Experimental investigation of the interplay between the sound field and the flow field in skewed low-pressure axial fans

Accepted Manuscript Experimental investigation of the interplay between the sound field and the flow field in skewed low-pressure axial fans Florian J. Krömer, Stéphane Moreau, Stefan Becker PII:

S0022-460X(18)30738-7

DOI:

https://doi.org/10.1016/j.jsv.2018.10.058

Reference:

YJSVI 14475

To appear in:

Journal of Sound and Vibration

Received Date: 13 April 2018 Revised Date:

24 August 2018

Accepted Date: 29 October 2018

Please cite this article as: F.J. Krömer, Sté. Moreau, S. Becker, Experimental investigation of the interplay between the sound field and the flow field in skewed low-pressure axial fans, Journal of Sound and Vibration (2018), doi: https://doi.org/10.1016/j.jsv.2018.10.058. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Experimental investigation of the interplay between the sound field and the flow field in skewed low-pressure axial fans Florian J. Kr¨ omera,∗, St´ephane Moreaub , Stefan Beckera a Friedrich-Alexander

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University Erlangen-N¨ urnberg, Institute of Process Machinery and Systems Engineering, Cauerstr. 4, 91058 Erlangen, Germany b Universit´ e de Sherbrooke, Chaire Industrielle d’A´ eroacoustique, 2500, boul. de l’Universit´ e, Sherbrooke J1K 2R1, Canada

Abstract

The type of fan-blade skew used in axial fans has a strong impact on the sound field, the flow field and their interrelations. In this study, the sound emission and the velocity distributions of three low-pressure axial fans with a similar design

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point and forward-, backward- and unskewed fan blades are investigated. The forward skewed fan is found to have best aerodynamic performance as well as the

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least sound emission over a broad operating range. More detailed investigations at the fan design point, based on sound pressure spectra and beamforming evaluations, reveal very dominant subharmonic narrowband components and

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increased turbulence-ingestion noise for the backward- and the unskewed fan. Moreover, an increase in the meridional velocity in the tip region is observed

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for the forward-skewed fan, which weakens the tip-vortex formation. For the backward- and the unskewed fan however, a reduced meridional velocity in the tip region is found, which is an indicator of an intensified tip gap flow. Additionally, values of the turbulent kinetic energy are substantially increased for the backward- and the unskewed fan, which also hints at unsteady flow phenomena in the tip region. These flow processes are linked to the subharmonic narrowband sound emission. Finally, unsteady flow features in the tip region ∗ Corresponding

author, Tel.: +49 9131 85 29462, Fax: +49 9131 85 29449 Email address: [email protected] (Florian J. Kr¨ omer)

Preprint submitted to Sound and Vibration

October 30, 2018

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lead to an increase in turbulence-ingestion noise. Keywords: Aeroacoustics, axial fan, skewed fan blade, sound emission, microphone array, laser Doppler anemometer

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Latin symbols

blade loading constant

b

blade loading constant

c0

speed of sound

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a

c1

absolute velocity at the inlet

c2

absolute velocity at the outlet

cm1

meridional velocity component of velocity c1 at the inlet

cm2

meridional velocity component

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of velocity c2 at the outlet

cr2

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cu1

radial velocity component

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cr1

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cu2

of velocity c1 at the inlet radial velocity component of velocity c2 at the outlet circumferential velocity component of velocity c1 at the inlet circumferential velocity component of velocity c2 at the outlet

d

blade loading constant

darray,l

large array diameter

darray,s

small array diameter

dduct

duct diameter

dfan

fan diameter

dhub

hub diameter

e

blade loading constant

f

frequency 2

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blade passing frequency

fs

sampling frequency

k

turbulent kinetic energy

k1

turbulent kinetic energy at the inlet

k2

turbulent kinetic energy at the outlet

lc

chord length

Lp

sound pressure level

Lp

averaged sound pressure level

Ms

shaft torque

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fBPF

N

total sample count

n

rotational speed

r

radius

stip

tip gap

tm

measurement time

circumferential velocity

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u V˙ w2⊥ x1 , x2 , x3

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Xp

TE

volume flow rate

zb

velocity perpendicular to the trailing edge

coordinate directions Fourier transform - linear spectrum number of fan blades

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Greek symbols α

rotational angle

∆pts

total-to-static pressure difference

ηts

total-to-static efficiency

λ

sweep angle

λ

wavelength

Λ

integral length scale

ν

dihedral angle

ρ

density

3

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flow-coefficient

ϕd

design flow-coefficient

ψts

total-to-static pressure-coefficient

Mathematical expressions

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ϕ

average

˜ •

phase-locked ensemble-average

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•

1. Introduction

Low-pressure axial fans are used in a variety of commercial applications for which more and more stringent specifications exist in terms of power consumption and noise emission, e.g. in [1]. Consequently, design optimizations now 5

focus on the one hand on the fan aerodynamics and on the other hand on the

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fan acoustics. These two features strongly interrelate, i.e. the flow field has a

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strong impact on the sound emission of axial fans. The flow field in modern lowpressure axial fans is greatly influenced by the fan-blade skew applied, which is a combination of fan-blade sweep and fan-blade dihedral [2, 3]. In a similar way, fan-blade skew affects the sound emission of low-pressure axial fans. The

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effect of fan-blade skew on the flow field and the sound field can be seen on

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various operating points. The focus in this study is on the effects at the fan design point; hence primarily phenomena in this operating range are taken into account.

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The impact of fan blade skew on the different sound generation mechanisms

in low-pressure axial fans is discussed in Section 2. In Section 3, the experimental setups and measurement methods are outlined, including the applied beamforming methodology, using a virtual rotating microphone array. The sound and flow fields and their interplay are assessed in Section 4, with emphasis on

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the individual characteristics of fans with different types of fan blade skew.

