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Turbocharger Aeroacoustics and Optimal Damping of Sound
Raimo Kabral [email protected]
Stockholm, Sweden 2017 The Marcus Wallenberg Laboratory for Sound and Vibration Research
Department of Aeronautical and Vehicle Engineering KTH Royal Institute of Technology
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framläggs till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 9:e juni 2017, kl 10:15 i sal E3, Osquars backe 14, Kungliga Tekniska Högskolan, Stockholm. Copyright: Raimo Kabral, 2017 TRITA-AVE 2017:36 ISSN 1651-7660 ISBN 978-91-7729-442-9
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Contents
List of publications .................................................................................................. 5
Abstract .................................................................................................................... 7
Sammanfattning ..................................................................................................... 8
Abbreviations and symbols .....................................................................................9
Introduction ........................................................................................................... 12
1 Centrifugal compressor aeroacoustics ............................................................ 18
Experiments ............................................................................................. 20
Reflection-free sound generation ........................................................... 22
1.2.1 Method ......................................................................................... 22
1.2.2 Results and discussion ................................................................. 24
Coupling between aerodynamic and acoustic fields .............................. 30
1.3.1 Method ......................................................................................... 30
1.3.2 Results and discussion .................................................................. 31
Validation of on-engine measurements ................................................. 34
1.4.1 Experimental setup ...................................................................... 34
1.4.2 Results and discussion ................................................................. 34
2 Acoustic characterization of twin-scroll turbine ............................................. 37
Method ...................................................................................................... 37
Experimental setup ................................................................................. 38
2.2.1 Peripheral systems ....................................................................... 38
2.2.2 Test rig for twin-scroll turbines .................................................. 39
2.2.3 Operating conditions ................................................................... 43
Results and discussion ............................................................................ 44
3 Optimization of compact flow duct silencer ...................................................45
Finite element model ............................................................................... 47
Method ..................................................................................................... 49
Results and discussion ............................................................................. 51
4 “Exact” Cremer impedance model ...................................................................54
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Method ...................................................................................................... 56
Wave propagation analysis ...................................................................... 57
Finite element analysis ............................................................................ 59
Sound attenuation mechanisms in optimized design ............................ 61
Results and discussion ............................................................................. 61
Conclusions ............................................................................................................ 68
References .............................................................................................................. 71
Acknowledgements ................................................................................................ 77
Appendix ................................................................................................................ 79
Paper I .................................................................................................................... 81
Paper II .................................................................................................................. 111
Paper III ............................................................................................................... 125
Paper IV................................................................................................................ 135
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List of publications
The present doctoral dissertation is based on the following peer reviewed publications:
Paper I Kabral, R., and Åbom, M. Investigation of turbocharger compressor surge inception by means of an acoustic two-port model. Journal of Sound and Vibration, submitted on March 21st, 2017.
Paper II Kabral, R., El Nemr, Y., Ludwig, C., Mirlach, R., Koutsovasilis, P., Masrane, A., and Åbom, M. Experimental acoustic characterization of automotive twin-scroll turbine. Proceedings of 12th European Conference on Turbomachinery Fluid dynamics & Thermodynamics ETC12, Stockholm, Sweden, April 3-7, 2017.
Paper III Kabral, R., Du, L., Åbom, M and Knutsson, M. A compact silencer for the control of compressor noise. SAE International Journal of Engines, 2014, 7(3), 1572-1578, doi:10.4271/2014-01-2060.
Paper IV Kabral, R., Du, L., and Åbom, M. Optimum sound attenuation in flow ducts based on the “exact” Cremer impedance. Acta Acustica united with Acustica, 2016, 102(5), 851-860, doi:10.3813/AAA.918999.
Copies of these articles are included in the Appendix.
Division of work between the authors:
Paper I Kabral planned and performed the experimental investigation based on an idea proposed by Åbom. Kabral also performed all the analyses and wrote the paper under the supervision of Åbom.
Paper II Kabral planned and performed the experimental investigation based on a proposal by El Nemr (V2C2), Ludwig (BMW Group), Mirlach (BMW Group), Koutsovasilis (BorgWarner Inc.) and Masrane (BorgWarner Inc.). Kabral also performed all the analyses and wrote the paper under the supervision of Åbom.
Paper III Kabral planned and performed the experimental and numerical investigation based on a proposal by Åbom and Knutsson (Volvo Car Corporation). Kabral also performed all the analyses and wrote the paper under the supervision of Åbom and Knutsson.
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Paper IV Kabral planned and performed the numerical investigation based on a proposal by Åbom. Kabral also performed all the analyses and wrote the paper under the supervision of Åbom.
Other related publications
1. Kabral, R., Rämmal, H., and Lavrentjev, J. Acoustic studies of micro-perforates for small engine silencers. – SAE Technical Paper Series, 2012, Paper no. 2012-32-0107, doi:10.4271/2012-32-0107.
2. Kabral, R., Rämmal, H., and Åbom, M. Acoustical Methods for Investigating Turbocharger Flow Instabilities. – SAE Technical Paper Series, 2013, Paper no. 2013-01-1879, doi:10.4271/2013-01-1879.
3. Kabral, R., Auriemma, F., Knutsson, M., Åbom, M. A new type of compact silencer for high frequency noise. – Online proceedings of the 9th International DAAAM Baltic Conference, 2014.
4. Kabral, R., Åbom, M., Ongoing acoustics research in the KTH-Competence Centre for Gas Exchange. – Proceedings of the Baltic-Nordic Acoustic Meeting 2014 BNAM 2014, 2-4th June 2014, Estonia.
5. Kabral, R., Bodén, H., Elnady, T. Determination of Liner Impedance under High Temperature and Grazing Flow Conditions. – Proceedings of the 20th AIAA/CEAS Aeroacoustics Conference, 16-20 June 2014, United States, Paper no. AIAA 2014-2956, doi: 10.2514/6.2014-2956.
6. Kabral, R., Åbom, M. Investigation of flow-acoustic interaction in automotive turbocharger. – Online Proceedings of the ISMA 2014, 15-17 September 2014, Belgium, ISBN 9789073802919.
7. Åbom, M., Kabral, R. Turbocharger noise - generation and control. – Invited key note lecture of the SAE Brasil International Noise and Vibration Colloquium 2014, 4-5 September 2014, Brazil, SAE Technical Paper Series, Paper no. 2014-10-25, doi:10.4271/2014-36-0802.
8. Bodén, H., Kabral, R. The Effect of High Temperatures and Grazing Flow on the Acoustic Properties of Liners. – Proceedings of the Euronoise 2015, ISSN 2226-514, 2015.
9. Kabral, R., Åbom, M. A compact efficient silencer based on the Cremer impedance. – Proceedings of the Baltic-Nordic Acoustic Meeting BNAM 2016, 20-22 June 2016, Sweden.
10. Kabral, R., Du, L., Åbom, M., Knutsson, M. Optimization of compact non-fibrous silencer for the control of compressor noise. – SAE Technical paper Series, 2016, Paper no. 2016-01-1818, doi:10.4271/ 2016-01-1818, 2016.
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Abstract
The use of centrifugal compressors has increased tremendously in the last decade, and they are now a key component in most modern IC engines. However, their useful operating range is restricted by the compression system surge phenomenon. The focus in previous investigations of surge inception has mainly been on the aerodynamic field while neglecting the acoustic field. In the present work, a new method based on the full acoustic 2-port model is proposed for investigation of centrifugal compressor stall and surge inception. Essentially, the compressor is acoustically decoupled from the compression system, hence enabling the determination of sound generation and the quantification of internal aeroacoustic coupling effects, both independently of the connected pipe system. These frequency-dependent quantities indicate whether the compressor is prone to self-sustained oscillations in the case of positive feedback when installed in a system. The method is demonstrated on the experimentally determined 2-port data of an automotive turbocharger centrifugal compressor under a variety of realistic operating conditions.
The experimental determination of automotive twin-scroll turbine acoustic performance is also considered. The unique test rig for automotive turbocharger acoustics at KTH CCGEx laboratory is further developed to enable testing of modern twin-scroll turbines under controlled laboratory conditions. It is shown how the passive acoustic properties of such turbines can be accurately characterized by means of an acoustic 3-port formulation. Governing equations along with the new test rig design are presented and discussed in detail. Furthermore, complementary results from the first experimental determination of twin-scroll turbine acoustic 3-port data are presented.
In the third part, a novel type of compact dissipative silencer developed to handle compressor noise problems is described and optimized. The silencer is based on a combination of a micro-perforated tube backed by a locally reacting cavity. The combined impedance of micro-perforate and cavity is chosen to match the theoretical optimum known as the Cremer impedance (Acustica 3, 1953) at the mid-frequency in the frequency range of interest. Due to the high damping achieved at the Cremer optimum (hundreds of dB/m), it is possible to create a compact silencer with a significant damping (say > 30 dB) in a range larger than an octave.
The Cremer impedance is the locally reacting boundary condition that maximizes the attenuation of a certain mode in a uniform wave guide taken as the lowest order mode or “plane” wave. The fourth part of the work analyzes the “exact” Cremer impedance model, i.e., the high frequency asymptotic results proposed by Tester for uniform mean flow (JSV 28(2), 1973) are extended to lower frequencies. It is shown that significantly larger attenuation per unit length can be obtained using the “exact” instead of the original asymptotic solution.
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Sammanfattning
Användning av centrifugalkompressorer har ökat kraftigt under de senaste tio åren då de introducerats som en nyckelkomponent i moderna förbränningsmotorer. Dock begränsas ett effektivt utnyttjande av problem med pulserande strömning vid låga massflöden så kallad ”surge”. Tidigare undersökningar av detta fenomen har fokuserat på de aerodynamiska effekterna och försummat det akustiska fältet. I detta arbete föreslås en ny metod som bygger på en fullständig akustisk 2-ports modell för att studera ”surge” hos centrifugalkompressorer. I princip innebär metoden att kompressorn blir frikopplade från det övriga drivsystemet, därav möjliggörs bestämning av reflexfri ljudalstring och kvantifiering av aeroakustiska kopplingseffekter, båda oberoende av det anslutna rörsystemet. Dessa frekvensberoende kvantiteter kan nyttjas för att analysera om kompressorn är benägen att hamna i ett tillstånd av självsvängning d.v.s ”surge”. Metoden har demonstrerats på experimentella 2-ports data för en personbils kompressor under en mängd realistiska driftsförhållanden.
Vidare har en ny metod utvecklats för att karaktärisera de passiva egenskaperna (reflektion/transmission) för så kallade ”twin-scroll” turbiner. I planvågsområdet kan denna typ av maskin ses som en 3-port. Den unika akustiska test riggen för att studera turboladdare hos KTH-CCGEx har vidareutvecklats för att klara dessa mätningar. Teori och detaljer kring det experimentella förfarandet samt data från mätningar på en twin-scroll turbin presenteras.
I den tredje delen, studeras en ny typ av kompakt dissipativ ljuddämpare som utvecklats för att hantera kompressorbuller. Ljuddämparen är baserad på en kombination av ett micro-perforerat rör som backas upp av en lokalt reagerande hålighet. Den kombinerade impedansen av rör och hålighet är vald att matcha den teoretiska optimala Cremer impedansen (Acustica 3, 1953) i mitten av frekvensbandet av intresse. På grund av att mycket hög dämpning uppnås vid den optimala Cremer impedansen (hundratals dB/m), är det lätt att skapa en kompakt ljuddämpare med en betydande dämpning (säg > 30 dB) i ett område större än en oktav.
Cremer impedansen är det lokalt reagerande randvillkor som maximerar dämpningen av den lägsta moden (”plan vågen”) i en vågledare. Den fjärde delen av arbetet analyserar en "exakt" Cremer impedans modell, d.v.s den högfrekventa asymptotiska modell som föreslås av Tester för system med flöde (JSV 28(2), 1973) utvidgas till lägre frekvenser. Av resultaten framgår att väsentligt högre dämpning kan erhållas om den korrekta exakta lösningen nyttjas istället för den asymptotiska.
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Abbreviations and symbols
BPF – Blade Passing Frequency
CCGEx – The Competence Center for Gas Exchange
FEM – Finite element method
FEA – Finite element analysis
IC – Internal combustion
JSV – Journal of Sound and Vibration
MGS – Minimum globally-stable
Mic. – Microphone
MPOW – Maximum potential acoustic power
MPP – Micro-perforated panel
MWL – The Marcus Wallenberg Laboratories for Sound and Vibration
Research
OP – Operating point
RO – Rotating order
RPM – Rounds per minute
S-matrix – Acoustic scattering matrix
SPL – Sound pressure level
TL – Transmission loss
WG – Waste gate
𝐴 – Area of the flow channel cross-section, m2
𝐷 – Diameter of the flow channel, m
𝑬 – Two by two unitary matrix
𝐺 – One sided cross-spectrum
𝑮𝐒 – Acoustic source cross-spectrum matrix, Pa2
𝐻m(n)
– Hankel function of n:th kind and m:th order
𝐿p – Sound pressure level, dB
𝑀x – Mean flow Mach number
𝑀g – The grazing flow Mach number of the micro-perforate
𝑃 – Acoustic power, W
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𝑄m – Acoustic monopole source, s-2
𝑅 – Acoustic reflection coefficient
𝑅e – The radius of the expansion chamber, m
𝑅s – The surface resistance of the micro-perforated panel, Pa∙s∙m-1
𝑹 – The reflection matrix of test rig terminations
𝑺 – Acoustic scattering matrix
𝑺𝐏 – Acoustic power scattering matrix
𝑇 – Acoustic transmission coefficient
𝑻 – Transformation matrix of acoustic waves
Z – Normalized acoustic impedance
𝑎 – The cross-section height of the rectangular channel, m
𝑐0 – The speed of sound, m∙s-1
𝑑 – The slit width of the micro-perforated panel, m
𝑓 – Frequency, s-1
𝑓01C – The lower cut-off frequency limit of the first radial mode in circular
channels, Hz
𝑖 – Unit imaginary number (𝑖2 = −1)
𝑘 – Wavenumber, m-1
𝑘s – The share wave number of the aperture
𝑙𝑟 – The length of the flow channel, m
𝒏𝐫 – The normal unit vector of the flow channel surface
𝑝 – Acoustic pressure, Pa
𝒑𝐬 – Acoustic source strength vector, Pa
𝑞d – Acoustic dipole source, N∙m-3
𝑟 – The radius of the flow channel, m
𝑟s – The normalized acoustic resistance of slit type micro-perforated panel
𝑡 – The time, s
𝑡h – The thickness of the micro-perforated panel, m
𝑥 – Axial co-ordinate, m
𝑥s – The normalized acoustic reactance of slit type micro-perforated panel
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𝛷 – Velocity potential, m2∙s-1
𝛽 – The grazing flow coefficient of the micro-perforated panel
𝛾S – Coherence between source components
𝜆 – Eigenvalue
𝜇 – Dynamic viscosity, Pa∙s
𝜈 – Kinematic viscosity, m2∙s-1
𝜌 – Density of the medium, kg∙m-3
𝜎 – The perforation ratio of the micro-perforated panel
𝜔 – Angular frequency, s-1
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Introduction
In modern internal combustion (IC) engine design, a large part is determined by the European Commission emission limits known as Euro 6 [1], and customer demand for continuously reduced fuel consumption while still preserving the power output. The achievement of these contradictory goals requires conceptual changes in the classical IC engine design. Therefore, today the concept of engine downsizing or rightsizing is a well-adapted industry standard [2, 3, 4, 5, 6, 7]. The essence of the concept relies on reducing the IC engine volumetric capacity while increasing the charge air pressure [8]. As a consequence, indicated fuel conversion efficiency is improved by increasing the indicated mean pressure. Although the same result can also be achieved by raising the volumetric compression ratio, it is not a preferable choice because of the higher combustion temperature, and thus increased NOx emissions.
