Fan Broadband Interaction Noise Prediction Using a Synthetic Turbulence Method

Fan Broadband Interaction Noise Prediction Using a Synthetic Turbulence Method

vorgelegt von M. Sc.

Carolin Anja Kissner ORCID: 0000-0003-1094-0939

an der Fakultät V – Verkehrs- und Maschinensysteme der Technischen Universität Berlin

zur Erlangung des akademischen Grades Doktorin der Ingenieurwissenschaften

– Dr.-Ing.–

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Dieter Peitsch Gutachter: Prof. Dr. Lars Enghardt Gutachter: Prof. Dr. Ennes Sarradj Gutachter: Prof. Dr. David Angland

Tag der wissenschaftlichen Aussprache: 13.09.2021

Berlin 2021

Acknowledgments

During my time as a doctoral researcher at the department of engine acoustics at the German Aerospace Center (DLR) in Berlin, I was fortunate to be surrounded by incredibly supportive and smart individuals. This made my work much more enjoyable and has motivated me, even when I experienced setbacks at times. Subse- quently, I want to express my gratitude but note that the following list is certainly not exhaustive.

Firstly, I would like to thank Dr. Sébastien Guérin, who has been my advisor during this thesis. I have very much enjoyed our scientific discussions and writing publications together. I found your passion for research to be infectious and your advice and encouragement made a lasting impression. Merci beaucoup!

I also want to express my thanks to Prof. Enghardt, whose support and advice had a positive impact on my work as a researcher. You have made my successful ap- plication for the ZONTA Amelia Earhardt Fellowship possible, which in turn opened many doors for me. In addition, I profited from participating in the TurboNoiseBB project, which was lead by you and helped me to establish an international network in the aeroacoustic community.

Next, I would like to acknowledge Dr. Attila Wohlbrandt, who has helped me to kick-start this thesis and entrusted me to continue the work on his brainchild - the fRPM-fan method. I learned a lot from you and it is only fitting that our

"handover" paper became publication I of this cumulative thesis.

Thanks also go to all of my other colleagues at the department of engine acous- tics, especially to my office mates throughout the years (Jakob Hurst, Dr. Karsten Knobloch, Robert Meier zu Ummeln), to the wonderful support staff (Balbir Kaur, Brig Pilger, Nico Seiffert), to my co-authors (Maximilian Behn, Dr. Axel Holewa, Henri Siller, Luciano Caldas), to my female colleagues for our occasional "girl" talks (Larisa Grizewski, Dr. Anita Schulz, Julia Genssler), and to the current and former

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members of NuP (Dr. Robert Jaron, Dr. Antoine Moreau, Stephen Schade, Martin Staggat). I consider myself lucky that I will continue working with many of you for a while longer.

I would also like to thank my parents Christine and Günter, who have supported and encouraged me throughout the years. I especially cherish our time together in Chicago, which has benefited me in so many ways.

Finally, I would like to express my gratitude to my husband Razmin. You have always been there for me and your unwavering belief in me and my abilities is truly humbling. Man toro cheili dust daram, joon!

Abstract

To address growing concerns regarding community noise due to air traffic, noise regulations are becoming increasingly stricter. Therefore, aircraft and engine man- ufacturers are motivated to develop more silent products. As fan noise is known to be a dominant source during critical flight phases, its reduction is a prerequisite. In recent years, fan tones were intensively studied and effective noise abatement mea- sures were implemented. As a result, the focus now shifts towards fan broadband noise.

RANS-informed synthetic turbulence methods are increasingly applied for study- ing this noise mechanism. They are computationally efficient without simplifying the flow or blade geometries. In this thesis, the fRPM-fan method, which is an fRPM-based synthetic turbulence method, was applied to three different transonic fans. Extensive parameter studies were performed to further the understanding of rotor-stator-interaction noise.

The 2D simulation approach was used to study the influence of cyclostation- ary effects for the NASA SDT fan. The key parameters, which are necessary to prescribe synthesized turbulence, were separately studied with respect to cyclosta- tionarity. The cyclostationary realization of the turbulent length scale proved to be critical. It caused a drop in noise levels at lower frequencies. Instead of a cir- cumferential averaging of the turbulent length scale, a spectral averaging technique was proposed. This new method ensures that the turbulent length scale is dictated by the energetically most dominant turbulence component. A constant simulation using a spectrally averaged instead of a circumferentially averaged turbulent length scale was thus capable of reproducing the sound power levels of a cyclostationary simulation.

The relevance of background versus wake turbulence was studied for the next- generation ASPIRE fan. For a purely 2D approach relying on inputs from a q3D URANS simulation on a streamline, the background turbulence was found to be dominant over wake turbulence. This finding was reversed when a correction tech- nique was applied to account for the difference in flow and turbulence characteristics between a q3D and a 3D CFD simulation. Neglecting the radial dimension in the former lead to significantly lowered wake turbulence levels. This study essentially showed that strip-based approaches can give questionable results and using inputs from a 3D CFD simulation is preferential. Furthermore, it highlighted that the

contribution of background turbulence may need to be considered for modern fan designs and for test rigs featuring non-negligible ingestion turbulence levels.

The 2D and 3D fRPM-fan methods were compared for the ACAT1 fan. While both approaches reproduced experimental trends with respect to the operating con- ditions, the 2D approach overestimated sound levels. A 2D–3D correction was pro- posed to address two main physical aspects: 1.) The transverse velocity frequency spectrum, which is critical for fan broadband noise, differs for 2D and 3D turbulence.

2.) Only supercritical gusts produce sound capable of propagating in a duct. Due to the absence of the third dimension, this mechanism cannot be captured by the 2D simulation.

Throughout this thesis, the fRPM-fan method was continuously improved in terms of accuracy and efficiency. The accuracy of the fRPM-fan method was as- sessed with respect to experimental data. A good agreement was achieved. Lastly, the computational cost of a 2D fRPM-fan simulation was decreased by a factor of 3.4. In fact, a comparison of the computational effort of the fRPM-fan method with other fan noise prediction methods showed that the method is competitive.

Zusammenfassung

Um der wachsenden Besorgnis über die Lärmbelästigung durch den Flugverkehr entgegenzuwirken, werden die Lärmvorschriften zunehmend strenger. Daher liegt es im Interesse der Flugzeug- und Triebwerkshersteller, leisere Produkte zu entwickeln.

Da der Fanlärm eine dominante Quelle während kritischer Flugphasen ist, ist des- sen Reduzierung eine wichtige Voraussetzung. In den letzten Jahren wurden Fantöne intensiv untersucht und wirksame Maßnahmen zur Lärmreduzierung entwickelt. In- folgedessen verlagert sich der Fokus nun auf den Fanbreitbandlärm.

RANS-basierte synthetische Turbulenzmethoden werden vermehrt zur Untersu- chung dieses Lärmmechanismus eingesetzt. Sie sind effizient, ohne dabei die Strö- mung oder die Schaufelgeometrie zu vereinfachen. In dieser Arbeit wurde die fRPM- Fan Methode, eine fRPM-basierte synthetische Turbulenzmethode, für drei verschie- dene transsonische Fans angewendet. Es wurden umfangreiche Parameterstudien durchgeführt, um das Wissen über den Rotor-Stator-Interaktionslärm zu erweitern.