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2. Impact of fan-blade skew on aerodynamics and aeroacoustics of low-pressure axial fans

The different sound generation mechanisms in low-pressure axial fans can be categorized – according to their radiation characteristics – into broadband, tonal

and narrowband sound sources. In general, the dominant sound sources are

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expected to be located in the outer part of the fan blade as the circumferential

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velocity increases from the hub to the fan blade tip [4, 5]. Accordingly, the fan-blade skew applied to the outer part of the fan blade has been shown to have the greatest impact on the sound emission of axial fans [6]. 30

Broadband sound sources

Potential broadband sound sources in low-pressure axial fans are boundarylayer noise, trailing-edge noise (for a turbulent boundary layer), tip noise and

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turbulence-ingestion noise.

Boundary-layer noise is induced by pressure fluctuations beneath the turbulent boundary layer of the fan blade. Fan blade skew has an impact on the

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35

boundary-layer development: in the case of backward-skewed fan blades, the boundary-layer thickness is increased owing to a longer travel path of the fluid

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before it reaches the trailing edge. The opposite applies to forward-skewed fan blades [7, 8, 9]. Hence, theoretically, boundary-layer noise is increased (backward-skewed fan) or decreased (forward-skewed fan). However, boundary-

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layer noise usually makes only a minor contribution to the overall emitted sound of low-pressure axial fans [10, 11, 12]. The radiation characteristics of trailing-edge noise is, among other param-

eters, dependent on the type of the boundary layer – laminar or turbulent. In

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the case of a turbulent boundary layer, broadband sound is generated by eddies that are convected past the trailing edge [13, 14, 15]. Trailing-edge noise prediction models, e.g. in [14, 16, 17, 18, 19], suggest that the level of trailingedge noise is dependent on the velocity perpendicular to the trailing edge w2⊥ (Fig. 1) [11, 20, 10, 21]. This velocity is dependent on the fan-blade skew, i.e. 5

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the fan-blade curvature at the trailing edge. It has been shown that this veloc-

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ity is of greater magnitude for forward-skewed fans than for backward-skewed

fans [22]. Accordingly, trailing-edge noise is expected to be more dominant for forward-skewed fans than for backward-skewed fans.

w2

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w2⊥

⊥

leading edge

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trailing edge

Figure 1: Velocity perpendicular to the fan-blade trailing edge w2⊥ for a forward-skewed fan blade.

Similarly to an airfoil that is fixed only on one end along the span, a tip 55

vortex develops on the fan-blade tips, which has a broadband sound characteristic [13, 14, 23]. Skewed fan blades are known to change the loading along

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the fan-blade span: forward-skewed fan blades tend to unload the tip blade sec-

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tions, whereas backward-skewed fan blades tend to upload the tip blade sections [24, 25, 26, 27, 4]. As a result, forward-skewed fan blades may weaken the tip60

vortex formation [28, 29, 8, 30]. The opposite applies to backward-skewed fan

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blades. With a reduced tip-vortex formation, broadband tip noise is decreased. Turbulence ingestion noise arises during the interaction of the fan blade with the inflow that usually incorporates a certain turbulence intensity. If the integral

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length scale of the inflow Λ is larger than the chord length lc , a varying total

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airfoil loading arises [10, 13, 15]. The resulting broadband sound cannot be assigned a specific fan-blade region as the fan blade is regarded as acoustically compact, i.e. the acoustic wavelength λ of the emitted sound is larger than the chord length lc [10, 13]. With the integral length scale Λ being of comparable size or smaller than the chord length lc , regions with pressure fluctuations are

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generated on the fan-blade leading edges, which are an efficient broadband noise generator [15, 10, 13]. Skewed fan blades tend to reduce turbulence-ingestion noise, compared with unskewed fan blades [31, 32, 7]. It has been shown that

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the impact on turbulence-ingestion noise is more pronounced for forward-skewed fans than for backward-skewed fans under inflow conditions with high turbulence 75

intensity values [33, 34, 3, 22]. Tonal sound sources

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Potential tonal sound sources in low-pressure axial fans are unsteady loading noise, noise from a feedback loop between the laminar boundary layer and vortex shedding on the trailing edge, Gutin noise and thickness noise.

The main tonal sound source for low-pressure axial fans is unsteady load-

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ing noise. This sound is generated by unsteady, i.e. fluctuating, blade forces [35, 36]. Such forces arise e.g. under unsteady and inhomogeneous inflow conditions, induced by upstream obstacles, such as struts or stator vanes for instance. Similarly to steady loading noise, this sound is tonal and occurs at the blade 85

passing frequency fBPF = n · zb and harmonics [35, 36]. Skewed fan blades tend to reduce the peak load as the interaction mechanisms between the fan

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blade and the inflow is changed [9, 37]. Accordingly, unsteady loading noise is

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reduced.

If the boundary layer is laminar, a feedback loop may be excited between 90

the sound from shed vortices and the boundary layer, which is tonal and could

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be linked to the vortex shedding frequency [14, 13]. Similarly to broadband trailing-edge noise, the velocity perpendicular to the trailing edge w2⊥ (Fig. 1) is

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an important parameter for these sound generation mechanisms. As the velocity w2⊥ is altered by fan-blade skew, so are the sound generation mechanisms.

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Owing to the forces produced by a fan blade under steady and homogeneous

inflow conditions, Gutin noise (steady loading noise) is generated [35, 15, 36]. This sound is tonal and radiates at the blade passing frequency fBPF and har-

monics. Fan blade skew leads to a dephasing effect of the sound from the hub to the tip [9, 38]. Thickness noise is induced by the fluid displacement of the fan

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blades and has a tonal characteristic [10, 39]. The generated pressure fluctuations are rotating with the fan rotational speed, which is substantially smaller than the speed of sound c0 for low-pressure axial fans. This leads to a small

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radiation factor. Fan blade skew again has a dephasing effect of thickness noise from the hub to the tip [9, 38]. However, similarly to boundary-layer noise, the 105

contribution of Gutin noise and thickness noise to the overall emitted sound of low-pressure axial fans is usually negligible [35, 36, 40, 15].

