength. dp ^ -cos 8 dS 4TTXC 6T p s p ( T ) (7) ' x_ c The d i s t r i bu t i on of source strength resu l t s i n an acoust ic model f i xed to the geometry of the sur face. The surface may then be considered as an array of acoust ic point sources of various strengths. I n i t i a l experiments showing the usefulness of th is approach were car r ied out by T. E. Siddon in 1969 1 1 in the invest igat ion of broad-band noise radiated 10 from a flat circular plate embedded at various positions in an air jet. The success of these experiments pointed the way towards the analysis of more complicated situations involving surface interaction noise. Typically the surface-related correlation functions p^p{ T) will have a characteristic antisymmetric shape, as shown in figure 3, for source fluctuations which are broad-band in nature. This trend results because the radiation is actually proportional to the time rate of change of p s > One merely evaluates the.slope of many such functions at appropriate values of T'(=X/C) in order to generate the contours of source strength over the surface. As will be discussed more fully later, in certain cases of anti-coherent sources, some elements of area may show an apparent negative source •^strength. .These-wdIT integnafce-*s©--.--«a-s • 'to^ e-an-ee-l• -a ••portion of the -pos-itive strength, but the residual integral will always be positive. In the special case where two counterphase sources exactly cancel one another, there will be no far field sound, and hence no correlation. Where there is a strong harmonic coupling between the source and the far field pressure spectrum, p"^ p(x) will not decay quickly with T , but will be periodic in nature, as depicted in Figure 4. 2.3 Periodic Correlation Functions It is sometimes useful, i f the far field spectrum is dominated by particular frequencies, or i f the distribution of a component frequency of broad-band noise is to be analysed; to f i l t e r both the surface pressure and. the far field signal with frequency and phase-matched band pass filters. This approach allows for the examination 11 of the distribution of sources producing the filtered frequency. For filtered source analysis, the relative pulsation phases of sources at various positions are important. If a simple example of two pistons vibrating out-of-phase with one another is considered, then the effect of phase on source strength analysis using cross-correlation becomes clearer. This example may be found in Appendix A. 2.4 Accounting for Phase Applying such considerations to the case of surface source pressure fluctuations, i t is evident that variation in the phase of the fluid dilatations on the surface at a particular frequency can prove to be important when relating the source distribution to the net far field sound by integration over the surface in question. If the source and far field signals are filtered, then the cross-correlation function. p~p,(.x,).-w.i.l 1 ,be ..sinusoidal having.a.,frequency identical ,..to the centre frequency of the band pass f i l t e r . The correlation function can be represented mathematically by the expression P~P (T ) H F P | S I N + <J>) (8) Here <j> is the phase angle between the correlation function, and a correlation function of the same period with a zero crossing of negative slope at the correct time delay T (Figure 4). Differentiation with respect to T gives: •.« t sin <t>) (9) v ( T } H p s p ' IF ( s i n w o f c o s * -12 Evaluation at the correct retarded time x = x /c g ives : ^-jP P| CO COS (J) (10) X T =" c and subst i tu t ing th is expression into-equation (7) y i e l d s : dS + c o s 8 c o s cj) ( 8 ) 4TTXC W P P s (ID Thus for a f i l t e r e d cor re la t ion , i t i s possible to predict the source strength for a pa r t i cu la r source locat ion by knowing the amplitude of the c ross-cor re la t ion func t ion , the frequency, the angle 6, between the surface normal and the f i e l d po in t , the phase angle cj), the speed of sound, and the distance to the f i e l d point r . o 13 III. EXPERIMENTAL METHOD 3.1 Apparatus All experiments were carried out in an anechoic chamber of inside dimensions 16 feet by 14 feet by 8 feet high. The chamber consists of an enclosure of steel-fibreglass sandwich constructed of panels 4 inches thick mounted on a spring isolated concrete pad. Inside the chamber, a fibreglass wedge pattern two feet deep gives the room a lower cut off frequency of 150 Hz. Removable hatch covers were incorporated into the design of the chamber to allow for experiments, such as fan noise studies, involving the circulation of air through the chamber. The fan was located in one corner of the chamber 18 inches from the wall wedges (Figure 5). The off-the-shelf unit (Figure 6) was manufactured by Woods of Colchester. It is a single stage, 19 inch, axial flow, seven bladed airfoil-type fan with no stator section. The fan motor is supported by two sets of four h inch diameter struts disposed at 90 degree intervals as shown in figure 6. The first set of struts is 7 inches downstream of the rotor. Complete vibration isolation of the fan from the chamber was achieved with a flexible coupling to the exhaust duct and spring mountings. The fan blades were set at a tip pitch angle of 20 degrees to the plane of rotation. The rotational speed of the fan was 3600 rpm, operating at a static head of .2 inches of H20 and a flow rate of 9300 CFM. These fixed operating conditions were maintained throughout the experiment. Far field sound measurements were made using a Bruel and Kjaer h inch microphone at a distance of 9.5 feet (about 6 fan diameters) from the leading edge plane of the rotor. 