Der 2D Simulationsansatz wurde verwendet, um den Einfluss von zyklostatio- nären Effekten für den NASA-SDT Fan zu untersuchen. Die Schlüsselparameter, die zur Definition der synthetischen Turbulenz notwendig sind, wurden separat hinsicht- lich Zyklostationarität untersucht. Die zyklostationäre Realisierung der turbulenten Längenskala erwies sich als kritisch. Sie bewirkte einen Abfall des Schallpegels bei niedrigen Frequenzen. Anstelle einer Umfangsmittelung der turbulenten Längenska- la wurde eine spektrale Mittelung vorgeschlagen. Diese neue Methode stellt sicher, dass die turbulente Längenskala von der energetisch dominantesten Turbulenzkom- ponente vorgegebenen wird. Eine konstante Simulation mit einer spektral gemittel- ten anstelle einer umfangsgemittelten turbulenten Längenskala war in der Lage, die Schallleistungspegel einer zyklostationären Simulation zu reproduzieren.

Die Relevanz von Hintergrund- und Nachlaufturbulenzen wurde für den ASPIRE Fan, der representativ für zukünftige Fandesigns ist, untersucht. Unter Verwendung eines reinen 2D Ansatzes, der Inputs einer q3D URANS Simulation auf einer Stromli- nie nutzt, wurde festgestellt, dass die Hintergrundturbulenz gegenüber der Nachlauf- turbulenz dominant ist. Dieses Verhältnis kehrte sich um, als eine Korrekturtechnik angewendet wurde, um den Unterschied in den Strömungs- und Turbulenzcharakte- ristiken zwischen einer q3D und einer 3D CFD Simulation zu berücksichtigen. Die Vernachlässigung der radialen Dimension in der Ersteren führte zu deutlich niedri- geren Nachlaufturbulenzwerten. Diese Studie zeigte im Wesentlichen, dass reine 2D

Ansätze fragwürdige Ergebnisse liefern können und dass die Verwendung von Inputs aus einer 3D CFD Simulation vorzuziehen ist. Darüber hinaus wurde hervorgeho- ben, dass der Beitrag der Hintergrundturbulenz bei modernen Fankonfigurationen und bei Prüfständen mit nicht vernachlässigbaren Nachlaufturbulenzwerten berück- sichtigt werden muss.

Die 2D und 3D fRPM-Fan Methode wurden für den ACAT1 Fan verglichen.

Während beide Ansätze die experimentellen Trends in Bezug auf die Betriebsbe- dingungen reproduzierten, überschätzte der 2D Ansatz die Schallpegel. Es wurde eine 2D-3D Korrektur vorgeschlagen, um zwei wesentliche physikalische Aspekte zu berücksichtigen: 1.) Das Frequenzspektrum der Transversalgeschwindigkeit, das für den Breitbandschall des Fans entscheidend ist, unterscheidet sich für 2D und 3D Turbulenz. 2.) Nur superkritische Gusts¹ erzeugen Schall, der sich in einem Kanal ausbreiten kann. Aufgrund des Fehlens der dritten Dimension kann dieser Mecha- nismus von der 2D Simulation nicht erfasst werden.

Im Laufe dieser Arbeit wurde die fRPM-Fan Methode kontinuierlich hinsichtlich Genauigkeit und Effizienz verbessert. Die Genauigkeit der fRPM-Fan Methode wur- de mithilfe von experimentellen Daten bewertet. Es konnte eine gute Übereinstim- mung erzielt werden. Zudem wurde der Rechenaufwand für den 2D Ansatz um einen Faktor von 3,4 reduziert. Tatsächlich zeigte ein Vergleich des Rechenaufwands der fRPM-Fan Methode mit anderen Ansätzen zur Fanbreitbandlärmvorhersage, dass die Methode konkurrenzfähig ist.

1Unter dem BegriffGust versteht man eine harmonische, konvektive Geschwindigkeitsfluktua- tion.

Contents

List of Abbreviations III

1 Introduction 1

1.1 Aircraft Development under Growing Environmental Constraints . . . 1

1.2 Fan Broadband Noise of Aircraft Engines . . . 3

1.3 Fan Broadband Noise Prediction Methods . . . 6

1.3.1 Overview of Existing Methods . . . 6

1.3.2 Prediction of Rotor-Stator-Interaction Noise with a CAA-based Synthetic Turbulence Method . . . 8

1.3.3 Generation of Synthetic Turbulence for CAA Applications . . 10

1.4 Research Objectives . . . 12

1.5 Contribution of the Publications . . . 13

1.5.1 Publication I . . . 14

1.5.2 Publication II . . . 16

1.5.3 Publication III . . . 18

2 Publications 21 2.1 Publication I . . . 22

2.2 Publication II . . . 45

2.3 Publication III . . . 59

3 Discussion 87 3.1 Key Findings of the Parameter Studies . . . 87

3.1.1 Influence of Cyclostationarity . . . 87

3.1.2 Relevance of Wake and Background Turbulence . . . 91

3.1.3 Comparison of the 2D and 3D Simulation Approaches . . . 93

3.2 Updated Comparison of the fRPM-fan Simulations . . . 95 I

3.2.1 Analysis of Interstage Flow and Turbulence Characteristics . . 95 3.2.2 Application of State-of-the-Art Corrections . . . 98 3.2.3 Comparison of Experimental and Numerical Fan Broadband

Noise . . . 100 3.2.4 Comparison of Mesh Resolutions and Computation Times . . 105 3.3 Summary . . . 108 3.4 Outlook . . . 109

Bibliography 121

Associated Publications 123

II

List of Abbreviations

2D Two-Dimensional 3D Three-Dimensional

ACARE Advisory Council for Aeronautics Research in Europe ACAT1 AneCom AeroTest Rotor 1

ATI Airfoil-Turbulence-Interaction

C Constant

CAA Computational AeroAcoustics CFD Computational Fluid Dynamics DES Detached Eddy Simulation DLR German Aerospace Center DNS Direct Numerical Simulation EPNL Effective Perceived Noise Levels FES Forced Eddy Simulation

fRPM fast Random Particle Mesh FWH Ffwocs-Williams-Hawkings

HW Hot-Wire

ICAO International Civil Aircraft Organization ISA International Standard Atmosphere LES Large Eddy Simulation

LN Low Noise

M2VP Multistage Two Shaft Compressor Test Facility NASA National Aeronautics and Space Administration OGV Outlet Guide Vanes

P Periodic

PPW Points Per Wavelength PW Pratt & Whitney

III

PWL Sound Power Level q3D Quasi-Three-Dimensional

RANS Reynolds-Averaged Navier-Stokes RPM Random Particle Mesh

RSI Rotor-Stator-Interaction SDT Source Diagnostic Test SLS Sea Level Static

SNGR Stochastic Noise Generation and Radiation SPL Sound Pressure Level

TKE Turbulent Kinetic Energy TLS Turbulent Length Scale UHBR Ultra-High Bypass Ratio

URANS Unsteady Reynolds-Averaged Navier-Stokes VAN Variable Area Nozzle

IV

Chapter 1 Introduction

1.1 Aircraft Development under Growing Environ- mental Constraints

Since the dawn of the jet age, the annual growth in passenger air travel averaged about 4-5% [31, 3]. In 2020, the COVID-19 pandemic abruptly halted this trend as airlines were virtually grounded due to travel restrictions, and global revenue passenger kilometers dropped by approximately 66% compared to the previous year [50]. Nonetheless, the aviation sector has proven to be resilient and has quickly rebounded from past downturns due to 9/11, SARS, and the global financial crisis.

