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Untersuchung des Liebeslebens der Windrder mit einem Mikrofonarray
Bachelor (Master-)Arbeit
Nr. Axx-y/z
vorgelegt von
Mina Mustermann
Matr.-Nr. 123456789
September 20zz
Naturwissenschaftlich-Technische Fakultt Department Maschinenbau
Institut fr Fluid- und Thermodynamik
Hier noch die unterschriebene Aufgabenstellung!Kurzfassung
ca. 0,5 Seiten!
Sauber geliedert in ca. drei Abschnitte
- Aufgabe und Ziel der Arbeit- Was wurde gemacht?
- Ergebnis und Schlussfolgerung
Abstract
Beispiel The effect of unavoidable tip clearance in axial fans is significant since a large clearance does not only degrade the overall aerodynamic performance, but it also increases the sound radiation into the far-field dramatically. The overall objective of this thesis is hence the detailed investigation of the tip clearance flow and subsequent of the sound generating mechanism, which can eventually pave the way for new and innovative low-noise fan designs.
In this study, comprehensive experimental and numerical investigations are conducted based on an impeller-only low pressure axial test fan in two tip clearance variations. Besides the overall aerodynamic and acoustic tests, the more detailed measurements of surface pressure fluctuations in the blade tip region show the footprints of the complex tip clearance flow. The underlying complete three-dimensional tip clearance flow field and its correlation with the acoustic field, however, can only be understood by carrying out advanced numerical simulations. Hence, various steady and unsteady Navier-Stokes based approaches with subsequent acoustic model as well as the Lattice-Boltzmann method are applied.
Both experimental results and numerical predictions confirm the aforementioned well-known effects of an increase in tip clearance. The effect of a large tip clearance on the sound pressure spectrum is twofold: (i) an increase in the broadband floor and, (ii) specifically at lower volume flow rates, the appearance of pronounced narrowband humps with center frequencies that are linked to the rotational speed of the impeller but that are not integer multiples of the blade-passing frequency. It is found that they result from the interactions of the impeller blades in the tip region with (i) the highly turbulent small vortex structures decayed from the tip clearance vortices during extending through the local blade passage and (ii) the global circumferentially coherent vortex structures(a superposition of circumferential modes of different mode orders, which rotate slower than the impeller blades.
The Lattice-Boltzmann method (LBM) also proved to be a suitable tool for the aeroacoustic prediction and investigation of the fan noise generating mechanism with a feasible computational effort.
Based on these findings, a novel casing treatment is designed that is able to substantially suppress tip clearance vortex structures and hence significantly reduce the tip clearance noise.
Danksagung
Inhaltsverzeichnis
TOC \o "2-4" \h \z \t "berschrift 1;1;berschrift 7;1;Sonderberschrift;1" HYPERLINK \l "_Toc521502856" Nomenklatur PAGEREF _Toc521502856 \h VII
HYPERLINK \l "_Toc521502857" 1 Einleitung PAGEREF _Toc521502857 \h 1
HYPERLINK \l "_Toc521502858" 1.1 Motivation PAGEREF _Toc521502858 \h 1
HYPERLINK \l "_Toc521502859" 1.2 Zielsetzung PAGEREF _Toc521502859 \h 3
HYPERLINK \l "_Toc521502860" 1.3 Gliederung der Arbeit PAGEREF _Toc521502860 \h 3
HYPERLINK \l "_Toc521502861" 2 Literatur- und/oder Patentbersicht PAGEREF _Toc521502861 \h 7
HYPERLINK \l "_Toc521502862" 3 Ihre eigentliche Arbeit PAGEREF _Toc521502862 \h 9
HYPERLINK \l "_Toc521502863" 4 Ergebnisse PAGEREF _Toc521502863 \h 10
HYPERLINK \l "_Toc521502864" 5 Diskussion der Ergebnisse und Schlussfolgerungen PAGEREF _Toc521502864 \h 11
HYPERLINK \l "_Toc521502865" Fakulativer Anhang A: z.B. Fehleranalyse PAGEREF _Toc521502865 \h 13