The idea of implementing the unexploited enthalpy of hot exhaust gases for driving the inlet charger dates from early 20th century aviation where the decrease of air density at high altitudes resulted in loss of the IC engine power output. Devices based on such a principle are referred to as turbochargers (Figure 1) and generally they consist of a turbine coupled to a centrifugal compressor. While the turbine transforms recovered enthalpy into mechanical energy, the centrifugal compressor utilizes this energy to provide high pressure charge air. Nowadays in the IC engine industry, turbochargers are used for efficiency reasons, and thus they carry a key role in the engine downsizing concept [9, 10].
Figure 1. A photo of a modern automotive turbocharger cutaway [11].
Shaft
Turbine outlet
Turbine inlet
Compressor inlet
Compressor wheel
Turbine wheel
Compressor outlet
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A large majority of automotive IC engines currently in production are based on the downsizing concept and are equipped with turbochargers. Therefore, the number of turbochargers manufactured has increased tremendously during recent years. Nevertheless, the problem of the compressor having a mass flux range that is narrower than the engine demand still remained [10, 12, 13]. In case of substantially downsized engines, the operation without high pressure charge results in significant and unaccepted deficiency in power output. Moreover, the future perspective is ultra-downsized engines [14] where the IC engine capacity is reduced even further, and thus the charge pressure must be even higher – three stages of turbochargers are planned.
The operating range of the centrifugal compressor can be visualized by the 2D graph referred to as a compressor map (Figure 2).
Figure 2. Compressor map visualizing the designed operating range of the
centrifugal compressor.
46
7
9
8
5
Corrected mass flow [kg s-1]
Pre
ssu
re r
atio
peak efficiency line
surge line
14
In the graph (Figure 2), the horizontal axis denotes mass flow (corrected according to the inlet temperature and pressure), while the vertical axis represents the ratio of total outlet pressure over the total inlet pressure. Consequently, the designed operating range is given as an “island” in the compressor map. Contours within the island indicate different efficiency levels of the compressor and solid lines across the map correspond to the constant rotational frequency of the rotor (Figure 1). In addition, the island of the designed operating range is bounded by a so-called “surge line” at the left-hand side and a “choke line” at the right.
In the designed operating range the compressor can provide continuous pressurized air delivery with acceptable efficiency. Exceeding the mass flow range, bounded by the choke line, the efficiency of the machine drops. In contrast, the whole system is driven into a destructive unstable state as the flow is reduced beyond the barrier posed by the surge line. Therefore, current industrial practice is to add preventive safety margins on the compressor map which can be as large as 20%. This unexploited part of the mass flow range could be efficiently implemented if the inception of the surge phenomena could be precisely predicted or if appropriate counteractions could be taken.
The maximum mass flow of the centrifugal compressor is determined by a choked flow, while the minimum stable mass flow is bounded by the inception of the surge phenomenon. When the back pressure of the coupled system becomes too high, the compressor cannot maintain continuous discharge pressure and a local flow reversal occurs. This leads to global self-sustained large amplitude pressure and mass flow oscillations across the entire compression system, making surge a system phenomenon [15, 16, 17]. The centrifugal compressor surge pathology was recognized directly after it was invented [see e.g. 18], and the main focus in the surge investigation has been on the inception process and root cause of surge occurrence. However, as many different static and dynamic stall scenarios can occur and lead to different types of instable operation, the investigation has proved to be challenging.
In 1976 Greitzer proposed a lumped parameter model for investigation of axial compression system instability [19]. This model was validated on centrifugal compressors by Hansen in 1981 [20]. From this model, it is apparent that the low mass flow instability in the compression system should occur at the Helmholtz frequency of the system. Global pressure and mass flow oscillations approximately corresponding to the Helmholtz frequency of the compression system have also been observed in a number of different experiments (See e.g. [21, 22, 23]). Moreover, the amplitude of the oscillations appears to be of progressive type with respect to the mass flow reduction, and can grow to relatively large amplitudes, eventually causing the blow-down of a coupled high pressure discharge volume [21]. However, it has been observed that the oscillations remain relatively small, even in the case of zero mass flow, if the coupled system is sufficiently small [17, 21], thus potentially extending the useful
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operating range. Based on the previous observation, it has been suggested that the stabilization of the system could be caused by higher damping within the system [23], however, it has not been shown or investigated further. Moreover, as the compressor must be coupled to the system to control its operating conditions, i.e. discharge pressure, the occurrence of surge within the system prevents the separation of damping and excitation.
Flow field changes inside the compressor under reduced mass flow conditions have also been studied in relation to surge inception. If the mass flow is continuously reduced, the compressor casing fixed stalled flow pattern first occurs at the inducer (compressor impeller inlet) annulus [21, 24]. By further reducing the mass flow, rotating stalled flow patterns are triggered [21, 24, 25]. In this case, one or more stalled flow cells propagate along the impeller annulus, and thus the resulting frequency of pressure oscillations is a fraction of the impeller rotational frequency. A rotating stall can occur at the inducer, in the impeller passages, or at the diffuser with corresponding characteristic frequency ranges [25]. Although associated low frequency elevated noise levels are observed in a number of works [17, 21, 22, 23, 26], the acoustic field has been neglected in the surge inception investigation while the focus has been on the aerodynamic aspects.
In general, the elevated low frequency noise level at low mass flows is a well-recognized problem of centrifugal compressors. However, an accurate determination of the sound generation of the compressor is difficult as it has to be coupled to a system that enables the control of the discharge pressure (throttle valve or IC engine). Such peripheral systems have a significant impact on the resulting sound field measured in the compressor inlet and outlet flow channels. Nevertheless, some measurement techniques with different levels of simplifications have been proposed in the literature [23, 26, 27, 28, 29, 30]. Although these methods can be effectively used in comparative measurements performed under different circumstances, they do not provide the “clean” source data necessary for surge inception investigation.
It is believed herein that not only is surge a system phenomenon, but also the initiation of the surge is related to the dynamics of the whole compression system, possibly involving acoustical properties of the compressor and the coupled system. Although the surge has been studied by many authors and institutions, the role of the acoustic field in the surge initiation has not been investigated. Therefore, it is of importance to investigate the in-duct acoustic field of the centrifugal compressor in detail.
In modern high efficient IC engine designs, twin-scroll turbines (Figure 1) are being implemented more frequently. The housing of the twin-scroll turbine incorporates two separated flow channels guiding exhaust gas to two different peripheral parts of the radial in-flow impeller. Such a design allows the separation of interfering exhaust channels of sequentially igniting cylinders,
16
resulting in higher turbine efficiency and better overall fuel conversion efficiency via improved scavenging effects. Moreover, because of geometrical differences between the two scrolls, designed for different flow conditions, the transient response and maximum flow capacity are both significantly improved.
As an essential element of the IC engine exhaust system, the presence of a turbine affects both the aerodynamic as well as the acoustic fields. While a number of aerodynamic field studies are reported on the twin-scroll type turbine, and a few studies have considered single-scroll turbine acoustics [31, 32, 33], the acoustic properties of a twin-scroll turbine have not been investigated. It is therefore of interest to extend the previous work on acoustic characterization of single-scroll turbines to twin-scroll turbines. One property of interest is the scattering of incident pressure pulses, which determines the effect the unit has on the exhaust system acoustics. Moreover, such acoustic data also contains information about the small amplitude (“linear”) dynamic response of the turbine to a pulsating flow that can provide useful information for optimizing the scavenging effects or exhaust pulse energy utilization in the turbine.
The implementation of a turbocharger on the IC engine also poses the problem of the high level of compressor noise reported by the passenger car as well as truck manufacturers. Noise control techniques currently applied to IC engine inlet systems are mainly based on the principle of the Helmholtz resonator, i.e. the generated sound is reflected back to the compressor. In this solution, the dissipation of the sound depends on the source absorbing ability. Moreover, the resonators are relatively sensitive to the varying flow rates and their location in the system. In addition, the attenuation provided is often of narrow band type which makes the design complicated when noise sources of varying frequency are considered. Therefore, substituting reflective resonators with dissipative noise control solutions could provide an advantage in terms of robustness and simplicity in the design process.
Traditionally, dissipative flow duct silencers are based on fibrous materials. Nevertheless, several problems can occur when materials of this type are integrated in the gas exchange system. For instance, the fibers can break and pollute the environment or cause failure of the engine and other essential components. Therefore, it is of interest to produce acoustic energy absorption by utilizing other innovative materials. Acoustic energy dissipation can be produced, for instance, by means of small apertures whose dimensions are in the order of the acoustic boundary layer [34]. Such innovative noise control materials are referred to as micro-perforated panels (MPP) and recent development of these materials has led to their mass-production. However, in order to effectively utilize the MPP losses, design has to be fine-tuned to the acoustic field, making an optimization strategy essential.
17
Objectives of the study
In this study, the main objectives are:
to carry out detailed investigations of the acoustic fields in the inlet and outlet channels of centrifugal compressors to investigate the initiation of compressor surge;
to develop the first 3-port characterization method for twin-scroll turbines;
to develop a new type of compact optimal dissipative silencer based on micro-perforated elements; and
to extend the asymptotic Cremer optimal impedance model (JSV 28(2) 1973) to the low frequency range by eliminating the assumption of well cut-on modes.
The work done to achieve these four objectives is treated in the following four chapters as well as in the appended Papers I…IV.
18
1 Centrifugal compressor aeroacoustics
In general, the accurate and detailed investigation of acoustic fields in flow channels can be performed by implementing well established methods for duct networks. However, because of the experimental limitations, such methods are limited to the zeroth channel mode frequency range. In this case, the acoustic pressure over the cross-section of the flow channel is nearly constant i.e. acoustic waves are planar. In the case of circular channels, the frequency of the first non-planar propagation is determined by the following relation [35]:
𝑓01𝑐 =
1.841𝑐0𝜋𝐷
√1 − |𝑀x|2 . (1.1)
Below that frequency (Eq. (1.1)), the acoustic wave propagation in the compressor inlet and outlet channels can conveniently be described by the harmonic solution of the homogeneous linearized wave equation for one-dimensional waves:
𝑝(𝑥) = �̂�+𝑒𝑖(𝜔𝑡−𝑘+𝑥) + �̂�−𝑒
𝑖(𝜔𝑡+𝑘−𝑥) , (1.2)
where
𝑘± =𝜔
𝑐0(1 ± 𝑀x) , (1.3)
and the 𝑥-axis is assumed to point out from the compressor inlet and outlet. As an example, the acoustic field is sketched in the centrifugal compressor inlet and outlet channels in Figure 1.1.
Figure 1.1. The simplified sketch of the experimental setup for compressor
aeroacoustic characterization, where mass flux refers to the mean flow.
Mass flux p a+s p b+
s Mass flux
p a+
p a–
p b–
p b+
Loudsp. a Loudsp. bMic. 1 Mic. 2 Mic. 3 Mic. 4
Ra 0 Rb 0
x3 x4 xx1 x2x
Inlet (a) Outlet (b)
19
In order to perform the wave decomposition of the planar acoustic field in a flow channel (Figure 1.1), the acoustic pressure has to be known in at least two axial positions. In addition, the information regarding the wave propagation between these two positions is essential. If such data is available, the complex opposite propagating acoustic pressure wave amplitudes can be found by means of the well-known two-microphone technique (see e.g. [36] or [37]):
[𝑝1𝑝2] = [𝑒
𝑖𝑘−𝑥1 𝑒−𝑖𝑘+𝑥1
𝑒𝑖𝑘−𝑥2 𝑒−𝑖𝑘+𝑥2] [𝑝−𝑝+] . (1.4)
Note that time dependence of exp(𝑖𝜔𝑡) is assumed in Eq. (1.4) and is also assumed through-out the present work. Further information about enhancing the robustness of the wave decomposition can be found in Paper I and Paper II.
By assuming time-invariant system, the compressor acoustic characterization can be given by a 2-port model [38] in the scattering-matrix (S-matrix) [37, 39] and source-strength-vector [40] form:
[𝑝a+𝑝b+
] = [𝑅aa 𝑇ba𝑇ab 𝑅bb
]⏟
𝑺
[𝑝a−𝑝b−
] + [𝑝a+s
𝑝b+s ]
⏟ 𝒑s
. (1.5)
The assumption of linearity implies a limit for the wave amplitudes typically stated as 1% of the static pressure. Assuming air at standard conditions, this implies pressure amplitudes of max 1000 Pa or 140 dB rel 20 µPa.
In general, the characterization of passive properties, i.e. determination of the S-matrix, in the presence of a non-zero source-strength-vector, requires uncorrelated external excitation of sufficient amplitude to dominate the acoustic field. By implementing a “clean” drive signal of external excitation in the well-known mathematical estimator of frequency response for the pressure [41], uncorrelated flow noise [37] and the source contribution [40] can be suppressed:
[𝑝a+𝑝b+
] = [𝑅aa 𝑇ba𝑇ab 𝑅bb
]⏟
𝑺
[𝑝a−𝑝b−
] . (1.6)
The S-matrix of a compressor (or single-scroll turbine) (Eq. (1.6)) consists of four unknown complex elements. However, performing a wave decomposition in both channels of the compressor (Figure 1.1) gives only two equations. Therefore, at least two test cases are required to determine the S-matrix:
[𝑝a+I 𝑝a+
II
𝑝b+I 𝑝b+
II ] = [𝑅aa 𝑇ba𝑇ab 𝑅bb
]⏟
𝑺
[𝑝a−I 𝑝a−
II
𝑝b−I 𝑝b−
II ] . (1.7)
20
Once the propagating acoustic wave amplitudes of the two test cases are available, the S-matrix can be found via a matrix inversion operation implying the linear independency condition of the cases:
det [𝑝a−I 𝑝a−
II
𝑝b−I 𝑝b−
II ] ≠ 0 . (1.8)
The overview of different methods for creating such linearly independent acoustic fields is given in Ref. [38]. In the present work, the two source-location method [42] is considered.