In fact, the aviation sector is projected to reach pre-crisis levels within three years and to return to the long-term growth trend a few years beyond that [17]. As a con- sequence, a further reduction of the negative environmental impact of air traffic is crucial in order to enable sustainable future aviation. Aside from carbon emissions, noise pollution continues to remain a major concern for communities around air- ports. This societal pressure on policy-makers has led to numerous regulations. The International Civil Aircraft Organization’s (ICAO) Annex 16 sets maximum Effec- tive Perceived Noise Levels (EPNL) for approach, sideline, and cutback conditions depending on the maximum take-off weight of airplanes. In successive "chapters", increasingly tougher standards must be met to certify new aircraft. Local airport rules, which include noise charges, curfews, noise exposure limits, restrictions on older and louder aircraft, etc., further reward the use of quieter aircraft. These reg- ulations and incentives prompted aircraft and engine manufacturers and associated

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2

CORE TURBINE JET FAN AIRFRAME

5 dB

PWL CORE TURBINE JET FAN AIRFRAME

5 dB

PWL

Figure 1.1: Breakdown of the noise sources of a typical aircraft equipped with turbofan engines at takeoff (left) and approach (right) operating conditions [Data obtained from Astley et al. [4]].

research institutions to intensify their efforts in developing more silent aircraft. This ambition was concretized by the European Union’s Advisory Council for Aeronau- tics Research in Europe (ACARE), which targets a 60% drop in the perceived noise level of an aircraft by the year 2050 relative to the noise emission of a new aircraft in the year 2000 [31].

A large portion of the noise reduction achievements of the past decades can be attributed to an increase in bypass ratio. Nowadays, the majority of the thrust is produced by the slower, moderately compressed bypass flow. The decrease in jet velocity significantly reduces the jet noise, which correlates with a power of 6 for coaxial jets [71] to 8 for single jets [66] with the jet velocity. Due to this reduction in jet noise, the relative importance of previously minor sources has increased. Relative weights of noise sources of a current engine at take-off and landing are shown in Fig. 1.1, which is based on the work presented by Astley et al. [4]. At take-off, the jet and fan noise have a similar magnitude and are the largest contributors to the total engine noise, which surpasses airframe noise by a wide margin. At approach conditions, the relative importance of airframe noise increases, but the total engine noise still dominates the total aircraft noise. The jet noise is significantly reduced and the fan is the most critical component. Previously, Airbus [2] had shown a similar breakdown of noise sources. The relative contribution of engine sources was

nearly identical, but the airframe noise contribution was higher. Nonetheless, both publications stress the importance of fan noise.

However, the noise reduction potential due to an increase of the bypass ratio is nearly exhausted. To accommodate the ever-increasing fan diameters, the nacelles are reduced in length and volume to minimize added weight and drag. As a con- sequence, there is less room for acoustic liners to absorb fan and core noise. In addition, the engines need to be installed directly underneath the wing for classi- cal tube-wing configurations. This makes the engines more susceptible to inflow distortions, which can create additional noise. Both measures counteract the noise reduction due to an increased bypass ratio. In fact, the decrease in noise levels of new aircraft relative to the year of certification shows an asymptotic behavior, i. e.

the rate of decrease has slowed in recent years as shown by Leylekian et al. [65]

and Jaron [51]. While the trend still conforms with ICAO Annex 16 regulations, a technological breakthrough is required to fulfill the ambitious goals set forth by the ACARE Flightpath 2050 [48]. The gradual optimization of conventional tube-wing configurations equipped with turbofans is no longer enough. Instead, the noise re- duction potential of radically different aircraft and propulsion architectures needs to be explored. Since the fan noise is expected to remain an important source for future configurations, a deeper understanding of the noise generation mechanism and the development and optimization of suitable noise prediction tools are essential.

1.2 Fan Broadband Noise of Aircraft Engines

Fan noise is comprised of tonal and broadband noise. Tonal noise has been exten- sively studied resulting in effective measures for reducing dominant tones at discrete frequencies. Noise abatement techniques include using liners, choosing an appro- priate blade-vane count combination, increasing the distance between the rotor and stator blades, operating the fan in the subsonic range, and improving the blade geometry. Gliebe et al. [43] predicted the maximum expected reduction in engine system noise of an ultra-high bypass ratio (UHBR) engine due to the elimination of fan tones to range between 0.5 and 1.5 EPNdB. Once fan tones are mostly elimi- nated, another 3 to 4 EPNdB in noise reduction can be achieved by decreasing the contribution of fan broadband noise. This highlights the need to further the un- derstanding of fan broadband noise mechanisms in order to develop suitable noise

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Figure 1.2: Schematic of fan broadband noise sources and of the respective turbu- lence components (indicated by circular markers) [Source of the fan picture: Rolls- Royce].

mitigation measures.

Fan broadband noise can be categorized into two groups: self-noise and interac- tion noise. Self-noise mainly consists of the noise produced by turbulent eddies in the boundary layer of a blade interacting with the trailing edge. This noise mechanism is relevant for rotor blades and outlet guide vanes (OGV’s) of a fan stage. Inter- action noise occurs when turbulence interacts with blade leading edges. Relevant turbulence components for the rotor are ingested or background turbulence (rotor ingestion noise) and boundary layer turbulence (rotor boundary layer noise). For the OGV’s, rotor wake turbulence, background turbulence, and boundary layer tur- bulence are relevant. In this work, self-noise and rotor interaction noise sources are neglected. The focus is to study the interaction noise sources at the stator vanes. In the context of this thesis, the terms fan broadband noise and rotor-stator-interaction (RSI) noise are used interchangeably. This is technically imprecise: Fan broadband noise typically describes all broadband noise components of a fan. The use of this collective term therefore implies that self-noise and rotor interaction noise sources are negligible. In addition, RSI noise is oftentimes used in literature to describe the interaction noise related to only the wake turbulence component. In publications II and III, the contribution of different turbulence components to stator interac- tion noise are discussed. Ingestion noise refers to the contribution of background

turbulence and boundary layer noise refers to the contribution of boundary layer tur- bulence. All mentioned fan broadband noise sources are depicted in Fig. 1.2. Note that the respective turbulence components are schematically indicated by circular markers: rotor wake turbulence (red), ingested or background turbulence (blue), boundary layer turbulence on the casing walls (green), and boundary layer tur- bulence on the blade surfaces (orange). The relevance of the different broadband noise sources to overall fan broadband noise levels is discussed in the subsequent paragraphs.

In the absence of interaction noise, self-noise can be understood as the minimum achievable level of fan broadband noise. In fact, Moreau and Roger [69] showed that self-noise is significantly lower than interaction noise for several applications. Yet, it is thought that this noise source can be relevant at low Mach number.

One of the main sources of interaction noise is RSI noise caused by the interaction of the rotor wake turbulence with the stator leading edges. Ganz et al. [37] studied an 18 inch model-scale fan in the Boeing Low-Speed Aeroacoustic Facility. They showed that the RSI noise is the loudest noise source for this fan configuration. For the NASA Source Diagnostic Test (SDT) fan, which was investigated in the NASA 9’ x 15’ Low-Speed Wind Tunnel, the RSI noise was also found to be the domi- nant fan broadband noise source [72]. This finding was confirmed in an analytical study performed by Envia et al. [30]. The authors used a RANS-informed ana- lytical technique, which is based on the work by Ventres et al. [89] and described in more detail by Nallasamy and Envia [72]. The code is restricted to the consid- eration of RSI noise but only slightly underpredicted the measured sound power levels. As measured data also contained some rotor noise, the slight discrepancy is reasonable and still shows that RSI noise is dominant. However, the authors also investigated two other fans: the NASA/PW Advanced Ducted Propulsor Fan 1 and the NASA/Honeywell Quiet High Speed Fan 2. For these two fans, the discrepancies between analytically predicted and experimental sound power level spectra were sig- nificantly larger at all operating points. This could indicate that other broadband noise sources significantly contribute to the overall fan broadband noise for these configurations.