14 Measurements of the blade pressure fluctuations were obtained by installing a miniature Kulite semi-conductor pressure transducer into a teflon plug which was subsequently pressed into one of several cylindrical cavities bored into the bottom of the blade. Five such cavities were machined at 1 inch spacings along a spanwise line located at a chordwise position 15% behind the leading edge (Figure 7). Each cavity communicated with the upper surface of the blade by a pin hole of .020 inch bore. The resonant frequency of the bore-hole-cavity resonator was calculated to be about 40,000 Hz, two orders of magnitude above the range of frequency dominant to the pressure spectrum. Shielded leads from the transducer were directed back to the hub of the fan through a slot milled in the underside of the blade. This slot was f i l l e d with modelling clay and smoothly faired to match the original blade surface. For the minimum anticipated pressure 'ampTitudev approximate'ly r03 vpsi j -the -KuTite- model '0QH-T25-5 pressure transducer was expected to produced a signal of only a few hundred microvolts. Thus, in preference to conventional slip rings, a low noise telemetry system was selected as a means to transfer the pressure signal from the rotating shaft to the analysis equipment. This system, built by the Acurex Corporation, was capable of accepting signals up to 1000 u volts, with a noise level of 5 y volts and a built in gain of 1000. The frequency response of the transducer telemetry system was flat and phase-matched with the far field microphone to a maximum deviation of 6 degrees over the frequency range of 20 Hz to 10,000 Hz (Figure 8). The telemetry transmitter was mounted on the front end of the fan shaft in a plexiglass housing which also contained batteries to provide power to the transducer and telemetry transmitter (Figure 6). All instrumentation mounted on the axis of the fan was statically balanced and enclosed by a 15 fibreglass nose cone. A Bruel and Kjaer narrow band spectrum analyser with a 6% band width and a PAR model 101 signal correlation computer were available for signal analysis (Figure 9). Calibration of the far field microphone was accomplished using a Bruel and Kjaer piston phone generating a pressure level of 124 dB. The piston phone was also used to calibrate the transducer-telemetry system; however, the transducer was mounted in a flat plate during calibration to ensure the special adaptor made for the piston phone seated properly around the pin hole. 3.2 Approach Initial objectives of this work were to establish a "means-by whi'ch -source distributions o'f "fan-noise "could be determined, and to collect some basic data for source strength analysis. The theory has 13 already proven to be useful and was readily available. The apparatus described above was designed and assembled prior to the collection and analysis of data. Investigation of broad-band noise was the fi r s t immediate concern; however, a strong blade passage frequency component at the on-axis location caused the correlation function to be periodic, and to mask the characteristic curve one might expect from a broad-band signal (Figure 10). The emphasis of the work was shifted at that time to determine the causes of the pure tones at the on-axis location which, as explained earlier, should be free from blade passage harmonics. 16 It was postulated that the on-axis blade passage frequency and its harmonics (Figure 11) were caused by one or more of the following mechanisms: geometric anomalies in either the fan inlet bell or the shroud, local inflow separation at the intake of the fan, interactions between the motor support struts and the rotor, and large inflow distortions such as geometrically fixed areas of excess velocity and large scale inlet turbulence or a concentrated inlet vortex. Each one of the mechanisms could produce a dipole directivity of sound with the maximum intensity at the on-axis position. Investigations of each of these possibilities were carried out using several analytical techniques. 17 IV. RESULTS AND INTERPRETATION The far field frequency spectrum revealed, a strong on-axis discrete tone at the fundamental blade passage frequency of 420 Hz, with lesser spikes at the higher harmonic frequencies and the strut interaction frequency of 240 Hzsas illustrated in Figure 11. The fundamental tone contains roughly 25% of the total acoustic output in the on-axis direction. Unfiltered cross-correlations between the blade and far field pressure signals were found to be sinusoidal in nature for holes near the leading edge, as shown in figure 10. Analysis of the blade pressure spectrum showed a strong spectral peak at the fan rotational frequency of 60 Hz and its fourteen higher harmonics (Figure 12). Inspection of the blade pressure wave form, indicated a once-per-revolution periodicity which seemed to be rather invariant, cycle to cycle, over periods of time of a few seconds, but with a slow rather erratic amplitude modulation over larger periods of time. Typical blade pressure wave forms are shown in figure 13 which also gives the spanwise variation of RMS fluctuating pressure (20 Hz to 20 KHz). Taken collectively this data suggested a dominant harmonic coupling between a once-per-revolution blade pressure anomaly and the seven times per revolution tone (and its harmonics) in the far field. Alternatively, however, the 420 Hz tone might have resulted from a seven times per revolution blade wake impingement on each motor support strut. Thus the seventh harmonic of the blade pressure fluctuation and to a lesser extent the fourteenth, twenty-first, etc. must contribute constructively to the on-axis discrete tone noise. At these characteristic frequencies the 18 radiation may be regarded as resulting from a time dependent dipole distribution at the location of the rotor disc or of the struts. Thus we might expect the sound level to be higher on the axis of the fan, as i t was (Figure 14). 