HYPERLINK \l "_Toc521502866" Appendix A : Arrangement of pressure transducers on the casing inner wall PAGEREF _Toc521502866 \h 17
HYPERLINK \l "_Toc521502867" Literatur PAGEREF _Toc521502867 \h 21
Nomenklatur
Lateinische Symbolea0speed of soundm/sAductcross-sectional area of the ductm2Aenvenvelope surface aream2Arefreference aream2b1, b2dimensions of the wire meshmznumber of blades-Griechische Symbole EMBED Equation.3 parameter of LBM turbulence model - Df f r e q u e n c y r e s o l u t i o n H z Df r e f r e f e r e n c e f r e q u e n c y r e s o l u t i o n H z te e m i s s i o n t i m e s te f f e f f e c t i v e r e l a x a t i o n t i m e s ti j R e y n o l d s R e y n o l d s s t r e s s t e n s o r ( m / s ) 2 tr e l a x r e l a x a t i o n t i m e s tw w a l l s h e a r s t r e s s k g / m s 2 w t u r b u l e n t f r e q u e n c y 1 / s x r e l a t i v e r e f e r e n c e f r a m e m yt s t o t a l - t o - s t a t i c p r e s s u r e c o e f f i c i e n t - A b k r z u n g e n A N N a r t i f i c i a l n e u r a l n e t w o r k s B E M b l a d e e l e m e n t m o m e n t u m B P F b l a d e - p a s s i n g f r e q u e n c y R A N S R e y n o l d s - a v e r a g e d N a v i e r - S t o k e s
E i n l e i t u n g
M o t i v a t i o n
B e i s p i e l F a n s h a v e a widespread field of application. For instance, fans are used in miniature computer cooling systems, compact mobile and stationary combustion engine cooling units, extended building heating, cooling and ventilation networks, large air and flue gas systems in thermal power plants and even in sophisticated aircraft engines. Yet, fans frequently represent one of the major noise sources in these applications and people need and call for a quiet environment. For decades, research and development efforts in the fan industry have therefore focused on the analysis and mitigation of flow induced fan noise on a par with a focus on increasing efficiency, range of operability and power density, etc.
EMBED Equation.3 .(1.1)
Among the numerous types of fans axial fans are indispensable for systems that require large flow rates and only a moderate pressure rise. Most axial fans consist of a impeller installed in cylindrical duct type casing, REF _Ref445211728 \h \* MERGEFORMAT Bild 1.1. Depending ....
Bild STYLEREF 1 \s 1. SEQ Figure \* ARABIC \s 1 1: Axial fan stage in a cylindrical (duct-type) housing.
Numerous sources of flow induced noise are known. Blake ADDIN EN.CITE Blake1986403[1]4034036Blake, W. K.Mechanics of Flow-Induced Sound and Vibration, Volume II: Complex Flow-Structure InteractionsVol. 17 in Applied Mathematics and Mechanics1986Orlando (FL), USAAcademic Press, Inc.[ HYPERLINK \l "_ENREF_1" \o "Blake, 1986 #403" 1] classified them into self noise and interaction noise, REF _Ref443577397 \h \* MERGEFORMAT Bild 1.2.
SHAPE \* MERGEFORMAT Bild STYLEREF 1 \s 1. SEQ Figure \* ARABIC \s 1 2: Classification of fan noise sources according to Blake ADDIN EN.CITE Blake1986403[1]4034036Blake, W. K.Mechanics of Flow-Induced Sound and Vibration, Volume II: Complex Flow-Structure InteractionsVol. 17 in Applied Mathematics and Mechanics1986Orlando (FL), USAAcademic Press, Inc.[ HYPERLINK \l "_ENREF_1" \o "Blake, 1986 #403" 1].
Self noise is the sound generated from fluctuating blade forces arising from the flow over the blades themselves. The Gutin noise arises from the potential flow around the blades, which essentially causes the desired forces on the blades steady in the rotational frame of reference, but unsteady when observed by a listener in the stationary laboratory system. The trailing edge noise is generated from the interaction of the turbulent boundary layer along a blade surface with its trailing edge. Vortex shedding is caused by a blunt trailing edge. Flow separation occurs on heavily loaded blades with high angle of attack, which are usually close to or in stall condition of a fan. Rotating stall is a particular case of flow separation that can generate tonal noise, Tab. 1.1.
