PHASED ARRAY MICROPHONE MEASUREMENT OF AN …tothbence/thesis.pdfPHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN v ACKNOWLEDGEMENTS I would like to thank Mr Tamás BENEDEK,

PHASED ARRAY MICROPHONE MEASUREMENT OF AN

AXIAL FLOW FAN

by

Bence Mihály TÓTH

/AGMES4/

Submitted to the

Department of Fluid Mechanics of the

Budapest University of Technology and Economics

in partial fulfilment of the requirements for the degree of

Master of Science in Mechanical Engineering Modelling

on the 16th May 2014

Project Report

Final Project /BMEGEÁTMWD2/

Supervisor:

Tamás BENEDEK, PhD student

Evaluation Team Members, advisors:

Dr János VAD, associate professor

Csaba HORVÁTH, assistant research fellow

Department of Fluid Mechanics

Faculty of Mechanical Engineering

Budapest University of Technology and Economics

PHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN

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iii

DECLARATION

Full Name (as in ID): Bence Mihály TÓTH

Neptun Code: AGMES4

University: Budapest University of Technology and Economics

Faculty: Faculty of Mechanical Engineering

Department: Department of Fluid Mechanics

Major/Minor: MSc in Mechanical Engineering Modelling

Fluid Mechanics major / Solid Mechanics minor

Project Report Title: Phased Array Microphone Measurement

of an Axial Flow Fan

Academic year of submission: 2013 / 2014 - II.

I, the undersigned, hereby declare that the Project Report submitted for

assessment and defence, exclusively contains the results of my own work assisted by

my supervisor. Further to it, it is also stated that all other results taken from the

technical literature or other sources are clearly identified and referred to according to

copyright (footnotes/references are chapter and verse, and placed appropriately).

I accept that the scientific results presented in my Project Report can be utilised by

the Department of the supervisor for further research or teaching purposes.

Budapest, 16th May, 2014

__________________________________

(Signature)

FOR YOUR INFORMATION

The submitted Project Report in written and in electronic format can be found

in the Library of the Department of Fluid Mechanics at the Budapest University of

Technology and Economics. Address: H-1111 Budapest, Bertalan L. 4-6. „Ae”

building of the BME.


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v

ACKNOWLEDGEMENTS

I would like to thank Mr Tamás BENEDEK, Dr János VAD and Mr Csaba

HORVÁTH for their help in the measurement process and the data analysis. I am

grateful to Ms Orsolya IGAZ for her cooperation in carrying out the velocity

measurements and to Mr Zsolt VÁRHEGYI for his help with the MATLAB

algorithm.

Köszönöm családom és barátaim segítségét, akik végig támogattak egyetemi

éveim alatt.


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vii

ABSTRACT

A method based on [1] is used to relate the radial distribution of aerodynamic

losses to the generated noise in case of an axial fan.

Aerodynamic characteristics are estimated based on geometry and inlet velocity

profile measurements. The blade sweep is accounted for in the calculations. Two

parameters are investigated: loss coefficient and Lieblein diffusion factor [2].

Both parameters were written in a level form.

Noise distribution was measured using a Phased Array Microphone (PAM).

Radially averaged plots were created for the third octave bands from 2000 Hz to

6300 Hz and a linear fit using the least squares method was carried out to find

parameters that best approximate the noise as a function of either or both on

suction and pressure sides. On the suction side the -dependent function seems

appropriate in the 2000 Hz – 3150 Hz range and the full band, too. The

approximation based on fails to reproduce the noise distribution. On the

pressure side the situation is similar, but the -dependent function preforms

better in the low frequency range. The full band estimation is acceptable in both

cases for both trial functions. Some measurement points do not support the

original assumption that increasing aerodynamic losses would lead to increasing

noise.

The ROSI [3] method was used to generate source maps of the fan from a co-

rotating coordinate system. The results show a significant noise source in the

vicinity of the leading edge tip, while on the pressure side the leading edge mid-

chord area generates more noise. In general, the pressure side is louder.

Further measurements are necessary to investigate the trial functions behaviour

as well as to determine the generation mechanism of the noise sources.


viii


ix

KIVONAT

A dolgozatban egy axiális ventilátor aerodinamikai veszteségeinek sugár menti

eloszlását hasonlítom össze a keletkezett zajjal [1] alapján.

Az aerodinamikai veszteségek becslése geometriai adatok és a belépő

sebességprofil mérése alapján történt. A számítások során figyelembe vettem a

lapátferdítés hatását. Két változót vizsgáltam: az veszteségi számot, illetve a

Lieblein diffúziós tényezőt [2]. Mindkét paramétert szintes írásmódban

használtam.

A zaj eloszlását mikrofontömb segítségével mértem. A mérési adatokat a

ventilátor forgása mentén átlagoltam, majd a sugár mentén forráserősség-eloszlási

diagramokat készítettem. Ezt mind a szívó, mind a nyomó oldalon elvégeztem a

2000 Hz-től 6300 Hz-ig terjedő tercsávokban. Ezekre a diagramokra mind , mind

felhasználásával hatványkitevős alakban írt próbafüggvényeket illesztettem. A

próbafüggvények paramétereit a legkisebb négyzetek módszerével határoztam

meg. Az eredmények alapján a szívó oldalon az -függő megoldás teljesít jobban

a 2000 Hz-3150 Hz tartományban illetve a teljes sávban is, míg a alapú közelítés

nem tudja visszaadni a függvények menetét. A nyomó oldalon hasonló a helyzet,

viszont a -függő megoldás is elfogadhatóan teljesít a mély tartományban. A teljes

sávban mindkét közelítés elfogadható. Néhány mérési pontban azonban a

közelítés eredménye ellentmond az eredeti feltevésnek, miszerint az

aerodinamikai veszteségek növekedése a zaj növekedésével járna együtt.

A ROSI [3] algoritmus segítségével zajtérképeket készítettem a ventilátorról

együttforgó koordináta-rendszerben. Az eredmények alapján a szívó oldalon a

belépőél csúcsa a legjelentősebb zajforrás, míg a nyomó oldalon a belépőél

középső része az. Általánosságban a nyomó oldalon keletkezik több zaj.

További mérések szükségesek az illesztett függvények viselkedésének

vizsgálata illetve a zajtérképeken látható források eredetének magyarázása

érdekében.