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Narrowband sound sources

Besides broadband and tonal components, additional sound sources occur in axial fans that have narrowband characteristics: sound from trailing-edge vortex shedding and subharmonic tip noise. Narrowband indicates that those

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contributions occur in the form of humps, rather than sharp tonal peaks Narrowband trailing-edge noise arises from vortex shedding on the fan-blade trailing edges. Thereby, the vortex-shedding frequency is dependent on the boundary-layer parameters and the trailing-edge geometry: the vortex-shedding 115

frequency increases for a decreasing trailing-edge thickness [13, 14, 15]. Another narrowband sound source is subharmonic tip noise. Thereby, sub-

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harmonic indicates that the peaks do not correspond to the blade passing fre-

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quency fBPF or harmonics. This mechanism is generated by coherent flow structures in the tip region that interact with the fan blades [41, 42, 43, 44, 45]. As 120

the coherent flow structures are rotating with a rotational speed that does not

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correspond to the fan rotational speed, subharmonic components are generated. The hump-like characteristic arises owing to a slightly varying rotational speed

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of the coherent flow structures. If any fan-blade skew is applied, a radial velocity component can be induced close to the fan-blade surface [7, 26]. The velocity

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is radially outwards directed for backward-skewed fans and radially inwards directed for forward-skewed fans [29, 46]. This possibly leads to a reduction (forward-skewed fan blades) or increase (backward-skewed fan blades) of the tip vortex, and in turn of subharmonic tip noise [28, 29, 8, 30]. It has been shown that there are several sound source mechanisms that

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are altered with an application of fan-blade skew and that there is a strong connection between the flow field and the sound field in low-pressure axial fans. However, a detailed side-by-side comparison of fans with different fan-blade

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skew and a common operating point, focused on the interplay between the sound field and flow field has not been done so far. Hence this study was aimed 135

at experimentally investigating the sound and flow fields of low-pressure axial fans with forward-, backward- and unskewed fan blades in order to provide a

deeper understanding of fan-blade skew and its impact on fan aeroacoustics and

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aerodynamics.

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3. Experimental setup-up and measurements 3.1. Axial fans and installation system

Three axial fans were investigated: an unskewed fan (U), a forward-skewed fan (F) and a backward-skewed fan (B) (Fig. 2).

Fan blade skew is the application of fan blade sweep, with sweep angle λ, and fan blade dihedral, with dihedral angle ν, see [22]. The sweep angle λ 145

characterizes the shift of a blade section upstream (forward/positive sweep) or

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downstream (backward/negative sweep) to the relative inflow and the dihedral

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angle ν the shift normal to the relative inflow towards the pressure side (positive dihedral) or the suction side (negative dihedral). The fans were designed according to the blade-element theory for low-solidity fans [47, 48] with identical stagger angles for each blade section of fans F and B and very similar

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stagger angles of fans U and F/B. By applying fan blade sweep, the effective inflow velocity is changed, which reduces the achievable pressure rise of a fan

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blade. Accounting for the reduced pressure rise, a sweep correction as proposed in [2] was applied in the fan design process. A detailed description of the design

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process including values for stagger and flow angles is given in [22].

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x2 x3

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x1

x2 x3

D

x1

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(a) Fan U

x3 x1

(c) Fan B

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(b) Fan F

x2

Figure 2: Investigated low-pressure axial fans: unskewed fan U (a), forward-skewed fan F (b) and backward-skewed fan B (c) with blade sections and stacking line (connecting the center

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of areas of each blade section) on one blade.

Except for the fan-blade skew, the fans differed in their blade-loading dis-

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tributions: fan U was designed with a free-vortex design (FV) [49, 50], whereas fans F and B were design with a controlled-vortex design (CV) [49, 51]. For a free-vortex design, the blade loading is constant along the fan blade span, rcu2 = const.

(1)

The blade loading for fan B and F, with a controlled-vortex design, follows 2

rcu2 = −a (br − d) + e,

(2)

with a, b, d and e being constant [22]. With the loading distribution in Eq. (2), the peak load of the fan blade can be shifted to a desired position along the fan 10

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blade span. In this case, the peak load is at r/rtip = 0.8 for fans F and B, see [22]. The basic fan design parameters are shown in Table 1. Table 1: Fan design parameters.

Parameter

fan U FV

Volume flow rate V˙ in m3 /s

Duct diameter dduct in m Rotational speed n in rpm Tip gap stip in m

Fan-blade airfoil 160

145

150

0...0

0 . . . 55

0 · · · − 55

0.2475 0.495 0.5 1486 0.0025 9

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D

Number of fan blades zb

CV

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Sweep angle λ from hub to tip in deg.

Fan diameter dfan in m

CV 1.4

Total-to-static pressure difference ∆pts in Pa

Hub diameter dhub in m

fan B

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Blade loading

fan F

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The aerodynamic and acoustic investigations were carried out in a standardized inlet test chamber, based on ISO 5801 [52], (Fig. 3). The chamber was built

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as an anechoic room with absorbing walls, ceiling and floor. The ambient noise level for f ∈ (0.1 kHz, 10 kHz) is Lp = 28 dB. 165

The test fans were installed in a short duct with an inlet bellmouth upstream

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of the fan (r = 0.1 · dduct ) and a diffusor downstream of the fan (Fig. 4). The fan mount was supported by four non-centric struts that were located

downstream of the fan at the diffusor exit (Fig. 5). Using a non-centric design and by placing the stator a considerable distance downstream of the fan – ap-

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proximately 180 mm from the fan-blade trailing edges with an axial rotor length of 70 mm (hub) and 20 mm (tip) – dominant rotor-stator-interaction tones are avoided.

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absorber

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12 3635

x3

x1

test fan x2

motor

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torque meter

diffusor

bellmouth inlet

standardized

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auxiliary fan

butterfly damper

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pressure tap

bellmouth inlet

straightener

flow

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splitter-type silencer

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2445 (depth: 2445)

Figure 3: Standardized inlet test chamber based on ISO 5801 [52]. Dimensions in mm.

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∅554

x1

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x3

∅170

x2

∅500

R

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Figure 4: Fan installation system. Dimensions in mm.

struts

x2

x3

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D

x1

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Figure 5: Strut configuration, downstream view.