The first experimental determination of the acoustic S-matrix, i.e. passive acoustic performance, of a turbocharger centrifugal compressor was successfully performed on the unique test rig at the Competence Center for Gas Exchange (CCGEx) laboratory by Tiikoja et al. in 2011 [28].
Experiments The experimental measurement campaign is carried out at CCGEx laboratory of the KTH Royal Institute of Technology [43]. The unique test rig for turbocharger acoustic characterization was first established in 2008 [44] and has being continuously developed since then. Photos of the current test rig, used in the experimental investigation herein, are presented in Figure 1.2, and detailed information regarding equipment and setup can be found in Paper I.
Figure 1.2. Photos of the test rig in the facility for turbocharger acoustic
measurements at CCGEx (www.ccgex.kth.se).
In the rig, turbochargers are not powered by IC engine exhaust gas; instead, investigations are carried out under idealized and controlled laboratory
21
conditions. The turbochargers are powered by means of a heated and compressed airflow to the turbine, and the realistic operating point of the compressor (See Figure 2) can be set by means of a throttle valve at the compressor outlet port. When a desired operating point (OP) is set and stabilized, the in-duct acoustic measurements are performed while maintaining the previously set OP.
The experiments herein are performed on a typical centrifugal compressor of a passenger car turbocharger. The compressor features an open-type impeller with splitter blades, vaneless diffuser, and external by-pass valve design, i.e. no by-pass channel in the compressor housing. Compressor design specifications are listed in Table 1.1 and corresponding photos are presented in Figure 1.3.
Table 1.1. Compressor design specifications.
Compressor housing (Scroll) inlet diameter, mm 44
Compressor housing (Scroll) outlet diameter, mm 42
Impeller inlet (inducer) diameter, mm 38.6
Impeller outlet (exducer) diameter, mm 52
Number of impeller blades 6 + 6
Figure 1.3. Photo of the turbocharger that is used in the experiments (Paper I)
with additional photos of its disassembled compressor housing and impeller.
In the experimental measurement campaign, the in-duct acoustic pressure data have been measured at six transducer positions along the compressor
22
contour while the external excitation has been provided by means of custom-designed loudspeakers at both branches. In addition, the acoustic pressure data have also been measured in the absence of external excitation. (Further details regarding measurement equipment and location can be found in Paper I.)
Reflection-free sound generation The peripheral components of the compression system, e.g., a throttle valve or IC engine inlet valves, cannot be considered as reflection-free terminations (�̂�− = 0 in the Eq. (1.2) and Figure 1.1) as reflections from flow channel discontinuities are highly significant in the plane wave frequency range. Therefore, the generated sound field, in the compressor inlet and outlet channels, is compression-system-dependent. In order to accurately determine the sound generation of the compressor, the passive properties of the entire system, including the compressor, have to be known. However, the measurement of passive properties of the compression system requires relatively strong external excitation, and therefore techniques with different levels of simplifications have commonly been used [See e.g. 23, 26, 27, 28, 29, 30]. Although such methods can provide the benefit of a simpler experimental setup, the assumption of reflection-free terminations is implicitly applied as a consequence. In general, such an assumption is invalid, especially in the low frequency plane wave range, and can lead to a significant error. In the present work, this assumption is eliminated by implementing a complete acoustic 2-port model (Eq. (1.5)) which acoustically decouples the compressor from the compressor system.
1.2.1 Method
The problem of determining the accurate aeroacoustic source data of ducted fans is not new. As early as 1971, Cremer suggested treating such devices as 2-port sources [45]. This was followed by the development of experimental methods by Terao et al. [46] and Lavrentjev et al. [40] in the 1990s. Although investigated fans in these works were mainly axial and of low-pressure type, the same methods will be adapted to the centrifugal compressor herein.
In the full 2-port formulation (Eq. (1.5)), the reflection-free conditions are assumed at the test-rig terminations. Since this is rarely the case, the terminations have to be characterized and accounted for. In order to describe the acoustic effects of test-rig terminations, the acoustic 1-port model is a convenient choice. In addition, by assuming passive behavior i.e. no additional sound generation behind test-rig terminations (Figure 1.1), the reflection coefficients
𝑅a =𝑝a−II
𝑝a+II and 𝑅b =
𝑝b−I
𝑝b+I . (1.9)
are completely adequate for the characterization.
23
Although the reflection coefficients (Eq. (1.9)) can readily be obtained from previously determined complex pressure wave amplitudes, the approach is limited to the two source-location measurement technique [42]. Because of the assumption of passive terminations, the external excitation must not be provided in respective branch while characterizing the termination (Figure 1.1). This requirement is fulfilled if at least two linearly independent test cases, necessary to compute the acoustic S-matrix (Eq. (1.7)), are realized by providing the external excitation sequentially in both branches.
After determining the passive properties of the test rig, the second acoustic pressure measurement has to be conducted in the absence of external excitation. By utilizing this pressure data and known passive properties of the test rig, the reflection-free source strength vector can be extracted from the overall sound field [40]:
𝒑s = (𝑬 − 𝑺𝑹)(𝑬 + 𝑹)−1𝒑 , (1.10)
where
𝑹 = [𝑅a 00 𝑅b
] , (1.11)
and 𝑬 is a 2 x 2 identity matrix. Note that the passive properties are determined in the reference cross-section of the flow channel, i.e. 𝑥 = 0 (See Figure 1.1), while the total sound field is measured at the microphone locations. Therefore, the passive properties are transformed from the reference cross-section to the corresponding microphone locations by means of transformation matrices:
𝑺x = 𝑻+𝑺𝑻−−1 and 𝑹x = 𝑻+
−1𝑹𝑻− , (1.12)
where
𝑻−(𝒙) = [𝑒𝑖𝑘a−𝑥a 00 𝑒𝑖𝑘b−𝑥b
] and 𝑻+(𝒙) = [𝑒−𝑖𝑘a+𝑥a 00 𝑒−𝑖𝑘b+𝑥b
] . (1.13)
Furthermore, the determined source strength vector can be transformed back to the original reference cross-section (𝑥 = 0) by implementing the transformation matrix of the positive propagation direction. This yields the expression of the source-strength-vector in the following form:
𝒑s = 𝑻+−1(𝒙)(𝑬 − 𝑺x𝑹x)(𝑬 + 𝑹x)
−1𝒑x . (1.14)
Acoustic pressure measurements performed without a reference signal can be contaminated by aerodynamic related pressure (“turbulence”) fluctuations under the microphone membrane. To reduce this error, one must avoid using auto-spectra and instead use cross-spectra. This will reduce errors from local aerodynamic pressures as long as the microphones at different locations of the flow channel are separated more than the correlation length for such
24
disturbances. By denoting terms associated with passive properties in Eq. (1.14) as:
𝑪x = 𝑻+−1(𝒙)(𝑬 − 𝑺x𝑹x)(𝑬 + 𝑹x)
−1 , (1.15)
the reflection-free source cross-spectrum matrix, where uncorrelated pressure fluctuations between different microphone locations are suppressed, can be written by means of directly measurable quantities [40]:
𝑮s = 𝒑s(𝒑s)† = 𝑪𝐱𝟏,𝟒 [𝐺x2x1 𝐺x3x1𝐺x2x4 𝐺x3x4
] (𝑪𝐱𝟐,𝟑)† , (1.16)
where 𝑥1…𝑥4 denoting the microphone positions (𝑥 co-ordinate in the Figure 1.1), and 𝐺xx are directly measurable cross-spectra between corresponding positions. Formally, the source cross-spectrum matrix is Hermitian, which is inconsistent with the estimate in Eq. (1.16). The Hermitian source cross-spectrum matrix estimate is obtained by combining the original estimate with its Hermitian transpose as:
𝑮s =𝑮s + (𝑮s)†
2 . (1.17)
Single-sided auto-spectra of reflection-free sound generation are in the main diagonal of the source cross-spectrum matrix while the cross-diagonal contains the cross-spectra between inlet and outlet channels with included phase information. This enables the computation of coherence between source-strength-vector components:
𝛾s =𝐺x2x4s 𝐺x3x1
s
𝐺x2x1s 𝐺x3x4
s . (1.18)
A coherence value close to unity can be interpreted as one compact source region while values close to zero as a distribution of uncorrelated sources. Finally, the reflection-free sound pressure level (SPL) spectra are computed by using corresponding auto-spectra in the main diagonal of the source cross-spectrum matrix as:
𝐿p = 10 log10 (𝐺xxs
𝑝ref2 ) , (1.19)
where 𝑝ref = 2 ∙ 10−5[Pa] .
1.2.2 Results and discussion
The S-matrix of the compressor (Eq. (1.6)) together with reflection coefficients of terminations (Eq. (1.9)) completely characterize the passive linear frequency response of the compression system. The systematic investigation of passive performance coefficients is outside the scope of this work. Nevertheless,
25
the example of passive results for the OP7 (Figure 2) is presented in Figure 1.4 in order to illustrate the significance of the passive properties in the determination of compressor sound generation.
Figure 1.4. The passive properties of the compressor – left graph, and test rig
terminations – right graph, measured in the OP7 located on the surge line in
the compressor map (Figure 2). The colors of the curves in the left graph are:
blue – (𝑅aa) the reflection coefficient at the inlet port; red – (𝑇ab) the
transmission coefficient in downstream direction, black – (𝑅bb) the reflection
coefficient at the outlet port; and green – (𝑇ba) the transmission coefficient in
the upstream direction. The colors in the right graph refer to the test rig
termination reflection coefficient in downstream direction (𝑅b) – red, and in
upstream direction
(𝑅a) – blue.
The compression system, i.e. the test rig, in the present work is equipped with termination silencers incorporating absorptive fibrous material. Nevertheless, high levels of termination reflection coefficients up to 2000 Hz are evident in the right graph of Figure 1.4. Moreover, this behavior in combination with the large variation of the compressor coefficients in the left graph of Figure 1.4 can have a significant impact, i.e. can create strong standing wave fields in the compressor inlet and outlet channels. These observations show that if accurate (“reflection-free” i.e. system-independent) compressor sound generation is sought, the passive properties cannot be neglected.
The compressor-generated sound pressure spectra for different mass flow conditions at constant 100 000 RPM shaft rotational frequency is presented in
0.0
0.2
0.4
0.6
0.8
1.0
0 1000 2000 3000
Mag
nit
ud
e
Frequency [Hz]
Compressor
0.0
0.2
0.4
0.6
0.8
1.0
0 1000 2000 3000
Mag
nit
ud
e
Frequency [Hz]
Terminations𝑅aa𝑇ab
𝑇ba𝑅bb
𝑅b 𝑅a
26
Table 1.2. In general, the sound generation spectra at the peak efficiency operation in Table 1.2 (OP6: green), representing the smallest aerodynamic losses, consist of a broadband level and narrowband rotor synchronous harmonics with higher level at the compressor outlet. A mass flow increase (Table 1.2 – OP5: blue) causes an increased broadband level, more significantly at the compressor outlet, and the level of the first rotor harmonic is also increased. While a slowly varying broadband level can be associated with flow noise of a turbulent nature, the origin of the rotor harmonics is not clear. Although it has been suggested that such harmonics can be the consequence of rotor geometrical imperfections [23], the harmonics have also been observed in Large Eddy simulations [47] where they have been associated with an oscillating radial pressure gradient of the non-axisymmetric volute. The coherence between inlet and outlet spectra (Table 1.2), in general, shows high values at the rotor harmonics while the broadband level remains close to zero. The broadband low level is an expected result as it shows that the sound is generated by the distribution of uncorrelated sources which is a characteristic property of turbulent flow noise.
The reduction of mass flow from peak efficiency operation to the manufacturer-stated surge line (Table 1.2 – OP7: red) and beyond, to the limit of globally stable operation (Table 1.2 – OP8: black), causes a large (up to ~25 dB) broadband increase in the SPL spectra. This is expectable as the impeller blade angle of attack at the impeller inlet increases with the reduction of mass flow, thus generating more disturbed turbulent flow in the impeller region. In addition, a trend for a low-frequency steep increase below ~150 Hz and other new spectral features (“humps”) below ~1 kHz are evident in the case of the minimum globally stable (MGS) mass flow (Table 1.2 – OP8: black). These features are more distinguishable at the outlet and the frequencies of the “humps” correspond to ~0.5, ~0.42 and ~0.2 times the impeller rotational frequency or rotating order (RO). The coherence between inlet and outlet spectra at the ~0.5 of the RO shows a well pronounced peak, indicating a coherent source that is radiating sound in the upstream as well as downstream directions. In contrast, at ~0.42 of the RO, where the peak occurs in the outlet SPL spectra, the coherence remains low, thus indicating a source at the outlet (diffuser region) that is radiating in the downstream direction while not radiating efficiently through the turbulent impeller flow in the upstream direction. In addition, the coherence becomes close to unity in the frequency range below ~250 Hz, hence making the distinction of a potential coherence peak at ~0.2 of the RO difficult.
In Table 1.3, compressor-generated sound spectra of three different ROs are compared in the case of the MGS mass flow, i.e. OP4, OP8 and OP9 (See Figure 2). The spectral features at ~0.2 and ~0.5 of the RO occur systematically in the case of all the tested impeller rotational frequencies, and it appears that the progressive SPL of these features is linearly related to the impeller rotational frequency. Although the pressure measurements of the aerodynamic field inside
27
the compressor are not conducted herein, the spectral features can be associated with different flow instabilities according to their characteristic frequencies determined in previous work [25]. Therefore, the spectral features systematically occurring at ~0.2 and ~0.5 of the RO are believed to be associated with the diffuser rotating stall and progressive impeller rotating stall respectively. Furthermore, as the impeller rotating stall is related to the mid-chord separation of the impeller blade [48] potentially radiating sound to upstream as well as downstream directions, the coherent sound generation at ~0.5 of the RO (Table 1.3) is also a consistent result. In addition to rotating stall related sound generation, a progressive steep trend below ~150 Hz, increasing towards lower frequencies, systematically occurs in the SPL spectra (Table 1.3). The coherence in this frequency range approaches unity and the SPL already at 80 Hz is ~120 dB, corresponding to ~28 Pa of instantaneous pressure fluctuation. From the compression system perspective, this is seen as progressive broadband coherent acoustic excitation in the low frequency range potentially leading to a system resonance if the compressor receives a positive feedback from the coupled system. It is also worth mentioning here that it is common belief that the sound generated by the centrifugal compressor in the plane wave frequency range merely consists of broad-band flow noise, since the BPF is beyond the plane wave range. Based on results presented herein (Table 1.2 and Table 1.3), it is clear that low frequency rotor harmonics are present at normal operating conditions.