Other potentially relevant interaction noise sources are ingestion and boundary layer noise. For a low-speed fan stage, which was studied in the low-speed fan rig at DLR in the framework of the PROBAND project, Jurdic et al. [54] reported

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that the stator ingestion noise due to background turbulence was several decibels louder than the RSI noise due to the wake turbulence. The significance of ingestion turbulence was also highlighted in a study by Moreau and Oertwig [68]. They analyzed the contributions of different broadband noise sources using the analytical tool PropNoise [70] for the DLR UHBR fan. This high-speed, low-pressure ratio fan was tested in the M2VP test facility in Cologne. Since this facility has no turbulence control screen, the rotor and stator ingestion noise were found to be significant, particularly at lower frequencies. Staggat et al. [87] scaled this fan and performed an analytical parameter study to investigate rotor boundary layer noise. They showed that the predicted rotor boundary layer noise increases with boundary layer thickness and shape factor. For an integrated turbofan, it was therefore postulated that the rotor boundary layer noise has the potential to be dominant compared to RSI noise at low and mid frequencies for approach and take- off conditions. The relevance of interaction sources like ingestion or boundary layer noise depends on the fan configuration, on test rig conditions and on the integration of an engine into the aircraft architecture. But even for these cases, RSI noise due to the wake turbulence is still an important contributor to the overall fan broadband noise levels. Its accurate prediction using analytical or numerical tools is therefore of great interest.

1.3 Fan Broadband Noise Prediction Methods

The availability of accurate and efficient fan broadband noise prediction methods is crucial for designing silent future engine and aircraft configurations. Due to the difficulty in computing turbulence characteristics, the prediction of fan broadband noise remains a challenge. Various methods ranging from advanced scale-resolving to purely analytical methods are currently used.

1.3.1 Overview of Existing Methods

Scale-Resolving Methods

Direct Numerical Simulations (DNS), which directly solve the Navier-Stokes equa- tions, and wall-resolved Large Eddy Simulations (LES), which directly solve the Navier-Stokes equations for large, energy-bearing eddies and model small, isotropic

eddies, are technically capable of precisely capturing the physical complexity of fan noise computations. Since these simulations require very fine meshes, the computa- tional effort quickly becomes prohibitive. The use of these simulations is restricted to simple cases with low Reynolds numbers. Typical fans feature a Reynolds num- ber between 10⁵ and 10⁷ and require complex setups for accurately predicting fan broadband noise. While no examples of DNS or wall-resolved LES are known to the author for fan applications, hybrid (U)RANS/LES approaches are becoming popular.

One of the earliest examples was presented by Greschner and Thiele [44], who performed a wall-modeled LES simulation for one passage on a reduced, spanwise domain. A Spalart-Allmaras model was used to simulate the inner-most portion of the boundary layer, and the grid contained 870 million grid points. A Ffowcs- Williams-Hawkings (FWH) method was required to extract fan broadband noise, and the agreement with measured data was not yet satisfactory.

For the ACAT1 fan, a wall-resolved LES [64] and a zonal Detached Eddy Simula- tion (DES) [78, 36] were performed at approach conditions. For the latter simulation, the DES mode, which switches between (U)RANS (using the Spalart-Allmaras tur- bulence model) and LES, is applied in a domain extending from slightly upstream of the rotor leading edge to the bypass outflow boundary. The rest of the domain is simulated using a simple (U)RANS formulation. For both simulations, the number of stator vanes was reduced to limit the computational domain to a periodic segment containing one rotor blade and two stator vanes. The wall-resolved LES required 90 million cells, while the zonal DES required 380 million cells. Note that a wall- resolved LES typically requires more cells than a zonal DES to achieve a comparable grid resolution. In fact, a grid refinement study was recommended for the LES [64].

Both simulations used a FWH method to predict sound power levels in the bypass and found a reasonable agreement with experimental results.

The full NASA SDT fan stage including the nacelle was simulated at approach and takeoff conditions using a DES technique [88]. Two grids were used containing 140 and 170 million grid points, which is small compared to the previous simula- tions featuring much smaller computational domains. Nonetheless, a satisfactory agreement between experimental and numerical sound power levels was shown for approach conditions. For take-off conditions, the numerically predicted levels were significantly lower than the experimental levels, especially at the fan inlet. A sim-

8

ilar domain was also simulated with a lattice-Boltzmann method [20]. A good agreement with experimental data was shown, if a suitable turbulence tripping was applied to the rotor blades and if the wakes were refined. The simulation times were comparatively short. Nevertheless, these advanced, partly scale-resolving methods are computationally expensive and therefore less suitable in a design context or for extensive parameter studies. However, their ability to provide detailed physical insights is impressive. In the future, these simulations could be seen as "virtual"

experiments, which can supplement real measurement campaigns.

Analytical Methods

On the other hand, analytical methods are comparatively fast and thus suitable for multidisciplinary fan design optimizations. Analytical models vary in complexity but typically rely on simplifying the flow and geometry. An overview over commonly used models is given by Guérin et al. [46]. These models often require flow and turbulence characteristics extracted from (U)RANS simulations as inputs. As a consequence, fan broadband noise predictions are highly dependent on the RANS simulation. The choice of the turbulence model was shown to have a significant impact on interstage turbulence and flow characteristics [58]. This is especially true at off-design operating conditions, where separated flow at the rotor leading edge can be significant for RANS simulations [79].

1.3.2 Prediction of Rotor-Stator-Interaction Noise with a CAA- based Synthetic Turbulence Method

Synthetic turbulence methods are hybrid, partly scale-resolving methods, which ad- dress each part of the physical problem with a different, highly optimized method.

Applying the linearity principle, flow variables are split into fluctuating and mean quantities. A typical approach used for predicting RSI noise or airfoil-turbulence- interaction (ATI) noise works as follows: The mean flow quantities are prescribed from a (U)RANS simulation, which can either be performed in three-dimensional or quasi-three-dimensional space. The extracted turbulence statistics and an assumed correlation function are used to synthesize a realistic, solenoidal fluctuating velocity field upstream of the stator vanes in a CAA domain. Common stochastic turbulence synthesis methods include superposing random Fourier modes [61, 11, 12], using syn-

Figure 1.3: Overview of the fRPM-fan method.

thetic eddies [52, 85, 56], or applying filters [19, 32]. A more detailed overview of these turbulence synthesis methods is given in the subsequent section 1.3.3. The convection of the synthesized turbulence, the sound generation at the stator leading edges, and the sound propagation are solved by a CAA code using linear or non- linear Euler equations. The generated noise in the far-field can either be directly determined at sensor positions within the simulation domain or computed by ap- plying a FWH technique, which uses the pressure fluctuations on the blade surface as inputs. A schematic of a typical workflow is shown in Fig. 1.3 for the fRPM-fan method. The fRPM-fan method is a hybrid synthetic turbulence method, which was initially developed by Wohlbrandt [90] and used throughout this thesis.

Synthetic turbulence methods can be seen as a compromise between accuracy and computational effort. They are fast enough to accommodate extensive param- eter studies to separately investigate different aspects of the fan broadband noise mechanism. This can be used to assess classical modeling assumptions made in analytical models. Realistic mean flows can be considered and real geometries are used. However, the reliance of these methods on (U)RANS simulations for determin- ing turbulence characteristics can be seen as a disadvantage as different turbulence models can produce quite different results [58]. Technically, experimentally deter- mined turbulence characteristics can also be prescribed, although it would restrict

10

the method to recomputing experiments rather than performing "blind" predictions.