3.2. Sound measurements

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To capture the sound emission on the suction side, seven 1/2 inch free-field

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microphones, type 4189-L-001 (Br¨ uel & Kjær) were used. They were arranged in a semicircle in a horizontal plane around the inlet bellmouth, at the same height as the fan rotational axis (Fig. 6). For each measurement, the fan operating point was kept stationary. The measurement time was tm = 30 s with a sampling

frequency fs = 48 kHz. The obtained spectra of the seven microphones were 180

energy-averaged, yielding an averaged spectrum and an averaged overall sound pressure level (for frequencies f ∈ (0.1 kHz, 10 kHz)). The microphone array setup consisted of two circular arrays – a small array

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1 2

R1

30 ◦

00 0

x2

x1

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3

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x3

5

6

TE

D

7

Figure 6: Microphone positions. Dimensions in mm.

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with 12 microphones (darray,s = 0.37 m) and a large array with 64 microphones (darray,l = 1.8 m) Fig. 7. More information about the microphone array charac185

teristics can be found in [6, 22]

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A TTL (transistor-transistor logic) signal was recorded synchronously to the

microphone signals to determine the fan angular position. The measurement time was tm = 30 s with a sampling frequency fs = 48 kHz. For the beamforming calculations, a three-dimensional focus grid was used [6, 22]. Three different

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beamforming integration regions were chosen for the three fans, incorporating the trailing edges (TE), the blade surfaces (BS) and the leading edges (LE) (Fig. 8). In post-processing, the integration regions TE and BS were consolidated as no dominant noise is expected from the boundary layer (Section 2). In general, beamforming methods are limited towards lower frequencies [53,

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large array plane darray,l = 1800 mm

small array plane

x2

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darray,s = 370 mm

x3

750

x1

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480

390

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Figure 7: Microphone array setup. Dimensions in mm.

54], hence integrated spectra will be shown only in the frequency range f ∈ (1

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kHz, 10 kHz). In this range, conclusive beamforming sound maps were obtained with the used array geometry.

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3.3. Sound-source localization

To identify the main sound-source regions and to quantify the contribution of these sound sources to the overall sound emission, a microphone array method

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was used. Owing to the rotation of fan, a motion-compensation of the rotating sound sources was necessary. This was done by using a virtual rotating microphone array [55]: prior to frequency-domain beamforming evaluations, the microphone data are transformed into a frame that virtually rotates with the same

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rotational speed as the investigated fan [56, 6, 22]. Therefore, the microphones need to be arranged on one or multiple rings, coaxial with the fan rotational axis. In this work, the CLEAN-SC deconvolution algorithm [57] was applied to improve the resolution and the dynamic range of the beamformer output. The obtained sound maps were post-processed by integrating the beamformer out15

BS

TE

PSfrag replacements

BS

TE

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(a) Fan U

PSfrag LE replacements

TE

BS

LE

(c) Fan B

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(b) Fan F

LE

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PSfrag replacements

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TE

Figure 8: Beamforming integration regions for fans U (a), F (b) and B (c).

put over certain source regions, yielding spectra for these regions. For the sound

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maps obtained with the CLEAN-SC deconvolution algorithm, this can be done without further processing as the beamforming result is already deconvoluted

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[58, 59].

3.4. Flow measurements

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The tip region is a very sensitive area in terms of sound production. To cap-

ture unsteady flow effects in this region, miniature differential pressure transducers, type XCS-093-1psi D (kulite semiconductor), were flush mounted in the duct wall (Fig. 9). In total 15 transducers, that were equally spaced with 10 mm distance from each other, were used. In Section 4, spectra will be shown of the

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transducer which is axially closest to the mid-chord position of the fan-blade tip sections, of the transducer three positions upstream of the mid-chord position

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transducers equally spaced with 10 mm distance from each other x2 x1

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x3

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Figure 9: Unsteady pressure transducer positions. Dimensions in mm.

and three positions downstream of the mid-chord position. Owing to the different fan-blade shapes, these sensor positions vary for each fan. The measurement time was tm = 30 s with a sampling frequency fs = 48 kHz. 225

The flow field was measured on the suction side and on the pressure side with

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a laser Doppler anemometer (LDA) [60, 61]. The LDA system incorporated an

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air-cooled 300 mW argon-ion laser, type Stellar-Pro-L (Modu-Laser), a FiberFlow transmitter, a two-component LDA probe in backscatter orientation and a BSA P80 burst spectrum analyzer (all Dantec Dynamics). For data processing, BSA Flow software v5.20 (Dantec Dynamics) was used. The measurement

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positions were adapted for each fan individually, so they were a distance of either 10 mm upstream of the fan-blade leading edges or 10 mm downstream of

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the fan-blade trailing edges (Fig. 10). Therefore, three different measurement setups were necessary: To measure the velocity components cm1 , cu1 , cm2 and

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cu2 , the probe was placed perpendicular to the duct. To measure the velocity component cr1 and cr2 , the probe was placed parallel to the fan rotational axis upstream of the fan (to measure velocity cr1 ) and downstream of the fan (to

measure velocity cr2 ) respectively (Fig. 10). In total 16 points from to the hub to duct were captured. To obtain spatial 240

information of the flow field, the velocity data were phase-locked ensembleaveraged in 2◦ bins [60, 61]. Three different measurement stop criteria were

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x2

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x1

10 mm from the trailing edge cr2

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x3

cr1

10 mm from the leading edge

cm2 , cu2

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cm1 , cu1

Figure 10: LDA measurement configurations.

set for each measurement point (the first one to be reached called the stop): a measurement time tm = 540 s, a total sample count N = 4 · 106 or a bin count N = 5 · 103 samples per bin.

The LDA measurement uncertainties (95 % confidence levels of the mean

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and fluctuation rms values [62]) are shown in Table 2.

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Table 2: LDA measurement uncertainties.