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CONTENTS

1. INTRODUCTION 5

2. AXIAL FANS, LOSSES AND NOISE 6

2.1. Fans 6 2.2. Fan types 6 2.3. Losses 7 2.4. Fan noise 8

3. PHASED ARRAY MICROPHONES 10

3.1. Time-domain beamforming 10 3.2. Frequency-domain beamforming 11 3.3. ROSI method [3] 13 3.4. Spatial resolution 15

4. GEOMETRY MEASUREMENT 16

4.1. Measured data 16 4.2. Calculated data 18 4.3. Uncertainties 19

5. AERODYNAMIC PROPERTIES 20

5.1. Inlet velocity measurement 20 5.2. Outlet velocity measurements 21 5.3. Calculations for unswept blades 21 5.4. Sweep correction 24 5.5. Uncertainties 25 5.6. Results 25

6. ACOUSTIC PROPERTIES 27

6.1. Equipment 27 6.2. Procedure 27 6.3. Delay-and-Sum results 29 6.4. Radial noise distribution 32 6.5. Source distribution on blades 38

7. SUMMARY 47

8. FURTHER AIMS 48

9. BIBLIOGRAPHY 49


xii

NOMENCLATURE

LATIN LETTERS

a speed of sound [m/s]

A, B function fitting coefficients [-]

AR aspect ratio [-]

d diameter [mm]

c chord [mm]

D diffusion factor [-]

e steering vector [-]

f blade curvature [mm]

fs sampling frequency [Hz]

Fourier operator

g tip clearance [mm]

h vector of signal spectra [Pa]

i unit vector in x direction [m]

j imaginary unit, √

L radial SPL distribution [dB]

M number of microphones

Ma Mach number [-]

n rotational speed [1/s]

N number of blades

p pressure [Pa]

P power [W]

q monopole intensity [kg/s2]

Q freq. domain monopole intensity

[kg/Hz2]

r radius [mm]

R outer radius [mm]

Rc camber radius [mm]

Rp pipe radius [mm]

R matrix of cross spectra [Pa2/Hz2]

s spacing [mm]

S auto spectrum [Pa2/Hz2]

t time [s]

u tangential velocity [m/s]

U tip tangential velocity [m/s]

v absolute velocity [m/s]

w relative velocity [m/s]

W weighting matrix

x observer location [m]

y source location [m]

z averaged PAM output [Pa]

Z freq. domain PAM output [Pa]

GREEK LETTERS

flow angle relative to blade [°]

sweep angle [°]

Dirac-delta function

difference

noise [Pa]

local flow number [-]

efficiency [-]

stagger angle [°]

wavelength [m]

PAM spatial resolution [m]

camber angle [°]

pressure number [-]

density [kg/m3]

retarded time [s]

circular frequency [rad/s]

SUBSCRIPTS / SUPERSCRIPTS

* complex conjugate K conjugate transposed

0 ambient conditions

1 suction side

2 pressure side

ax axial

is isentropic

m microphone index

mid medium value

re real

sw sweep corrected


1

LIST OF FIGURES

Figure 2.1. Axial (left) and radial (right) fan schematics 6

Figure 4.1. The investigated fan [1] 16

Figure 4.2. Fan geometry 17

Figure 5.1. Nondimensional axial velocity profile 20

Figure 5.2. Characteristic curve of the investigated fan [12] 21

Figure 5.3. The relative deflection ε/ε* versus (i-i*)/ε* recreated from [13] 23

Figure 5.4. Aerodynamic properties along radius 26

Figure 6.1. The measurement setup 27

Figure 6.2. Comparison of source maps acquired with 30 s (left) and 20 s (right) averaging 28

Figure 6.3. DS source map at 2000 Hz mid-frequency 29






Figure 6.9. DS source map at full band 31

Figure 6.10. A-weighting spectrum 33

Figure 6.11. SPL versus radius at 2 kHz on suction side 33

Figure 6.12. SPL versus radius at 2500 Hz on suction side 34





Figure 6.17. SPL versus radius at full band on suction side 35

Figure 6.18. SPL versus radius at 2000 Hz on pressure side 36






Figure 6.24. SPL versus radius at full band on pressure side 38

Figure 6.25. Suction side source location at 0.5 m distance 39

Figure 6.26. Pressure side source location at 1 m distance 39

Figure 6.27. Synthetic algorithm source map 40

Figure 6.28. Suction side source map at 2000 Hz 41






Figure 6.34. Suction side source map at full band 43

Figure 6.35. Pressure side source map at 2000 Hz 44




2




Figure 6.41. Pressure side source map at full band 46


3

LIST OF TABLES

Table 4.1. Geometric data along radius 17

Table 4.2. Interpolated 18

Table 4.3. Calculated data 19

Table 4.4. Dimensional uncertainties 19

Table 5.1: Uncertainties 25

Table 5.2: Calculated efficiencies, pressure numbers and diffusion factors 26

Table 6.1. Suction side function fit parameters 32

Table 6.2. Pressure side function fit parameters 36


4


5

1. INTRODUCTION

Noise of turbomachinery is a growing concern. These pieces of equipment are

widely used in urban areas, buildings and offices; therefore reducing their noise is

of great importance.

The connection between aerodynamic losses and generated noise is investigated

in case of a short-ducted industrial fan following the methods described in [1].



parameters are investigated: loss coefficient and Lieblein diffusion factor [2].

Both parameters are written in a level-like, i.e. logarithmic form.

Noise distribution is measured using a Phased Array Microphone (PAM).

Radially averaged plots are created for the third octave bands from 2000 Hz to 6300

Hz and a linear fit using the least squares method is carried out to find parameters

that best approximate the noise as a function of either or both on suction and

pressure sides. The correctness of these approximations is investigated through the

R2 value as well as their behaviour.

The ROSI [3] method is used to generate source maps of the fan from a co-

rotating coordinate system. These maps are analysed to find the most important

noise sources. An attempt is made to explain their origin.

Finally, recommendations for further work are given.


6

2. AXIAL FANS, LOSSES AND NOISE

Turbomachinery are pieces of equipment that transfer energy between a rotor

and a fluid [4]. This can happen in two ways: either energy is transported from the

fluid to the rotor (turbines) or from the rotor to the fluid. Machines realising the

latter method can be divided into three groups. In increasing order of pressure

ratio, these machines are: fans, blowers and compressors.

2.1. FANS

Fans are devices whose operation is based on Euler’s turbine equation [5]. They

are used to transport gases by generating a pressure ratio of

or lower. In

this case, because of the low pressure increase, fluid density and temperature can be

regarded as constant.

2.2. FAN TYPES

Fans are characterised by the direction of the flow and the rotational axis. The

two most common types are axial and radial fans, shown on Figure 2.1.

Figure 2.1. Axial (left) and radial (right) fan schematics

In the present thesis an axial fan transporting air from an open space to another

open space are investigated. In such a scenario, the total static pressure rise is 0,

since the static pressure on both sides is p0, the ambient pressure. The total pressure

rise is

(

)

(2.1)

Axial fans are capable of producing less total pressure rise than radial ones;

therefore their transported volume flow rate per unit power is larger.

Axial fans may come in several configurations: with flat plate blades or airfoil

profile blades, with our without nose cones and hub diffusers, with direct or

indirect drive etc. The investigated fan had flat plate blades. This has the advantage

of easier construction, but has aerodynamic drawbacks. Profiled blades are more


7

apt since in that case the separation point can move on the leading edge under off-

design operating conditions, thus the efficiency in these cases is higher.

2.3. LOSSES

The different losses of axial fans are described here based on [5].

2.3.1. Friction loss

Due to friction, the air on the suction side of the blades loses some of its velocity.

The boundary layer thickens and the losses grow. This loss can be minimised by

choosing a blade profile with the highest lift-to-drag ratio.