4.1 Inflow Separation The fan was delivered equipped with a short inlet bell mouth made from rolled sheet metal. This transition piece was terminated by a sharp edged lip at the outer surface (Figure 6). Flow visualization and a velocity survey of the flow in the region of the lip showed that flow separation was occurring intermittently in this region. To determine whether a local flow separation was causing the periodicity on the fan blade pressure signal, a plane baffle disc of 4 feet outside diameter was fitted around the sheet metal bell mouth, as may be seen in Figure 15. Subsequent spectra taken of the surface pressure and the far field acoustic pressure (Figure 11 and Figure 12) showed a drop in the broad-band noise level of about 5 decibels. The blade pressure signature became less erratic in its variation in amplitude. As may be seen from figure 11, addition of the baffle effected a reduction in spectrum levels at nearly all frequencies with a larger effect on the broad-band radiation than on the discrete tones. An even greater reduction is anticipated with the addition of a carefully designed bell mouth inlet in place of the crude baffle plate arrangement described above. The foregoing observation is consistent with results from similar experiments described by Filleul in his paper "An Investigation of Axial Flow Fan Noise".4 19 4.2 Geometric Anomolies in the Fan While the suppression of the inflow separation clearly had a significant effect on the broad-band sound radiation, the decrease in level of the pure tone context was quite small. As the periodicity in the blade pressure signal was now very regular, cycle-to-cycle, i t was postulated that the anomaly in pressure on the blade may occur at a fixed circumferential position relative to the stationary fan annulus. The passing of the spinning rotor blades through this fixed anomaly would produce a far field radiation at 420 Hz and its higher harmonics. A time mark generator was keyed to a circumferential position at r/R = .97, This marker consisted of a tiny air jet impinging on the rotor disc at a known angular position. As the instrumented blade passed the jet, a spike of very short time compared to the period of the blade pressure signal appeared on the oscilloscope. Storage of a number of periods of revolution produced polar plots such as those shown in Figure 16, confirming that the mechanism producing the blip in the blade pressure signal was fixed circumferentially to the fan. 4.3 Tip Clearance Modulation The surface dipole strength measured in the spanwise direction as shown in Figure 17 suggested that much of the radiation was coming from the tip of the blade (reasons for negative source strengths in this region will be discussed later). Close examination of the fan showed that the shroud in which the rotor spun, constructed of rolled sheet metal, was not entirely concentric with the rotor. It was off-round in a number of places. With a dial deflection indicator, i t was determined that over a short portion of the circumference, in the vicinity of the welded longitudinal seam, (220*) the blade tip clearance decreased to a 20 small value and increased quickly again. Figure 18 depicts the measured tip clearance modulation as a function of circumferential position. Modulation amplitudes of ± .025 inches were apparently superimposed on an average clearance of about .050 inches. The pattern shown was typical of all chordwise points at the blade tip. Comparison of the blade pressure polar (Figure 16) with the clearance modulation curve (Figure 18) showed a surprising similarity, particularly for circumferential positions between 120 degrees and 130 degrees, although the valley in the vicinity of 210 degrees was somewhat deeper on the pressure plot. Where the clearance decreased, the pressure became more negative and vice versa. This variation would be the expected result for a negatively loaded blade upper surface i f the clearance modulation were to influence the shedding of tip vorticity and hence the short circuiting of tip loading as a function of "time. To determine the effect of the tip clearance modulation, an annular section machined from a cast billet of hardened aluminum was fitted to replace a section of the shroud cut away around the rotor. The baffle and rolled bell mouth were attached as before. The overall sound level was decreased by only about two more decibels. Subjectively, however, the fan appeared to be less noisy. Inspection of the blade surface pressure and far field sound pressure spectra (Figures 12 and 11) showed that the discrete frequency components were decreased by 5 decibels or more in the far field spectrum while the high frequency level actually increased for frequencies above 4000 Hz. A similar trend was noted on the blade pressure spectra although the reductions at multiples of the 60 Hz rotational frequency were not as pronounced as in the far 21 field sound. The high frequency broad-band noise was more intense, and so masked the discrete tones more effectively when the tip clearance modulation was eliminated. The reason for the enhancement of the high frequency levels was not immediately evident. It was postulated that communication between the lower and upper surface pressures 'of the blade in the region of the tip causes a discrete frequency vortex structure to be shed from the tip of the blade for the case of a uniform clearance around the circumference of the fan. A crude calculation based on the assumption that this vortex sheet was formed by a jetting of air through the slot between the blade tip and the shroud indicated that such an effect would produce frequencies in the order of 10,000 Hz corresponding to the blip on the high frequency part of the dotted curve in Figure l l . (Appendix B) It is also plausible to argue that by regularizing the tip clearance, the shedding of trailing edge vorticity becomes more coherent in the vicinity of the blade extremities thus increasing the level of high frequency noise generation. 