Tab. 1.1: Distribution of the monitoring points in the blade passages and on the stationary inner wall (R=150mm).DirectionStart-Pos.
(Notation)End-Pos.
(Notation)DistributionSpanwise(Radial)R=150mm
(R150)R=110mm
(R110) DR = 4 m m C h o r d w i s e L e a d i n g E d g e
( C 0 1 ) T r a i l i n g E d g e
( C 1 0 ) 1 0 p r o b e s u n i f o r m l y d i s t r i b u t e d f r o m L E t o T E a l o n g t h e p r o f i l e c h o r d a t b l a d e t i p A z i m u t h a l 5 r o w s o f p r o b e s ( C 0 1 - C 1 0 ) i n e a c h b l a d e p a s s a g e , a r o u n d f u l l 3 6 0 ( 5 b l a d e p a s s a g e s ) Dq = 1 2 ( i n e a c h blade passage)(Az01)(Az25)
Zielsetzung
The overall objective of this thesis is the detailed investigation of the tip clearance flow and subsequent of the sound generating mechanism. The aim is to achieve a better understanding of the mechanism responsible for the tip clearance noise, which can eventually pave the way for new and innovative low-noise fan designs. This study is restricted to...
Gliederung der Arbeit
Following this introduction, Chapter REF _Ref423878825 \r \h \* MERGEFORMAT 2 presents results from a literature review on tip clearance noise from axial fans. Chapter REF _Ref409439190 \r \h \* MERGEFORMAT 3 introduces the strategy for the design of the generic test fan, the test rigs as well as the experimental methods. Chapter REF _Ref446017377 \r \h \* MERGEFORMAT 4 provides an overview of the diverse numerical approaches adopted in this study. Chapters REF _Ref441054207 \r \h \* MERGEFORMAT 5 and REF _Ref443760134 \r \h \* MERGEFORMAT 6 present the results: Chapter REF _Ref441054207 \r \h \* MERGEFORMAT 5 deals with the effect of the "macroscopic" parameters on the overall aerodynamic and acoustic fan performance, whereas Chapter REF _Ref443760134 \r \h \* MERGEFORMAT 6 analyzes the details of the tip flow interaction and its impact on specific spectral sound components. Chapter 7 investigates various geometrical modifications in the tip clearance region of the fan to suppress the tip clearance noise. Chapter REF _Ref410994774 \r \h \* MERGEFORMAT 8 summarizes the results and presents the key conclusions of this work.
Literatur- und/oder Patentbersicht
Beispiel Numerous investigations have addressed tip clearance secondary flow phenomena in axial flow machines. Studies from the early 1950s focused predominantly on aerodynamic effects. However, it was soon recognized that both stability and sound emission of axial fans and compressors are also crucially affected by tip clearance flows. Apart from a few selected studies on aerodynamic effects, this literature review concentrates on tip clearance noise studies. The chapter concludes with a critical assessment of the results of existing studies.
The results from the literature are often presented in terms of dimensionless numbers; of special importance are the flow rate coefficient
EMBED Equation.3 ,( STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 1)the pressure rise coefficient
EMBED Equation.3 ,( STYLEREF 1 \s 2. SEQ Equation \* ARABIC \s 1 2)
Hierher gehrt auch Ihre kritische Einschtzung des Stands des Wissens oder der Technik nach dieser bersicht und die Bekrftigung der obigen Zielsetzung der Arbeit.
Ihre eigentliche Arbeit
Ergebnisse
Die ....
Diskussion der Ergebnisse und Schlussfolgerungen
Hier ist es unbedingt wichtig, auf die Zielsetzung am Anfang Bezug zu nehmen!
Ist das Ziel erreicht, in welcher Form?
Ihre persnliche Einschtzung der in dieser Arbeit erzielten Ergebnisse!
Wo sind noch offene Fragen, die in knftigen Arbeiten angegangen werden sollen.