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Value

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Mean value

Fluctuation value

Suction side

pressure side

c1: ±0.05 m/s

c1: ±0.02 m/s

c2: ±0.02 m/s

c2: ±0.01 m/s

c3: ±0.07 m/s

c3: ±0.02 m/s

c01: ±0.04 m/s

c01: ±0.01 m/s

c02: ±0.01 m/s

c02: ±0.01 m/s

c03: ±0.05 m/s

c03: ±0.02 m/s

4. Results and discussion This study is focused on the sound field and the flow field at the fan design point. To give a general overview of the fan characteristics, aerodynamic and 18

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acoustic characteristic curves are discussed. In the following, only results at the

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fan design volume flow rate V˙ = 1.4 m3 /s (this corresponds to a flow-coefficient ϕd = 0.252, Eq. (3)) are considered. 4.1. Characteristic curves

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The aerodynamic and acoustic characteristic curves (Fig. 11) are displayed in dimensionless numbers. The flow-coefficient ϕ is calculated according to, π (d2fan

4V˙ , − d2hub ) π n dfan | {z }

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ϕ=

(3)

u

the total-to-static pressure-coefficient ψts according to ψts =

2∆pts ρu2

(4)

and the total-to-static efficiency ηts according to

D

ηts =

V˙ ∆pts , Ms 2 π n

(5)

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torque Ms .

TE

with the circumferential velocity at the fan tip u, the density ρ and the shaft

Based on similar design parameters, all fans achieve a comparable pressure-

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coefficient ψts at the design flow-coefficient ϕd (Fig. 11(a)). Small discrepancies are attributed to effects that are neglected during the fan design procedure, such

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as losses due to the tip leakage flow or the inlet geometry. 260

In general, the pressure-coefficient curves of the three fans are similar. The

characteristics for fans U and B show a flat progression in the range ϕ ∈ (0.14, 0.24), i.e. at lower flow-coefficients than the design point. In contrast, fan F shows a higher pressure rise. This effect has been observed in previous investigations [7, 28, 8, 63] and was attributed directly to the forward-skew of

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the fan blade and its benefits in terms of stall onset. The maximum efficiency of fans U and B is achieved at the design flowcoefficient ϕd , whereas the maximum efficiency for fan F is observed at a slightly lower volume flow rate (Fig. 11(b)). Fan F has the highest overall efficiency, 19

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8 9 -

0 .3

7

0 .2

8

0 .1 0

0 .1 0 .2 0 .3 flow-coefficient ϕ

-

0 .4

B

0

ϕd

0 .1 0 .2 0 .3 flow-coefficient ϕ

0 .4

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U F

80

70

ϕd

B

-

0 .2

(b) Efficiency

90 Lp in dB

6

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efficiency ηts

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(c) Averaged sound pressure level

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Figure 11: Aerodynamic and acoustic characteristic curves for fans U, F and B.

followed by fans U and B. Particularly noticeable is the substantial lower efficiency of fan B compared with fans U and F at the design flow-coefficient ϕd .

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This will be further discussed when showing the characteristic differences in the flow field of the fans.

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Major differences between the three fans are observed for the acoustic char-

acteristic curves (Fig. 11(c)). Except for ϕ < 0.12, fan U has the highest sound

275

emission. This is reasonable as fan-blade skew has the potential of reducing various sound source mechanisms (Section 2). Fan F has the least sound emission in a broad region of ϕ ∈ (0.16, 0.28). A particularly large difference of the averaged sound pressure values Lp between fans U and B is observed at ϕd . This will be discussed below on the basis of averaged sound pressure and integrated

280

sound pressure spectra. At ϕ < 0.12, the relations change with fan B showing the lowest Lp values. However, this region does not correspond to the typical

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operating conditions of the three fans, as stall on the fan blades is very likely to occur at such low flow-coefficients. 4.2. Sound field 285

1

Averaged sound pressure spectra for the three fans at the design flow-

7

9 -

f = 1.55fBPF

60

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5

80

B

U F

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3

sound pressure level Lp in dB

coefficient ϕd = 0.252 are shown in Fig. 12.

40

f = 1.46fBPF

fBPF = 223 Hz 20

103 frequency f in Hz

102

.

104

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Figure 12: Averaged sound pressure spectra for fans U, F and B at a flow-coefficient ϕ = 0.252.

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The arrows indicate the levels of the tonal peaks.

The most distinctive effects in the averaged sound pressure spectra are the very dominant subharmonic components at f = 1.55fBPF = 345 Hz and

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f = 2.15fBPF = 479 Hz (fan U) and f = 1.46fBPF = 325 Hz and f = 2.1fBPF = 468 Hz (fan B), with fBPF = 223 Hz. They are the first harmonics of the sub-

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hamronic components observed below the blade passing frequency (f = 173 Hz for fan U and f = 168 Hz for fan B). Such a component can also be seen for fan F at f = 1.6fBPF = 357 Hz, albeit to a much smaller extent. The first indicator of these subharmonic components can be seen already at f = 0.77fBPF = 172 Hz

295

for all fans. This sound generation mechanism is linked to a backflow from the pressure side to the suction side in the tip-gap region (Section 2). Forwardskewed fan blades tend to weaken the tip-vortex formation [64, 30, 28, 29, 65], which leads to a lower magnitude of this sound generation mechanism. Tonal noise is most likely connected to inflow distortions, as no turbulence

300

control screen was used [66, 67]. The levels of the tonal component at the 21

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blade passing frequency fBPF are slightly lower for fan F than for fans U and B. Consequently, the blades of fan F are experiencing lower unsteady blade

forces than the other fan blades. It is expected that these higher forces are mainly induced by flow phenomena in the tip region: with an intensified tip305

gap flow, a high unsteadiness is introduced, which can be a reason for higher

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tonal components [8, 30]. Higher levels of the BPF harmonics (2 · fBPF and

3 · fBPF ) can be seen for fan U compared with fan B. From this, one can draw the conclusion, as discussed in Section 2, that fan-blade skew has a potential

310

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for reducing unsteady blade forces.

The broadband levels of fan F in Fig. 12 are substantially lower for f < 2 kHz. In this range, broadband sound is expected to be induced by turbulenceingestion noise, coming from the turbulent flow in the tip gap [68]. As mentioned in Section 2, dominant sound sources are expected to be located in the outer part of the fan blade, owing to the higher circumferential velocity. In the case of fans U and B, the intensified tip gap flow and the high unsteadiness in the

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tip region is very likely to increase turbulence-ingestion noise. These effects,

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in combination with the high circumferential velocity at the fan tips, are a reasonable explanation for higher turbulence-ingestion noise and in turn for the higher broadband components for f < 2 kHz of fans U and B. Sound at higher frequencies is usually governed by trailing-edge noise (Section 2). From

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f > 2 kHz, fan B has the lowest broadband levels. Hence the difference in the

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trailing-edge curvature seems to play an important role for this sound generation mechanism. As mentioned in Section 2, the trailing-edge sound production is strongly dependent on the velocity perpendicular to the trailing edge w2⊥ .