4.4 Inlet Velocity Distortions Although the machined annulus provided a partial reduction in discrete tone content, a significant residual fraction was found to persist. Elimination of clearance modulation removed some of the erraticity of the blade pressure wave form, but a prominent negative dimple was s t i l l evident over about 100 degrees of arc, centered at the 210 degree position. Cycle to cycle variations were also noted in the region included between angles of 30 and 120 degrees (Figure 16). Recently Lowson et al^ have given an account of the effect of gross inflow distortions on the noise generated by an isolated, unshrouded, fan 22 rotor. Natural turbulence is found to raise the lower frequency part of the broad band spectrum and to some extent'the discrete frequency peaks. Other workers have described how geometrically fixed distortions of inlet 9 velocity will accentuate only the discrete frequency tones Calculations based on quasi-steady pressure coefficients over the blade show that an axial fluctuation of inflow of only about 2 feet per second superimposed on the mean flow of 75 feet per second will cause a pressure fluctuation on the blades of about 1250 y bar. This value is of the same order as the fluctuating pressure amplitude being measured on the blade at 15% chord. (Appendix C) For circumferential positions in the vicinity of 30 to 120 degrees, the blade pressure wave form is quite erratic (Figure 16). Here the -pressure- -fluctuateons^may be -eaused by a time-varying flow' distortion caused by the proximity of the fan to the wedged wall of the anechoic chamber. Autocorrelations of the far field acoustic pressure performed on the fan noise while a wake was introduced into the opposite side of the fan from the wall showed the emergence of a double frequency of 840 Hz (Figure 19), indicating the possibility of a discrete frequency generating mechanism in the vicinity of the wall. An occasional increase in velocity caused by intermittent flow around the wedges would produce on the upper surface of the blade a drop in surface pressure corresponding to the dashed curve in Figure 16. Traverses of dynamic pressure gave no indication of fixed localized regions of gross starvation over the inflow plane. The time-averaged velocity profiles were found to be uniform and axisymmetric. The cross-correlation measurements indicated a region of zero source strength at about the 3/4 23 span location (Figure 17). This reading was rechecked several times. Oh the outboard side of this position, the source strength is negative, and on the inboard side, positive. The negative source strength (as described in appendix 1) indicates that the pressure at that point is out of phase with the far field sound, and so is a detractor from the gross far field sound level. 4.5 Inlet Vortex The counter phase source strength curve could be explained by the presence of a concentrated inlet vortex being periodically chopped by subsequent blade passages. The nulle at r/R = .75 would correspond to the vortex core. The negative and positive source strength on either side of the nulle would be caused by respective increases and decreases in blade angle of attack relative to the flow, caused by swirl in the vortex (Figure 20) as i t passes intermitantly over the blade. If such a vortex were ingested at the 210 degree circumferential position, this would give rise to a positive dimple on the blade pressure signal (for points outboard of the core). To suppress any possible circulation in the inflow, a circular disc of honeycomb was placed over the inlet of the fan and attached to the baffle. Comparative tests were run with the machined annulus on and with the fan in its off-the-shelf configuration. Results showed that with the honeycomb over the inlet of the fan, the source strength remained positive over the entire blade span. The case where the machined annulus was in position showed a slightly lower source strength in the region of the tip; however, the lack of enough pressure 24 tapping points in this region makes this result open to question (Figure 17). More points would have to be provided before a conclusion regarding effect of the machined annulus on tip source strength could be made with more confidence. This fact also holds true for the case of the fan with no honeycomb. Unfortunately,due to the inconvenience of relocating the blade pressure transducer several times, only five spanwise points were used in the present experiments. The overall sound level increased when the honeycomb was attached. Crowding of the flow through the honeycomb near the-extremities of the fan rotor was caused by the taper of the sheet metal bell mouth (Figure 6). This crowding of the honeycomb "jetlets" may explain the higher source strength in the region of the blade tips and the higher far field sound pressure levels observed for the case of the honeycomb attached. The elusive properties of inlet vortices are well known. Their suspected influence on fan noise tests conducted under confined conditions 1 has been discussed by others. Attempts to visualize a vortex using smoke filaments were relatively successful, showing what could be a concentrated vortex at the 210 degree position (Figure 15). In this figure, the apparent wrapping of smoke filaments around each other may be a result of the presence of a vortex at this position. 4.6 Motor Support Struts The spectrum of the far field sound (Figure •-11) shows a noticeable strut interaction tone at four times the rotational frequency of 60 Hz. This frequency is a result of the upstream potential distortions imposed by the strut on the fan blades. These give rise to a four-times-per revolution force modulation on the blades. 