Computational Aeroacoustics of an axial fan with leading edge serrations

Stefan SCHODER(1), Florian KRÖMER(1,2), Michael WEITZ(1), Manfred KALTENBACHER(1), Stefan BECKER(2)

(1)Institute of Mechanis and Mechatronics, TU Wien, Austria, stefan.schoder@tuwien.ac.at(2)Institute of Process Machinery and Systems Engineering, Friedrich-Alexander University Erlangen-Nürnberg, Germany

AbstractIn recent years, a trend towards modifications of the leading edge geometry in airfoils to reduce the sound emission andimprove the stall behavior has been observed. However, low-pressure axial fan design methodologies for a decreasedsound radiation rely almost exclusively on the use of fan blade skew rather than on leading edge modifications so far.Therefore, with this study we aim to investigate the sound reduction capabilities of leading edge serrations applied tolow-pressure axial fans using the efficient perturbed convective wave equation. For this purpose, we use a referencefan with straight leading edges and a fan with serrated leading edges that has been studied in experimental investiga-tions before. The comparison of the CFD and CAA simulations with experimental results show excellent agreement.Furthermore, we analyze the sound reduction mechanisms of leading edge serrations based on the CAA results. Ingeneral, a sound reduction is obtained with leading edge serrations without influencing the fan operating point. Thestudy demonstrates the applicability of this aeroacoustic approach for axial fans with modified leading edges.Keywords: Hybrid aeroacoustics, Numerical simulation, Leading edge serrations, Fan noise

INTRODUCTIONBy increasing performance and efficiency, axial fans contribute to many technical systems encountered in ev-eryday life, e.g. computers, cars, trains, ventilation systems, and powerplants. For example, to reduce the effectof increasing temperature on humans in urban regions, the demand of cooling systems increases significantly[1, 2]. Hence the number of axial fans and the sound emission rises in urban regions, which in turn also inter-fere with our lives. To reduce the sound emissions of axial fans, there are several approaches among which theapplication of leading-edge serrations shows promising capabilities. Therefore, we demonstrate the applicabilityof aeroacoustic simulations and present an outlook towards hybrid aeroacoustic using the perturbed convectivewave equation [17].

1.1 Sound reduction with leading-edge serrationsUnder distorted flow conditions with high turbulence intensity, leading-edge serrations of an airfoil effectivelyreduce airfoil noise [3, 4, 5, 6, 25, 8, 9, 10]. Recently, the investigations support that the sound-reductionmechanisms also apply for axial-fan blades.A reduction of the sound power level of 2.3dB was observed with sinusoidal leading-edge serrations only onthe outer 20% of the blade span width [11]. A similar relationship was found for ducted, unskewed low-speed axial fans with sinusoidal leading-edge serrations under various inflow conditions [12]. Sound is reducedmainly below 2kHz and for serrations with the smallest wavelength and the highest amplitude, a maximumoverall reduction of 3.4dB was identified. Krömer et al. [13] performed a study on the sound emission of aforward-skewed fan with sinusoidal leading-edge serrations of varying amplitude and wavelength under free anddistorted inflow conditions. Leading-edge serrations reduced the emitted sound for both inflow conditions. Basedon this study, a comprehensive investigation on different leading-edge modifications was carried out [14, 15, 16],including sinusoidal, double-sine and random-amplitude serrations. The sinusoidal leading-edge serrations leadto the most effective sound reduction, namely 7dB for distorted inflow conditions and 11dB for free inflowconditions compared to the reference fan with straight leading edges. As indicated by Biedermann et al. [12],the sound emission decreases with increasing serration amplitude and lower serration wavelength.