2.3.2. Secondary loss

The term “secondary loss” refers to the losses that occur because of the real flow

being different from the ideal designed one, inside the region enclosed by two

blades, the hub and the duct. In modern fan design the whole flow is considered as

one 3D phenomenon, so that such distinctions are not used anymore.

2.3.3. Annulus loss

Pressure loss caused by friction on the hub surface and the casing surface is

called annulus loss.

2.3.4. Tip clearance loss

The name refers to the pressure loss that occurs because of unwanted tip

clearance flow. This is the most important source of loss and has a significant

contribution to noise, too.

2.3.5. Guide vane loss

The presence of guide vanes causes two types of losses: friction and secondary

loss. But since the relative velocity is lower, the losses are lower too, than that of the

rotor.

2.3.6. Swirl loss

This loss occurs when guide vanes are not applied, or when the fan in operated

in an off-design point. The rotational loss equals to the kinetic energy of the rotating

jet per unit time. It can be avoided by a contra-rotating arrangement, but that is an

expensive and very noisy solution.


8

2.3.7. Diffuser loss

Diffuser loss occurs in two cases. Firstly, in case of a ducted fan, the flow

between the hub and the duct is decelerating, which may cause separations and

pressure losses to occur. This can be avoided by using a hub diffuser that extends

into the pipe and helps to slowly increase the cross section, thus avoids separation.

Secondly, when the air enters free space: in this case the outlet velocity should be

chosen as low as possible, so that the Borda-Carnot loss is minimised.

2.4. FAN NOISE

Fans are responsible for the most noise in ventilation systems. There are several

noise generation mechanisms that are detailed here based on [6].

2.4.1. Mechanical noise

Mechanical noise originates mainly from two sources: bearing noise and the

noise of unbalanced rotating parts.

In most cases ball bearings are used to support the shaft. Ball rotation causes

vibration in the structure that is radiated from the housing as noise. This is the case

for unbalanced rotors. too. Usually mechanical noise is only important at slowly

rotating fans because at higher speeds aerodynamic noise increases significantly. In

the domain below 25 [m/s] however, mechanical noise is an important source

especially because of the high frequency and presence of tonal components that

make it more annoying than broadband low frequency aerodynamic noise.

2.4.2. Vortex noise

Behind a bluff body submerged in a flow a separation bubble might appear that

causes the formation of vortices. When the Reynolds number is high, viscosity

cannot dissipate these and vortex shedding occurs behind the body. This causes a

fluctuating force that is a source of dipole noise. The noise power is found to be

proportional to the sixth power of velocity.

(2.2)

Already in a non-separated flow the turbulent boundary layer (BL) on the blades

acts as a noise source. This is a dipole source too, since the fluctuating pressure

acting on the blade surface generates a fluctuating force, therefore the power is

again proportional to the sixth power of the velocity.

(2.3)


9

The incoming turbulent flow serves as a noise source too, since the velocity

fluctuations perpendicular to the mean velocity direction create a time-varying

fluctuation and a dipole source, too. The power is again proportional to the sixth

power of the velocity.

(2.4)

The most important contribution is usually from the vortices shed behind the

blade trailing edge. These vortices are formed as the interaction of different

pressure and suction side flow velocities. The trailing edge noise power scales with

velocity6, too.

(2.5)

2.4.3. Rotational noise

The periodic motion of the rotor causes a pressure fluctuation that is the cause of

rotational noise. The intensity and frequency dependence of this contributor

depends heavily on the tip clear size between the rotor and the casing. Rotational

noise is however not important in the velocity range in which axial fans usually

operate as it only becomes significant at about 100 [m/s] of tangential velocity.

2.4.4. Turbulent noise

The turbulent flow itself can be a significant noise source. Its intensity is

proportional to the eighth power of velocity [7] since it is described as a

quadrupole. As such it only becomes important at fairly high velocities (above 50

[m/s]). It is important to note that the spectrum shape is velocity-dependent too: a

two-fold increase in velocity means a six-fold frequency increase.

(2.6)

2.4.5. Rotor-stator interaction noise

The rotor wake impinging on a nearby object creates the rotor-stator interaction

noise. This can be a very significant noise source, especially if the number of the

stators (engine supports etc.) equals to the number of blades. The generated noise is

tonal, therefore it is very annoying. Rotor-stator interaction can be avoided by

placing the supports far from the rotor or if that is not possible, the rotor and stator

number should be chosen to be relative primes to each other.


10

3. PHASED ARRAY MICROPHONES

For a long time, acoustic experiments were limited to the measurement of overall

noise. With the rapid development of computers however, the identification of and

spatial differentiation between noise sources has become possible. This process is

carried out by Phased Array Microphones (PAM). In most cases, the delay-and-sum

(DS) technique is used, either in time or in frequency domain to provide data about

the positions of the most important noise sources.

Beamforming consists of recording several microphone signals, then

decomposing the spatial domain into focus points, calculating the time delays for

each of them and calculating the output value by assuming a source at the actual

focus point. If the value of the output is large, it means that the source was at the

focus point, if it is small then there was no source at the focus point. Using this

method it is possible to reconstruct the spatial distribution of sound sources.

3.1. TIME-DOMAIN BEAMFORMING

The operation of time-domain beamforming is described here based on [8].

A sound field of a monopole source at y0 is described by the following equation:

( ) ( ) (3.1)

where p is the pressure, is the speed of sound, q is the monopole intensity, t is

the temporal, x is the spatial coordinate and δ is the Dirac-delta function. The

solution in the free field is the well-known Green function:

( )

( | |

)

| | (3.2)

This expression means that the emitted signal arrives to the observation point

after a time delay or retarded time | |

and its magnitude is multiplied by a factor

of

| | accounting for the decrease in intensity as the cross section area grows in

case of spherical wave propagation.

Time-domain beamforming uses a set of M microphones placed at locations xm

that record the pressure fluctuations. The retarded time

| |

(3.3)

is the time when the signal reaching the microphone m=1…M was emitted by the

source. Assuming a source at the yf focus position, time difference is


11

| |

(3.4)

The recorded pressure fluctuations are compensated for this time difference and

the microphone signals are summed, with amplitude correction taking the different

source―microphone distances into account. The output z is then

( )

∑

| |

| |

( ) (3.5)

The expression means that the output signal z for an assumed source can be

given as a function of time by averaging the contributions of each microphone. Each

contribution consists of q source output taken at . This is to assure

that signals from the same phase are summed even though the sound waves have

to travel different paths towards each microphone. Then the amplitude is corrected

by a factor corresponding to the distance of the microphone and the source to

balance the effects of decreasing amplitude over propagation length.

If the focus position coincides with the source position , ( ) ( ) is

obtained, otherwise the signal in different phases should result in an average of a

lower value.

3.2. FREQUENCY-DOMAIN BEAMFORMING

The previously discussed DS technique can also be applied in the frequency

domain as described in [8] for a stationary source.

The discrete Fourier transform of the time-domain signal recorded by

microphone m=1…M at location xm using sampling frequency fs is given as

( ) ∑ ( )

(3.6)

where

(3.7)

are the discrete frequencies at which the transformation is done, N is the number

of samples, n is the current sample index and j is the imaginary unit.