1.3.3 Generation of Synthetic Turbulence for CAA Applica- tions

Historically, an analytically motivated approach of injecting harmonic gusts into a CAA domain was used in order to study turbulence interacting with a single airfoil or blades in an annular cascade [8, 47, 84]. While this approach continues to be used [29, 83, 5, 6, 7, 49, 62], stochastic methods for synthesizing turbulence are increasingly favored. The three most common methods are subsequently discussed.

Random Fourier Mode Method

Random Fourier mode methods are sometimes also denoted as Stochastic Noise Gen- eration and Radiation (SNGR) methods. Based on the work of Kraichnan [61], the method was adapted for the use in CAA applications [11, 10, 9, 12, 13]. A fluctu- ating velocity field is generated by superposing a finite number of random, discrete Fourier modes in order to realize a specific turbulence wavenumber spectrum. The method is commonly used due to its relative simplicity in realizing divergence-free turbulence and its conceptual similarity to gust forcing techniques. However, the method struggles with heterogeneous flows, and the required computational effort is directly related to the number of discrete frequencies and to the number of random modes generated for each frequency. In order to fully resolve a turbulence spectrum for complex cases, the method tends to become expensive.

A first application for computing ATI noise was shown by Clair et al. [21], who validated the method and studied a wavy stator leading edge on a reduced span- wise segment. Only the upwash velocity component was considered. Gill et al. [42]

presented an expansion of the method to include streamwise and spanwise compo- nents but concluded that only the transverse component is necessary to accurately capture the ATI noise of a symmetric airfoil at zero angle of attack. Polacsek et al. [76] also restricted the method to the upwash velocity component and applied the method to a fan. To reduce the cost, the simulation domain was limited to a single stator vane passage for more complex cases. The azimuthal dependency of the synthetic turbulence was thus discarded to permit the use of periodic boundary conditions in circumferential direction. As a consequence, the direct acoustic field

can no longer be directly computed by the CAA code and a FWH extrapolation was applied to the blade surface pressures instead. Reboul et al. [80] later simulated the NASA SDT fan with and without wavy leading edges and studied the impact of limiting the simulation to one stator vane and of reducing the number of radial grid points. Recently, Cader et al. [18] extended the two-dimensional turbulence spectrum to three dimensions. The disadvantage is that a larger periodic domain has to be considered to include a sufficient number of angular wave number compo- nents, which significantly increases the simulation cost. Most recently, Polacsek et al. [77] studied a novel leading edge serration design for the ACAT1 fan. The work highlighted the numerical difficulties due to flow inhomogeneities and due to mesh distortions for such a complex case.

Synthetic Eddy Method

The synthetic eddy method was originally proposed by Jarrin et al. [52, 53]. Sescu and Hixon [85] adapted this approach for aeroacoustic simulations and introduced a synchronized convection of the turbulence with the mean flow in the CAA domain.

The method randomly distributes eddies, which are described by an eddy shape function (vector potential). A divergence-free velocity field is realized by taking the curl of the eddy shape function. Kim and Haeri [56] created a sponge-layer technique for injecting the turbulence into the CAA domain. They calibrated the method to generate realistic turbulence and applied the proposed model to a three-dimensional simulation of ATI noise. While this method is very promising for realizing three- dimensional and fully realistic turbulence, a large number of parameters have to be set in order to obtain realistic turbulence characteristics.

Filtering Method

Based on the works of Careta et al. [19] and Klein et al.[60], Ewert [32] developed the Random Particle Mesh (RPM) method. The method realizes divergence-free velocity fluctuations on a source patch in the CAA domain by applying spatio-temporal filters to convecting white noise signals. Contrarily to the random Fourier mode method, the RPM method focuses on the realization of spatio-temporal cross-correlations, thus implicitly specifying turbulence spectra instead of directly prescribing them.

Moreover, the RPM method simulates a continuous turbulence spectrum rather than discrete frequencies, more easily facilitates the realization of inhomogeneous

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turbulence, and considers spatial mean flow variations. The fast RPM (fRPM) method [86] relies on fast recursive Gaussian filter formulations, and the convolution is performed on an auxiliary grid, which enables to filter each dimension separately.

The RPM method was used to study various sources, e. g. jet noise [33], slat noise [32], haystacking [86], and airfoil self-noise [22]. Reiche et al. [81] even expanded the method to realize anisotropic vorticity fluctuations based on the Reynolds stresses determined by an adequate turbulence model.

A first application for predicting ATI noise in a two-dimensional domain was shown by Dieste and Gabard [27, 28]. They also derived complex filter kernels to model more realistic turbulence spectra, i. e. Liepmann and von Kármán spectra.

These filter functions are spatially coupled and therefore, the effort scales relative to the number of grid points n and the dimension d as follows: n^d. For complex, three-dimensional cases, these non-Gaussian filters can become expensive. An al- ternative was therefore proposed by Wohlbrandt et al. [92], who superposed several Gaussian filters of different length scales to realize a target spectrum. The variance of each filter depends on an analytical weighting function. Since recursive, spatially decoupled Gaussian filters are used, the computational effort scales with NG·n·d, where N_G denotes the number of superposed Gaussian filters.

The so-called advanced digital filter technique [38] has recently emerged. It can be seen as a mixture of the RPM and synthetic eddy methods. Instead of applying filters to white noise, Gaussian eddies are directly prescribed in the CAA domain and can be superposed to generate realistic spectra. This bypasses the need for an auxiliary grid but the eddies are spatially coupled and no recursive formulation can be used. The computational effort is therefore expected to be similar to non- Gaussian filter formulations. Gea-Aguilera et al. [39, 40] superposed anisotropic eddies of various length scales to realize homogeneous, axisymmetric Kerschen and Gliebe turbulence [55]. The method was also expanded to cyclostationarity [41]

using a similar approach as Dieste and Gabard [27], who modeled rotor wakes as a train of Gaussian functions.

1.4 Research Objectives

In this thesis, the so-called fRPM-fan method, which is an fRPM-based synthetic turbulence method specifically optimized for predicting fan broadband noise, is ex-

panded and applied to three different fan configurations. Simulations are performed to address the following objectives:

1. To further the general understanding of this noise generation mechanism, three issues are specifically investigated:

• the influence of cyclostationary effects,

• the relevance of wake versus background turbulence,

• and the difference in results between the 2D and 3D simulation ap- proaches.

2. To enable realistic yet efficient fan broadband noise predictions, the simulation settings are continuously improved, the 2D simulation approach is designed to be as representative as possible for the 3D fan configuration, and the level of necessary complexity is evaluated based on the findings of the above parameter studies.

In order to achieve "blind" predictions, all simulations rely on inputs from (U)RANS simulations. Measurement data or results of other prediction methods are used to evaluate the outcomes of the simulations.

1.5 Contribution of the Publications

The thesis is comprised of three journal publications:

Publication I

A. Wohlbrandt, C. Kissner and S. Guérin. Impact of cyclostationarity on fan broadband noise prediction. Journal of Sound and Vibration, 420:142–164, 2018.

ISSN 0022-460X.https://doi.org/10.1016/j.jsv.2018.01.039. (publisher’s ver- sion, see Section 2.1)

Publication II

C. Kissner and S. Guérin. Influence of Wake and Background Turbulence on Predicted Fan Broadband Noise. AIAA Journal, 58(2):659–672, 2020. ISSN 0001- 1452. https://doi.org/10.2514/1.J058148. (publisher’s version, see Section 2.2)

14

Publication III

C. Kissner and S. Guérin. Comparison of predicted fan broadband noise using a two- versus a three-dimensional synthetic turbulence method. Journal of Sound and Vibration, 508, 2021. ISSN 0022-460X. https://doi.org/10.1016/j.jsv.