28
Table 1.2. Power spectral density and coherence spectra of the reflection-free sound generation at 100 000 RPM shaft rotational frequency (OPs: Figure 2).
At 100 000 RPM L
eg
en
d
5 (blue) : 0.113 kg∙s-1; 7 (red) : 0.039 kg∙s-1; 6 (green) : 0.076 kg∙s-1; 8 (black) : 0.029 kg∙s-
1;
Inle
t so
un
d g
en
era
tio
n
[dB
]
Ou
tlet
so
un
d g
en
era
tio
n
[dB
]
So
un
d s
ou
rce c
oh
ere
nc
e
8
5 7
6
5 7
6
8
5
7 6
8
29
Table 1.3. Power spectral density and coherence spectra of the reflection-free sound generation at minimum globally stable mass flow (OPs: Figure 2).
At minimum globally stable mass flow
Leg
en
d
4 (green) : 80 000 RPM;
8 (red) : 100 000 RPM;
11 (black) : 120 000 RPM
Inle
t so
un
d g
en
era
tio
n
[dB
]
Ou
tlet
so
un
d g
en
era
tio
n
[dB
]
So
un
d s
ou
rce c
oh
ere
nc
e
9
8
8
8 4
4
4 ~0.2 RO
~0.5 RO
~0.5 RO
9
9
30
Coupling between aerodynamic and acoustic fields If a stable flow field in the centrifugal compressor is considered, the coupling is expected to occur in the form of strong dissipation of incident acoustic waves in small-scale turbulence. However, when the mass flow is reduced beyond the surge line, the flow in different parts of the compressor will stall. While this abnormal compressor flow causes the occurrence of local flow instabilities, the global mass flow in the system still remains constant. Therefore, it is expected that these local flow instabilities can modulate incident acoustic waves resulting in the amplification of out-going waves.
1.3.1 Method
The acoustic 2-port with flow can be divided into two different regions: an outer region relatively far upstream and downstream, where acoustic and aerodynamic fields are “fully developed and uncoupled”, and an internal region with strong interaction between aerodynamic and acoustic fields [49]. The unstable flow, associated with flow separations and vorticity inside the compressor, is normally associated with the dissipation of sound but can also feed energy to an incident acoustic wave. This interaction and possible dissipation or amplification is captured in the 2-port S-matrix [50]. Note that the source term in Eq. (1.5) in contrast is independent of the incident sound field. At this point, for the sake of convenience, a new acoustic state variable that is related to the time-averaged acoustic power as:
𝒑P±† 𝒑P±
= ⟨𝑃±⟩ , (1.20)
is introduced. The acoustic power output, i.e. amplification or dissipation, of the 2-port or compressor can now be expressed as:
⟨𝑃out⟩ = 𝒑P−† (𝑺P
†𝑺P)𝒑P− − 𝒑P−† 𝒑P− . (1.21)
Note that the time-averaged acoustic power output in Eq. (1.21) depends on the magnitude and phase relation between incident sound waves from downstream and upstream directions as well as on the S-matrix. Without the loss of any generality, the time-averaged incident acoustic power in Eq. (1.21) can be normalized to 1 W [49]:
⟨𝑃out⟩ = 𝒑P−† (𝑺P
†𝑺P)𝒑P− − 1 . (1.22)
In addition, the Hermitian matrix (𝑺𝐏†𝑺𝐏) is diagonalizable by means of real and
positive eigenvalues as:
𝑻†(𝑺P†𝑺P)𝑻 = diag(𝜆1, 𝜆2) , (1.23)
31
where the transformation matrix 𝑻 is unitary and its columns are the
eigenvectors of the Hermitian matrix (𝑺𝐏†𝑺𝐏), i.e. the quadratic form
𝒑P−† (𝑺P
†𝑺P)𝒑P− can be reduced to a sum of squares [49]:
𝒑P−
† (𝑺P†𝑺P)𝒑P− =∑𝜆q
q
|𝑝q′ |2 . (1.24)
The vector 𝒑′ is defined as:
𝒑′ = 𝑻†𝒑P− . (1.25)
Finally, the maximum and minimum potential power outputs are obtained by substituting Eq. (1.24) into Eq. (1.22):
⟨𝑃outmax⟩ = 𝜆max − 1 and ⟨𝑃out
min⟩ = 𝜆min − 1 , (1.26)
and the eigenvectors, i.e. columns of the transformation matrix 𝑻 give the corresponding relative combination of incident acoustic waves.
Eq. (1.26) considers all the possible amplitude and phase combinations of incident sound waves [50], and predicts amplification (𝜆 > 1) or dissipation (𝜆 < 1) of incident acoustic power. The compression system can become unstable in the case of eigenvalues larger than unity if the reflections from the outside boundaries combined with the amplification create a positive feedback. This will then cause the inception of self-sustained oscillations, i.e., compression system surge. While the method can predict the potentiality for such self-sustained oscillations as a function of frequency [50, 51, 52], the actual amplitude of the resulting pressure oscillations is controlled by non-linear phenomena, and thus of course cannot be predicted by means of linear analysis.
1.3.2 Results and discussion
The method has been applied on experimental acoustic pressure data from the automotive centrifugal compressor operating under realistic conditions (Figure 2). The maximum and minimum potential acoustic power output spectra under the MGS mass flow conditions at different impeller rotational frequencies of 80 000, 100 000 and 120 000 RPM, i.e. OP4, OP8 and OP9 respectively in Figure 2, are presented in Figure 1.5.
32
Figure 1.5. The maximum (solid) and minimum (dashed) normalized acoustic
power output (Eq. (1.26)) spectra at minimum globally stable mass flow in the
case of different shaft rotational frequencies (80 000 – green, 100 000 – red,
120 000 – black RPM). OP4, OP8 and OP9 in Figure 2.
In general, the maximum potential acoustic power (MPOW) output remains negative in the measurement frequency range (Figure 1.5) indicating no net amplification of incident acoustic power. The substantial dissipation of incident acoustic power is evident instead, except in a low frequency range. One can also observe the well pronounced peak that can be distinguished at ~0.5 of RO. By contrast, no such behavior can be noticed at ~0.2 or ~0.45 of RO. It is believed that the flow instability at ~0.5 of the RO, probably being progressive rotating impeller stall as characterized in [25], can locally amplify the incident acoustic waves; however, the amplification is not sufficient to overcome the overall strong dissipation of the compressor (Figure 1.5). While the reduction in the dissipation, i.e. a deviation from the trend, appears to grow with increasing impeller speed, the level of the MPOW output remains approximately at -0.3 as the overall broadband dissipation also increases in this frequency range. Therefore, the compression system remains well damped (~30% of the incident time-averaged acoustic power) at ~0.5 of the RO, and it is believed that the flow instability associated with this frequency range, likely being progressive impeller rotating stall, does not cause the inception of self-sustained oscillations. As the rotating stall flow instability plays a significant role in the surge inception of the multistage axial turbomachines, it has been suspected that it could also be of importance in the case of centrifugal compressors [53]. However, in [21] it was suggested that the rotating stall has little importance in the compression system surge inception, which is also consistent with the result in Figure 1.5, i.e. dominating overall losses over local amplification by the rotating stall.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0 500 1000 1500 2000 2500 3000 3500
No
rm. a
cou
stic
po
wer
ou
tpu
t
Frequency [Hz]
Dissipation
Amplification
33
The MPOW output curves of the tested impeller rotational frequencies approximately collapse below ~350 Hz (Figure 1.5), and the level below ~150 Hz is systematically very close to zero, i.e. negligible dissipation in the case of the MGS mass flow. In addition, a slightly positive level or small amplification of incident acoustic waves can be observed at 80 Hz in the case of 120 000 RPM of impeller rotational frequency. In this frequency range, the compression system is not damped and is therefore prone to the inception of self-sustained oscillations, i.e. compression system surge. On the other hand, the difference between the maximum and minimum (dashed curves) power output curves in the frequency range below ~150 Hz shows a great potential for increasing the dissipation by modifying the incident sound field, which could lead to possible avoidance of self-sustained oscillations in the compression system.
The normalized incident acoustic wave (Eq. (1.25)) magnitude spectra required to produce the MPOW output under peak efficiency mass flow and the MGS mass flow conditions at 120 000 RPM of impeller rotational frequency are compared in Figure 1.6. Note that for this comparison an additional measurement of the passive part of 2-port (Eq. (1.6)) on the peak efficiency line at 120 000 RPM of impeller rotational frequency is conducted.
Figure 1.6. Incident acoustic pressure wave amplitudes (“eigenvector”) for
maximum normalized power output in the case of designed (dashed curves)
and minimum globally stable mass flow (solid curves) under 120 000 RPM
shaft rotational frequency. Red: outlet; Blue: inlet.
Clear changes in the normalized incident acoustic wave magnitudes at ~0.5 of the RO and below ~150 Hz are evident when mass flow is reduced from peak efficiency operation to the MGS mass flow (Figure 1.6). In both frequency ranges,
0.0
0.2
0.4
0.6
0.8
1.0
0 500 1000 1500 2000 2500 3000 3500
No
rm. i
n-g
oin
g w
ave
amp
l.
Frequency [Hz]
34
the incident sound wave magnitude at the outlet port becomes strongly dominant.
Validation of on-engine measurements In the CCGEx test rig (Figure 1.2), the turbochargers are characterized under idealized laboratory conditions, i.e. turbochargers are isolated from the IC engine. This is different in principle from on-engine operation in terms of various aspects, the most relevant being pulsating mass flow and significantly higher temperature at the turbine inlet. Therefore, it is of interest to determine whether these differences in operating conditions have an appreciable impact on the S-matrix of the compressor.
1.4.1 Experimental setup
The on-engine measurements are carried out at the IVT Institute of Internal Combustion Engines and Thermodynamics of TU Graz. The engine test-cell, based on the BMW P4U turbocharged R6 engine with direct petrol injection and Valvetronic™, is modified for acoustic characterization of turbocharger compressor. Herein, only the photo of the test rig is presented in Figure 1.8 and further information about the set-up can be found from [54].
1.4.2 Results and discussion
The same turbocharger compressor (See Figure 1.8) is measured in two different laboratories, IVT TU Graz and KTH CCGEx, under different operating conditions, i.e. on-engine and under idealized laboratory conditions, in the same mean operating points of the compressor. The acoustic transmission loss (TL) spectra, based on the transmission coefficients of the S-matrix (Eq. (1.6)), of these measurements are computed as:
𝑇𝐿io = 10 log10𝑊in𝑊out
= 10 log10 [𝐴i ∙ 𝜌o ∙ 𝑐o ∙ (1 ± 𝑀i)
2
|𝑇io|2 ∙ 𝐴o ∙ 𝜌i ∙ 𝑐i ∙ (1 ± 𝑀o)
2] , (1.27)
and are compared in two OPs in Figure 1.7.
35
Figure 1.7. Comparison of compressor TL results between the CCGEx test rig
(solid curves) with steady flow and the on-engine measurements at IVT with
pulsating mean flow and high turbine inlet temperature (dotted curves). The
OP I corresponds to low mass flow and ~85% of the highest designed pressure
of on-engine operation – left graph, and the OP II corresponds to ~30% more
mass flow and ~88% of full designed pressure. The colors of the curves refer to
downstream (blue) and upstream (red) direction.
In general (for more details see [54]), the TL results of the compressor between two basically different test rigs replicate each other remarkably well. From these results, it is evident that the results obtained from CCGEx test rig are of better quality, and moreover, are directly useable on-engine without the necessity for further compensations.
0
10
20
30
40
50
60
0 1000 2000 3000
Mag
nit
ud
e
Frequency [Hz]
OP I
CCGEx: test-rig downstreamCCGEx: test-rig upstreamIVT: on-engine downstreamIVT: on-engine upstream
0
10
20
30
40
50
60
0 1000 2000 3000M
agn
itu
de
Frequency [Hz]
OP II
CCGEx: test-rig downstreamCCGEx: test-rig upstreamIVT: on-engine downstreamIVT: on-engine upstream
36
Figure 1.8. Photo of the modified engine test rig for acoustic on-engine
measurements of turbocharger.
37
2 Acoustic characterization of twin-scroll turbine
The turbocharger turbine is an essential element of the exhaust system of the IC engine having significant impact to both aerodynamic and acoustic fields. To develop an accurate acoustic prediction model, accurate experimental validation data is essential. Therefore, it is of interest to extend the previous work on single scroll turbines [55] to modern twin-scroll-type turbines where all the flow channels have significant interaction with two other channels. In the present work, the method is suggested for obtaining accurate experimental data for in-detail investigation of acoustic wave interaction, and numerical model validation of the twin-scroll type of turbines.
Method A simplified sketch of the experimental characterization set-up of a twin-scroll turbine is presented in Figure 2.1.
Figure 2.1. Sketch of a twin-scroll turbine treated as an acoustic three-port.
The characterization of passive acoustic performance is based on the determination of acoustic state in each flow channel of the twin-scroll turbine. If propagating acoustic pressure plane wave amplitudes (Eq. (1.2)) are selected as acoustic state variables, the method is a direct extension of the acoustic 2-port model, i.e. an acoustic 3-port model in the S-matrix form:
p b–
p b+
pa+
pa–
Loudsp. I
Rb 0
x
x5 x6
Outlet (b)
pc+
pc–
Mic. 1 Mic. 2
Mic. 6Mic. 5x3 x4
Mic. 3 Mic. 4
Mean flow out
Mean flow in
xInlet (c)
Mean flow in
Inlet (a) x1 x2x
Loudsp. III
Loudsp. II
Rc 0
Ra 0
38
[
𝑝a+𝑝b+𝑝c+
] = [
𝑅aa 𝑇ba 𝑇ca𝑇ab 𝑅bb 𝑇cb𝑇ac 𝑇bc 𝑅cc
] [
𝑝a−𝑝b−𝑝c−
] . (2.1)
In the case of an acoustic 3-port, the S-matrix consists of nine unknown complex coefficients. Therefore, determination of the S-matrix requires at least three test cases where wave decomposition (Eq. (1.4)) is performed simultaneously, i.e. with common phase reference, in all three ports:
[
𝑝a+I
𝑝b+I
𝑝c+I
𝑝a+II
𝑝b+II
𝑝c+II
𝑝a+III
𝑝b+III
𝑝c+III
] = [
𝑅aa 𝑇ba 𝑇ca𝑇ab 𝑅bb 𝑇cb𝑇ac 𝑇bc 𝑅cc
] [
𝑝a−I
𝑝b−I
𝑝c−I
𝑝a−II
𝑝b−II
𝑝c−II
𝑝a−III
𝑝b−III
𝑝c−III
] , (2.2)
where the test cases have to be linearly independent, i.e.
det [
𝑝a−I
𝑝b−I
𝑝c−I
𝑝a−II
𝑝b−II
𝑝c−II
𝑝a−III
𝑝b−III
𝑝c−III
] ≠ 0 . (2.3)
A convenient method for realizing three test cases is to extend also the two source-location method [42] to a three source-location method, i.e. to excite sound fields sequentially in all the channels of a twin-scroll turbine.