After transforming equation (2.6) the following is obtained:

( )

∑

| |

| |

( )

( ) (3.8)

As usual, the distance was chosen as the weighting factor in order to cancel the

amplitude reduction due to the intensity change. In the expression above, Q is the


12

frequency-domain monopole source intensity, yf is the focus location, y0 is the

source location, is the time delay between microphone m and the source,

while is the time delay between microphone m and the focus point.

Z variable then gives the frequency-domain output at a chosen focus point as

a function of discrete frequencies as a sum over each microphone. The summed

contribution of each microphone is the Q source intensity at the frequency in

question normalized by the distances of the microphone to the focus and the source

to account for the decreasing intensity because of the spherical wave propagation.

The exponential part modifies the phase. This is important because the sound

waves have to travel different paths to each microphone that would modify the

result. By this method, we can assure that the summation is carried out with the

same emitted signal phase.

It is still true that the expression has a maximum when the source is at the

investigated focus point:

( )

∑ ( )

( ) (3.9)

The array output in (3.8) is reformulated using a matrix notation:

( ) (3.10)

where ( ) denotes the conjugate transposed of a vector or matrix. In the vector h

the Fourier transformed microphone signals m=1…M are collected:

( ) (

( ) ( )

( )

) (3.11)

e is called the steering vector, a phasor with exponents chosen to cancel the phase

shifts due to wave propagation:

(

) (3.12)

The microphone weights are summarized in the diagonal matrix W:

(

( ) ( ) ( )

) (3.13)


13

In practical applications the signal and therefore the results in Z are very noisy.

To reduce the noise, the output is averaged over a certain K number of windows. It

can be shown that as the number of averages goes to infinity, the average Z goes to

zero. The auto spectrum is calculated as

( )

∑

( ) ( )

(3.14)

where the asterisk denotes the complex conjugate and ( ) is the array output

for the ith window. This can be summarised as

( ) (3.15)

where ( ) is the matrix of cross spectrum density estimates:

( )

∑

( ) ( )

(3.16)

In the expression above, W is a correction factor that takes into account the

energy loss caused by the window function and ( ) is the ith sample recorded

by microphone m. These values are arranged into matrix R in the following way:

(

( )

( ) ( )

( )

( ) ( )

( ) ( )

( ))

(3.17)

In some cases the signal-to-noise ratio (SNR) may still be low. This can be

increased by removing the main diagonal from matrix R, since the values there

contain auto cross spectra [9]. These spectra are more vulnerable to external noise

since they are computed from one microphone signal only. The SNR can then be

increased by applying a modified matrix R’:

(

( )

( )

( )

( )

( ) ( ) )

(3.18)

3.3. ROSI METHOD [3]

The previously discussed beamforming method is only applicable to stationary

sources. The theory and, based on that, a computer program called ROSI was

developed that can handle moving sources too [3]. In the current investigation

about fans, the emphasis is of course on rotary motions.


14

First, the equation for the sound pressure field of a moving monopole is given

using the notation of Equation (3.1):

( ) ( ( )) (3.19)

In the current case, the source position y is a function of time. The convective

derivative is defined as

(3.20)

where Ma is the Mach number of the flow. Using that and the results of Dowling

and Ffowcs Williams [10] the T(x, y(τe), t, τe) transfer function between the moving

source and the receiver at x is written as

( ( ) )

( ( ( ) )) (3.21)

In the expression above, the emission time τe is defined using the x direction unit

vector i in the following way:

| ( ) ( ) | (3.22)

while Q is the inner product

( ( ) ) ( ( ) ( ) ) (3.23)

Using transfer function T, the pm signal recorded by microphone m can be written

as

( ) ( ( ) ) ( ) ( ) (3.24)

where ( ) is the noise and the contribution from other sources. This can be

written briefly as

( ) ( ) ( ) ( ) (3.25)

using the different tm receiver times for different microphones from (3.22).

A reconstructed array output signal ( ) can be found using the DS procedure:

( )

∑ ( )

(3.26)

where the reconstructed source signal is

( )

( )

( ) (3.27)


15

The frequency spectrum is calculated as the discrete Fourier transform of the

source signal:

( )

∑ ( )

(3.28)

The auto power spectrum is then

| ( )|

|∑ ( )

|

∑ ∑ ( )

( )

(3.29)

The theory and the ROSI computer programme were tested on a rotating whistle,

a model-scale helicopter and a wind turbine rotor and it proved its value in the

identification of noise sources on rotating objects.

3.4. SPATIAL RESOLUTION

The spatial resolution of a phased array microphone is [11]

(3.30)

where is the target distance from the PAM, is the wavelength

corresponding to the mid-frequency of interest and is the characteristic

dimension of the PAM.


16

4. GEOMETRY MEASUREMENT

In order to be able to calculate aerodynamic properties along the blade radius of

the assigned fan, geometrical measurements had to be taken at several points.

Measured were the chord c, the curvature f, the stagger angle γ, and the sweep

angle at each point. Additional measurements were also taken to help calculate

the necessary quantities. These are listed below. Measurement uncertainties were

estimated as well.

Figure 4.1. The investigated fan [1]

4.1. MEASURED DATA

The following data were measured. Duct diameter Dp=315 [mm] corresponding

to a duct radius Rp=157.5 [mm]. Fan diameter Df=300 [mm], therefore the fan radius

is R=150 [mm]. Hub diameter dh=94 [mm], therefore hub radius rh=47 [mm]. The tip

clearance was g=7.5 [mm], constant along the circumference. Number of blades is

N=5. Figure 4.2 shows the interpretation of geometric data.


17

Figure 4.2. Fan geometry

Table 4.1 contains the chord c, curvature f, stagger angle γ and axis-normal

sweep angle β’ values at five radii nondimensionalised with Rp hub radius.

r/Rp=0.30 is the hub radius, r/Rp=0.63 is the midspan radius and r/Rp=0.95 is the

outermost blade radius (tip). As seen above, β’ is measured in the plane normal to

the axis of rotation.

Table 4.1. Geometric data along radius

r/Rp [-] r [mm] c [mm] f [mm] γ [°] β’ [°]

0.30 47 88 12 35 0

0.46 73 97 9 33 23

0.63 99 108 9 31 31

0.79 124 118 8 29 39

0.95 150 130 8 27 44

The data were measured using a ruler, a calliper and a Leica Racer 100 electric

angle measurement device.


18

In order to provide a smoother distribution of the dimensions and account for

measurement error the data – with the exception of f – were fitted with second-

order polynomials and the interpolated values were used in the following. In

addition to that, the value of β’ was modified to obtain β, the angle in the plane of

the blade (rotated by the stagger angle). This was done based on Equation (4.1).

(4.1)

Table 4.2 contains the interpolated values.

Table 4.2. Interpolated geometric data

r/RP [-] r [mm] c [mm] f [mm] γ [°] β [°]

0.30 47 87.93 12 35.00 1.81

0.46 73 97.45 9 33.00 23.19

0.63 99 107.77 9 30.98 37.04

0.79 124 118.46 8 29.03 44.52

0.95 150 130.38 8 26.99 47.06

4.2. CALCULATED DATA

Knowledge of the geometric data made possible the calculation of the spacing s,

the solidity c/s, the camber radius Rc and the camber angle θ. The formulae are the

following.