25 On the other hand, the impingement of the wakes from the seven blades of the rotor on each of the motor struts will produce a fundamental tone at seven times the rotational frequency of the fan (420 Hz) and its harmonics (provided all blade wakes are identical). This strut radiation may or may not over-ride the blade radiation at corresponding frequencies (blade passage frequencies and its harmonics). The question arises, which contributes more to the on axis discrete tone at the blade passage frequency, radiation from the blades, or from the struts? The answer to this question may be determined by integrating the source strength distributions at 420 Hz over the surfaces of interest. A h inch Bruel and Kjaer microphone was embedded in a motor support strut with 0.020 inch pin hole communicating to the outside surface of the strut. The strut was rotated through 360 degrees to obtain a circumferential distribution of source strength. A frequency analysis of the pressure spectrum at the strut surface for an angle, 9, of 120 degrees to the fan axis, showed a peak at 420 Hz (Figure 21) as was to be expected. The peak at 60 Hz is probably caused by variation of the pitch angle and length of the rotor blades. Changes from blade-to-blade in these two parameters occur once per revolution-Repetitions of identical wake deficits and velocity profiles once per revolution would give rise to periodic noise generation at the rotational' frequency. Source strength at 420 Hz was measured around the circumference of the strut at r/R = .89, yielding the result shown in Figure 22. This distribution was determined in a similar manner to that of the blade span line using equation 11. The source strength is greatest at the -15 degrees position and in the 90 degrees to 240 degrees region. In both these areas, the 26 source strengths are negative, indicating that these pressure fluctuations are out-of-phase with the dominant far field sound by more than ±90 degrees. Thus this source strength reduces the net value of p^ on axis. The regions of positive source strength correspond to areas of oscillating flow separation. Thus, because of the varying velocity of on coming flow, the separation bubble will oscillate back and forth in this region causing a pressure fluctuation out of phase with the rest of the strut pressure, but in phase with the far field sound. The plot of overall rms pressure (Figure 23) suggests that separation occurs in the region of 60 degrees and 285 degrees, when compared to steady flow pressure distributions around circular cylinders. The 420 Hz filtered pressure fluctuations show stronger peaks at about 120 and 260 degrees, with a null near 180 degrees. These are probably associated with fluctuating side forces and drag forces imposed on the strut-by wake impingement at -420 jHz or vortex shedding at a nearby frequency. It is interesting to note that i f one calculates the Strouhal frequency for the fan mean flow of 75 feet per second passing over a strut of h inch diameter, one finds that the frequency of vortex shedding from the struts would be about 360 Hz. It is therefore possible that not only are the rotor wakes impinging on the struts at 420 Hz, but also they may be amplifying the vortex shedding frequency phenomenon at the strut (increasing strut sound radiation at the blade passage frequency to a level not normally expected). To calculate the contribution from the struts to the far field sound rigorously i t would be necessary to measure source strength distributions over the entire length and circumference of all four struts and to integrate these values over the total surface. The result would then establish whether or not the sound radiated by the struts is contributing in a dominant way to the far field sound. 27 4.7 Integral Check on Source Strength (Rotor/Strut) Source strengths were calculated on two surface lines: firs t along the span of the fan blade at 15% chord, and secondly around the strut at r/R = .89. The resulting distributions are shown in Figure 17 and Figure 22 respectively. Both plots are source strength distributions for the blade passage frequency, 420 Hz. The curves of the blade source strength distributions were extended smoothly to the root of the blade as shown in Figure 17, and integrated over the span. An approximation of chordwise distribution was based on a straight line decrease at 15% chord to zero source strength at the trailing edge. This distribution would roughly approximate the static pressure curve for the pressure variation over the upper surface of a thin airfoil at incidence (Figure 26). Sound radiation from the upper surface is assumed to be-equal to-that -from''the Tower. Assuming the distribution is the same for all blades, this approximation predicts 65.5 decibels of sound radiated from the rotor at 420 Hz with the machined annulus on and 65.0 decibels from the rotor with the basic fan shroud around the rotor. The chord-wise pressure distribution approximation limits the confidence that can be placed in the above figures especially in the case where the integration over the span involves taking the difference of two large areas to arrive at a relatively small result (Figure 17). It is very probable that the chordwise distribution of source strength is not well approximated by the straight-line function used, for all span-wise locations. Small inaccuracies resulting from, the approximation may comprise a large percentage of the resultant net source strength after the integration over the blade surface is performed. More points in both the spanwise and chordwise directions would alleviate this limitation. The far field frequency spectrum shows 58 Db at. 420 Hz with the machined annulus 28 on and 64 decibels with the basic shroud. (Fig 11) C lear ly the blade t i p region expected to be most effected by the addi t ion of the annulus was not adequately surveyed by the f i ve span-wise po in ts , and so the source strength in tegrat ion approximation does not show a suppression of the blade passage generated frequency s im i l a r to the far f i e l d spectrum. The cases where the honeycomb was placed across the i n l e t to the fan show that an increase of about 8 decibels in the 420 Hz tone would be expected using the same approximations as for the case of no honeycomb. Source strengths are higher near the t i p of the fan as a resu l t of the previously discussed crowding of j e t l e t s through the honeycomb, and are always of pos i t i ve s i gn . JaMe 1 ^Gont*ribut4ons to ;tota'l sound at 4 2 0 Hz COMPONENT NO ANNULUS ANNULUS HONEYCOMB BLADES CALCULATED 6 5 . 