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1.2 Aeroacoustic modelFor a deeper understanding of the physical processes causing the sound reduction, numerical simulations of theflow and sound field are performed. Based on a highly resolved CFD simulation of the fan, radiated sound ispropagated by Ffowcs Williams-Hawkings analogy (FW-H) [18]. We used the implementation of Star-CCM+(Siemens PLM software, Plano, TX/USA).Besides FW-H, one can use a special hybrid aeroacoustic workflow for low Mach number applications. Startingfrom the acoustic/viscous splitting technique [19], many different linear and non linear wave equations havebeen derived [20, 21, 22, 23]. All these methods have in common that the flow field quantities are split intocompressible and incompressible parts

p = p̄+ pic + pc = p̄+ pic + pa (1)vvv = v̄vv+ vvvic + vvvc = v̄vv+ vvvic + vvva (2)ρ = ρ̄ +ρ1 +ρ

a . (3)

First, the field variables are decomposed into mean ( p̄, v̄vv, ρ̄) and fluctuating parts. Additionally, the fluctuatingparts are further split into acoustic (pa, vvva, ρa) and flow components (pic, vvvic). Finally, a density correction ρ1is built according to (3). An ALE (Arbitrary Lagrangian-Eulerian) description for the operators

DDt

=∂

∂ t+(vvv− vvvr

)·∇ , (4)

where vvvr is the relative velocity of the grid, yields the perturbed convective wave equation (PCWE) for rotatingsystems (see [17])

1c2

D2ψa

Dt2 −∆ψa =− 1

ρ̄c2Dpic

Dt. (5)

This scalar convective wave equation describes aeroacoustic sources generated by incompressible flow structuresand wave propagation through moving media, as it occurs in the axial fan configuration. Compared to otherconvective wave equations, the PCWE reduces the number of unknowns (acoustic pressure pa = ρ̄

Dψa

Dt andparticle velocity vvva = −∇ψa) to just one scalar unknown, the acoustic velocity potential ψa. All computationsof the PCWE are exectued in CFS++ [24] and the modeling strategies for rotating system can be found in [17].

1.3 Motivation and outlineIn this study, we aim to investigate the sound-reduction capabilities of leading-edge serrations by aeroacousticsimulations. In Sec. 2, the fan design and the leading-edge parameters are outlined and the most importantfacts of the experimental investigation are described. A comparison of the simulated noise reduction and themeasurement data is given Sec. 3. Final conclusions are drawn in Sec. 4.

EXPERIMENTAL INVESTIGATIONThe experimental investigation used for the validation of the simulation results have been previously publishedand are described in [15]. Upon that, we briefly describe the most important facts of these measurements.

2.1 Fan designThe investigated reference fan has straight leading edges and unskewed fan blades (see Fig. 1). Nine fan bladesare mounted on the hub (hub diameter dhub = 247.5mm) and the axial fan is operated at a constant rotationalspeed n = 1486rpm. The outer diameter of the axial fan is dfan = 497mm. During the investigations, the fanswere installed in a duct with a diameter of dduct = 500mm, resulting in a tip gap stip = 1.5mm. As illustratedin Fig. 1, the turbulent structures are controlled by a turbulence grid that is mounted inside the duct. Further

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y

z

xγ

Figure 1. Simplified axial fan with straight leading edges.

details on the fan design can be found in [14]. The laser-cut blades are made of t = 6mm thick aluminumplates and have a constant stagger angle γ = 20◦ along the fan blade span without any camber or twist. Thestacking line of the blades connects the fan-blade leading edges that are centric towards the axis of rotation.

2.2 Leading edge parameterLeading-edge modifications affect the aerodynamic and the acoustic properties of lifting sections. We use themost common form of such modifications, that is, a sinusoidal leading edge. This sinusoidal modification canbe described by two leading edge parameters, the wavelength λLE and the amplitude aLE as a percentage of themean chord length lc = 69.6mm (see Fig. 2). Figure 2 shows the used leading-edge serrated fan blade used inthese investigations with the parameters being λLE = 16.7%lc and aLE = 6.7%lc.

λLE

aLE

fans were investigated. One fan blade of each fan blade set is shown in Fig. 3. Thereby, the mean chord length for all fanblades is identical.