Experimental setup The measurement campaign is carried out at the CCGEx laboratory for fluid mechanics and acoustics. The available test rig for turbocharger acoustic characterization is developed further to enable three-port measurements of twin-scroll turbines.
2.2.1 Peripheral systems
In order to determine the passive acoustic three-port data (Eq. (2.1)), the system has to be stationary i.e. the turbine operating point is kept constant throughout the acoustic measurement. This is done by controlling the OP of the turbine by means of pneumatic throttle valves at the inlet of the turbine as well as at the outlet of the compressor (See Figure 2.2). The compressed air is supplied by an external compressor plant with capability of up to 500 g per second at 5.5 bar via a 25 m3 stagnation tank for pressure stabilization. Moreover, the incoming air temperature is also increased by the 18 kW electric pre-heater system to approximately 50 °C at the turbine inlet in order to avoid ice formation at the turbine outlet due to the high rate of enthalpy extraction. The oil supply for turbocharger shaft journal bearings is provided by an oil system with independent pressure and temperature control. The peripheral hardware is schematized in Figure 2.2.
39
Figure 2.2. Peripheral hardware scheme of the CCGEx turbocharger test rig.
2.2.2 Test rig for twin-scroll turbines
The measurement equipment, i.e. sensors and drivers, are specified in the following Table 2.1 and complementary layout sketch is shown in Figure 2.3.
The synchronous data acquisition and signal generation is performed by means of a customized NI cRIO 9074 embedded control and monitoring system. Acoustic pressure signals from pressure transducers and microphones are pre-conditioned by Dewetron DAQP-Bridge-B and B&K Nexus Type 2690-A conditioners accordingly, while the generated excitation signal is amplified by means of two Zachry XP-600 professional series amplifiers. The stepped sine excitation signal is used to concentrate all the output power available to one single frequency. Moreover, three measurements on sufficiently different frequencies are performed simultaneously i.e. the external excitation with different frequencies in different turbine channels is provided simultaneously. As a consequence, the measurement time is reduced by approximately three times, and thus the stability of the turbine OP during relatively long measurement time is also improved. In the present work, the frequency difference between simultaneous measurements is 50 Hz. Photos of the test rig are presented in Figure 2.4.
40
Figure 2.3. The location layout sketch of test-rig sensors and drivers. The
reference cross-sections of the determined acoustic scattering matrix data are
indicated with red arrows. All lengths in mm.
Ref.
RPM
p1
p2
p3
ea
pa
pa0
ta
ec
pc
pc0
tc
p7
p8
p9
p4 p5 p6
pCa
pCa0
tCa
pCb
pCb0
tCb
pb
pb0
tb
eb
55
311 2855
5
39
62
85
41
Table 2.1. The list of measurement equipment with corresponding symbols in the layout sketch.
Sensor/Driver Type or model Measured or
generated quantity
Symbol in the sketch (Fig. 2.3)
Condenser microphone
B&K 4941-A-011 Acoustic pressure, Pa
p1…p3
Piezoresistive abs. pressure transducer
Kulite WCT-312M Acoustic pressure, Pa
p4…p9
Electrodynamic driver (loudspeaker)
Custom design
External excitation of acoustic pressure, Pa
ea…ec
Differential pressure sensor
NXP MPX5050DP Quasi-static pressure, Pa
pa0−pa; pb0−pb; pc0−pc; pCa0−pCa, pCa pCb0−pCb
Gauge pressure sensor
Gems 2200SGA6001A3UA
Quasi-static pressure, Pa
pa0; pb0; pc0; pCb0
Thermocouple Type-K Temperature, °C
ta; tb; tc; tCa; tCb
Revolution counter system
Micro-epsilon turboSPEED 135
Shaft rotational frequency, RPM
RPM
42
Figure 2.4. Photos of the unique test rig for acoustic characterization of
automotive twin-scroll turbines at the KTH CCGEx laboratory
(www.ccgex.kth.se).
43
2.2.3 Operating conditions
The experimental determination of the acoustic three-port data is performed on a typical modern automotive twin-scroll turbine (See Figure 1.8 and Figure 2.4), originating from a turbocharged R6 petrol BMW P4U engine unit equipped with direct petrol injection and Valvetronic™. The operating conditions of the turbocharger in the test rig are set according to the reference OP of the complete engine unit (BMW P4U). Since currently the turbine air inlet temperature in the test rig is significantly lower than the exhaust gas temperature of the engine, the characteristic operating map, referred to as the turbine map, cannot be used to accurately determine the OP. Nevertheless, on the compressor side, the realistic operating conditions are met, and the OP can be matched to the reference point in the original compressor map. Therefore, the OP of the turbocharger is set for acoustic characterization by first matching the wastegate (WG) (turbine by-pass valve that short-circuits the inlet and outlet channels of the turbine) valve position to the reference OP of the complete engine unit, and thereafter matching the compressor OP in the compressor map by means of pneumatic throttle valves (Figure 2.2). The position of the WG is determined by the translation length of the WG actuator.
In addition to the operating point that is set according to the complete engine unit reference point, the comparison OP with the WG position of 20 mm, corresponding to fully open position, is also measured while keeping the turbine total mass flow constant. The physical quantities determining the operating points are tabulated below (Table 2.2).
Table 2.2. The physical quantities of the turbocharger operating points during measurements.
Ref. OP to complete engine unit OP
Comparison OP with open WG
Wastegate actuator translation length, mm
2 20
Compressor mass flow, kg∙s-1 0.080 0.060
Compressor pressure ratio (total to total)
1.61 1.06
Turbine total mass flow, kg∙s-1 0.200 0.200
Pressure ratio: channels a and b (total to total)
1.78 1.18
Pressure ratio: channels c and b (total to total)
1.77 1.17
Averaged shaft rotational frequency, RPM
91 166 38 780
44
Results and discussion The acoustic transmission loss spectra of two operating points (Table 2.2) with different WG valve positions are presented in Figure 2.5.
Figure 2.5. The spectra of acoustic transmission loss between turbine channels
(a), (b) and (c) (See Figure 2.1). Two different wastegate positions, determined
according to the actuator translation length of 2 mm – left graph, and of 20 mm
– right graph, are considered under constant total mass flow conditions
(See Table 2.2).
In general, the quality of the results (Figure 2.5) is remarkably good. The acoustic transmission loss peak values reach as high as 50 dB while the broadband level remains > 10 dB (Figure 2.5 left graph), thus having a significant impact on the exhaust system acoustic performance. Furthermore, the TL spectra show no difference between the two non-symmetrical inlet channels below ~1 kHz (Figure 2.5 left graph). In addition, the TL between the inlet channels unexpectedly remains the same regardless of the propagation direction (Figure 2.5 left graph).
The opening of the wastegate valve causes a noticeable change in the character of the TL spectra (Figure 2.5 left graph) by making narrowband peaks more pronounced while lowering the broadband level (Figure 2.5 right graph), except for the TL between two inlets.
0
10
20
30
40
50
60
0 600 1200 1800 2400
Tra
nsm
issi
on
Lo
ss [
dB
]
Frequency [Hz]
WG translation 2 mm
a → b a → cb → a b → cc → a c → b
0
10
20
30
40
50
60
0 600 1200 1800 2400
Tra
nsm
issi
on
Lo
ss [
dB
]
Frequency [Hz]
WG translation 20 mm
a → b a → cb → a b → cc → a c → b
45
3 Optimization of compact flow duct silencer
The concept of a compact flow duct silencer, treated herein, is the result of several works investigating the possibility of using a mass-production micro-perforated sheet material Acustimet™ [56] for vehicle applications. A new type of flow duct silencer, based on the micro-perforated tube, made of Acustimet™ panels, was proposed by Allam and Åbom in [57]. A sketch of this silencer is presented in Figure 3.1.
Figure 3.1. Geometry for the MPP silencer proposed in [57]. Circular symmetry
is assumed and the outer chamber is sub-divided into two or several cavities by
rigid walls.
It was concluded in [57] that such a silencer (Figure 3.1) can provide a non-fibrous alternative to the classical dissipative silencer. However, the expected drawback of having negligible sound attenuation at frequencies where the chamber length equals half wave-length multiples, was recognized. Therefore, the implementation of impenetrable separating baffles inside the cavity was suggested (Figure 3.1), and as a consequence, the minima in sound attenuation was shifted to the higher frequency. In order to eliminate the minima completely, the locally reacting limit was formulated by Åbom and Allam in [58]. Essentially, the cavity is locally reacting up to the frequency where the length of the cavity is smaller than half the wavelength. In addition, a custom Acustimet™ panel with larger apertures was also considered in [58] and it was concluded that the higher attenuation of sound in such a silencer is achievable in the case of larger apertures, i.e. smaller acoustic resistance.
The starting point of the optimization herein is the silencer based on the previously described development. In addition, it is decided to study an application related to IC-engine intake compressor noise. Based on this, a set of initial design constraints are formulated in co-operation with Volvo Car Corporation, tabulated in Table 3.1, and geometrical constraints are sketched in Figure 3.2.
46
Table 3.1. Design constraints for the compressor noise problem studied.
Parameter Inlet/outlet
duct radius, m
Average Mach
number
Temperature, °C
Target frequency,
kHz
Value 0.03 0.05 20 2.0
155
105
1
Ø6
0
Ø9
0
Figure 3.2. Geometry of the prototype MPP silencer studied. The arrow,
marked 1, points at the micro-perforated sheet tube (Acustimet™), separating
the main flow channel from the outer cavities.
In order to predict and compare the acoustic performance of different compact silencer configurations, modeling has to be performed. For the application in mind, an incident plane wave can be assumed and in earlier works simple 1D models were tested [57]. But it was found that the periodic structure of the outer volume created nearfields, which even far below the “cut-off” for higher modes influenced the results. Therefore, it is necessary to use an acoustic FEM model to accurately model this silencer. Here, the FEM software COMSOL Multiphysics® [59] is used. In addition, the prototype built at the Volvo Car Corporation by means of rapid prototyping and employing a standard Acustimet™ panel, is used for validation purposes. Moreover, the cavity of the prototype is also used (Paper IV) to experimentally evaluate the results of the optimization (Table 4.1). The photo of this prototype silencer is presented in Figure 3.3.
47
Figure 3.3. Photo of the compact silencer rapid prototype with magnified view
of the micro-perforated (Acustimet™) sheet tube. Dimensions as in Figure 3.2.
Finite element model The modeling in [57] was carried out by means of FEM. In the model, the MPP was substituted by a pre-computed acoustic transfer impedance boundary condition. Thus, the resulting model consisted of two separate domains connected by the pre-defined boundary condition (Figure 3.1). In addition, the convective flow effects were neglected in the main flow channel while the grazing flow effects on the MPP were accounted for in the computation of the boundary condition. Such an approach is reasonable for low mean flow Mach number applications [57].
In the present work, the mean flow velocity is relatively small compared to the speed of sound (Table 3.1). Therefore, applying the approach also used in [57] is adequate. Moreover, as the cavity of the compact silencer considered is locally reacting, it can be modeled analytically and included in the boundary condition. It results in the complete acoustic boundary condition of the flow channel inside the cavity (Figure 3.2). Consequently, the modeling domain consists only of the air volume in the flow channel of the silencer (Figure 3.4).
48
Figure 3.4. Acoustic pressure distribution at 2 kHz plotted on the FEM modeling
domain for the prototype silencer with the standard MPP, i.e. not optimized
configuration.
In the modeling domain, the inhomogeneous Helmholtz equation is solved in the lossless medium:
∇1
𝜌(∇𝑝 − 𝒒𝐝) −
𝑘2𝑝
𝜌= 𝑄m . (3.1)
The main flow channel is assumed to be impenetrable by sound waves and along the cavity section (Figure 3.2) the wall boundary is set as:
−𝒏𝐫 [−1
𝜌(∇𝑝 − 𝒒𝐝)] = −𝑝
𝑖𝜔
𝑍wall𝜌𝑐0 . (3.2)
In order to evaluate the acoustic performance of the silencer, the TL (Eq. (1.27)) is chosen. The TL considers one-way propagation of sound, and thus it is conveniently obtained by using reflection-free terminations in the axial direction. By assuming that the reflected sound waves are negligible, the incident and transmitted acoustic power is obtained by integrating the sound intensity over respective cross-sections.
Locally reacting surface (Eq. (3.3))
49
Method In order to optimize the compact silencer (Figure 3.3), it has to be realized that the acoustic performance is completely controlled by the acoustic impedance of the locally reacting surface (𝑍wall) inside the cavity section of the flow channel (Figure 3.2 and Figure 3.4). This impedance is a consequence of the perforate and the adjoining cavity, acting together so that:
𝑍wall = 𝑍MPP + 𝑍cav . (3.3)
Guo et al. gave an overview in Ref. [60] of the semi-empirical modeling of micro-perforate transfer impedance. They also investigated the effect of flow and, based on experiments at MWL, KTH, they suggested correction terms for the acoustic impedance under grazing flow conditions. In addition, they showed that the acoustic mass end-correction term for the slit types of MPP, e.g. as the Acustimet™ panel used here, can be neglected. The linear acoustic resistance Re(ZMPP) of the slit type MPP can be computed from:
𝑟s = 𝑅𝑒 {𝑖𝜔𝑡h𝜎𝑐0
[1 −tanh(𝑘s√𝑖)
𝑘s√𝑖]
−1
} +4𝑅s𝜎𝜌𝑐0
+ 𝛽𝑀x𝜎 , (3.4)
and the reactance Im(ZMPP) from:
𝑥s = Im {𝑖𝜔𝑡h𝜎𝑐0
[1 −tanh(𝑘s√𝑖)
𝑘s√𝑖]
−1
} . (3.5)
The shear wave number, which relates the aperture dimensions to the acoustic boundary layer thickness, is defined as:
𝑘s = 𝑑√𝜔
4𝜐 . (3.6)
Finally, the surface resistance, which is a consequence of the oscillating motion of the fluid on the surface of a perforated panel, can be found from:
𝑅s =1
2√2𝜌𝜔𝜇 . (3.7)
The normalized linear resistance (Eq. (3.4)) is the sum of three terms. The first term analytically relates acoustic losses with viscous effects inside the apertures (propagation in “narrow” tubes), whereas the last two terms empirically describe the acoustic losses outside the apertures. As also seen from Eq. (3.4) and Eq. (3.5), a grazing flow will affect (increase) the resistance but not affect the reactance. Here, the non-linear term in the MPP impedance has been omitted. It is possible to include it in the analysis of the compact silencer as shown by Allam and Åbom [57].