2021.116221. (publisher’s version, see Section 2.3)

In this section, their contributions in addressing the previously stated research objectives are presented.

1.5.1 Publication I

The primary objective of publication I is to identify and to quantify the influence of cyclostationary effects on fan broadband noise. Cyclostationarity describes a pe- riodically recurring signal, which can be found in the rotor wakes of a fan stage.

In a first step, the expansion of the method to cylclostationarity is presented and verified. The method uses complex Fourier coefficients, which are determined via a URANS simulation, to reconstruct mean flow and turbulence characteristics at each time step. The periodic wake structure can thus be fully realized. A preliminary version of this expansion was presented by Wohlbrandt et al. [91]. In this work, the method is refined and fully defined in the absolute frame of reference. In a second step, a parameter study is performed to separately study the influence of the cyclostationarity in terms of the three input variables that directly determine the turbulence synthesis: the mean velocity u0, the turbulent kinetic energy k (TKE), and the turbulent length scaleΛ(TLS). Different cyclostationary simulation settings are illustrated in Fig. 1.4, which shows contour variables dimensionalized with the speed of soundc0 ∼340.3m/s and with the reference lengthLref. = 1 m. Note that the background turbulence is very small for this case. Therefore, no vorticity is vis- ible between the wakes. The parameter study is performed for the NASA SDT fan at approach conditions. A 2D simulation approach on a streamline positioned at the stator midspan is applied. A 3D RANS simulation is used to extract the streamline position, and the in- and outflow conditions of the quasi-3D (q3D) URANS simu- lation are tuned to approximate the wake structure in the rotor domain of the 3D RANS simulation at the respective streamline position.

To reduce the simulation costs of the fRPM-fan simulations for the parameter

Figure 1.4: Comparison of 2D fRPM-fan simulations with the following settings from top left to bottom center: P-PP (periodic u0, k, and Λ), C-PP (constant u0, periodic k and Λ), and C-CC (constant u0, k, and Λ). The contours show dimensionless, instantaneous mean velocities u0 and the vorticity magnitudes |Ω|.

study, several measures are applied:

• An eddy relaxation term [34] is used to locally inject the synthesized turbulence into the CAA domain. In contrast to using a modified radiation boundary or a specific sponge zone at the inflow boundary condition, the portion of the mesh capable of fully resolving the turbulence can be smaller resulting in an overall reduction in grid size.

• The number of stator vanes is reduced to 5 stator vanes.

• It is assumed that the blades are acoustically uncorrelated. Therefore, the patch is restricted to one stator pitch and the synthesized turbulence only interacts with one stator vane. The other stator vanes ensure the correct, acoustic radiation.

The validity of the latter two points are verified in the paper. All simulations are evaluated using stationary spectral analysis techniques. A correction is considered

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Figure 1.5: Wake and background turbulence for a cyclostationary 2D simulation at 50% stator height for the ASPIRE fan at approach conditions. The contours show instantaneous vorticity magnitudes |Ω| and pressuresp⁰ dimensionalized with ISA values and a reference length Lref. = 1 m.

to account for differences in the definition of the 2D and 3D upwash velocity fre- quency spectra as the upwash velocity component is the most critical for this noise generation mechanism.

1.5.2 Publication II

Based on the results of the parameter study presented in publication I, the authors postulate that the background, i. e. ingested, turbulence can be relevant for the fan broadband noise under certain circumstances. As a consequence, the focus of publication II is to investigate the relevance of wake and background turbulence on the predicted fan broadband noise levels. For this study, a next-generation fan, which was designed by Schnell et al. [82] for the European project ASPIRE, is chosen. This fan features a bypass ratio of 16 at the aerodynamic design point and is equipped with a variable area nozzle (VAN). At off-design operating points, the VAN maintains an acceptable stall margin by increasing the nozzle area, which decreases the fan loading. While the fan loading at approach conditions is still

relatively high, only a weak leading edge separation develops at the rotor leading edge, which is roughly restricted to the upper 20% of the rotor height. Both Prasad and Prasad [79] and Kissner et al. [58] reported more pronounced leading edge separations spanning a larger portion of the rotor for more conventional fan designs at approach operating conditions. It is hypothesized that this can lower the wake turbulence, which in turn can increase the relative contribution of the background turbulence to the overall fan broadband noise. For the CFD simulations, an inflow turbulence, which roughly approximates test bed conditions, is prescribed. The parameter study to investigate background and wake turbulence consists of several cylostationary simulations but also included constant simulations, i. e. simulations relying on circumferentially averaged values. In Fig. 1.5, wake and background turbulence are shown at one time step for a cyclostationary simulation at the stator midspan position. In contrast to publication I, several modifications regarding the 2D fRPM-fan simulations are made:

• (U)RANS simulations are preformed using a Reynolds stress turbulence model as the turbulence characteristics between the wakes cannot be correctly real- ized by a Boussinesq-based two-equation turbulence models for cases featuring larger turbulent length scales in the engine intake.

• To compute more representative fan broadband noise levels, 2D fRPM-fan simulations are performed at three spanwise positions at 20%, 50%, and 80%

of the stator height and an averaging of the spectral levels are performed.

• Instead of arbitrarily adjusting the boundary conditions of the q3D URANS simulations to approximate the rotor wake of the 3D RANS simulation, the incidence angles at the rotor leading edge at the respective streamline positions are held constant. In 2D flows, the incidence angle is decisive for the wake development. The wake structure of 3D flows in fans can be strongly influenced by spanwise velocities, which can e. g. be induced by areas of flow separation at the rotor leading edge. To account for such differences, a correction technique based on transverse velocity frequency spectra is formulated.

• For the cyclostationary simulation approach, it is not possible to impose the turbulence characteristics close to the stator leading edge, which are critical for the sound mechanism. Instead, the turbulence characteristics at the fRPM

18

patch position, which is upstream of the stator vanes, are extracted from the CFD simulations. Since the synthesized turbulence is modeled as frozen turbulence, the changes in wake structure with an increasing distance from the rotor cannot be considered in the simulation. A correction analogous to the one used to account for 3D flow effects is applied.

Similar to publication I, the number of stator vanes is reduced. The computational setup and the respective settings were chosen almost analogously. As no experimen- tal data are available for this fan, the feasibility of the predicted results is determined by comparing to the scaled, experimental data of the SDT and ACAT1 fans. An overview of these fans is given in Table 5 of publication II.

1.5.3 Publication III

In the preceding publications, the parameter studies are conducted using a 2D sim- ulation approach. 2D simulations are convenient for such studies as they can be performed within hours on a regular computer. Nonetheless, the question remains if these 2D simulations can be truly representative for a 3D fan stage. On the one hand, they are restricted to a specific streamline position. On the other hand, no well-established 2D–3D correction technique for fan broadband noise exists. To re- solve this issue, 2D and 3D simulations are performed for the ACAT1 fan at two approach operating conditions on two different working lines. The expansion of the fRPM-fan method to three-dimensional space and a first working example for a re- alistic fan configuration were initially presented by Kissner and Guérin [57]. Since 3D simulations tend to require significantly more computational effort than 2D sim- ulations, the authors also performed parameter studies on simple 3D test cases to optimize the simulation settings in terms of accuracy and efficiency. Instead of the more conservative settings applied in publications I and II, this optimized routine is used to design the simulation setups for all 2D and 3D simulations of this pub- lication. In addition, the so-called 3D-equivalent approach, which was proposed by Kissner et al. [59], is applied for the 2D simulations. Instead of arbitrarily picking streamline positions as for publications I and II, the 3D-equivalent approach relies on the analysis of flow and turbulence characteristics near the stator leading edge to determine a streamline featuring representative flow characteristics and to com- pute turbulence statistics based on a radially averaged upwash velocity frequency

Figure 1.6: Comparison of 3D and 2D fRPM-fan simulations at approach operating conditions on the sea level static working line. The contours show instantaneous vorticity magnitudes |Ω| and pressures p⁰ dimensionalized with ISA values and a reference length Lref. = 1 m.