325

Based on the curve progressions in 12, it is reasonable to assume that the highest w2⊥ values occur for fan U and the lowest for fan B. This will be further discussed on the basis of integrated sound pressure spectra. Integrated sound pressure spectra for different fan-blade regions are shown in Fig. 13. They are based on sound maps, as shown in Figs. 14 and 15 for the

330

third-octave bands with center frequencies fc = 2.5 kHz (Fig. 14) and fc = 5 kHz

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Lp in dB

50 6 30 U 10

F

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.

30 U 10

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104

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.

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8

70

4

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70

4

6

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(Fig. 15).

Lp in dB

2

0

(a) Leading edges

(b) Blade surfaces and trailing edges

Figure 13: Integrated spectra for the leading-edges integration regions (a) and the bladesurfaces and trailing-edges integration regions (b) at a flow-coefficient ϕ = 0.252.

From Fig. 13(a), it is obvious that turbulence-ingestion noise, radiated from the fan-blade leading edges, is very pronounced for fan U: the levels are consider-

range f ∈ (1 kHz, 10 kHz). This also relates to the higher broadband levels of

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ably higher than for fan F and partially also for fan B in the considered frequency

fan U in the averaged sound pressure spectra (Fig. 12) for f ∈ (1 kHz, 5 kHz). It is also noticeable that the levels for fan B are higher than for fan F below

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f = 1.7 kHz. Similarly to the averaged sound pressure spectra, this suggests that the unsteady flow field in the tip regions of fans U and B leads to increased 340

turbulence-ingestion noise and that fan-blade skew has the potential of reducing

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this sound source mechanism. Above f = 4 kHz, fan U shows the highest levels of sound originating from the ”blade surfaces/trailing edges” integration regions (Fig. 13(b)). This has also been observed in Fig. 12 and indicates again that the trailing-edge curvature is an important factor for trailing-edge noise generation.

345

However, no major differences are observed for fans F and B. Below f = 4 kHz,

no clear trend is noticeable – in this context, it has to kept in mind that inflow conditions with large length scales Λ leads to broadband sound sources that cannot be assigned to a specific fan-blade region (Section 2).

23

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Lp in dB 45 6

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Figure 14: Beamforming sound maps for the third-octave band with center frequency fc = 2.5 kHz for fans F (a), U (b) and B (c) at a flow-coefficient ϕ = 0.252.

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Figure 15: Beamforming sound maps for the third-octave band with center frequency fc = 5 kHz for fans F (a), U (b) and B (c) at a flow-coefficient ϕ = 0.252.

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4.3. Interplay between the sound field and the flow field The sound field has been discussed in Section 4.2. In this section, the focus is on the interplay between the sound and flow fields. Wall pressure fluctuations

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Spectra of wall pressure fluctuations on the duct are shown in Fig. 16.

For all spectra, dominant tonal components at the fBPF and harmonics oc355

cur. These pressure peaks are created as the fan blades pass the transducers at

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a steady frequency. In general, fan F has the lowest broadband levels. Similarly to the averaged sound pressure spectra (Fig. 12), subharmonic narrowband humps arise in the wall pressure spectra of the upstream position at identical frequencies: f = 1.55fBPF and f = 2.15fBPF (fan U) and f = 1.46fBPF and 360

f = 2.1fBPF (fan B).

At the mid-chord position, only the first hump can be seen, while the humps

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vanish at the downstream position. The occurrence of subharmonic humps both in the averaged sound pressure spectra and in the wall pressure spectra

365

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is a clear indicator that the subharmonic humps originate from the tip region and that there is an interrelation between the unsteady wall pressure and the sound radiation. Higher broadband levels for fans U and B hint also at a more

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efficient interaction of tip gap flow with blade tip for fans U and B. Velocity distribution on the suction side and the pressure side

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Plots of the phase-locked ensemble-averaged velocity values are shown in

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Fig. 17. The contour represents the out-of-plane velocity c˜m and the vector field

the in-plane velocities c˜r and c˜u as seen from the fan suction sides. Furthermore, plots of the phase-locked ensemble-averaged meridional velocity on the pressure side c˜m2 for all fans and for a varying dimensionless radius r/rduct (in the tip region) are shown in Fig. 18.

375

For fan U, the maximum c˜m1 velocity is located in the hub to mid-span region, while there is no pronounced maximum for fan B. For fan F, the c˜m1 maximum is located in the outer part of the fan blade, whereas c˜m1 is decreased

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7 8 0 9 12.

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101 10−1 10−3 2 10

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(a) Upstream

8 0 9 12.

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frequency f in Hz (c) Downstream

Figure 16: Spectra of wall pressure fluctuations upstream of the fans (a) at mid-chord position (b) and downstream of the fans (c) at a flow-coefficient ϕ = 0.252.

in the hub region. Forward-skewed fans are known to change the blade loading along the fan-blade span [24, 25, 26, 27, 4], which explains this velocity dis380

tribution. With increasing c˜m1 , the effective angle of attack is reduced, which

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leads to an unloading of the tip blade sections [22] and in turn to a weaker tip-vortex formation. Owing to the weaker tip vortex, no dominant subhar-

monic components are noticeable in the averaged sound pressure spectra. The opposite applies for fans U and B. Zhu et al. [45] clearly showed the interplay 385

between the tip flow, particularly the turbulent coherent structures that lead

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to characteristic pressure modes also known as rotational instabilities, and the

subharmonic humps in the tip noise. Since the flow field in the tip region is similar for fans B and U, so is the magnitude of the subharmonic components

390

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in Fig. 12.