50
The analytical model for the acoustic cavity impedance 𝑍cav has been derived and proposed in Ref. [58] and is given by:
𝑍cav =
𝑖 [H0(1)(𝑘𝑟) −
H1(1)(𝑘𝑅e)
H1(2)(𝑘𝑅e)
H0(2)(𝑘𝑟)]
H1(1)(𝑘𝑟) −
H1(1)(𝑘𝑅e)
H1(2)(𝑘𝑅e)
H1(2)(𝑘𝑟)
. (3.8)
It was discovered in 1953 by L. Cremer that the maximum damping of a pair of sound wave modes in an infinite rectangular duct with definite acoustic impedance on one side is obtained when the modes merge in the complex plane. The optimal wall impedance, so-called Cremer impedance, was derived for zeroth channel mode, and expressed in [61] as:
𝑍Cr = (0.91 − 0.76𝑖)𝑘𝑎
𝜋 . (3.9)
By following the same principles as Cremer, B. J. Tester derived the optimal wall impedance expression for circular ducts in 1973. In addition, the mean flow correction was added under a uniform mean flow assumption in [62] as:
𝑍Cc = (0.88 − 0.38𝑖)𝑘𝑟
𝜋(1 + 𝑀x)2 . (3.10)
The essence of the optimization method proposed herein is the matching of a locally reacting surface impedance to the Cremer optimum (Eq. (3.10)). It should be noted that the reactance is produced by means of both the cavity (Eq. (3.8)) and the MPP (Eq. (3.5)) while the acoustic resistance is produced only by the MPP (Eq. (3.4)). Therefore, the resistance is matched first by determining the corresponding MPP geometrical parameters. As a consequence, certain mass reactance is produced i.e. the reactance is positive and increasing with the frequency while the Cremer optimum suggests the negative reactance (Eq. (3.10)). This discrepancy is then eliminated by introducing the corresponding cavity with the required negative reactance (Eq. (3.8)).
While the concept of a compact silencer as such is general, i.e. the acoustic resistance can be produced by any means, in the present work the resistance is produced by implementing the MPP. Since the resistance of the MPP can be approximated to a constant value across the frequency range, linearly increasing optimum resistance (Eq. (3.10)) can be realized only at the frequency where the maximum sound damping is desired (Table 3.1). (A detailed discussion regarding the described issue can be found in Paper III.)
It should be noted that the optimal wall impedance expression (Eq. (3.10)) is derived by assuming an infinite duct, i.e. in the zeroth duct mode frequency range reflected waves cannot exist. Therefore, it is assumed that the proposed
51
optimization technique will lead to a dissipative silencer. On the other hand, the locally reacting surface in the compact silencer is of definite length. Thus, the occurrence of reflections at the cavity interfaces are expected, resulting in reactive silencer effects. In addition, the Cremer optimum impedance (Eq. (3.10)) equals zero in the trivial case of zero frequency (𝑘 = 0) i.e. a perfect resonator with total reflection.
Results and discussion The experimental validation of the TL spectrum predicted by the simplified FEM model in the absence of a mean flow is presented in Figure 3.5. In addition, the theoretical TL spectrum computed by assuming the Cremer impedance (Eq. (3.10)) across the frequency range is plotted for reference purposes.
Figure 3.5. The results of experimental validation of sound transmission loss
obtained by the simplified modeling approach (green and blue curves) for the
prototype silencer (Figure 3.3). The MPP is of standard type, with 𝑟s ≈ 1.5, used
for room acoustics. The red curve shows the theoretical maximum damping for
the silencer using the so-called Cremer impedance.
As can be observed in the TL graph (Figure 3.5), the experimental spectrum is well-captured by the simplified FEM model in the absence of mean flow. Moreover, the predicted theoretical maximum TL curve shows that a much higher peak value at target frequency (2 kHz) is obtainable by implementing the optimization method.
According to the proposed optimization technique, the appropriate set of MPP geometrical parameters is determined by considering the initial design constraints (Table 3.1) and required resistance (Eq. (3.10)) while preserving the
0
20
40
60
80
100
0 500 1000 1500 2000 2500 3000 3500
Tra
nsm
issi
on
loss
[d
B]
Frequency [Hz]
ExperimentSimplified ModelCremer Maximum
Transmission loss under no flow conditions
52
original MPP thickness 𝑡h. The resulting parameters are given and compared to the standard Acustimet™ MPP, used in the first prototype (Figure 3.3), in Table 3.2. Corresponding cavity radius 𝑅e = 49 mm, to match the reactance, is also determined.
Table 3.2. The geometrical parameters of the MPPs studied. The optimized MPP is designed to match the Cremer resistance at 2 kHz for 𝑟 = 30 mm.
MPP panel
Thickness [mm]
Perforation ratio
Averaged slit width
[mm]
The resistance
at 2 kHz
Standard 1 0.043 0.095 ~1.54
Optimized 1 0.062 0.210 ~0.34
The predicted TL spectra of the new optimized design (Table 3.2), of the first prototype and also of theoretical Cremer impedance across the frequency range, at Mach 0.05 mean flow conditions, is presented in Figure 3.6.
Figure 3.6. Predicted sound transmission loss for the prototype silencer for
different configurations of MPP + cavity impedance. The optimized result is
obtained by tuning the wall impedance based on Cremer’s impedance at a
target frequency 2000 Hz. By splitting the silencer in 2 or 3 sections tuned to
1500, 2500 Hz and 1500, 2000 and 2500 Hz, respectively, a more broadband
damping behavior is possible; see Table 3.3.
0
20
40
60
80
100
0 500 1000 1500 2000 2500 3000 3500
Tra
nsm
issi
on
loss
[d
B]
Frequency [Hz]
Transmission loss at Mach number 0.05
First PrototypeOptimizedCremer MaximumTwo Optimized SectionsThree Optimized Sections
53
As expected, the much higher TL peak value of the optimized design (Figure 3.6), compared to the first prototype, touches the theoretical reference curve at the target frequency of 2 kHz. Moreover, as the cavity is of locally reacting type, the total cavity length available can be divided into separately optimized sections at different target frequencies, thus producing close to a constant wideband attenuation. In addition, such a high attenuation as > 60 dB would be challenging to achieve in industrial applications because the in-duct air-borne sound transmission is reduced due to other transmission mechanisms.
In order to produce wideband dissipation around the original target frequency (Table 3.1), the optimization has been reconsidered by splitting the total reacting length (Figure 3.4) into separately optimized sections with different target frequencies. The new constraints are listed in Table 3.3 and the corresponding predicted TL spectra are presented in Figure 3.6.
Table 3.3. Design constraints for the optimized sections shown in Figure 3.6.
Configuration name
Section 2 Section 1 Section 3
length, mm
freq., kHz
length, mm
freq., kHz
length, mm
freq., kHz
Optimized - - 96 2.0 - -
Two optimized sections
48 1.5 - - 48 2.5
Three optimized sections
48 1.5 20 2.0 28 2.5
As can be observed in Figure 3.6, by further dividing the compact silencer into separately optimized sections, a high TL (>20 dB) in a wide frequency band (more than an octave) is possible.
54
4 “Exact” Cremer impedance model
The specific problem considers the propagation and attenuation of sound in an infinite uniform two-dimensional wave guide, with a locally reacting wall impedance and a uniform (plug) flow; see Figure 4.1. The boundary condition is the classical Ingard–Myers condition [63, 64], i.e. the acoustic normal displacement and the acoustic pressure are continuous at the wall.
x
y
r
Z
Figure 4.1. Sketch of the studied uniform 2D wave guide with a locally reacting
wall.
The propagation of sound in an axisymmetric wave guide can be described by superposition of complex acoustic modes of well-known form:
𝑝n = 𝐴n𝑒𝑖(𝜔𝑡−𝑘xn𝑥)J0(𝑘rn𝑟) . (4.1)
Following Cremer and Tester [61, 62], it is assumed that the least attenuated acoustic mode in the problem is the zeroth order or so-called fundamental plane wave mode (Eq. (1.1)). Hence, the mode number 𝑛 is abandoned in further expressions. In addition, the specific acoustic impedance of the air is used to normalize all the acoustic impedance expressions.
The damping of the mode is directly related to the axial decay rate of the propagating acoustic mode in the wave guide and is given by the imaginary part of the corresponding longitudinal wave number. The expression of the normalized longitudinal wave number in the wave guide is:
𝑘x𝑘=−𝑀x ± √1 − (
𝑘𝑟𝑘)2
(1 − 𝑀x2)
1 − 𝑀x2 .
(4.2)
By assuming no dissipation in the medium, i.e. 𝑘 is real, the imaginary part of the longitudinal wave number 𝑘x is controlled only by the radial wave number 𝑘r as the only complex quantity in the longitudinal wave number expression (Eq. (4.2)). The existence of an optimal radial wave number, leading to the maximum axial decay rate of the propagating acoustic zeroth mode was first addressed by Cremer [61] for rectangular wave guides. In 1973, Tester [65]
55
further generalized the work by Cremer to any acoustic mode and included both annular and circular wave guides. In addition, it was shown that under optimum condition two sequential order acoustic modes merge in the complex 𝑘r plane, thus making the optimal transverse wave numbers a branch point of the wave guide eigenvalue equation. Moreover, the effect of a uniform or “plug” flow was also included by Tester [62].
By following Tester’s work [62], the optimum wave number for a circular uniform wave guide, carrying a uniform mean flow, is the solutions of the corresponding branch point equation:
d
d(𝑘r𝑟)[(1 −𝑀x
𝑘x𝑘)−2 𝑘r𝑟 ∙ J0
′ (𝑘r𝑟)
J0(𝑘r𝑟)] = 0 . (4.3)
From the branch point equation, it is clear that the optimum radial wave number is frequency- and Mach-number-dependent. In order to significantly simplify the derivation of the optimum impedance, the high frequency range assumption of “well cut-on” modes was proposed by Tester [62]. This assumption corresponds to:
(𝑘r𝑘)2
(1 − 𝑀x2) → 0 , (4.4)
and thus
𝑘x ≈𝑘
1 ± 𝑀x . (4.5)
By applying the “well cut-on” frequency range assumption, i.e. Eq. (4.5), to the branch point equation (Eq. (4.3)), a significantly simplified equation is obtained:
d
d(𝑘r𝑟)[(1 ± 𝑀x)
2𝑘r𝑟 ∙ J0
′ (𝑘r𝑟)
J0(𝑘r𝑟)] = 0 . (4.6)
The wave number resulting from Eq. (4.6) is independent of frequency and Mach number i.e. the solution with this approximation is identical to the no flow case. Based on this, the optimal impedance for non-zero mean flow simply involves the zero mean flow impedance [62]:
𝑍opt = (0.88 − 0.38𝑖) ∙𝑘𝑟
𝜋 (4.7)
corrected by the term (1 ±𝑀x)2 as:
𝑍optA |
𝑀x=
𝑍opt(1 ± 𝑀x)
2 . (4.8)
56
Method In the present work, the high frequency assumption used by Tester [62] is eliminated, and the “exact” expression for the longitudinal wave number (Eq. (4.2)) is used instead in the branch point equation (Eq. (4.3)). This modification of the Tester high frequency asymptotic model is vital for obtaining accurate optimal radial wave numbers, especially in the low frequency range and under appreciable Mach number conditions, where the deviation from the high frequency asymptotic model is expected to be the most significant.
The “exact” longitudinal wave number expression (Eq. (4.2)) contains a square root with two possible sign options. To choose the correct sign, the approach suggested by Eversman [66] is used herein. The approach is based on the assumption of propagating acoustic modes with decaying amplitude in their direction of propagation, i.e. the imaginary part of the longitudinal wave number must be negative in the case of spatial dependence of – 𝑖𝑘x𝑥 and Re(𝑘x) > 0 (see Eq. (4.1)). Therefore, if the principal square root function is evaluated in the upper half of the complex plane, i.e. with a positive imaginary part, the minus sign in Eq. (4.2) has to be selected consistently throughout the analysis.
By defining the mean flow related term in the branch point Eq. (4.3) as:
𝑓1 = 1 −𝑀x𝑘x𝑘 , (4.9)
and carrying out essential manipulations (see Paper IV), the branch point equation takes the following form:
d𝑓1d(𝑘r𝑟)
∙2 ∙ J1(𝑘r𝑟)
𝑓1− J0(𝑘r𝑟) −
J12(𝑘r𝑟)
J0(𝑘r𝑟)= 0 , (4.10)
where
d𝑓1d(𝑘r𝑟)
=−𝑀x𝑘r𝑟
(𝑘𝑟)2√1 − (𝑘r𝑘)2
(1 − 𝑀x2)
. (4.11)
Computing the optimal radial wave numbers involves finding the roots to the non-linear transcendental equation (Eq. (4.10)). Here the “vpasolve” solver from MatLab® is used with initial values defined by the asymptotic (“high frequency”) known solution. In general, an unlimited number of solutions and their complex conjugates satisfying the Eq. (4.10) can be found. These solutions correspond to increasing order of sequential acoustic mode pairs merging at a branch point in the 𝑘r plane. Nevertheless, only the first solution corresponding to the first radial mode pair, referred to by Tester [62] as “(0, 1)”, is considered here to maximize the longitudinal decay rate of the zeroth or “plane wave” mode. Once the
57
optimum radial wave number is available, the attenuation level of time averaged acoustic power per duct radius (𝑟) can be computed:
𝑇𝐿∞r = 20 log10[𝑒
𝐼𝑚(𝑘x)𝑟]−1 . (4.12)
The corresponding optimum acoustic impedance of the locally reacting wall is computed by utilizing the Ingard–Myers boundary condition and the previously obtained optimum radial wave number:
𝑍opt|𝑀x=𝑖𝜋 ∙ (1 − 𝑀x
𝑘x𝑘)2
∙ J0(𝑘r𝑟)
𝑘r𝑟 ∙ J1(𝑘r𝑟)∙𝑘𝑟
𝜋.