(4.2)

(4.3)

( ) (4.4)

Inlet and outlet flow angles are:

(4.5)


19

(4.6)

Table 4.3 contains these values along the radius.

Table 4.3. Calculated data

r/RP [-] s [mm] c/s [-] Rc [mm] θ [°] α1’ [°] α2’ [°]

0.30 59.06 1.49 86.54 61.07 85.53 24.46

0.46 91.73 1.06 136.38 41.86 77.93 36.07

0.63 124.41 0.87 165.81 37.93 77.98 40.05

0.79 155.82 0.76 223.27 30.77 76.35 45.58

0.95 188.50 0.69 269.60 27.99 77.00 49.01

4.3. UNCERTAINTIES

Measurement uncertainties were estimated by measuring each dimension ten

times. The uncertainties are listed in Table 4.4.

Table 4.4. Dimensional uncertainties

c [mm] f [mm] γ [°] β [°]

±2 ±1 ±0.2 ±1

In each case except for the blade angle, the interpolated values were found to be

inside of the uncertainty region.


20

5. AERODYNAMIC PROPERTIES

Aerodynamic properties of the fan were evaluated along the radius to be

comparable with phased array microphone noise measurements. The inlet velocity

profile was measured, and then the characteristic variables, such as the Ψ pressure

number, the η efficiency and the D diffusion factor were calculated. The data were

corrected to account for the skewed blades based on literature.

5.1. INLET VELOCITY MEASUREMENT

The inlet velocity was recorded at several points to allow the calculation of the

aerodynamic properties of the fan. These measurements were carried out using a

“Mini-Air” Dostmann P670 turbine anemometer. In total, four radii were examined

and the velocity profiles were found to be in good agreement with each other.

Then tangential velocity of the fan u was determined:

(5.1)

where n=23.29 [1/s] is the rotational speed measured by a stroboscope.

The local flow number is calculated as the measured axial velocity divided by the

tip tangential velocity:

(5.2)

The average profile is shown on Figure 5.1 versus the nondimensional radius

along with a second order polynomial fit. The error bars indicate 5% error, which is

a characteristic value of Mini-Air measurements in this velocity range.

Figure 5.1. Nondimensional axial velocity profile

0.10

0.20

0.30

0.40

0.50

0.00 0.25 0.50 0.75 1.00

φ [

-]

r/Rp [-]

♦ measured

▬ fitted


21

The volume flow rate calculated based on the velocity measurements is 1948

[m3/h], which is in good agreement with the findings of a previous report [12].

Figure 5.2 shows the characteristic curve of the investigated fan.

Figure 5.2. Characteristic curve of the investigated fan [12]

5.2. OUTLET VELOCITY MEASUREMENTS

The outlet velocity was measured along four radii using the same Mini-Air

probe. The results were however found to be erroneous. This is because of the large

separation bubble behind the fan hub that causes backflow. The Mini-Air is not able

to differentiate between directions when measuring velocity, thus the data could

not be used. Velocity measurements would have been possible using Laser Doppler

Anemometry (LDA), but this technique was not available.

5.3. CALCULATIONS FOR UNSWEPT BLADES

In order to calculate efficiency and pressure number distribution along the radius

r the following calculations were carried out.

The real inlet angle was determined on the basis of the velocity magnitudes

assuming :

(5.3)

The angle difference i can then be determined as the difference of the two angles:

(5.4)

Assuming nominal operating conditions, α1=α1*. The nominal outlet angle α2* is

calculated as follows [13]:

0

10

20

30

40

50

60

500 750 1000 1250 1500

Δp

[Pa]

Q [m3/h]

♦ measured

▬ fitted


22

(

) (5.5)

The value of m is:

(5.6)

assuming circular blade profiles. With this, δ* is:

(

)

(5.7)

The angle α2’* is then

(5.8)

while α1’* is

(5.9)

The nominal angle of incidence i* is defined as the following:

(5.10)

while

(5.11)

and

(5.12)

Values of flow deflection can be read from Figure 5.3 taken from [13] as a

function of the dimensionless parameter group

.


23

Figure 5.3. The relative deflection ε/ε* versus (i-i*)/ε* recreated from [13]

Using this figure to calculate ε, α2 is given as:

(5.13)

The outlet axial velocity is assumed to be identical to the inlet velocity:

(5.14)

Thus the relative outlet velocity is

(5.15)

The tangential component of the outlet velocity is

(5.16)

It was assumed that the air exits at the same radius where it entered the fan. The

total isentropic pressure rise is then calculated from Euler’s turbine equation

(5.17)

While the total real pressure rise in case of a fan blowing from free space to free

space is

(

) (5.18)

The efficiency is defined as the real-to-isentropic pressure rise ratio:

(5.19)

The pressure numbers are defined as the pressure rise at the given radius

divided by the dynamic pressure calculated at the outermost radius, that is:

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

ε/ε*

[-]

(i-i*)/ε* [-]


24

(5.20)

where

(5.21)

5.4. SWEEP CORRECTION

The results of the previous calculations have to be corrected in case of swept

blade fans. This is done based on [14].

First, the angle λ is calculated

(

) (5.22)

Then, using the midspan value of the M parameter is calculated as

(5.23)

The blade aspect ratio AR is

(5.24)

where cmid is the chord value at midspan. Using these, A=0.5 can be found from

[14] so that

(5.25)

Using CF, the isentropic pressure number after sweep correction is

(5.26)

The tangential component of the absolute outlet velocity after sweep correction is

(5.27)

The real pressure number after sweep correction is

(5.28)

The outlet angle after sweep correction

(5.29)


25

The D diffusion factor is calculated to take the losses attributed to the widening

blade channels and the adverse pressure gradient into account

( ) (5.30)

The diffusion factor after sweep correction is

( ) (5.31)

The efficiency after sweep correction

(5.32)

5.5. UNCERTAINTIES

Since the estimation of uncertainties would have been very difficult, a simplified,

strongly conservative approach was used. First, all measured variables were set to

their measured values minus the measurement uncertainty and the calculated

values were recorded. Then the measured variables were set to their measured

values plus the uncertainty and the calculated values were recorded again. The

difference of the two values was regarded as the uncertainty. These are given in

Table 5.1 below.

Table 5.1: Uncertainties

η

[-]

Ψis

[-]

Ψre

[-]

D

[-]

ηsw

[-]

Ψis,sw

[-]

Ψre,sw

[-]

Dsw

[-]

0.06 0.02 0.01 0.04 0.07 0.01 0.01 0.04

5.6. RESULTS

The results of the aerodynamic calculations are given below in Table 5.2.