20

spectrum. The analysis of turbulence characteristics also shows that the expected contribution of background turbulence to the overall fan broadband noise is about 1% to 2%. Therefore, cyclostationary effects are neglected for this fan configuration.

To ensure a meaningful comparison of 2D and 3D simulations in terms of tur- bulence realization and acoustics, the 2D and 3D simulation setups are designed as analogously as possible. In order to facilitate the validation of an appropriate 2D–3D correction technique, constant turbulence characteristics (determined by the 3D-equivalent approach) instead of radially varying turbulence characteristics (ex- tracted directly from the 3D RANS simulation) are applied for the 3D simulations.

The 3D fRPM-fan simulations are restricted to 11 stator vanes and the radial domain is reduced to about one-third of the stator height to lower the computational effort.

The underlying assumptions are verified with separate simulations. Instantaneous vorticity magnitudes and fluctuating pressures are shown in Fig. 1.6. While Fig. 1.6 is of a qualitative nature, it can already be seen that the synthetic turbulence of both simulations has a similar vorticity magnitude. However, the magnitude of the fluctuating pressure appears to be significantly higher for the 2D simulation than for the 3D simulation. Based on in-depth analyses of the discrepancies between the 2D and 3D simulation results, a suitable 2D–3D correction technique is formulated. The results are compared to experimental data and to predictions using RANS-based an- alytical methods, which were discussed in detail by Guérin et al. [46]. Furthermore, the 2D simulation approach is applied for cutback and sideline operating condi- tions to confirm the suitability of the method for higher rotational speeds and to substantiate the plausibility of the proposed 2D–3D correction technique.

Chapter 2 Publications

This chapter contains the main publications in chronological order:

Publication I

A. Wohlbrandt, C. Kissner and S. Guérin. Impact of cyclostationarity on fan broadband noise prediction. Journal of Sound and Vibration, 420:142–164, 2018.

ISSN 0022-460X.https://doi.org/10.1016/j.jsv.2018.01.039. (publisher’s ver- sion, see Section 2.1)

Publication II

C. Kissner and S. Guérin. Influence of Wake and Background Turbulence on Predicted Fan Broadband Noise. AIAA Journal, 58(2):659–672, 2020. ISSN 0001- 1452. https://doi.org/10.2514/1.J058148. (publisher’s version, see Section 2.2)

Publication III

C. Kissner and S. Guérin. Comparison of predicted fan broadband noise using a two- versus a three-dimensional synthetic turbulence method. Journal of Sound and Vibration, 508, 2021. ISSN 0022-460X. https://doi.org/10.1016/j.jsv.

2021.116221. (publisher’s version, see Section 2.3)

21

Journal of Sound and Vibration 420 (2018) 142–164

Contents lists available atScienceDirect

Journal of Sound and Vibration

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j s v i

Impact of cyclostationarity on fan broadband noise prediction

A. Wohlbrandt , C. Kissner , S. Guérin ^*

Institute of Propulsion Technology, Engine Acoustics Department, German Aerospace Center (DLR), Müller-Breslau-Str.8, 10623 Berlin, Germany

a r t i c l e i n f o

Article history:

Received 23 May 2017 Revised 12 January 2018 Accepted 17 January 2018 Available online XXX

Keywords:

Cyclostationary turbulence Isotropic turbulence

Fan broadband noise simulation Computational aeroacoustics Fast Random Particle Mesh Method

a b s t r a c t

One of the dominant noise sources of modern Ultra High Bypass Ratio (UHBR) engines is the interaction of the rotor wakes with the leading edges of the stator vanes in the fan stage. While the tonal components of this noise generation mechanism are fairly well understood by now, the broadband components are not. This calls to further the understanding of the broadband noise generation in the fan stage. This article introduces a new extension to the Random Par- ticle Mesh (RPM) method, which accommodates in-depth studies of the impact of cyclosta- tionary wake characteristics on the broadband noise in the fan stage. The RPM method is used to synthesize a turbulence field in the stator domain using a URANS simulation characterized by time-periodic turbulence and mean flow. The rotor-stator interaction noise is predicted by a two-dimensional CAA computation of the stator cascade. The impact of cyclostationarity is decomposed into various effects, which are separately investigated. This leads to the finding that the periodic turbulent kinetic energy (TKE) and periodic flow have only a negligible effect on the radiated sound power. The impact of the periodic integral length scale (TLS) is, how- ever, substantial. The limits of a stationary representation of the TLS are demonstrated making this new extension to the RPM method indispensable when background and wake TKE are of comparable level. Good agreement of the predictions with measurements obtained from the 2015 AIAA Fan Broadband Noise Prediction Workshop are also shown.

©2018 Elsevier Ltd. All rights reserved.

1. Introduction

Current and future engines used in civil aviation have large bypass ratios meaning that the fan plays an ever increasing role as a noise source. Fan noise, in particular rotor-stator-interaction (RSI) noise, is one of the most dominant noise sources of an ultra-high bypass ratio (UHBR) engine. It has the largest contribution during the approach phase and is only surpassed by jet noise during the take-off phase. Its prediction is of an increasing importance for the development of new technologies in light of the overall growth in air traffic and progressively more stringent noise regulations.

The tonal components of this noise generation mechanism have been researched extensively. As a result, different methods were successfully applied to reduce the tonal RSI noise. These approaches include reducing the tip circumferential speed to sub- sonic speeds, using acoustic liners in the engine duct, increasing the rotor-stator gap, choosing certain blade count combinations to strategically use acoustic cut-off effects, and modifying the blade geometry to e.g. reinforce destructive radial interferences.

Due to the reduction of tonal noise, the relative contribution of the broadband noise has significantly increased over the last decades. Hence, a greater understanding of the broadband noise generation mechanism in the fan stage is required to further reduce the RSI noise.

However, the prediction of fan broadband noise is still considered to be a challenge: On one hand, analytical models are restrictive as they require strong assumptions. On the other hand, CFD computations that fully resolve turbulent scales are

* Corresponding author.

E-mail address:sebastien.guerin@dlr.de(S. Guérin).

https://doi.org/10.1016/j.jsv.2018.01.039 0022-460X/©2018 Elsevier Ltd. All rights reserved.

22

exceedingly demanding in computational resources. To advance the current understanding of broadband noise generation in a fan stage, methods are needed that are both fast and affordable without being overly restrictive.

The use of hybrid approaches can help to fill the gap. It required to divide the physical problem into individual phenomena which can be calculated sequentially. This results in a process chain where every task is completed by the most efficient method.

Hybrid approaches can combine numerical, analytical and empirical methods. In fan broadband noise predictions the two most prominent ones are Large Eddy Simulations (LES) coupled to an acoustic analogy and stochastic methods coupled to a Com- putational AeroAcoustics (CAA) method. This paper focuses on the latter method. Allan and Darbyshire [1] compared the two mentioned approaches for noise predictions in two different media: air and water. The cases considering air are an airfoil slat and a bent duct with a simplified valve at the exit; the cases considering water are a bent and a t-junction pipe. They concluded for these cases that the hybrid approach relying on a stochastic method yields satisfactory noise results at a fraction of the cost of LES.