5 6 5 73 STRUTS CALCULATED 6 5 6 5 -OVERALL MEASURED 64 58 The s t ru t source strength d i s t r i bu t i on shown in Figure 22 ind icates that the strongest regions of surface in te rac t ion generated noise a t 4 2 0 Hz occur at the forward surface near the stagnation po in t , and around the rear of the s t r u t , because of the modulations in the base pressure and overa l l s t ru t drag, driven by the unsteady approach ve loc i t y f i e l d . For a flow approaching along the 0 degrees a x i s , the d i s t r i bu t i on of 29 source strength may be expected to appear more symmetrical. The presence of the spinning rotor situated between the source point and the far field receiving microphone may have some effect on the distribution of the strut source strength due to alternations of the sound travel time as a function of blade circumferential position. This effect was difficult to verify because of the complex nature of the fan, and the large number of sources of 420 Hz tones. Checks of the travel time, however, using a point source near the surface pressure measuring points showed that the travel time did not change appreciably as the rotor was spun by hand in front of the source. When the distribution of source strength was integrated around each strut, and along its length (assuming a uniform lengthwise distribution of strength), the net sound radiation at 420 Hz from the four struts was predicted at 65 decibels. This figure is almost certainly.too high, since a lengthwise phase shift along the strut might be expected. This shift could result because the trailing edge of the wake shedding rotor blade is skewed at an angle relative to the longitudinal axis of the strut. Data collected at this time pertinent to the origins of the on-axis discrete tones is not sufficient to conclusively identify all mechanisms producing the on-axis anomaly. To gain more positive evidence of the mechanisms several additional experiments are possible. In particular i t will be necessary to do a detailed source distribution survey over the entire blade surface (upper and lower) and over the length of the strut. Having accomplished this task,which is by no means a simple task, one could more confidently state which was the major contributor to the on-axis sound radiation, the strut or the fan rotor, and where the strongest sources are concentrated. 30 V. CONCLUSIONS . Experiments conducted in this fan noise research have shown how causality correlation techniques employing cross-correlation functions can be useful in identifying causes of on-axis discrete tone fan noise, and has isolated some mechanisms of the on-axis tones for this axial flow fan. For the present experiments, the spatial resolution was inadequate to enable a detailed analysis of the contributions from various areas of the fan blade. To establish an accurate surface source strength distribution, the spacing between measured points will have to be decreased, especially in the region of the tip where the change in magnitude of the source strength is strongest. Strength over both upper and lower surfaces of the blade and from blade to blade, will be necessary to reveal both spatial and -spectral origins of the far field sound. A more detailed analysis of the strut source strengths will determine which was the major contributor to the far field blade passage noise, the struts or the rotor. Results to date suggest that because the strut 420 Hz sound radiation is counter phase with the far field sound, and the rotor 420 Hz sound.is in phase (at least over inboard sections of the blade), the rotor probably contributes more to the on-axis pure tone than the struts, but not by very much. As mentioned earlier, the presence of the rotor upstream of the struts may affect the cross-correlation between the strut pressure and far field sound. Further research into this matter will be required. Despite these few problems, experiments performed using causality 31 correlations as a diagnostic tool have proven that this method presents a powerful and effective means of identifying areas which contribute °greatly to noise from rotating rotor blades. Data has shown almost conclusively that an inlet vortex or similar flow distortion is being ingested into the fan near the 210 degree circumferential position. - This vortex produces blade pressure fluctuations concentrated near the outer extremities of the blades which are related to the far field discrete tone sound. The on-axis radiation results from harmonic components of a once-per-revolution blade load modulation, with only those integral multiples of blade passage frequency being significant radiators. On-axis radiation may a,lso .result from -fluctuations..in'the inflow velocity caused by the proximity of the fan to the anechoic chamber wedged wall. The effect of these large scale velocity distortions on the discrete tone fan noise have been discussed by others''' ^ , but requires further exploration. Random blade load fluctuations result from flow , separation at a poorly designed bell mouth and from the ingestion "of natural turbulence results in an increase in the broad-band noise. Experiments conducted with an accurately machined shroud showed that geometrically fixed load variations resulting from the cyclic modulation of tip clearance can be suppressed. The regularization of clearance reduces the pure tone content slightly (5 db), but does not, by an means, eliminate i t . 