λLE

aLE

Fig. 2 Leading-edge sine parameters: amplitude aLE and wavelength λLE.

(a) USK (b) USK_A133λ67 (c) USK_A167λ67 (d) USK_A133λ100 (e) USK_A167λ100

(f) FSK (g) FSK_A133λ67 (h) FSK_A167λ67 (i) FSK_A133λ100 (j) FSK_A167λ100

(k) BSK (l) BSK_A133λ67 (m) BSK_A167λ67 (n) BSK_A133λ100 (o) BSK_A167λ100

Fig. 3 Fan blades with straight and sinusoidal leading edges: USK (a - e), FSK (f - j) and BSK (k - o).

Table 1 Leading-edge serration parameters.

name aLE in % lc λLE in % lc

A133λ67 13.3 6.7A133λ100 13.3 10A167λ67 16.7 6.7A167λ100 16.7 10

5

Figure 2. Serration wavelength λLE and amplitude aLE for a sinusoidal leading edge (right) and a leading-edgeserrated fan blade A167λ67.

2.3 Experimental setupAll experimental investigations were carried out in a standardized inlet test chamber [14]. The fans were casedby a short duct with a diffuser on the pressure side and an inlet bellmouth on the suction side. The fan motorand a torque meter were installed outside the duct. Improving the measurement conditions, the measurementchamber is built as an anechoic chamber with absorbers on the walls, the floor and the ceiling. To avoiddistinctive noise from rotor-stator interactions, four non-centric struts were used as fan support.

2.4 Sound fieldSeven 1/2inch free-field microphones, type 4189-L-001 (Brüel & Kjær), connected to microphone conditioners,type NEXUS 2690-A (Brüel & Kjær), arranged in a semicircle aligned with the axis of rotation (Fig. 3), were

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used to measure the sound field. A PXIe-1075 front-end with 24-bit PXIe-4496/PXIe-4492 data-acquisitionmodules (National Instruments) was used for data acquisition. The measurement time was tm = 30s with a

M4: 0◦

M1: +90◦

M7: −90◦

M3: +30◦

M2: +60◦

M5: −30◦

M6: −60◦

100030◦

Figure 3. Microphone positions, schematic (left) and photograph (right). Dimensions in mm.

sampling frequency fs = 48kHz. Further details on the measurement procedure can be found in [14].

SELECTED RESULTS AND DISCUSSIONThis section visualizes aeroacoustic quantities based on an accurate CFD simulation and an aeroacoustic prop-agation simulation. First, the sound sources of the flow simulation are determined and thereafter the soundemission is computed using FW-H analogy and the PCWE. The analysis of the aeroacoustic sources on the fanblades reveals the sound reduction mechanism. Due to unexpected issues, we show only results of the FW-Hanalogy.

3.1 Impact of the leading-edge serrations on the aeroacoustic sourcesIn order to propagate sound using the FW-H analogy, we defined the fan surface as propagation origin and theregion where the main sources are located. Sources in the fluid region are neglected. Figure 4, comparing the

5.2 Ffowcs Williams-Hawkings Methode

direkt vor dem Ventilator befindet, sollen die Ergebnisse an dieser Position betrachtet und dis-kutiert werden. In Abbildung 5.4 werden die ermittelten Oberflächenquellen am gesamten Lüfterfür beide Modelle dargestellt.

Abbildung 5.4: Quelltermformulierung nach der FW-H Methode am kompletten Lüfterrad zumZeitpunkt t=0,48 s für den Mikrofonpunkt Mic4.

Anhand von Abbildung 5.4 lässt sich bereits erkennen, dass das Referenzmodell deutlich mehrQuellterme mit höheren Werten aufweist, als der Ventilator A167λ67. Für eine genauere An-sicht wird in Abbildung 5.5 ein Lüfterblatt vergrößert dargestellt und anhand dessen weitereUntersuchungen durchgeführt.