Fakulativer Anhang A: z.B. Fehleranalyse
In general, the result of a measurement is only an approximation or estimate of the value of a quantity and thus is complete only when accompanied by a statement of the uncertainty of that estimate. The quantification of measurement uncertainty, as described in this study, is defined by the "Guide to the expression of uncertainty in measurement (GUM)" ADDIN EN.CITE ISO International Organization for Standardization2008107[104]10710758ISO International Organization for Standardization,Guide 98-3:2008: Uncertainty of Measurement - Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995)2008Geneva, Switzerland[ HYPERLINK \l "_ENREF_104" \o "ISO International Organization for Standardization, 2008 #107" 104], which is based on the standards DIN V ENV 13005 ADDIN EN.CITE DIN Deutsches Institut fr Normung e.V.1999104[105]10410458DIN Deutsches Institut fr Normung e.V.,DIN V ENV 13005: Leitfaden zur Angabe der Unsicherheit beim Messen1999Berlin, GermanyBeuth Verlag[ HYPERLINK \l "_ENREF_105" \o "DIN Deutsches Institut fr Normung e.V., 1999 #104" 105], DIN 1319-3 ADDIN EN.CITE DIN Deutsches Institut fr Normung e.V.1996105[106]10510558DIN Deutsches Institut fr Normung e.V.,DIN 1319-3: Grundlagen der Metechnik, Teil 3: Auswertung von Messungen einer einzelnen Megre, Meunsicherheit1996Berlin, GermanyBeuth Verlag[ HYPERLINK \l "_ENREF_106" \o "DIN Deutsches Institut fr Normung e.V., 1996 #105" 106] and DIN 1319-4 ADDIN EN.CITE DIN Deutsches Institut fr Normung e.V.1999106[107]10610658DIN Deutsches Institut fr Normung e.V.,DIN 1319-4: Grundlagen der Metechnik, Teil 4: Auswertung von Messungen, Meunsicherheit1999Berlin, GermanyBeuth Verlag[ HYPERLINK \l "_ENREF_107" \o "DIN Deutsches Institut fr Normung e.V., 1999 #106" 107].
The uncertainty in the result of a measurement generally consists of several components which may be grouped into two categories based on their method of evaluation ADDIN EN.CITE ISO International Organization for Standardization2008107[104]10710758ISO International Organization for Standardization,Guide 98-3:2008: Uncertainty of Measurement - Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995)2008Geneva, Switzerland[ HYPERLINK \l "_ENREF_104" \o "ISO International Organization for Standardization, 2008 #107" 104]:
- Type A, those which are evaluated by statistical methods,
- Type B, those which are evaluated by other means.
For a measured quantity Xi, the uncertainty component obtained from a TypeA evaluation is characterized by the estimated variance u2(xi), which is calculated from series of repeated observations. The estimated standard deviation u(xi) (the positive square root o f u 2 ( x i ) ) i s t h u s c a l l e d a T y p e A s t a n d a r d u n c e r t a i n t y a n d , i s t h e n g e n e r a l l y d e f i n e d a s
E M B E D E q u a t i o n . 3 , ( A . S E Q ( A . \ * A R A B I C 1 ) w h e r e x i a r e t h e e s t i m a t e s o f t h e q u a n t i t y X i , s(x i ) i s t h e r e s p e c t i v e s t a n d a r d d e v i a t i o n a n d N m e a s i s t h e n u m b er of repeated observations (i.e. measurements).
For an uncertainty component obtained from a Type B evaluation, the estimated variance u2(xi) is evaluated using scientific judgement based on all of the available information on the possible variability of Xi, and the estimated standard deviation u(xi) is called a TypeB standard uncertainty. The pool of information may include ADDIN EN.CITE ISO International Organization for Standardization2008107[104]10710758ISO International Organization for Standardization,Guide 98-3:2008: Uncertainty of Measurement - Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995)2008Geneva, Switzerland[ HYPERLINK \l "_ENREF_104" \o "ISO International Organization for Standardization, 2008 #107" 104]
- previous measurement data,
- experience with the behaviors and properties of relevant materials and instruments,
- specifications of the manufacturer,
- data provided in calibration and other certificates,
- uncertainties taken from handbooks based on reference data.