The in-plane velocity vector of c˜r1 and c˜u1 is in general directed towards the c˜m1 maximum. The flow field in the tip region of fan B is substantially different compared with the other fans: Whereas the in-plane velocity at upstream is mainly oriented against the rotational direction for fans U and F, this component is oriented in circumferential direction in the tip region for fan B. Furthermore, the meridional velocity c˜m1 is reduced in the tip region for fan B. This reduced

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through-flow in the tip region can also be associated with an intensified gap flow

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for fan B. Owing to the backflow from the pressure side to the suction side, c˜m1 is reduced and the flow deflects towards lower radii. The in-plane velocity on the suction side for fan U is also directed inwards, similar to fan B. On the pressure side, the flow field is driven by a strong circumferential

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velocity c˜u2 owing to the fan rotation. For all fans, there is a band with reduced

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c˜m2 velocity in the tip region. This band is more pronounced, i.e. further distributed inwards with lower flow velocities, for fans U and B than for fan F. An explanation for this is again the gap flow that partially blocks the meridional

405

through-flow, which leads to lower velocities c˜m2 . The differences in the tip-

flow field are also clearly visible in Fig. 18. At a larger dimensionless radius (Fig. 18(a)), the meridional velocity c˜m2 is greatest for fan F, followed by fans

B and U. Towards lower dimensionless radii, the curve progressions for the different fans converge (Figs. 18(b) and 18(c)) until no obvious deviations can 410

be seen anymore (Fig. 18(d)). This clearly shows the impact of the blocking effect owing to the intensified tip gap flow for fan B and U compared with fan 28

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F. Another indicator of unsteady flow processes is the turbulent kinetic energy k˜ (Fig. 19). There are bands with increased k˜1 and k˜2 values on the suction and 415

on the pressure sides respectively. These bands are induced by beginning flow

fan blades (pressure side) respectively.

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partitioning in the different blade channels (suction side) and the wake of the

Similarly to the velocity plots, a substantial difference of the turbulent kinetic energy is observed in the tip region. On the suction side, k˜1 values are generally in the tip region low for fan F, whereas there is a slim band (fan U)

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420

and a wide band (fan B) with increased k˜1 values. On the pressure side, bands with increased k˜2 values are observed for all fans, however the bands for fans U and B are wider than for fan F.

As discussed above, fans U and B show subharmonic sound components that 425

can be related to the flow phenomena in the tip region. Additionally, a high

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unsteady flow field in the tip region leads to an increase in turbulence-ingestion noise, which explains the elevated low-frequency broadband components in the

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averaged sound pressure spectra for fans U and B.

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5

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10 m/s

7

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12 10 8 7 6 4 9 2 0 -

.

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. (a) Fan U, suction side

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12 10 8 6 4 2 0

. (d) Fan F, pressure side

c˜m1 in m/s

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(b) Fan U, pressure side

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5 12 10 8 7 6 4 9 2 0 -

10 m/s

x3 x2

12 10 8 6 4 2 0

.

(e) Fan B, suction side

(f) Fan B, pressure side

Figure 17: Phase-locked ensemble-averaged distribution of the meridional velocity c˜m (contour) and the mean plane velocity components c˜r and c˜u (vector-field) for fans U ((a) and (b)), F ((c) and (d)) and B ((e) and (f)) at a flow-coefficient ϕ = 0.252. The index 1 denotes properties on the suction side and the index 2 properties on the pressure side.

30

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F

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.

velocity c˜m2 in m/s

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B

15 10 5

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60 120 180 240 300 360rotational angle α in deg. .

0

(a) r/rduct = 0.952

-

(b) r/rduct = 0.936

10 5 0

7

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velocity c˜m2 in m/s

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60 120 180 240 300 360rotational angle α in deg. .

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.

B 15

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(c) r/rduct = 0.904

B 15

U

F

10 5 0

0

60 120 180 240 300 360 rotational angle α in deg. (d) r/rduct = 0.872

Figure 18: Phase-locked ensemble-averaged meridional velocity on the pressure side c˜m2 for all fans and for varying dimensionless radius r/rduct (a)-(d)).

31

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10 m/s

10 m/s

6 7 10 m/s8 9

10 9 5 0 .

x3

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k˜2 in m2 /s2 35 30 25 20 15 10 5 0

(d) Fan F, pressure side

k˜1 in m2 /s2 4 35 30 6 25 20 7 15 8 10 9 5 0 .

(e) Fan B, suction side

x3 x2

k˜2 in m2 /s2 35 30 25 20 15 10 5 0

(f) Fan B, pressure side

˜ Figure 19: Phase-locked ensemble-averaged distribution of the turbulent kinetic energy k (contour) for fans U ((a) and (b)), F ((c) and (d)) and B ((e) and (f)) at a flow-coefficient ϕ = 0.252. The index 1 denotes properties on the suction side and the index 2 properties on the pressure side.

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5. Conclusion The sound flow fields of three fans with forward-, backward- and unskewed fans were studied with a focus on the impact of different flow phenomena on

the sound emission of axial fans at the fan design points. The pressure rise

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of the fans was similar, except for a region at lower flow-coefficients than the

fan design point: here, the unskewed fan U and the backward-skewed fan had 435

a flat curve progression, whereas the forward-skewed fan had higher pressure-

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coefficient values. The forward-skewed fan F also had the highest efficiency of the three fans. The least efficiency was observed for the backward-skewed fan. Major differences were found for the acoustic characteristic curves: the forwardskewed fan F had a substantial lower sound emission than the other fans over a 440

very broad range.

Averaged sound pressure spectra showed an increased low-frequency broadband sound for the unskewed fan U and the backward-skewed fan B compared

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with the forward-skewed fan F. Additionally, very pronounced subharmonic nar-

445

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rowband components occurred for fans U and B. The high-frequency broadband sound levels were most dominant for the unskewed fan U and least for the backward-skewed fan B.