Abbildung 5.5: Quelltermformulierung nach der FW-H Methode am einzelnen Lüfterblatt zumZeitpunkt t=0,48 s für den Mikrofonpunkt Mic4.

Es wird ersichtlich, dass die Quellen besonders an den Blattoberflächen deutliche Unterschiedeaufweisen. Betrachtet man das Referenzmodell, so erkennt man, dass die auftretenden Oberflä-chenterme über die gesamte Fläche im oberen Bereich der Schaufel auftreten. Im Vergleich dazutreten beim Modell A167λ67 kaum dominante Quellterme auf der Saugseite auf. Ein Grund hier-für könnte sein, dass durch die veränderte Vorderkantengeometrie die auftretenden Quellterme sobeeinflusst werden, dass diese sich gegenseitig auslöschen und somit über die Oberfläche zerfallen

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Figure 4. Aeroacoustic source terms of the FW-H analogy of the reference axial-fan (left) and the leading-edgeserrated axial fan(right), with respect to M4 (see Fig. 3).

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aeroacoustic source of the two different blade types, shows a significant reduction in the source terms on thesuction side of the fan blade. As indicated in previous studies [25], the reduction is a result of the decorrelationeffect of the aeroacoustic sources. However, small sources are visible at the base line of the serrations and themost dominant sources occur at the tip of the serrated blade.

3.2 Impact of the leading-edge serrations on the sound emissionIn order to compare the measurement results and the simulation results, the sound field is exported at the sevenmicrophone positions during the simulation. The data is then Fourier-transformed and energetically averaged.Figure 5 shows the averaged spectrum of the reference fan (left) and the leading-edge serrated fan (right). Thered graph denotes the measurements and the blue graph the simulated results, respectively. From the simulationresults of the reference fan we see that a maximum frequency of 5kHz is resolved, where the broadband noiseis generally underestimated since the volume contributions to FW-H are neglected. The first blade passingfrequency at 223Hz is captured well by the simulations. Overall, the trend of the sound emission is resolved.

Kapitel 5 Numerische Untersuchung der Akustik

und keinen größeren Einfluss mehr für die Schallabstrahlung darstellen. Diesen dekorrelieren-den Effekt durch die Verwendung von serrations konnte bereits durch Lau et al. [8] bewiesenwerden. Betragsmäßig kleinere Quellen können dennoch am Grund der serrations festgestelltwerden. Das Lüftermodell A167λ67 weist den Schwerpunkt der dominanten Schallquellen amäußeren Bereich der Schaufeln auf, welche höher ausfallen als die des Referenzmodells.Die Darstellung der Oberflächenquellterme an den anderen Mikrofonpositionen ist der Vollstän-digkeit halber im Anhang B für das Referenzmodell und in Anhang C für das LüftermodellA167λ67 zu finden.

5.2.2 Vergleich der Schallemission und Validierung

Um die in der Simulation erhaltenen Ergebnisse auswerten zu können, werden die Datensätzeder sieben Mikrofonpunkte exportiert und in Matlab über eine Fast-Fourier-Transformation vomZeitbereich in den Frequenzbereich übertragen. Im Anschluss werden die Frequenzdaten für diesechs Umdrehungen energetisch richtig gemittelt.In Abbildung 5.6 sind die gemittelten Spektren für das Referenzmodell REF dargestellt. Dabeientspricht die rote Linie dem Spektrum der Messung und in der Farbe Blau ist das simulierteErgebnis aufgetragen. Die maximal auflösbare Frequenz beträgt circa 5000 Hz. Man erkennt,dass gemessene und simulierte Ergebnisse gut übereinstimmen, wobei die Simulation den Breit-bandschall leicht zu gering vorhersagt. Die erste Blattfolgefrequenz bei 223 Hz kann durch dieFW-H Methode gut abgebildet werden.