(4.13)
Wave propagation analysis The Eversman [66] approach sign selection in Eq. (4.2) is adequate only in the case where waves have decaying amplitude in their propagation direction, and can lead to errors if amplifying waves, e.g. aerodynamic Kelvin-Helmholtz instability modes, exist. To this end, frequency domain wave propagation analysis, based on Eq. (4.13), is carried out by considering the following dispersion relation for the infinite wave guide (Figure 4.1):
𝐻(𝑘x, 𝜔) = 0 , (4.14)
where
𝐻 = 𝑍opt|𝑀x−𝑖𝜋 ∙ (1 − 𝑀x
𝑘x𝑘)2
∙ J0(𝑘r𝑟)
𝑘r𝑟 ∙ J1(𝑘r𝑟)∙𝑘𝑟
𝜋 ,
(4.15)
and the radial wave number is derived from Eq. (4.2) as:
𝑘r𝑘= ±√
1 − [𝑘x𝑘(1 − 𝑀x
2) +𝑀x]2
1 − 𝑀x2 .
(4.16)
As in the case of Eq. (4.2), Eq. (4.16) also contains the square root operation, implying sign selection. However, Eq. (4.15) is an even function with respect to the radial wave number 𝑘r, i.e.
J0(𝑘r𝑟)
𝑘r𝑟 ∙ J1(𝑘r𝑟)|𝑘r𝑟
=J0(𝑘r𝑟)
𝑘r𝑟 ∙ J1(𝑘r𝑟)|−𝑘r𝑟
, (4.17)
and therefore the sign selection in Eq. (4.16) has no effect.
58
As mentioned previously, in the presence of instability modes, a more comprehensive analysis than the Eversman sign convention is required to determine the direction of propagation. The physical requirement of causality is transformed to a study of 𝑘x as a function of the complex frequency ω [67] [68]. For the numerical determination of 𝑘x, the argument principle is used, which states that the argument of the analytic function 𝐹(𝑧) increases with 2N 𝜋⁄ when 𝑧 traverses a closed curve in the positive direction, where N is the number of zeros of 𝐹(𝑧) inside this curve. A consequence is that the zeros are clearly shown in a graph of the isocontours of arg(𝐹(𝑧)) and abs(𝐹(𝑧)) on a rectangle in the complex 𝑧-plane. This isocontour plot is created with the MatLab® script “contour”. In the case considered herein,
𝑧 = 𝑘x𝑟 and 𝐹(𝑧) = 𝑘r𝑟 ∙ J1(𝑘r𝑟) ∙ 𝐻 (4.18)
that is analytic in the complex 𝑧 region of interest.
When one mode has the same stability properties for all frequencies-- stable, neutrally stable, or alternatively unstable, the following simplified stability
analysis can be employed [67]: The 𝜔 is set as 𝜔 = 𝜌ω𝑒−𝑖𝜃, and 𝜃 is varied
continuously from 0 to 𝜋 2⁄ while 𝜌ω is kept constant. A mode with
Im[𝑘x𝑟(𝜃 = 𝜋 2⁄ )] > 0 is propagating to the negative 𝑥 direction, and
Im[𝑘x𝑟(𝜃 = 𝜋 2⁄ )] < 0 is propagating to the positive 𝑥 direction.
A wave propagating to the positive 𝑥 direction with
Im[𝑘x𝑟(𝜃 = 0)] < 0 is stable while the one with
Im[𝑘x𝑟(𝜃 = 0)] > 0 is unstable.
For the case when the stability properties vary with the (real) frequency, it is the sign of Im[𝑘x𝑟(𝜃 = 𝜋 2⁄ )] for 𝜌ω tending to infinity that determines the direction of propagation.
The instability discussed so far is termed a convective instability meaning that the amplitude is growing in the direction of propagation. A so-called absolute instability means that the solution tends to infinity with time for a fixed point in space. Such an absolute instability is created when 𝑘x for the modes propagating to the negative and positive 𝑥 direction are merging in the physical half-plane (Im(𝜔) < 0). For such a situation, it cannot be assured that 𝑘x is an analytical solution of 𝜔 in the physical half-plane, which causality requires. A consequence is that the mode does not exist for real frequencies, indicating the absolute instability property.
59
Finite element analysis The analytical modeling considers a uniform wave guide with infinite length (Figure 4.1). The effect of a finite length and reflection at the inlet/outlet as well as scattering to other modes is investigated by means of FEM. The FEM computations are carried out by means of the commercial software COMSOL Multiphysics® [59]. The linearized acoustic field in a lossless medium with a mean flow (assumed to be potential) is determined by solving the equation:
−𝑖𝑘(𝑘𝛷 +𝑀x ∙ ∇𝛷) + ∇ ∙ [∇𝛷 − (𝑖𝑘𝛷 +𝑀x∇𝛷)𝑀x] = 0 (4.19)
The geometry of the studied wave guide (see Figure 4.1) is axisymmetric, hence an efficient truncated 2D modeling domain with axisymmetric boundary condition is used. The resulting modeling domain with an example of the acoustic pressure distribution is presented in Figure 4.2.
The locally reacting wall impedance boundary condition is simulated at the outer radius of the modeling domain using the Ingard-Myers condition implemented in COMSOL Multiphysics® [59]. In addition, an 8 cm long section with a so-called “sound-hard” boundary condition is used before and after the locally reacting segment (See Figure 4.2) by setting the velocity in radial direction to zero. In the longitudinal direction at both terminations (inlet/outlet), reflection-free boundary conditions are imposed with an incident plane wave at the inlet side (𝑥 = 0).
The computation grid consists of regular 2D rectangular-shaped elements. Although satisfactory convergence is obtained by using as few as five elements per highest frequency wave length, the conservative approach of twenty five elements per wave length is used herein. Nevertheless, the model still remains inexpensive in terms of computational resources.
Once the velocity potential field is computed, time-averaged acoustic power can be obtained from the incident (imposed) and transmitted (computed) velocity potential. The acoustic transmission loss (in the plane-wave range) is given by the square of the velocity potential amplitude:
𝑇𝐿FEM = 20 log10|𝛷in|
|𝛷out| , (4.20)
where the subscripts in/out refer to the incident/transmitted wave amplitudes. The transmitted amplitude is computed as the surface average at the reflection-free termination of the modeling domain. To compare with results for an infinitely long wave guide (Eq. (4.12)), the transmission loss is reduced to a length of 1 𝑟:
𝑇𝐿FEMr =
𝑟 ∙ 𝑇𝐿FEM𝑙r
. (4.21)
60
Figure 4.2. The modeling domain of the finite element analysis with indicated
locations of boundary conditions and acoustic pressure distribution plotted on
the first half of the modeling domain. Length scale is in meters and color legend
is in pascals.
Locally reacting wall impedance
“Sound-hard” wall
Reflection free termination
61
Sound attenuation mechanisms in optimized design In the robust noise control solution of a flow channel network, the property of attenuation should preferably be achieved in a dissipative manner. Moreover, as was discussed previously (Figure 1.5), the reflected sound waves in the inlet system of modern IC engines can be responsible for triggering the surge condition. In a uniform wave guide, no longitudinal reflections occur as the impedance boundary condition is continuous, i.e. the attenuation is caused by the dissipation of acoustic power at the wave guide wall. By contrast, in a finite length flow-duct, as the compact silencer in Figure 3.2, longitudinal reflections does occur at the interfaces of wall impedance discontinuities, i.e. at the inlet and outlet. As a consequence, the total transmission loss is caused by the reflection and dissipation of time-averaged acoustic power. In order to evaluate whether dissipation or reflection dominates the TL behavior, the distribution of sound power is followed by studying the acoustic S-matrix data. The transmission loss associated with dissipation can be determined as:
𝑇𝐿dis = 10 log10 [1 − |𝑅|2
(1 −𝑀x)2
(1 +𝑀x)2
|𝑇|2] . (4.22)
In Eq. (4.22), it is assumed that the differences in aerodynamic pressure, temperature, air density and Mach number between the silencer inlet and outlet are negligible. From Eq. (4.22) it follows that the TL that is caused only by the reflection is given by:
𝑇𝐿ref = −10 log10 [1 − |𝑅|2(1 − 𝑀x)
2
(1 + 𝑀x)2] . (4.23)
Note that by combining Eqs. (4.22) and (4.23), the total TL, i.e. the classical definition of TL (Eq. (1.27)), is obtained. The set of these logarithmic parameters (Eq. (4.22), (4.23) and (1.27)) give a detailed characterization of the silencer acoustic performance, and the quantification of attenuated, dissipated and reflected sound power.
Results and discussion
The radial wave number (Eq. (4.10)) traces on the complex 𝑘r𝑟 plane, computed for different Mach numbers by varying the Helmholtz number 𝑘𝑟, are presented in Figure 4.3a, and corresponding maximum attenuation rates per channel length of 1 𝑟 are in Figure 4.3b.
The high frequency asymptotic model by Tester is based on the constant radial wave number 𝑘r𝑟 value of (3.0+1.3i) [62]. A very close value of (2.98+1.28i) as high frequency asymptote or zero mean flow value is obtained from the numerical solution here. This constant value can be observed as a point
62
in Figure 4.3a. In contrast, a large variation of optimal radial wave number 𝑘r𝑟 can be observed in the case of non-zero mean flow, i.e. a significant deviation of optimal wave guide wall impedance from the constant-value-based high frequency model (Eq. (4.8)). In addition, the existence of low frequency asymptotic values, (0, 0𝑖) for positive Mach number and (4.47 + 1.47𝑖) for negative Mach number, are evident from Figure 4.3a. As a consequence of the existence of high and low frequency asymptotic values, a different mean flow Mach number only changes the path on the complex plane between these two points. This Mach-number-dependent difference appears to be most significant near the high frequency asymptotic value and becomes negligible in the low frequency range.
Figure 4.3. a – Analytical optimum radial wave number trace for varying
Helmholtz number (𝑘𝑟) and different Mach numbers (M) computed from
Eq. (4.10). The + denotes the “cut-off” Helmholtz number (𝑘𝑟) of first higher
order mode in a hard-walled duct. b – Theoretical maximum attenuation rate
per channel length of 1 𝑟 computed by means of the “exact” radial wave
number. The X denotes the Helmholtz-number where the real part of the
Cremer impedance becomes negative (See Figure 4.4).
The TL spectra in Figure 4.3b are based on the imaginary part of the longitudinal wave number 𝑘𝑥, computed according to Eq. (4.2). As is mentioned previously, the imaginary part is controlled by the radial wave number 𝑘r as the only complex quantity in Eq. (4.2). Therefore, a meaningful comparison between the “exact” and asymptotic (constant) radial-wave-number-based models cannot be produced as the TL of the latter becomes independent of flow direction (±𝑀x). Although similar behavior of the “exact” model can be observed in the asymptotic
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4
Im
Re
M = -0.3 M = -0.2 M = -0.1 M = -0.042 M = 0 M = 0.042 M = 0.1 M = 0.2 M = 0.3
a
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5
Tra
nsm
issi
on
loss
[dB
/r]
Helmholtz number
M = -0.3M = -0.2M = -0.1M = -0.042M = 0M = 0.042M = 0.1M = 0.2M = 0.3
b
63
high frequency range (Figure 4.3b), for 𝑘𝑟 < 4 a significant difference exists between the up- and downstream directions.
The optimum Cremer impedance of the “exact” and asymptotic models [62] is compared in Figure 4.4.
Figure 4.4. Theoretical optimum Cremer impedance for a circular wave guide
wall for negative mean flow direction (See Figure 4.1) – a, and for positive
direction – b. “A.” denotes the asymptotic model [62] (Eq. (4.8)).
In general, a clear difference between the optimal impedance spectra of the asymptotic and the “exact” models can be observed. The difference between the models predictably increases with mean flow Mach number and toward lower Helmholtz numbers. From the perspective of a passive noise control, a rather undesirable feature of negative resistance can also be observed in Figure 4.4. The low frequency band of negative resistance is Mach-number-dependent, and is wider, i.e. reaching to higher frequencies, in the case of higher Mach number values. In this frequency band, the wall of the wave guide has to be active in order to produce the maximum attenuation of the propagating wave. The transition values of Helmholtz numbers where the resistance changes from positive to negative, i.e. zero resistance, are also denoted (with X) in Figure 4.3b to show the low Helmholtz number limit of a passive wave guide wall.
-1.5
-0.5
0.5
1.5
2.5
3.5
4.5
5.5
0 1 2 3 4 5
No
rmal
ized
imp
edan
ce
Helmholtz number
Re: M = -0.042 Re: M = -0.042, A. Im: M = -0.042 Im: M = -0.042, A. Re: M = -0.3 Re: M = -0.3 A. Im: M = -0.3 Im: M = -0.3, A.
a
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5
No
rmal
ized
imp
edan
ce
Helmholtz number
Re: M = 0.042 Re: M = 0.042, A. Im: M = 0.042 Im: M = 0.042, A. Re: M = 0.3 Re: M = 0.3, A. Im: M = 0.3 Im: M = 0.3, A.
b
64
The mean-flow-dependent locations of wave guide modes in the longitudinal wave-number 𝑘x𝑟 plane (i.e. the zeros of Eq. (4.15)) are presented for the original Cremer impedance model (Eq. (4.8)) in Figure 4.5a and for the constant “exact” Cremer impedance for the Mach 0.3 mean flow case, in Figure 4.5b.
Figure 4.5. Longitudinal wave numbers 𝑘x𝑟 of wave guide (Figure 4.1) modes
at constant Helmholtz number 𝑘𝑟 = 1 (i.e. the zeros of the Eq. (4.15)) in the
case of the original Cremer impedance model (Eq. (4.8)) – a, and in the case of
constant “exact” optimal impedance for Mach 0.3 mean flow
(i.e. 𝑍opt|𝑀=0.3= 0.1035 + 0.2994𝑖) – b.
It is clear from Figure 4.5a that the original asymptotic Cremer impedance model (Eq. (4.8)) does not cause the wave guide modes to merge in the low frequency range (𝑘𝑟 = 1). By contrast, the “exact” Cremer impedance value for Mach 0.3 mean flow conditions causes the merging of two modes, denoted as (0, 0) for plane wave and (0, 1) for the first radial mode, under corresponding mean flow conditions (Figure 4.5b). In addition, the attenuation rate, i.e. the imaginary part of (0, 0) mode in the lower half-plane, is noticeably improved over the original asymptotic model. Moreover, the constant “exact” Cremer impedance gives a higher attenuation rate when mean flow Mach number > 0.1 (Figure 4.5: green dotted line) regardless of the fact that the impedance is computed for the Mach 0.3 mean flow case. The previous observation indicates the potentiality of increasing design robustness, with respect to mean flow changes, by using the “exact” Cremer impedance for the highest designed mean flow range.