In most cases, a output quantity Y, is not measured directly, but is determined from N measured input quantities X1, X2, ..., XN through a functional relationship EMBED Equation.3 :
EMBED Equation.3 .(A. SEQ (A. \* ARABIC 2)To determine the standard uncertainty of Y, the functional relation EMBED Equation.3 needs to be considered. This is achieved with the combined standard uncertainty, uc(y), determined by the law of propagation of uncertainty
EMBED Equation.3 .(A. SEQ (A. \* ARABIC 3)In Equation REF _Ref424740027 \h (A.3), the partial derivatives of the functional relation f are termed sensitivity coefficients. They describe how the output variable y varies with changes in the input quantities xi ADDIN EN.CITE ISO International Organization for Standardization2008107[104]10710758ISO International Organization for Standardization,Guide 98-3:2008: Uncertainty of Measurement - Part 3: Guide to the Expression of Uncertainty in Measurement (GUM:1995)2008Geneva, Switzerland[ HYPERLINK \l "_ENREF_104" \o "ISO International Organization for Standardization, 2008 #107" 104]. Each u(xi) is a standard uncertainty evaluated as Type A or Type B. The second term in Equation REF _Ref424740027 \h (A.3) is obsolete if input quantities xi and xj are uncorrelated.
The combined standard uncertainty uc(y) (or standard uncertainty u(y)) can be also described in terms of relative combined standard uncertainties uc,r(y) (or relative standard uncertainties ur(y))
EMBED Equation.3 ,(A. SEQ (A. \* ARABIC 4)where yref is either the actual measured value or the full measuring range.
Assuming a normal distribution, the combined standard uncertainty uc(y) has a confidence interval of approximately 68%, i.e. the measured value y falls into the interval yuc(y) with a probability of 68%. To achieve a higher confidence interval, the expanded standard uncertainty ue(y) can be determined by multiplying the combined standard uncertainty uc(y) with the so-called coverage factor kcov,
EMBED Equation.3 .(A. SEQ (A. \* ARABIC 5)The coverage factor for a confidence interval of 95% an d a n o r m a l d i s t r i b u t i o n i s k c o v = 2 . T h e u n c e r t a i n t y o f a m e a s u r e m e n t c a n t h e n b e r e p r e s e n t e d a s y - u e ( y ) d" Y d" y + u e ( y ) w i t h a c o n f i d e n c e i n t e r v a l o f 9 5 % .
I n t h i s s t u d y , t h e T y p e B s t a n d a r d u n c e r t a i n t y i s u s e d . A l l u n c e r t a i n t i e s o f t h e i n d i v i d u a l s e n s ors are based on the information of the manufacturer.
Acoustic Measurements. Before each measurement, all microphones were calibrated via a Brel & Kjaer acoustic calibrator (model type 4231), which has an standard uncertainty of 0.2dB. The aeroacoustic test rig meets the requirements of ISO 5136 ADDIN EN.CITE ISO International Organization for Standardization2003366[41]36636658ISO International Organization for Standardization,ISO 5136: Acoustics - Determination of Sound Power Radiated into a Duct by Fans and Other Air-Moving Devices - In-duct Method2003Geneva, Switzerland[ HYPERLINK \l "_ENREF_41" \o "ISO International Organization for Standardization, 2003 #366" 41] for the determination of sound power radiated into a duct by fans. The reproducibility of the overall sound power level on different days and with a rebuilt setup is in the range of 1dB. The far-field measurements are conducted in a semi-anechoic chamber. The semi-anechoic chamber is designed according to the highest accuracy class of DIN 45635-1 ADDIN EN.CITE DIN Deutsches Institut fr Normung e.V.1984367[42]36736758DIN Deutsches Institut fr Normung e.V.,DIN 45635-1: Measurement of Airborne Noise Emitted by Machines; Enveloping Surface Method; Basic Requirements for 3 Accuracy Classes1984Berlin, GermanyBeuth Verlag[ HYPERLINK \l "_ENREF_42" \o "DIN Deutsches Institut fr Normung e.V., 1984 #367" 42] for acoustic measurements of machines via enveloping surfaces. The standard uncertainty given is s d" 1 . 5 d B , w h i c h r e s u l t s i n a n e x p a n d e d s t a n d a r d u n c e r t a i n t y o f u e d" 3 d B w i t h a c o n f i d e n c e i n t e r v a l o f 9 5 % .