26

Table 5.2: Calculated efficiencies, pressure numbers and diffusion factors

r/Rp

[-]

η

[-]

Ψis

[-]

Ψre

[-]

D

[-]

ηsw

[-]

Ψis,sw

[-]

Ψre,sw

[-]

Dsw

[-]

0.30 0.84 0.08 0.07 0.01 0.36 0.85 0.08 0.07

0.46 0.57 0.17 0.10 0.07 0.42 0.58 0.17 0.10

0.63 0.50 0.25 0.13 0.12 0.38 0.51 0.24 0.12

0.79 0.50 0.31 0.15 0.16 0.33 0.50 0.30 0.15

0.95 0.47 0.46 0.21 0.24 0.35 0.47 0.45 0.21

The spanwise distribution of these values along the radius is demonstrated on

Figure 5.4.

Figure 5.4. Aerodynamic properties along radius

One may observe that the sweep correction hardly modifies the efficiencies and

the diffusion factors. The efficiency is highest at the innermost radius and decreases

as the coordinate tends towards the blade tip. The diffusion factors have a smaller

variation along the radius, starting from low, reaching a plateau and the slightly

decreasing again. The pressure numbers are increasing along the radius, which is

understandable given the increasing tangential velocity. There is a significant

difference between the real and the isentropic pressure numbers, and the difference

grows with the radius.

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.25 0.5 0.75 1

η [

-]

ψis

, ψ

v ,

ω, D

, φ

[-]

r/Rp [-]

x η x ηsw

● ψis ● ψis,sw

♦ ω ♦ ωsw

■ D ■ Dsw

▲ψv ▲ψv,sw

+ φ


27

6. ACOUSTIC PROPERTIES

The acoustic properties of the fan were measured using a phased array

microphone. The acoustic investigation had two aims. Firstly, to acquire the

averaged radial noise distribution of the fan in order to compare with the radial

distribution of aerodynamic properties as described above. Secondly, to create noise

maps of the fan in a co-rotating system of coordinates. This would allow the

identification of noise sources on the fan blade geometry.

6.1. EQUIPMENT

The measurement setup is shown on Figure 6.1. The measurement setup The

noise signals were recorded using a 24-channel phased array microphone (PAM).

The PAM was attached to amplifier and to a device responsible for sampling and

digitizing the microphone data (ADC). The digital data was fed into a personal

computer (PC) that saved the measurement files. In order to measure rotation

speed, an optical tachometer (TACH) was attached to the fan (FAN), whose output

was connected to the sampler in the place of one of the microphones.

Figure 6.1. The measurement setup

FAN denotes the investigated fan, TACH is the optical tachometer, ADC is the sampler and

analogue-to-digital converter, PC is the computer used to gather the data.

6.2. PROCEDURE

Radial noise distribution was recorded using the phased array measurement

technique. 30 [s] long noise samples were recorded at a sampling frequency of 44.1

[kHz]. When measuring the suction side, the microphone array was placed at a

distance of 0.5 [m] from the fan in order to achieve good spatial resolution. On the

pressure side however, this distance was not applicable as the aerodynamic

pressure fluctuations caused the overload of the amplifier, therefore the distance


28

had to be increased to 1 [m]. An optical tachometer was attached to the fan to

record the instantaneous angular velocity.

The effect of sample length was evaluated as seen on Figure 6.2. It was

concluded that no significant difference can be seen between a 20 [s] and a 30 [s]

long sample, as seen on the figures.

Figure 6.2. Comparison of source maps acquired with 30 s (left) and 20 s (right) averaging.

The two images were taken with the same colour bar settings.

The samples were processed using the Acubeam software programmed by Péter

TÓTH and the results were then averaged along concentric circles in Tecplot using

100 nodes in both radial and circumferential directions.

From here, a procedure described in [1] was applied. The spanwise noise

pressure distribution was assumed to be a monotonically increasing function of

aerodynamic loss. Two quantities were considered to describe this loss: the loss

coefficient and the D diffusion factor. The two test functions were written in a

power form as follows:

(6.1)

(6.2)

Since the measured quantity is sound pressure level (SPL), it is convenient to

write the above equations in a level-form, taking their base-10 logarithm and

multiplying them by 20. This gives the following expressions for the sound pressure

levels depending on the loss coefficient ( ) and the diffusion factor ( ):

( ) (6.3)

( ) (6.4)


29

Introducing the “loss level”

(6.5)

and the “diffusion level”

(6.6)

the equations can be written in the following form:

(6.7)

(6.8)

The new parameters and were found by applying a least-

squares fit onto the measured radial SPL distribution at the five known values of

and calculated above.

6.3. DELAY-AND-SUM RESULTS

DS results were obtained using the ImageJ program and its special plugins for

each third-octave band at both pressure and suction sides.

Figure 6.3. DS source map on suction side (left) and pressure side (right)

at 2000 Hz mid-frequency


30








31






at full band


32

As seen on the figures, the DS method is not able to handle rotating sources. The

output is such a case is a smoothed, radially almost symmetric map that is due to

the rotating fan. It can still be used to illustrate some radiation characteristics of the

fan though. It is clearly visible that the outer radius of the fan is the dominant noise

source, which is expected because of the increasing tangential velocity. This can

only be observed on the suction side maps however, as on the pressure side the

larger target distance causes the decreases of PAM spatial resolution. The DS

method is able to give an estimate of the source strengths as well.

6.4. RADIAL NOISE DISTRIBUTION

6.4.1. Suction side results

Table 6.1 shows the parameters and the R2 values of the function fit for the

different third octave frequency bands on the suction side.

Table 6.1. Suction side function fit parameters

fmid [Hz] A2,ω B2,ω R2ω A2,D B2,D R2D

2000 68.18 3.21 0.94 60.59 -9.17 0.05

2500 65.04 1.06 0.47 64.34 1.01 0.00

3150 61.89 3.87 0.93 51.77 -13.21 0.07

4000 52.32 1.59 0.21 36.08 -32.43 0.60

5000 47.66 -0.69 0.06 48.44 0.04 0.00

6300 44.60 -2.24 0.26 47.55 1.14 0.00

full band 75.97 1.98 0.95 70.55 -7.31 0.09

The results show agreeable R2 values for the loss coefficient (ω) dependency in

the low frequency range. This is a welcomed result, since from the viewpoint of

human comfort, the 2000-3150 Hz frequency range is the most important regime.

This can be seen from the large positive weighting in the dB(A) scale in this

frequency range show on Figure 6.10. The fan also radiates with a much higher

intensity in this deep range that causes the full band data to fit well onto the ω

dependent trial function but worse on the diffusion factor dependent one.


33

Figure 6.10. A-weighting spectrum

It is important to note that the negative coefficients occurring for the loss

coefficient dependent approximations at 5 kHz and 6.3 kHz, and for the diffusion

factor dependent approximations at 2 kHz, 3150 Hz, 5 kHz and the full band mean

that increasing aerodynamic loss leads to decreasing noise. These measurement

points do not support the original theory that noise is an asymptotically increasing

function of aerodynamic loss.

On the figures below, LM is the source intensity distribution acquired with

diagonal removal on, while LM’ is without diagonal removal.