102 103 104

10

20

30

40

50

60

70

Abbildung 5.6: Schallspektrum der Messung (rot) und des Lüftermodells REF (blau).

52

Frequency in Hz

Aver

aged

sou

nd p

ress

ure

leve

l Lp

in d

B

5.2 Ffowcs Williams-Hawkings Methode

102 103 104

10

20

30

40

50

60

70

Abbildung 5.7: Schallspektrum der Messung (rot) und des Lüftermodells A167λ67 (blau).

In Abbildung 5.7 sind die gemittelten Spektren für das Lüftermodell A167λ67 dargestellt. Dabeientspricht die rote Linie dem Spektrum der Messung und in der Farbe Blau ist das simulierteErgebnis aufgetragen. Die maximal auflösbare Frequenz beträgt ebenfalls circa 5000 Hz. DesWeiteren erkennt man, dass gemessene und simulierte Ergebnisse ebenso gut übereinstimmen,wobei die Simulation den Breitbandschall auch zu gering vorhersagt. Es fällt auf, dass die erstensieben Blattfolgefrequenzen korrekt abgebildet worden sind aber der Pegel zu gering vorherge-sagt worden ist. Im Vergleich zum Referenzmodell weist das Lüftermodell A167λ67 höhere tonaleKomponenten an der Blattfolgefrequenz und deren harmonischen auf. Dieser Effekt könnte da-durch erklärt werden, dass durch die serrations die effektive Länge der Vorderkante größer istals beim Referenzmodell und somit auch eine größere Angriffsfläche für die auftreffende Strö-mung bietet, was akustische Auswirkungen zeigt.Zusammenfassend kann gesagt werden, dass vor allem der breitbandige Anteil der Schallemis-sion des Lüftermodells A167λ67 durch den Einsatz von serrations reduziert werden konnte.Betrachtet man beide Frequenzspektren, so kann geschlussfolgert werden, dass die Schallvor-hersagemethode nach Ffowcs Williams-Hawkings die Blattfolgefrequenzen gut abbildet, jedochbei beiden Modellen einen leicht unterschätzten breitbandigen Anteil des Schalls aufweist. Dieskönnte daran liegen, dass für die FW-H Methode nur die Lüfterblätter und die Nabe als schall-abstrahlende Oberflächen angegeben wurden. Betrachtet man den realen Systemaufbau mitwelchem die Messungen durchgeführt worden sind, so wird klar, dass auch die anderen Kompo-nenten des Systems, wie zum Beispiel das Turbulenzgitter, an den erzeugten Schallemissionenbeteiligt sind.

53

Frequency in Hz

Aver

aged

sou

nd p

ress

ure

leve

l Lp

in d

B

Figure 5. Comparison of simulation (blue) and measurements (red) of the averaged sound pressure level of thereference axial-fan (left) and the leading-edge serrated axial fan(right).

Moving on to the discussion of the simulation results of the leading-edge serrated axial fan, the grid resolvesa maximum frequency of 5kHz. In general the trend of the sound emission is captured well and again thebroadband components are underestimated. The tonal components are well represented in the simulation resultsand compared to the reference configuration the tonal components dominate the sound radiation. This increasein the tonal components may be partly addressed to the increasing contour line of the leading-edge. However,the broadband sound emission as well as the overall sound emission is decreased by the leading-edge serratedaxial fan.

CONCLUSIONSAccording to the theory, we see a sound reduction of the broadband components in both the measurementsand the acoustic simulations. A comparison of the aeroacoustic sources on the fan blade shows a significantreduction in the source terms on the suction side of a fan blade with leading-edge serrations. For a leading-edge serrated axial fan, the tonal components become more dominant since the broadband sound emission issubstantially decreased. We attribute the slight underestimation of the broadband components to the neglectedvolume terms in the FW-H formulation. The tonal components are well represented in the FW-H simulationresults. In the future, we will use the PCWE to compute sound emissions of leading-edge serrated fans and wewill compare the findings with the present study.

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