A e r o d y n a m i c P e r f o r m a n c e C h a r a c t e r i s t i c s . T h e a e r o d y n a m i c p e r f o r m a n c e o f t h e f a n i s d e t e r m i n e d o n a s p e c i a l c h a m b e r t e s t r i g f o r a e r o d y n a m i c p e r f ormance testing according to the standard DIN 24163 ADDIN EN.CITE DIN Deutsches Institut fr Normung e.V.1985368[39]36836858DIN Deutsches Institut fr Normung e.V.,DIN 24163-2: Ventilatoren, Teil 2: Leistungsmessung - Normprfstnde (Fans, Part 2: Performance Tests - Standardized Test Rigs)1985Berlin, GermanyBeuth Verlag[ HYPERLINK \l "_ENREF_39" \o "DIN Deutsches Institut fr Normung e.V., 1985 #368" 39]. The relative random uncertainty of the single quantities measured at this chamber test rig to determine the performance characteristics and the resulting combined uncertainties of the coefficients are given in REF _Ref426097082 \h \* MERGEFORMAT Table A.1 according Beiler ADDIN EN.CITE Beiler1996243[108]2432436Beiler, Michael G.Untersuchung der dreidimensionalen Strmung durch Axialventilatoren mit gekrmmten SchaufelnFortschritt Berichte VDI Reihe 7 Nr. 2981996DsseldorfVDI VerlagDissertation[ HYPERLINK \l "_ENREF_108" \o "Beiler, 1996 #243" 108].
Table A. SEQ Table_A. \* ARABIC 1: Relative uncertainty of quantities measured at the chamber test rig ADDIN EN.CITE Beiler1996243[108]2432436Beiler, Michael G.Untersuchung der dreidimensionalen Strmung durch Axialventilatoren mit gekrmmten SchaufelnFortschritt Berichte VDI Reihe 7 Nr. 2981996DsseldorfVDI VerlagDissertation[ HYPERLINK \l "_ENREF_108" \o "Beiler, 1996 #243" 108] Quantity
Unit
Relative standard
uncertainties, ur(y)
Relative combined uncertainty, uc,r
total-to-static pressure rise Dp t s
[ P a ]
0 . 5 %
-
d e n s i t y r
[ k g / m 3 ]
d" 0 . 5 %
-
r o t a t i o n a l s p e e d n
[ m i n - 1 ]
0 . 0 5 %
-
f l o w r a t e E M B E D E q u a t i o n . D S M T 4
[ m 3 / s ]
1 . 0 %
-
t o r q u e T
[ N m ]
0 . 3 %
-
p r e s s u r e c o e f f i c i e n t y
[ - ]
-
1 . 6 %
f l o w r a t e c o e f f i c i e n t f
[ - ]
-
1 . 0 %
t o t a l - t o - s t a t i c e f f i c i e n c y hts
[-]
-
2.0%
Blade Pressure Fluctuations. The transducers are calibrated with a white noise signal, as described in REF _Ref444848263 \n \h Appendix B. As specified by the manufacturer, the applied pressure transducers show a constant behavior in a frequency range between 100 Hz and 10 kHz. The sensitivity varies by 3dB (relative to 1V/0.1Pa). Preliminary tests have shown that additional noise generated by the slip ring transducer, which transfers the signal from the rotating system to the stationary system, is negligible. Also, flush-mounted installation of the transducers on the blades do not impact on the acoustic and aerodynamic performance ADDIN EN.CITE Zhu2012130[44]13013027Zhu, TaoAkustische Nachberechnung von Ventilatoren - Hauptarbeitspaket C: Aeroakustisches Validierungsexperiment. FLT Nr.: L236, Final reportF60 001 B2012SiegenUniversity of Siegen, Institute of Fluid- and Thermodynamics[ HYPERLINK \l "_ENREF_44" \o "Zhu, 2012 #130" 44].
For the determination of mode orders, the phase shift between two transducers is required. Since only integer values of the mode order are valid, the results are rounded if necessary. Only errors in phase that are larger than half of the circumferential distance between two transducers would affect the results. The circumferential distance between two transducers is at least 72 for all cases. Since errors in the phase data are generally smaller than 5, the phase are not expected to have any effect on the results ADDIN EN.CITE Bendat1980404[46]4044046Bendat, J. S.Piersol, A. G.Engineering Applications of Correlation and Spectral Analysis1980New York, USAJohn Wiley & Sons[ HYPERLINK \l "_ENREF_46" \o "Bendat, 1980 #404" 46].