32 By preventing inflow separation, and by eliminating clearance modulation, a sound level reduction in the far field of 7 decibels was achieved. An even greater reduction is expected i f a carefully designed bell mouth is installed to reduce inflow separation further, i f the fan is positioned so that the effect of the proximity of the wall is eliminated, and i f the inlet vortex being injected by the fan is eliminated. 5.1 Recommendations for Further Work Experiments to this point have been carried out on an off-the-shelf fan which has many noise sources inherent in its design due to considerations of economy and utility. It would be useful to modify the fan so that many of the mechanisms of noise generation described above would no longer exist. Having accomplished this task, controlled flow distortions, and geometric anomalies could be imposed upon the fan and the resulting effect on source strengths and the far field sound pressure level could be determined. More work should be conducted in the determination of the effect of noise generating obstructions in the source-far field path. The case of the spinning rotor between the source on a fan strut and the far field measuring point from the fan is an example of this problem. Further work on the nature of sound radiation generated by a strut when in the modulating velocity field of spinning rotor wakes could be accomplished by swinging an instrumented bar in and out of the flow field of a turbulent jet. Using the causality correlation techniques described, source strength distributions could be determined. A more detailed analysis of blade source strength distribution is 33 r e q u i r e d i n v o l v i n g t h e s u r v e y i n g o f many more p o i n t s . A more e f f i c i e n t means o f s a m p l i n g p r e s s u r e s a t v a r i o u s p o i n t s on t h e b l a d e s u r f a c e s would have t o be d e v e l o p e d t o overcome t h e l i m i t a t i o n s o f t i m e now e x p e r i e n c e d because o f the g r e a t c a r e r e q u i r e d when c h a n g i n g t h e p o s i t i o n o f t h e t r a n s d u c e r f r o m one h o l e t o a n o t h e r . T h i s p r o c e d u r e i n v o l v e s r e m o v i n g the r o t o r f r o m the f a n , e x t r a c t i n g t h e t r a n s d u c e r and l e a d s from t h e m i l l e d s l o t , r e p l a c i n g i t i n a new h o l e , and i n s e r t i n g new m o d e l i n g c l a y i n t h e empty h o l e s and m i l l e d s l o t s . B e f o r e t h e r o t o r i s put back on t h e motor, new t a p e must be p l a c e d o v e r the t r a n s d u c e r and l e a d s t o keep them i n s i d e t h e i r m i l l e d c a v i t i e s . 34 REFERENCES 1. Colehour, J.L. and Farquhar, B.W., "Inlet Vortex", J. Aircraft, 8(1) p. 39-42, (1971). 2. Curie, N., "The Influence of Solid Boundaries Upon Aerodynamic Sound", Proc. Roy. Soc. A, 231, 505-514, (1955). 3. Kraichnan, R. H., "Noise Transmission from Boundary Layer Pressure Fluctuations", JASA 25, P. 65-80, (1957). 4. Filleul, N., "An Investigation of Axial Flow Fan Noise", Journal of Sound and Vibration, 3(2), p. 147-165, (1966). 5. Gutin, L., "On the Sound of a Rotating Propeller", Translation of "Uber da Schallfeld einer rotierenden Luftschraube" Physikalische Zeitschr i f t der Sonjetunion, Band 9, Heft 1, 1936, NACA Tech. Memor. No. 1195 (1945). 6. Lee, H. K., "Correlation of Noise and Flow of a Jet", UTIAS Rep. 168 (1971); also AFOSR-TR-71-2572 (1971). 7. Lowson, M.V., Whatmore, A.R., Whitfield, C.E., "Studies of Noise ..Radiation Jay,Ro.t.ating.s.BJtadding", ^ Interagency.,Symposium'.on .University Research in Transportation Noise, Proceedings p. 211, Mar. (1973). 8. Rackl, R., "Two Causality Correlation Techniques Applied to Jet Noise", PhD. Thesis, Dept of Mech. Eng., University of British Columbia, April (1973). 9. Savell, C. T., Knott, P.R., "Effect of Fan Parameters on Turbulence-Fan Interaction Noise. General Electric Technical Memorandum, March (1972).. 10. Scharton, T. D., White, P.H., "Simple Pressure Source Model of Jet Noise", JASA 52(1), July (1972). 11. Siddon, T. E., "Surface Dipole Strength by Cross-Correlation Method", JASA Vol 53 No. 2, p 619-633, Feb. (1973). 12. Siddon, T. E., Leggat, L. J., "Blade Load Modulation as a Source of Discrete Frequency Fan Noise", Proceedings, Internoise '73, Aug. (1973). 13. Siddon, T. E., "Noise Source Diognostics Using Causality Correlations". Specialists Meeting on Noise Mechanisms, AGARD Fluid Dynamics Panel, Belgium, Sept (1973). 14. Tyler,J.M.,Sofrin, T.G.,"Axial Flow Compressor Noise Studies", SAE Trans.,70,p.309-332(1962). 35 ' APPENDIX A Two pistons are mounted as shown in Figure 24 equidistance from a far field microphone. Both pistons are vibrating with the same frequency; however, the rate of change of pressure at the surface of piston one is held constant at a value of unity while the rate of change of pressure for piston two is caused to vary from 0 to 3 by increasing the driving force. Piston one is vibrating counterphase to piston two and both pistons are of equal area. At the far field microphone, the net pressure will be the residual after cancelation of waves from both pistons. The pressure detected at the far field microphone may then be represented by the equation: P(r.t) « a^r 5 ( I f ) • ds 4irx v 3.t ' ' " ° ' A l p The net sound pressure p n e t ( t ) is the sum of the source strengths of pistons one and two multiplied by their respective radiating areas. ? n e t - < f # • S >1 + < # ' S '2 A2 Substituting from equation (11) ~2 _ s • cose p net 4TTXC Pc- P + Pc P s l s2 A3 T=X/C Take k as the ratio of source pressure amplitudes such that p = -kp and p = const =1.0 AA  s2 1 s l 36 The far field pressure decreases in proportion to the increase of radiation from piston 2 which cancels part of the