Figure 6.11. SPL versus radius at 2 kHz on suction side

-25

-20

-15

-10

-5

0

5

20 200 2000 20000

A [

dB(A

)]

f [Hz]

60

62

64

66

68

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=2 kHz

─ LM

─ LM' ■ LPω

▲LPD

62

64

66

68

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=2.5 kHz

─ LM

─ LM' ■ LPω

▲LPD


34

Figure 6.12. SPL versus radius at 2500 Hz on suction side




52

54

56

58

60

62

64

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=3150 Hz

─ LM

─ LM' ■ LPω

▲LPD

48

50

52

54

56

58

60

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=4 kHz

─ LM

─ LM' ■ LPω

▲LPD

44

46

48

50

52

54

56

58

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=5 kHz

─ LM

─ LM' ■ LPω

▲LPD


35


Figure 6.17. SPL versus radius at full band on suction side

Figure 6.11 through Figure 6.17 show the estimated SPL distributions and the

actual measured one versus the radius. The estimations are agreeable at 2000, 2500

and 3150 Hz mid-frequencies, but above that they fail to follow the trends in the

SPL function. The full band estimation is good due to the fact that most of the

intensity is radiated in the low frequency domain, where the estimations work

relatively well.

6.4.2. Pressure side results

Table 6.2 shows the parameters of the fitted functions on the pressure side.

42

44

46

48

50

52

54

56

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=6.3 kHz

─ LM

─ LM' ■ LPω

▲LPD

70

72

74

76

78

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

full band

─ LM

─ LM' ■ LPω

▲LPD


36

Table 6.2. Pressure side function fit parameters

fmid [Hz] A2,ω B2,ω R2ω A2,D B2,D R2D

2000 65.86 -1.60 0.72 73.53 13.26 0.33

2500 65.05 -0.63 0.50 68.63 6.47 0.36

3150 62.79 0.82 0.68 61.40 -1.11 0.01

4000 59.29 0.20 0.03 61.77 6.02 0.16

5000 55.17 1.46 0.44 55.90 5.17 0.04

6300 48.71 0.18 0.01 57.34 19.70 0.44

full band 76.69 -0.46 0.20 80.61 7.66 0.39

On the pressure side the R2 values are generally lower than on the suction side. It

is again important to highlight the frequency bands with negative coefficients, such

as 2 kHz and 2.5 kHz for the loss coefficient dependent approximation and 3150 Hz

for the diffusion factor dependent approximation. In these cases, increasing

aerodynamic loss leads to decreasing noise. This is against our initial assumption

stating that there should be a monotonically increasing relationship between the

losses and noise.

Figure 6.18. SPL versus radius at 2000 Hz on pressure side


66

67

68

69

70

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=2 kHz

─ LM

─ LM' ■ LPω

▲LPD

64

65

66

67

68

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=2.5 kHz

─ LM

─ LM' ■ LPω

▲LPD


37




60

61

62

63

64

65

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=3150 Hz

─ LM

─ LM' ■ LPω

▲LPD

58

59

60

61

62

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=4 kHz

─ LM

─ LM' ■ LPω

▲LPD

50

52

54

56

58

60

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=5 kHz

─ LM

─ LM' ■ LPω

▲LPD


38


Figure 6.24. SPL versus radius at full band on pressure side

Figure 6.18 through Figure 6.24 show the calculated and the measured radial SPL

distribution. Both approximations, but especially the diffusion factor dependent

one, seem to give acceptable results in the low frequency range. Besides that the

agreement is quite poor. Again, because of the high relative intensity in the low

range, the full band approximation is acceptable.

Effects of diagonal removal can also be deduced from the figure. The method

decreases the signal amplitude but increases its dynamic range. Besides that, it

barely modifies the shape of the functions; therefore it can be used well to obtain

information about source distribution.

6.5. SOURCE DISTRIBUTION ON BLADES

The Acubeam ROSI algorithm was used to create blade source maps in the co-

rotating system. This allows the identification of significant noise sources on the

blade.

46

48

50

52

54

56

58

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

fmid=6.3 kHz

─ LM

─ LM' ■ LPω

▲LPD

76

77

78

79

80

0.25 0.50 0.75 1.00

LP [

dB]

r/Rp

full band

─ LM

─ LM' ■ LPω

▲LPD


39

6.5.1. ROSI rotation tests

Before taking any actual measurements, it had to be examined where the

Acubeam algorithm places the sources on the circumference of their rotation path,

i.e. what is the phase difference between the phase used to display the sources and

the phase when the tach signal arrives.

To achieve this, test measurements were taken with a localized source. The test

source was placed on the same radial line as the reflective dot used for the optical

tachometer. This allowed the determination of the phase difference between the

tach signal and the rotated source on the output image. Several setups were

analysed: multiple distances and both the pressure and the suction side was

investigated. Source maps of very low dynamic range were created and the rotation

angle was then obtained. Several results were analysed to establish a reliable value

with uncertainties.

The results show that the algorithm rotates the source map by about the

following amounts:

on the pressure side at a distance of 1 m, by -13.30°±2.15°

on the suction side at a distance of 0.5 m, by 6.15°±1.35°.

These pictures of the localised source are shown on Figure 6.25 and Figure 6.26.

The dot indicates the midpoint axis of the PAM, the small circle is the theoretical

location of the source and the colourful area is the measured source location. The

dashed circle indicates the source path, while the arrow shows the direction of

rotation.

Figure 6.25. Suction side source location

at 0.5 m distance

Figure 6.26. Pressure side source location

at 1 m distance


40

6.5.2. Synthetic source

In order to further investigate the rotation effects of Acubeam, an algorithm was

developed in MATLAB that generates the noise recorded by each microphone in

the presence of a monopole source rotating at a given radius with a given angular

velocity in a plane parallel to the PAM plane. This solution allows the investigation

of several variables, like angular velocity, direction of rotation, distance from the

PAM etc. in a controlled manner. The algorithm can generate signals of different

sampling rates and accounts for the variable distances and reception phases during

the monopole movement. It also incorporates the Doppler effect.

The output noise from this algorithm was fed into the Acubeam software and

source maps similar to the previous ones were created. These source maps show the

synthetic source exactly at its place at the start time, at 0 rotational phase, on the

horizontal axis. This suggests that the Acubeam algorithm places the sources

exactly to the place where it assumed it at the time of the tach signal. Such a source

map is shown on Figure 6.27.

Figure 6.27. Synthetic algorithm source map

In this case, the angle differences found above have to be explained in some way,

since according to this result all measured sample noise sources should lay on the

horizontal axis. A possible explanation is that the swirling flow coming from the fan

is able to modify the path of the sound waves. This effect together with the fact that

the sample source is not a geometrical point but has a finite size and with the

PAM’s finite spatial resolution may account for the experienced rotation angles.

Since the main aim is to correctly evaluate the experimental results, in the

following the rotation angles obtained using the sample noise source are used, i.e.

those listed in Section 6.5.1.


41

6.5.3. Source maps

Source maps were created for the fan from suction and pressure side as well. The

position of the fan blades is marked along with 3° uncertainty (dotted lines).

The black dot indicates the position of the index signal while the arrow the

direction of rotation. The left image was obtained with diagonal removal switched

on, while the right without it. Diagonal removal is expected to reduce the

amplitude and increase the dynamic range, therefore the two diagrams have

different scale settings. This allows the comparison of the shapes on the two figures.