-9
-7
-5
-3
-1
1
3
5
7
9
-3 -2 -1 0 1 2 3
Im
Re
M = 0M = 0.1M = 0.2M = 0.3
(0, 0)(0, 1)
(0, 0)
(0, 1)
a-9
-7
-5
-3
-1
1
3
5
7
9
-3 -2 -1 0 1 2 3
Im
Re
M = 0M = 0.1M = 0.2M = 0.3
(0, 0)
(0, 1)
(0, 0)
(0, 1)
b
65
In addition to previously described differences in the lower half-plane (Figure 4.5), the mode denoted (0, 1) in the higher half-plane has changed location significantly while switching from the original asymptotic model (Figure 4.5a) to “exact” Cremer impedance (Figure 4.5b). A relatively large real part and strong mean flow Mach number dependence indicate a low mean-flow-dependent phase velocity, while the large imaginary part suggests a high amplification rate. Nevertheless, the propagation speed does not scale with the mean flow Mach number, and thus does not have the properties of an amplifying Kelvin-Helmholtz aerodynamic instability.
The longitudinal wave numbers for different “exact” Cremer impedance values at different frequencies 𝑘𝑟, corresponding to small positive, zero, and small negative resistance (see Figure 4.4b) in the case of Mach 0.3 mean flow, are presented in Figure 4.6a, while the case with zero resistance is further analyzed in the Figure 4.6b by introducing losses in the media, i.e. in the case of complex frequency 𝜔 as discussed in section 4.2.
Figure 4.6. Longitudinal wave numbers 𝑘x𝑟 of wave guide (Figure 4.1) with the
“exact” Cremer impedance boundary condition and Mach 0.3 mean flow
conditions: a – different frequencies 𝑘𝑟 selected in the vicinity of resistance
sign change (See Figure 4.4b), and b – the complex angle variation of
frequency ω in the lower half-plane in the case of constant magnitude
corresponding to 𝑘𝑟 = 0.81 i.e. zero resistance. Dash-dotted line denotes the
symmetry respect to real axis (i.e. Im = 0) at 𝑘𝑟 = 0.81 i.e. Re (𝑍opt|𝑀=0.3) = 0
(See Figure 4.4).
-9
-7
-5
-3
-1
1
3
5
7
9
-3 -2 -1 0 1 2 3
Im
Re
kr = 1kr = 0.8kr = 0.7
(0, 0) = (0,1)
(0, 1)
(0, 0)
a-9
-7
-5
-3
-1
1
3
5
7
9
-3 -2 -1 0 1 2 3
Im
Re
θ = 0θ = 0.1 πθ = 0.2 πθ = 0.3 πθ = 0.4 πθ = 0.5 π
(0, 0) = (0,1)
(0, 1)
(0, 0)
b
66
It can be observed in Figure 4.6a that the condition of merged (0, 0) and (0, 1) modes is also fulfilled in the case of zero resistance (𝑘𝑟 = 0.81) as well as in negative resistance frequency range (𝑘𝑟 = 0.7). Furthermore, in the case with zero resistance (𝑘𝑟 = 0.81), the mode (0, 0) in the upper half-plane moves from the IInd quadrant to the Ist, implying the sign change of the real part, and it merges to the (0, 1) mode in the upper half-plane, forming the symmetrical solution with respect to the real axis (Im = 0). The stability properties for these two modes are studied in Figure 4.6b by keeping 𝑘𝑟 fixed at 0.81 and increasing 𝜃 from 0 to 𝜋 2⁄ . The result of this analysis shows that the (0, 0) mode propagate to the negative 𝑥 direction and is stable, whereas (0, 1) propagate to the positive 𝑥 direction and is unstable, i.e. amplified. The fact that these two modes merge does not mean an absolute instability since the merging occurs for real frequencies, i.e. outside the physical half-plane Im(𝜔) < 0. In addition, the merged modes in the lower half-plane, so-called optimized modes, propagate to the intended positive direction showing that the Eversman approach [66], used previously to compute the optimal radial wave numbers, leads to the correct solution in this case.
In Table 4.1, the TL results are presented with determined distribution between dissipation and reflection, thus revealing the character of attenuation. While the first column (Table 4.1) considers theoretical results, i.e. optimum impedance across the frequency span, the second column (Table 4.1) considers realizable results, i.e. optimum impedance at target frequency as discussed in chapter 3; see Table 3.2 and Figure 3.6, and in Paper III.
It can be observed in the first column of Table 4.1 that the simulated TL of the asymptotic (Eq. (4.8)) and “exact” models is predominantly caused by dissipation. Moreover, a significantly improved TL of the “exact” model is achieved via the increased level of dissipation and not the reflection, regardless of the lower level of wall resistance (Figure 4.4b). Although the reflection is significantly increased in the case of a realistic duct length of 5 𝑟, the level still remains negligible compared to the dissipation. In other words, the Cremer impedance also leads to dominantly dissipative TL in the case of finite length channels.
The same trends, dominating high level of dissipation and negligible reflection, are also observed in the case of the silencer prototype (the second column of Table 4.1), i.e. the experimental results of “exact” Cremer impedance realization. (More details regarding the realization can be found in Paper IV)
67
Table 4.1. Dissipation, reflection and total attenuation of the Cremer impedance.
FEM: FEA results for flow channels of different length.
Experiments: Silencer prototype optimized using the
Cremer impedance.
Leg
en
d
To
tal att
en
uati
on
Dis
sip
ati
on
(E
q.
(4.2
2))
Refl
ecti
on
(E
q.
(4.2
3))
024681012141618202224
0 0.20.40.60.8 1 1.21.41.61.8
Tra
ns
mis
si…
Helmholtz number
FEM, M = 0.3, lz = 100r FEM, M = 0.3, lz = 100r, A. FEM, M = 0.3, lz = 5rTheor., M = 0.3, lz = ∞
0102030405060708090100
1000 2000 3000Tra n…
Frequency [Hz]
M = -0.042, experiment M = -0.042, FEM model
0
4
8
12
16
20
0 0.6 1.2 1.8Helmholtz number
Transmission loss [dB∙r
-1]
0
20
40
60
80
1000 2000 3000Frequency [Hz]
Transmission loss [dB∙r
-1]
0
4
8
12
16
20
0 0.6 1.2 1.8Helmholtz number
Transmission loss [dB∙r
-1]
0
20
40
60
80
1000 2000 3000Frequency [Hz]
Transmission loss [dB∙r
-1]
0
2
0 0.6 1.2 1.8Helmholtz number
Transmission loss [dB∙r
-1]
0
10
1000 2000 3000Frequency [Hz]
Transmission loss [dB∙r
-1]
68
Conclusions
In the first part of this work, the acoustic field in the automotive centrifugal compressor inlet and outlet branches is investigated. It is supposed that the acoustic field could play a significant role in the initiation of compressor surge. Therefore, a new method for centrifugal compressor stall and surge investigations is proposed and experimentally demonstrated on the centrifugal compressor of a commercial automotive turbocharger. The method is based on the full acoustic 2-port model and enables in-detail investigation of stall and surge by acoustically de-coupling the compressor from the compression system. First, it is shown how the compression-system-independent (“reflection-free”) sound generation of a centrifugal compressor is obtained, and then how the acoustic power production/dissipation characteristics, associated with the internal coupling between aerodynamic and acoustic fields, are determined from the sound scattering. It is found that dynamic-stall-related flow instabilities at 0.2, 0.42 and 0.5 of the RO generate a high level of sound, and can also locally further amplify incident sound waves at 0.5 of the RO. Nevertheless, the high level of overall dissipation dominates the amplification, and hence the system remains well damped in this frequency range. By contrast, the dissipation becomes negligible and a high level of broadband sound is generated in the low frequency range below ~150 Hz in the case of minimum globally stable mass flow, i.e. the system is prone to the inception of self-sustained oscillations if receiving a positive feedback in this frequency range, e.g. a feedback from a natural frequency of the compression system. The above results suggest that strong surge or self-sustained oscillations in centrifugal-compressor-systems will only occur below a certain critical frequency, where the flow instabilities in the compressor can amplify sound at any frequency. In the amplifying range reflections at the outlet (high pressure) side are mainly critical for creating a positive feedback loop.
In the second part, the experimental determination of the acoustic frequency response to incident sound waves of a twin-scroll turbine is considered. This is an extension of previous works [55] concerning accurate measurements of turbocharger acoustics, which have only covered 2-port (one inlet/outlet) configurations, to 3-port. By presenting and discussing the measurement methodology and test rig design in detail, it is shown how high quality data can be experimentally obtained under controlled laboratory conditions. The experimental determination of turbine acoustic data from on-engine test rigs has proved to be challenging [31]. Therefore, building a dedicated acoustic turbocharger test rig as is described in the present work is a way to secure high quality data, which is essential in order to validate numerical models, both reduced order models [33] and more advanced models [47]. In addition, the first high quality results of measurements on a twin-scroll turbine are presented and briefly discussed.
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In the third part, an optimization technique for a compact silencer, based on the so-called Cremer impedance and the use of micro-perforated panels, is proposed. The optimization of this type of silencer is performed by means of a simplified FEM model according to the design constraints of a particular application. It is demonstrated that, by following the proposed optimization technique, a very high level of dissipative attenuation is achieved at the desired target frequency. Moreover, an almost constant high level of damping in a wide frequency band (~an octave) can be realized by splitting the silencer into separately optimized sections. Such a modular and wideband silencer is convenient for noise control in limited space conditions and can also handle sources with varying frequency signature, e.g. automotive compressors.
In the fourth part, the Cremer optimal impedance model [61, 62, 65] is presented and analyzed from the perspective of non-fibrous silencer optimization (Paper III). The original asymptotic model proposed by Tester [62] leads to a significant deviation from “exact” optimal radial wave number (𝑘𝑟𝑟) in the presence of mean flow and frequencies well below cut-on. Based on these results, plots for the “exact” Cremer impedance as well as the corresponding attenuation rates are provided for a range of Mach numbers. In addition, a numerical FEM model, validated by experiments, is used to also study a finite length duct with a Cremer wall impedance. The results show that a significantly larger transmission loss can be achieved using the “exact” Cremer impedance rather than the asymptotic model. Furthermore, a way to split transmission loss data for silencers (2-ports) into a pure reflection and a pure dissipation part is proposed. Applied to the optimal Cremer impedance, it shows that silencers based on this concept will have a transmission loss strongly dominated by dissipation, i.e. it represents a true dissipative type of silencer solution.
Further work
Although the experimental results presented and discussed herein shed some new light on the physics behind the compression system surge, a further systematic investigation involving different compression systems and compressors by employing the proposed method is required. Furthermore, the method can also be implemented in CFD modeling of centrifugal compressors, enabling more in-depth identification of internal flow phenomena causing the different characteristics discussed herein.
It can be noted that the 3-port tests of the twin-scroll turbine are not performed under realistic operating conditions. This is not considered a problem since currently the data is intended for model validation. Nevertheless, one can consider scale the data from the rig to transfer the results to a corresponding realistic operating case. Furthermore, based on the passive data, the reflection-free sound generation of the twin-scroll turbine, i.e. the source data independent of the coupled duct system, can further be determined as the passive data test
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procedure also characterizes the test rig response. The reflection-free source data can be extracted from the total measured in-duct sound field by direct extension of the complete 2-port theory which is presented in the first part of the work.
An interesting feature of the “exact” Cremer impedance is that the optimal impedance requires a negative real part in the low frequency range, i.e. an active boundary. In practice if only passive walls are accepted this creates a low frequency limit below which the "exact" Cremer solution cannot be used. Even if active walls are considered the existence of the steady state solution for this case needs to be proven, e.g. using the method outlined in section 4.2. It is also worth note that the solution shows a significant difference in the low frequency behavior for the up- and down-stream cases. For the downstream case, the limiting radial wave-number is (0 + 0𝑖), implying no damping. Further analysis of this result as well as the negative real part would be an interesting continuation of the present work. One limitation in the underlying theory is also the assumption of a plug flow and the use of the Ingard-Myer boundary condition. It could be interesting to eliminate these assumptions and investigate how the optimum impedance is modified.
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Acknowledgements
This work was accomplished at KTH CCGEx in Stockholm within the framework of the initial training project FlowAirS (http://www.flowairs.eu) funded under the European Commission 7th Framework Program within People work program (Marie Curie actions). The author would also like to acknowledge the involvement of Swedish Energy Agency, Virtual Vehicle Research Center, Borg Warner Inc., BMW, Scania, Volvo GTT, Volvo Cars and Audi AG. In addition, the financial support from the Competence Center for Gas Exchange at KTH Royal Institute of Technology is gratefully acknowledged.
The author also expresses his personal sincere gratitude to Prof. Mats Åbom for the most constructive supervision, exciting opportunities, and inspiring discussions taking place independently of time and location. In addition, the author would like to thank Dr. Magnus Knutsson from Volvo Car Corporation for his kind support during this work, and Prof. Börje Nilsson for most fruitful consultations regarding wave propagation studies.
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Appendix
81
Paper I
Kabral, R., Åbom, M. Investigation of turbocharger compressor surge inception by means of an
acoustic two-port model. Journal of Sound and Vibration, JSV-D-17-00556, submitted 21.03.2017.
111
Paper II
Kabral, R., El Nemr, Y., Ludwig, C., Mirlach, R., Koutsovasilis, P., Masrane, A., and Åbom, M.
Experimental acoustic characterization of automotive twin-scroll turbine. Proceedings of 12th European Conference on Turbomachinery Fluid dynamics
& Thermodynamics ETC12, Stockholm, Sweden, April 3-7, 2017.
125
Paper III
Kabral, R., Du, L., Åbom, M., and Knutsson, M. A Compact silencer for the control of compressor noise.
SAE International Journal of Engines, 2014, 7(3), 1572-1578, doi:10.4271/2014-01-2060.
Reprinted with permission from SAE paper 2014-01-2060 Copyright © 2017
SAE International. This paper may not be reprinted, copied, distributed, or
saved on any retrieval system without prior permission from SAE.
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Paper IV
Kabral, R., Du, L., Åbom, M. Optimum sound attenuation in flow ducts based on
the “exact” Cremer impedance. Acta Acustica united with Acustica, 2016, 102(5), 851-860,
doi:10.3813/AAA.918999.