radiation from piston 1. Thus: P f f ( k ) = P f fk = 0 ( 1 " k ) A5 * n A . T 2 - Scose 3 -—- ,, .x2 . a n d : P net - 4^c~ — P s / . n ( 1 " k ) A6 T 1 k=0 As long as k < 1 that is that p.. < p<.,, then the far field sound ' 52 1 radiation will be dominated by contributions from piston 1 and the correlation function ps^p(r) will display a negative slope at the correct time delay as shown in Figure 24, (Indicating a positive source strength ). In contrast the correlation function ps^p(r) will have a positive, but flatter slope at the correct time delay, indicating a weaker, and negative source strength. When k exceeds 1, then the far field pressure will be dominated by contributions from piston 2 and the reverse of the above situation is true. By varying k from zero to 5, the net pressure is seen to vary as shown in the dashed curve of figure 25. For values of k less than unity, the far field pressure will be dominated by contributions from piston one and will have the same phase. Where k is one, contributions from both pistons are felt equally at the far field, but their opposite phase causes complete cancellation, and a resultant net pressure of zero (see table, Figure 25). As k becomes greater than one, the sound radiation from piston 2 dominates the far field pressure, and will determine the phase. It can be seen from this example then that because of phase differences, in this case counterphase sources, the net far field sound pressure level is not determined with the sum of the absolute values of source strengths but by consideration of relative phasing of sources and their cancelling effect in the far field. 37 APPENDIX B The calculation for the discrete frequency expected from the jetting of air through the slot between the blade tip and shroud is based on the formula for the characteristic frequency for a slotted jet: f = .2 ^  t =slot width In the case of the fan, the slot width is .050 inches and the velocity through the slot is assumed to be 200 feet per second, 70 per cent of the blade tip velocity. This calculation leads to an expected frequency of 9,600 Hz. APPENDIX C The preS'sure 'on the bTade *a-t *T5% chord is-"given -by: r 1 II 2 p15% c a = blade angle of attack dp dcp 1 n 2 do" " da 2 p UR Un = blade relative velocity a value of dcp/da at 15% chord of .04 based on quasi-steady pressure coefficients and a relative velocity of 310 feet per second gives: 3a ~ degree a fluctuation of inflow velcoity (U) of 2 feet per second produces a da of 36 degrees resulting in a dp of 1,250 yBar. surface pressure fluctuations resulting from strut passing through flow deficiencies in wakes wake Figure 1 Periodic Noise Generation Mechanisms turbulence in inflow and shroud boundary layer i u y i ~ blade surface pressure fluctuations induced by turbulent flow / blade wake blade boundary layer Figure 2 Broad Band Noise Generation Mechanisms T-msec Figure 3 typical Antisymmetric Cross-Correlation Function Figure 4 Cross-Corelation Function of Filtered Signals «< O'IO' S C A L E J_> l ' 4 Figure 5 Anechoic Chamber Showing Fan Installation ro o Figure 6 strut motor Experimental Fan Rig Figure 7 Instrumented Fan Blade 6D pressure transducer -transmitter receiver amplifier narrow band frequency analysis • and cross ^co r re l a t i on amplifier far field microphone Figure 9 Schematic of Apparatus and Analysis Instruments CD Figure 10 Unfiltered Cross-Correlation Function Showing Strong Harmonic Content 8 0 CQ Q C O or L U I -L U < Q < L L . CD II X C O 7 0 6 0 5 0 4 0 3 0 2 0 10 FUNDAMENTAL BLADE PASS F R E Q U E N C Y B A F F L E O F F B A F F L E ON STRUT INTERACTION FREQUENCY B A F F L E AND MACHINED ANNULUS ON 10 10 10 F R E Q U E N C Y , Hz ( 6 % B . W . ) 10 -F=. CO Figure 11 Far Field Noise Spectrum 130 r Q 120 Is-cq w no z o r-CO o CL U l o < ID CO _J CL 100 9 0 80 7 0 6 0 BAFFLE OFF BAFFLE ON BAFFLE AND MACHINED ANNULUS ON 10' FREQUENCY,Hz (6% B.W.) 10° 10* Figure 12 Blade Surface Pressure Spectrum OS D B 85^ Figure 14 Fan Noise Forward Directivity b a f f l e smoke filament Figure 15 Flow Visualization of Intake Velocity Field 53 2 0 0 0 H Y D R O D Y N A M I C P R E S S U R E (/iBARS) Figure 16 Circumferential Blade Pressure Fluctuation (Three random trials) O annulus , no h oneycomb* g no honeycomb.no annulus A annulus, honeycomb O honeycomb, no annulus r s radius to tronsducer position R = radius of f an Spanwise Source Strength of 4 0 0 hz T o n e at 15% Chord Figure 17 Spanwise Source Strength, at 15% Chord • t o 55 0.10" 0.05" ta.oo" b l 270c o O 00 90° C L E A R A N C E (INCHES) gure 18 Clearance Between Fan Tip and Shroud T - msec Figure 19 ' Autocorrelation Functions of Far Field SPL Showing Emergence of Double Freauency for Inflow Distortion at Fan Circumferential Angle of 270 Degrees •• " , cn a lower induced angle of attack Figure 20 Effect of Ingested Vortex on Blade Lift Characteristics cn Figure 21 Strut Surface Pressure Spectrum 61 M LLJI P(t) FROM PLATE I lL = L A R G E R AND+VE dJS ~ T FROM PLATE 2 ££- = SMALLER AND - V E dS as i as <-Illustrative Example of concept of negative Source Strength Using Vibrating pistons Figure 24 Vibrating Piston Example of Negative Source Strength 2 — ( dp _ cosaTpp(c)"] dS = 4mrc Is J j . j . pn2et = s-cosenp;p)-n"PjF)'] 4rtTC L * JjL c P (k) = P x U - k ) V k = 0 K [£••1 P 2 0 1 0 1 . 2 5 . 7 5 - . 1 9 . 5 6 . 5 • • 5 0 - . 2 5 . 2 5 1 . 0 0 0 0 where p = -kp, 2 ' p Scose  n c t 4tr rc R p p ) - (1-k) [ J . k»o p = const =1.0 - ( BP), ( l - k ) ( k ) l V 'k 2 2 P n p. = S - c o s g ( p p ) ( l - k ) T h e o r e t i c a l Resul ts From Illustrative Example Figure 25 Theoretical Results From Piston Example Figure 26 approximation of chordwise source strength distribution static pressure distribution over upper surface of thin airfoil at incidence Approximation of Source Strength Distribution co 

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