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Integrated sound pressure spectra for different fan-blade regions revealed that turbulence-ingestion noise from the leading-edge regions is very pronounced for the unskewed fan U and also for the backward-skewed fan B (at lower frequencies though). Furthermore, the unskewed fan showed increased trailing-

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edge noise, which was attributed to the trailing-edge curvature and its impact on the velocity perpendicular to the trailing edge. Similar subharmonic component to those in the averaged sound pressure

spectra for the unskewed fan U and the backward-skewed fan B were also found

455

in the wall pressure fluctuation spectra. This clearly indicates that the subharmonic components originate from the tip region, induced by coherent flow structures that interact with the fan blades. These subharmonic are far less pronounced for the forward-skewed fan F as this type of fan-blade skew weakens the

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tip-vortex formation and accordingly reduces this sound generation mechanism. The velocity distributions on the suction side and the pressure side showed an increased meridional velocity in the tip region for the forward-skewed fan F, compared with the unskewed fan U and the backward-skewed fan B. This

leads to an unloading of the tip blade sections and accordingly to a weaker

465

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tip-vortex formation, as suggested by [28, 29, 30]. Low values of the meridional velocity as well as bands with high turbulent kinetic energy on the suction side

and the pressure side for fans U and B suggest a high unsteady flow field in

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the tip region and an intensified gap flow. This is again in accordance with the occurrence of the subharmonic narrowband sound components for these fans. Besides this, an unsteady flow field in the tip region leads also to an 470

increase in turbulence-ingestion noise, which can be seen clearly on comparing the low-frequency sound emission of fans U and B with fan F, which features substantially lower broadband sound levels.

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Characteristic flow features were observed in this study that were dependent on the fan-blade skew. It was shown that there is a strong connection between these flow phenomena and the sound radiation of the investigated axial

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fans. All investigations were made under homogeneous inflow conditions without any obstructions upstream of the fan. The forward-skewed fan showed the

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best performance – both in terms of aerodynamics and aeroacoustics – under these inflow conditions. The tip gap flow was identified to have a major impact on both the sound field and the flow field. The findings provide a better

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understanding of the interplay between these two domains and show means for predicting relevant flow and sound phenomena for fans with different fan-blade skew.

[1] European Union, Commission Regulation (EU) No 327/2011, Official Jour-

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nal of the European Union. [2] M. Beiler, Untersuchung der dreidimensionalen Str¨omung durch Axialventilatoren mit gekr¨ ummten Schaufeln [Investigation of the three-dimensional

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flow through axial fans with skewed fan blades], Ph.D. thesis, University Siegen, Germany (1996). 490

[3] F. Zenger, G. Herold, S. Becker, Acoustic characterization of forward- and backward-skewed axial fans under increased inflow turbulence, AIAA Jour-

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nal 55 (4) (2017) 1241–1250. doi:10.2514/1.J055383.

[4] F. A. Agboola, T. Wright, The effects of axial fan noise control by blade sweep on the radial component of velocity, in: Proceedings of 5th AIAA/CEAS Aeroacoustics Conference, AIAA Paper 99-1862, Bellevue,

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USA, 1999. doi:10.2514/6.1999-1862.

[5] T. Fukano, C.-M. Jang, Tip clearance noise of axial flow fans operating at design and off-design condition, Journal of Sound and Vibration 275 (2004) 1027–1050. doi:10.1016/S0022-460X(03)00815-0. [6] F. Kr¨ omer, J. M¨ uller, S. Becker, Investigation of aeroacoustic properties of

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low-pressure axial fans with different blade stacking, AIAA Journal 56 (4)

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(2018) 1507–1518. doi:10.2514/1.J056324. [7] T. Wright, W. Simmons, Blade sweep for low speed axial fans, Journal of

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Turbomachinery 112 (1990) 151–158. doi:10.1115/1.2927413. [8] J. Vad, Aerodynamic effects of blade sweep and skew in low-speed axial flow rotors at the design flow rate: an overview, Proceedings of the Institution

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of Mechanical Engineers, Part A: Journal of Power and Energy 222 (1) (2008) 69–85. doi:10.1243/09576509JPE471.

[9] T. Carolus, M. Beiler, Skewed blades in low pressure fans: a survey of noise

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reduction mechanisms, in: Proceedings of 3rd AIAA/CEAS Aeroacoustics Conference, AIAA Paper 97-1591, Atlanta, USA, 1997, pp. 47–53. doi: 10.2514/6.1997-1591.

[10] T. Carolus, Ventilatoren - Aerodynamischer Entwurf, Schallvorhersage, Konstruktion [Fans - aerodynamic design, sound prediction, engineer-

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ing], 3rd Edition, Springer Vieweg, Wiesbaden, 2013. 978-3-8348-2472-1.

doi:10.1007/

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[11] R. E. Hayden, Some advances in design techniques for low noise operation

of propellers and fans, in: Proceedings of the National Conference on Noise

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Control Engineering, Hampton, USA, 1977.

[12] W. C. Meecham, On noise produced by boundary-layer turbulence, Journal of the Acoustical Society of America 35 (1963) 116–117. doi:10.1121/1.

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[13] S. Wagner, R. Bareiß, G. Guidati, Wind turbine noise, Springer, Berlin, 1996. doi:10.1007/978-3-642-88710-9. 525

[14] T. F. Brooks, S. D. Pope, M. A. Marcolini, Airfoil self-noise and prediction, NASA Reference Publication 1218.

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[15] W. K. Blake, Mechanics of flow-induced sound and vibration: Complex

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flow-structure interactions, Vol. 2, Academic Press, New York, 1986. [16] M. V. Lowson, Assessment and prediction of wind turbine noise, Flow 530

Solutions Report 92/19, ETSU W/13/00284/REP.

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[17] I. J. Sharland, Sources of noise in axial flow fans, Journal of Sound and Vibration 1 (3) (1964) 302–322. doi:10.1016/0022-460X(64)90068-9.

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[18] R. K. Amiet, Noise due to turbulent flow past a trailing edge, Journal of Sound and Vibration 47 (3) (1976) 387–393. doi:10.1016/0022-460X(76)

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[19] M. Roger, S. Moreau, Addendum to the back-scattering correction of amiet’s trailing-edge noise model, Journal of Sound and Vibration 331 (24) (2012) 5383–5385. doi:10.1016/j.jsv.2012.06.019. [20] N. A. Brown, The use of skewed blades for ship propellers and truck fans,

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[21] S. Moreau, M. Roger, Competing broadband noise mechanisms in low-speed axial fans, AIAA Journal 45 (1) (2007) 48–57. doi:10.2514/1.14583.

[22] F. J. Kr¨ omer, Sound emission of low-pressure axial fans under dis545

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