: Arrangement of pressure transducers on the casing inner wall
SHAPE \* MERGEFORMAT Figure C. SEQ Figure_C. \* ARABIC 1: Technical drawing of the arrangement of pressure transducers on the casing inner wall
Literatur
ADDIN EN.REFLIST [1] Blake, W. K., Mechanics of Flow-Induced Sound and Vibration, Volume II: Complex Flow-Structure Interactions. Vol. 17 in Applied Mathematics and Mechanics, Academic Press, Inc., Orlando (FL), USA, 1986.
[2] Lighthill, M. J., On Sound Generated Aerodynamically I. General Theory. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 211, No. 1107, pp. 564-587, 1952.
[3] Lighthill, M. J., On Sound Generated Aerodynamically II. Turbulence As a Source of Sound. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 222, No. 1148, pp. 1-32, 1954.
[4] Carolus, T., Zhu, T. and Sturm, M., A Low Pressure Axial Fan for Benchmarking Prediction Methods for Aerodynamic Performance and Sound. Noise Control Engineering Journal, 63, 6, 2015.
[5] Marcinowski, H., Einflu des Laufradspaltes und der Luftfhrung bei einem Khlgeblse axialer Bauart. Motortechnische Zeitschrift (MTZ), 14, 9, 259-262, 1953.
[6] Longhouse, R. E., Control of Tip-Vortex Noise of Axial Flow Fans by Rotating Shrouds. Journal of Sound and Vibration, 58, 201-214, 1978.
[7] Fukano, T., Takamatsu, Y. and Kodama, Y., The Effect of Tip Clearance on the Noise of Low Pressure Axial and Mixed Flow Fans. Journal of Sound and Vibration, 105, 2, 291-308, 1986.
.
.
.
[109] Hesselmann, N., Digitale Signalverarbeitung. 2nd Edition, Vogel Verlag, 1987.
In terms of the acoustic analogy coined by Lighthill, Curl and Ffowcs Williams and Hawkings ADDIN EN.CITE Lighthill1952398[2, 3]39839817Lighthill, M. J.On Sound Generated Aerodynamically I. General TheoryProceedings of the Royal Society of London. Series A, Mathematical and Physical SciencesProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciencespp. 564-587Vol. 211No. 11071952Lighthill195439939939917Lighthill, M. J.On Sound Generated Aerodynamically II. Turbulence As a Source of SoundProceedings of the Royal Society of London. Series A, Mathematical and Physical SciencesProceedings of the Royal Society of London. Series A, Mathematical and Physical Sciencespp. 1-32Vol. 222No. 11481954[ HYPERLINK \l "_ENREF_2" \o "Lighthill, 1952 #398" 2, HYPERLINK \l "_ENREF_3" \o "Lighthill, 1954 #399" 3], these sources are "dipole sources", i.e. fluctuating forces on solid boundaries which eventually radiate sound.
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Contents STYLEREF Sonderberschrift \l \* MERGEFORMAT PAGE VII
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STYLEREF Sonderberschrift \l \* MERGEFORMAT PAGE XI
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PAGE 4 STYLEREF "berschrift 1" \l \n \* MERGEFORMAT 1 STYLEREF "berschrift 1" \l \* MERGEFORMAT Einleitung
STYLEREF "berschrift 2" \l \n \* MERGEFORMAT 1.3 STYLEREF "berschrift 2" \l \* MERGEFORMAT Gliederung der Arbeit PAGE 3
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PAGE 36 STYLEREF "berschrift 1" \l \n \* MERGEFORMAT 7 STYLEREF "berschrift 1" \l \* MERGEFORMAT Summary und Conclusions
STYLEREF "berschrift 7" \l \n \* MERGEFORMAT Appendix A STYLEREF "berschrift 7" \l \* MERGEFORMAT : Experimental Uncertainty Analysis PAGE 125
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PAGE 14 STYLEREF "berschrift 7" \l \n \* MERGEFORMAT 0 STYLEREF "berschrift 7" \l \* MERGEFORMAT Fakulativer Anhang A: z.B. Fehleranalyse
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