For RSI noise, a hybrid approach can be divided into three main tasks: Firstly, the sound generation mechanisms are mod- eled either directly or by synthesizing a turbulent field which impinges on the blade row. Secondly, the sound is propagated considering complex duct geometries and flow. Lastly, the sound is radiated into the far field, i.e. to an observer. The two last mentioned parts can be realized by a CAA simulation applying the Linearized Euler Equations (LEE). The first part, however, has proven to be the crux of the matter. For many years, the only way of modeling the sound sources was to use discrete harmonic gusts to generate the turbulent field [2–5]. This method is still in use to model RSI noise. In fact, Lau et al. [6] have recently investigated the impingement of harmonic gusts in a three-dimensional (3D) CAA simulation in order to quantify the influence of wavy leading edges.

Aside from this analytically motivated method, two classes of stochastic methods are used to model broadband noise: the Stochastic Noise Generation and Radiation (SNGR) method and the Random Particle Mesh (RPM) method.

The SNGR methods apply a random set of superposed Fourier modes to realize a target model spectrum, e.g. a von Kármán or a Liepmann spectrum. The SNGR methods can be traced back to the work of Kraichnan [7], who proposed the theoretical framework, and to Bechara et al. [8], who was the first to apply it to predict noise generated by free turbulence. Clair et al. [9]

predicted the effects of wavy leading edges (LE) of isolated airfoils, while Gill et al. [10] investigated real symmetric airfoils at zero angle of attack. To predict RSI noise Polacsek et al. [11] have presented an approach simulating only one stator vane with periodic boundary conditions in circumferential direction. The far-field signature is obtained by extrapolating the instantaneous pressure on the blade surface.

The RPM method by Ewert et al. [12] synthesizes the turbulent fluctuations by spatially filtering white noise. An advantage of this method compared to the SNGR method is that it can more easily represent inhomogeneous stochastic fields and consider spatial mean flow variations. The mean turbulent quantities are taken from a preceding RANS simulation. This method is now established and has been successfully applied to model different sources such as jet noise [13], slat noise [14], haystacking [15]

or airfoil self noise [16]. The method is also applied for the prediction of fan noise. The first reported application was shown by Dieste and Gabard [17,18], who investigated the interaction of turbulence with a two-dimensional flat plate.

Kim and Haeri [19] applied it to investigate the turbulence interaction with a flat plate in two- and three-dimensional space.

They generated a von Kármán model spectrum by an optimization technique utilizing a set of Gaussian and Mexican hat fil- ters. The divergence-free turbulence is coupled into a CAA domain by a sponge-layer technique. For centrifugal fans Heo et al.

[20] have applied the RPM method to time-periodic flow with cyclostationary turbulence. The synthetic fluctuations are used as sources in an acoustic analogy solved by a boundary element method. A sufficient agreement with measurements is only achieved if cyclostationarity is considered.

To compare the results to experimental data, it is crucial to use realistic model spectra. Dieste and Gabard [18] have derived complex filter stencils to model von Kármán spectra directly. This turns out to be computationally intensive. A more efficient solution is the empirical weighting of Gaussian filters with different length scales and amplitudes [19,21]. Wohlbrandt et al.

[22] have derived analytical weighting functions in order to realize typical isotropic turbulence spectra by the superposition of Gaussian spectra. They also showed that the reconstruction with five logarithmically distributed, discrete realizations is suffi- cient to cover a frequency range spanning one order of magnitude. The current article will show how this technique can be used to simulate length scales varying in space and time while realizing temporally and spatially constant Gaussian filtered fields.

Broadband noise in the fan stage is caused by the interaction of the turbulence in the rotor wakes with the surfaces at the leading edges of the stator vanes in the presence of a time-periodic mean flow.

The first objective of the current paper is to utilize the RPM method to include time-periodic turbulence variations and mean flow, which are essential in studying broadband noise generation of rotating parts. This method allows for an in-depth study of cyclostationary turbulence and therefore contribute to a greater understanding of broadband noise generation in fans. This is especially important for the development and improvement of analytical tools. The second objective is to separately study the impact of the different effects due to cyclostationarity. A preliminary study utilizing this method was presented by Wohlbrandt et al. [23]. This article consolidates the method and applies it to another fan, for which measurement data have been made available.

This paper is structured as follows: The used hybrid approach, the extensions for including cyclostationarity, the general procedure for the setup of such a computation as well as evaluation methods are discussed in Section 2. In Section3, the method extension is demonstrated by applying it to the NASA Source Diagnostic Test (SDT) fan. The effects of cyclostationary wake characteristics on the fan broadband noise are discussed in Section4. Additionally, the numerical sound power spectra are compared to experimental data. Key features of the method as well as significant findings are summarized in Section5.

A. Wohlbrandt et al. / Journal of Sound and Vibration 420 (2018) 142–164 144

Fig. 1.Overview of the tools involved in the hybrid approach.

2. Method

2.1. Cyclostationarity

“A cyclostationary signal is a random signal whose statistical characteristics vary periodically in time” [24]. This is especially relevant in a fan. Although the stochastic signal is different at each revolution of the fan, its characteristics reappear periodically.

This is valid for rotor-triggered mean values but also for the turbulent statistics.

By replacing the ensemble average with a cycle average [25], the subsequently used hybrid method is expanded to reproduce cyclostationary processes. Hence, the mean flow and stationary turbulent characteristics are extended to a periodically changing background flow and cyclostationary turbulence. Although the changes to the underlying governing equations are small as discussed inSubsection 2.2, the resulting level of complexity is very much increased. The possible combinations are shown in Subsection 2.3. The influence of periodically changing background flow, variance and length scale is investigated in Section3.

2.2. Hybrid approach

The hybrid approach, which simulates broadband RSI noise using both stationary and cyclostationary turbulence, is depicted inFig. 1. It consists of three methods: The (U)RANS method computes the background flow and turbulence statistics. The RPM method synthesizes the turbulence in the time domain. The CAA method convects the synthetic turbulence into the source region and radiates the resulting broadband noise to the sensor positions.

Solely the geometry and operating condition of the turbomachine and the shape of the correlation function are needed as inputs for this hybrid approach. It outputs broadband time signals at the desired microphone positions, which are converted into sound power levels (PWL) in an equivalent duct.

Next, the separate methods of the hybrid approach and the post-processing are explained.

2.2.1. (U)RANS: background flow and turbulence statistics

The in-house Computational Fluid Dynamics (CFD) solver TRACE was used [26]. The mean flow and mean turbulent statistics were predicted by a Reynolds-Averaged Navier Stokes (RANS) simulation, while the periodic flow, periodic turbulent statistics, and the tonal noise were predicted by an unsteady RANS (URANS) simulation.

In this investigation, the (U)RANS calculations were performed on a quasi-3D (q3D) domain. A q3D computational domain consists of a few cells in the radial direction and its radial boundaries follow streamlines of a preliminary 3D RANS simulation.

In most cases, the aerodynamic results of such a q3D computation closely resemble the 3D results at the same position [27].

2.2.2. Random Particle Mesh method: synthesized turbulence

The Random Particle Mesh method [12] allows to synthetically realize the time-space-dependent turbulent fluctuations based on the background flow, the local turbulent kinetic energy (TKE), and the local turbulent length scales (TLS) provided by the (U)RANS simulation. In general, the RPM method is able to generate anisotropic, evolving synthetic turbulence of local integral turbulence length scaleΛrealizing arbitrary model spectra. The turbulence is generated by spatially filtering a random stochastic field with a Gaussian filter of the aforementioned length scale. The turbulence is scaled with the local variance, which corresponds to the turbulent kinetic energyk_tfor this particular application, and convects with the local background velocity

24