The maps were created using 5 dB dynamic range below which the data was

cropped (white areas). The straight line on the source maps shows the theoretical

spatial resolution of the PAM.

DS source strengths obtained with ImageJ and with the ROSI method should not

be compared directly, because the two softwares have different calibration settings.

This is not a problem though, since our main interest is in describing the relative

importance of the source regions.

Suction side

Figure 6.28. Suction side source map at 2000 Hz with (left) and without (right) diagonal removal


42





43



Figure 6.34. Suction side source map at full band with (left) and without (right) diagonal removal

The source maps indicate significant noise peaks in the vicinity of the leading

edge tips. Two possible explanations exist for this. One of them is that the outer

radius has the highest velocity and the leading edge tip has a geometric

discontinuity. These factors together could make this region the loudest noise

source. It may also be the effect of a vortex separating from one blade and

impinging on the leading edge of the other. Another possible explanation is that the


44

noise sources are in fact the vortices separating behind the plane of the fan and they

are visible because of the bad z-direction resolution of the PAM.

Pressure side

Figure 6.35. Pressure side source map at 2000 Hz with (left) and without (right) diagonal removal




45





46

Figure 6.41. Pressure side source map at full band with (left) and without (right) diagonal removal

On the pressure side, the maximum SPL is about 2 dB higher than on the

pressure side. The source maps generally have a higher spatial resolution due to the

fact that measurements had to be taken from a larger distance. Blade periodicity can

still be observed on the maps except for the lowest frequencies. On the pressure

side the most significant source regions are the leading edges. This is probably

because of the wake from the previous blade impinging on the next leading edge.

6.5.4. Effects of diagonal removal

The maps with and without removal show similar geometric noise level

distributions, so the removal is a reliable method that does not neglect any useful

data. As expected, the method reduces the maximum amplitudes and increases the

dynamic range of the source maps. As such, it is a very useful tool in creating maps

that are easier to understand and contain the necessary information without the

noise effects coming from the autospectra in the main diagonal.


47

7. SUMMARY

A method based on [1] is used to relate the radial distribution of aerodynamic

losses and generated noise in case of an axial fan.



parameters are investigated: loss coefficient and diffusion factor. Both

parameters were written in a level-like form.

Noise distribution was measured using a Phased Array Microphone (PAM).

Radially averaged plots were created for the third octave bands from 2000 Hz to

6300 Hz and a linear fit using the least squares method was carried out to find

parameters that best approximate the noise as a function of either or both on

suction and pressure sides. On the suction side both functions seem appropriate in

the 2000 Hz – 3150 Hz range and the full band, too. Above that the agreement is

quite poor. On the pressure side, the dependent function preforms better and

gives good results in the low frequency range, but again, at higher frequencies both

functions fail to reproduce the chordwise distribution of noise. The full band

estimation is acceptable in both cases for both trial functions due to the fact that

most of the noise is radiated in the low frequency range, where the intensity

approximation is quite good. It is important to note however, that some

measurement points show negative function fit coefficients that do not support the

original theory that states that increasing aerodynamic losses would lead to

increasing noise generation.

The ROSI method was used to generate source maps of the fan from a co-rotating

coordinate system. The results show a significant noise source in the vicinity of the

leading edge tip, while on the pressure side the leading edge mid-chord area

generates more noise. In general, the pressure side is louder.

The results show that the phased array measurement technique can effectively be

applied to study the noise of turbomachinery.


48

8. FURTHER AIMS

Measurements of another, unswept fan have been carried out in a similar

manner. Those shall be evaluated in order to gain more insight into the noise

generation mechanisms present in axial fans.

It should be determined whether the noise sources in the blade tip region result

from the tip vortices or from the geometric discrepancy. Some preliminary

measurements were taken with a decreased tip clearance but their results were not

conclusive and they should be repeated. These measurements with a reduced tip

clearance will be carried out in order to determine its effects on the source intensity

and thus show the origin of noise.

A code generating a synthetic noise from an orbiting monopole source was

designed to test the ROSI algorithm and allow the more exact determination of the

angle by which ROSI rotates the source map. This could easily be enhanced to be

able to simulate a source of a given spectrum. With some further work, it could be

enabled to simulate several sources rotating together, each having different

spectrum.

A program based on the genetic algorithm (evolution strategy) was proposed

that would be able to calculate the most efficient blade geometry for an axial fan of

given pressure rise and volume flow rate. This code shall be completed. If the

results regarding the connection of aerodynamic losses and noise show agreement,

that could be used to design axial fans taking both efficiency and noise level into

account.


49

9. BIBLIOGRAPHY

[1] T. Benedek and J. Vad, “Concerted Aerodynamic and Acoustic

Diagnostics of an Axial Flow Industrial Fan, Involving the Phased Array

Microphone Technique (Draft),” in ASME Turbo Expo 2014, Düsseldorf,

2014.

[2] S. Lieblein, F. C. Schwenk and R. L. Broderick, “Diffusion Factor for

Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor

Blade Elements,” National Advisory Comittee for Aeronautics,

Washington, 1953.

[3] P. Sijtsma, S. Oerlemans and H. Holthusen, “Location of rotating sources

by phased array measurements,” in 7th AIAA/CEAS Aeroacoustics

Conference, Maastricht, 2001.

[4] “Turbomachinery,” [Online]. Available:

http://en.wikipedia.org/wiki/Turbomachinery.

[5] J. Vad, “Ipari légtechnika”.

[6] J. Gruber, Ventilátorok, Budapest: Műszaki Könyvkiadó, 1974.

[7] M. J. Lighthill, “On Sound Generated Aerodynamically. I. General

Theory,” Proceedings of the Royal Society of London. Series A, vol. 211, no.

1107, pp. 564-587, 1952.

[8] L. Koop, “Beam forming methods in microphone array measurements.

Theory, practice and limitations,” in von Kármán Institute Lecture Series,

Rhode Saint Genèse, 2007.

[9] P. Tóth, “Mikrofontömbös méréstechnika,” 2012.

[10] J. E. Ffowcs Williams and A. P. Dowling, Sound and Sources of Sound,

Wiley, 1983.

[11] J. Hald, “Combined NAH and Beamforming Using the Same Array,”

Brüel & Kjær Technical Note, 2005-1.

[12] “Comparative Measurements on Axial Flow Fans,” Department of Fluid

Mechanics, BME, Budapest, 2012.

[13] S. L. Dixon, Fluid Mechanics and Thermodynamics of Turbomachinery,

Butterworth-Heinemann, 1998.

[14] P. V. Ramakrishna and M. Govardhan, “On loading corrections and loss

distributions in low-speed forward swept axial compressor rotors,”

Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power

and Energy, vol. 225, no. 1, pp. 120-130, 2011.


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Documents

PHASED ARRAY MICROPHONE MEASUREMENT OF AN …tothbence/thesis.pdfPHASED ARRAY MICROPHONE MEASUREMENT OF AN AXIAL FLOW FAN v ACKNOWLEDGEMENTS I would like to thank Mr Tamás BENEDEK,